University of Southern California Dissertations and Theses

Genome-scale modeling of macrophage activity in the colorectal cancer microenvironment

(USC Thesis Other)

Genome-scale modeling of macrophage activity in the colorectal cancer microenvironment

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content
Genome-Scale Modeling of Macrophage Activity in the Colorectal Cancer Microenvironment

By

Patrick Gelbach

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
THE UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)

August 2023

Copyright 2023 Gelbach

ii

Dedication

This dissertation is dedicated to my family,
in gratitude for their continuous love and support

iii
Acknowledgements

This dissertation reflects the incredible amount of support and love I have received over
the past years. I can’t fully express my gratitude, but I hope you all know how appreciative I am
for your impact on my life and particularly on this work.
I first would like to thank my advisor, Professor Stacey Finley. Being a member of her
lab was among the best decisions of my life and made my time in grad school so enjoyable.
Stacey has an incredible ability to mentor well- she knows exactly the right balance between
being supportive and understanding and being firm to demand the best out of me. I am truly
grateful for her impact on my personal and professional development, and I owe a great deal of
my personal success to her continued and enthusiastic encouragement.
I have been blessed that my research projects ended up being relatively broad in scope, as
that led to a range of meaningful and impactful collaborations. In particular, I would like to thank
Professors Scott Fraser, Shannon Mumenthaler, and Nicholas Graham, who comprised the rest of
my dissertation committee. Their guidance, encouragement, support, and interest in my work
made a huge difference.
Next, I am grateful to Drs. Jason Papin and Anna Blazier, who gave me my first
experience doing research while I was an undergraduate at UVA. Together they inspired my
decision to pursue science research and helped set me down my path.
I am forever indebted to the other members of the Finley Lab who made the daily work
enjoyable and greatly improved these research projects. I am glad to have worked with lab
alumni such as Dr. Mahua Roy, Dr. Jess Wu, Dr. Min Song, Dr. Sahak Makaryan, Dr. Junmin
Wang, Ryland Mortlock, and Ariella Simoni. Dr. Colin Cess and I entered the lab at the same

iv
time and have become great friends. Current members of the lab have also made the days
particularly wonderful, and I want to thank them all- Holly Huber, Vardges Tserunyan, Niki
Tavakoli, Lynne Cherchia, Diamond Mangrum, Dr. Geena Ildefonso, Handan Cetin, and Neel
Tangella. I am truly grateful to each member of the lab for their impact on me personally and
scientifically.
I am so grateful for my family- my parents Mary and Doug Gelbach, who encouraged me
to pursue this degree and provided so much encouragement and support. Thank you to my
siblings- Max Gelbach, Aidan and Sam Bray, Margaux Gelbach, and Finn Gelbach, I love you
all.
Finally, I want to thank my wife, Reniah. The demands of doing a PhD were made much
easier to manage because of your support and encouragement- you push me to be my best and
have sacrificed a lot to make this degree work for our family. Claire, Luke, and I are blessed to
have you.

v
Table of Contents
Dedication………………………………………………………………………………………...ii
Acknowledgements………………………………………………………………………………iii
List of Tables…………………………………………………………………………….………vii
List of Figures…………………………………………………………………….……………..viii
Abstract…………………………………………………………………………….……………..ix

Chapter 1: Introduction....................................................................................................................1
1.1. Macrophages play an important role in the colorectal cancer microenvironment..............1
1.2. Macrophage metabolism defines different subgroups of cells ...………………................3
1.3. Systems biology approaches enable mechanistic understanding of cellular metabolism...4
1.4.Genome-scale metabolic modeling integrates large-scale datasets to predict the
metabolic activity of cells..……………...…………………………………………….…..6
1.5. Dissertation Outline…………………………………………………………...……….....7

Chapter 2: Ensemble-based genome-scale modeling predicts metabolic differences
between macrophage subtypes in colorectal cancer………………………………………………10
2.1. Abstract…………………………………………………………………………..…..….10
2.2. Introduction……………………………………………………………………...………11
2.3. Materials and Methods…………………………………………………………………..15
2.4. Results…………………………………………………………………………………...21
2.5. Discussion……………………………………………………………………………….39

Chapter 3: Generation and analysis of single-cell genome-scale metabolic models of
macrophage activity in the colorectal cancer microenvironment………………………………..43
3.1. Abstract…………………………………………………………………………..…..….43
3.2. Introduction……………………………………………………………………...………44
3.3. Methods…………..……………………………………………………………...………46
3.4. Results…………..……………………………………………………………...………..49
3.5. Discussion……………………………………………………………………………….58
3.6. Conclusion………………………………………...…………………………………….59

Chapter 4: Flux Sampling in Genome-scale Metabolic Modeling of Microbial Communities….60
4.1. Abstract………………………………………………………………………………….60
4.2. Introduction……………………………………………………………………………...60
4.3. Methods………………………………………………………………………………….64
4.4. Results…………………………………………………………………………………...68
4.5. Discussion……………………………………………………………………………….78
4.6. Conclusions……………………………………………………………………………...81

Chapter 5: Conclusion………………………………………………………………………..…..82
5.1 Overview…………………………………………………………………………….…...82
5.2 Summary…………………………………………………………………………….…...82

vi
5.3 Future Directions………………………………………………………………………...83

References…………………………………………………………………………..………..…..85

Appendices...……………………………………………………………………………………106
A. Kinetic and data-driven modeling of pancreatic beta cell central carbon
metabolism and insulin secretion…………………………………………………….…106
B. Supplementary Information for Chapter 2……………………………………………....137
C. Supplementary Information for Chapter 3………………………………………………147
D. Supplementary Information for Chapter 4………………………………………………154

vii

List of Tables
Table 2-1. Qualitative comparison of model predictions and experimental observations…. 34
Table 3-1: Highly variable flux distributions by cell group………………………………...56

viii

List of Figures
Figure 2-1: Size of context-specific genome-scale models………………………….…..…...…23
Figure 2-2: Comparison of model ensembles…………………………………….……...……...25
Figure 2-3: Characteristics of the consensus models………………………….…………...........28
Figure 2-4: Model flux predictions………………………………………….……………..…....31
Figure 2-5: Reaction knockout analysis……….…………………………….……………..…....38

Figure 3-1: Characteristics of single-cell GEMs...........................................................................51
Figure 3-2: Differentially represented model components............................................................53
Figure 3-3: GBT-identified important reactions............................................................................55
Figure 3-4: ROBO- and ROBO+ flux differences.........................................................................57

Figure 4-1: Approaches for genome-scale metabolic modeling of communities..........................62
Figure 4-2: Pairwise analyses of the AGORA/AGORA2 set of models.......................................70
Figure 4-3: Pooled model analyses................................................................................................74
Figure 4-4: Costless secretion analysis..........................................................................................76

ix
Abstract
Macrophages are immune cells that play a critical role in the body’s response to illness,
particularly colorectal cancer (CRC). Macrophages show high versatility, as they can adapt to
different microenvironments and conditions. Their plasticity makes them challenging to
categorize definitively; however, broad groupings have emerged based on differences in
observed behavior. Cell behavior is increasingly understood to be driven by the metabolic state
of the cell; macrophage metabolism in CRC therefore warrants further study.
Traditionally, activated macrophages are classified into two general phenotypes, an "M1"
pro-inflammatory condition, and an "M2" immunosuppressive state. The M1/M2 paradigm is
relatively understudied, particularly in cancer. In the first section of this work, I use
computational modeling to understand the subtype-specific metabolic differences between the
pro- and anti-immune macrophage states. Cancer cells show distinct behavior depending on their
genetic state- certain mutations can cause the cancer cell to be more aggressive, thereby leading
to worse patient outcomes. Those cancer cell mutations also cause the associated macrophages to
act differently. One CRC mutation that is understudied but is known to drive poor patient
prognosis is the loss of the ROBO gene. In this second portion of this work, I study the metabolic
differences between macrophages surrounding CRC cells with and without the ROBO mutation
to identify potential therapeutic interventions. Finally, I develop a novel computational approach
to study the metabolic interactions between cells, enabling future work to study the way
macrophages interact with CRC cells and other cell types in the tumor microenvironment.
Altogether, this work captures macrophage metabolic activity, providing a framework to help
predict and study novel therapies in colorectal cancer

1
Chapter 1

Introduction

1.1 Macrophages play an important role in the colorectal cancer microenvironment.
Colorectal carcinoma (CRC) is among the leading causes of cancer deaths, with less than
a 10% survival rate for patients with metastatic disease
1,2
. One of the major contributors to the
progression of CRC is the immune system's failure to identify and eliminate cancer cells,
indicating a significant need to study the cells in the tumor-immune microenvironment in order
to develop more effective treatment strategies
3
.
Macrophages, immune cells responsible for engulfing and eliminating foreign substances,
play a critical role in the body’s immune response. Macrophages are highly versatile immune
cells that can adapt to different microenvironments and conditions. Their plasticity makes them
challenging to categorize definitively; however, broad groupings have emerged based on
differences in observed behavior. Traditionally, activated macrophages are classified into two
general phenotypes, an "M1" pro-inflammatory condition, and an "M2" immunosuppressive
state. The classification into the two phenotypes can be based on a range of observations,
including cell surface markers (such as CD11c or MHC II for M1 and CD163 or CD206 for M2),
extracellular factors that induce differentiation (such as IFN‐γ or LPS for M1 and IL-4 or TGF‐β
for M2), and factors secreted by macrophages themselves (such as TNF‐α or IL-6 for M1 and IL-
10 or VEGF for M2)
4–7
. In a healthy person, an increase in the number of cells exhibiting the M1
state is often seen in response to bacterial infections. In contrast, an increase in the presence of
M2 cells often occurs during the process of wound healing or angiogenesis, as the pro-

2
inflammatory and immunosuppressive states of M1 and M2 cells, respectively, provide needed
support for maintaining health in those distinct contexts.
This M1/M2 paradigm is particularly important in CRC Macrophages are the most
common immune cell type in the CRC microenvironment and are influenced by the local
microenvironment and interactions with cancer cells. The pro-inflammatory state of M1
macrophages is an effective contributor to the anti-tumor immune response in CRC
8,9
. On the
other hand, the immunosuppressive and pro-angiogenic behavior of M2 cells is utilized by the
cancer cells to promote their survival and proliferation. For this reason, M2 cells in the cancer
microenvironment are often referred to as “tumor-associated macrophages” (TAMs)
4,7,8
. An
abundance of M2 cells in the tumor microenvironment is correlated with worse prognosis for
CRC patients. Additionally, M2 macrophages can oppose the effects of chemotherapy by
providing survival factors and activating anti-apoptotic programs in cancer cells. A more
comprehensive understanding of macrophages and their role in CRC may provide key insights
into developing more effective treatments. Furthermore, intentional targeting and converting of
TAMs toward an anti-cancer phenotype may substantially improve patient response to treatment.
While the traditional M1/M2 classification system has provided a useful framework for
characterizing macrophages, the characteristics that define each phenotype remain to be fully
understood. There is substantial overlap in the features of M1 and M2 macrophages due to the
cells’ intrinsic plasticity
10
. No single classification method sufficiently accounts for all the
functional characteristics of macrophages. Thus, although being able to properly identify distinct
subgroups of macrophages, this is a challenging task. There is a need to better characterize the
heterogenous macrophage population to develop more precise immunotherapeutic strategies,

3
while simultaneously developing a more nuanced understanding of macrophage heterogeneity,
especially in the tumor microenvironment.
1.2 Macrophage metabolism defines different subgroups of cells.
The role of metabolism is beginning to be understood as a vital driver for the functional
activity of immune cell response in the two distinct phenotypes
11–13
. Macrophages alter their
metabolic pathways to meet specific functional demands in response to environmental signals,
which in turn enable inflammatory or immunosuppressive activity. That rapid adjustment in
metabolic behavior as an adaption to the local microenvironment is crucial for their proper
functioning in immune responses.
In general, the two major macrophage activation states (M1 and M2) have different
metabolic profiles. M1 macrophages, classically activated by pro-inflammatory cytokines such
as IFN-γ, use glycolysis as their primary energy source to generate ATP, which is needed for
their phagocytic and bactericidal activities. M1 macrophages also exhibit high levels of
mitochondrial respiration and oxidative phosphorylation (OXPHOS) to produce reactive oxygen
species (ROS) and reactive nitrogen species (RNS), which are necessary for microbial killing.
However, excessive ROS and RNS production may cause oxidative stress and inflammation,
which can contribute to tissue damage and pathogenesis
10
. On the other hand, M2 macrophages,
alternatively activated by anti-inflammatory cytokines such as IL-4 or IL-13, rely more on
oxidative metabolism, including fatty acid oxidation (FAO) and OXPHOS, to produce ATP. M2
macrophages also exhibit higher rates of mitochondrial biogenesis. In addition, M2 macrophages
produce anti-inflammatory mediators, such as IL-10 and TGF-β, which contribute to tissue repair
and remodeling
10
.

4
Much of our understanding of the differences in M1- and M2-like metabolism comes
from emergent “-omics” technologies. Genomics, transcriptomics, proteomics, fluxomics, and
metabolomics techniques have all been used to study macrophage metabolism, providing
valuable insight into metabolic pathways and regulatory mechanisms that are activated in
different macrophage states
14–16
. This -omics characterization is valuable and has revolutionized
our understanding of biology in many contexts. However, there are limitations in the utility of
such data. The different types of collected -omics data are unfortunately often difficult to couple
together, for example, because it is hard to bridge scales and meaningfully connect
transcriptomics and metabolomics. Furthermore, -omics data may be limited in scope, as in some
cases, it is extremely difficult to obtain whole-cell data. Finally, relevant biological insights
obtained from -omics characterization in a specific experimental condition are often difficult to
extend or apply to novel contexts. Computational modeling has emerged as a method to address
each of these limitations, thereby enabling broader utilization of -omics data to make new
predictions and generate novel biological insights.

1.3 Systems biology approaches enable mechanistic understanding of cellular metabolism.
Systems biology approaches allow one to probe and predict metabolic behavior
analytically. Systems biology combines qualitative experimental data with an in silico modeling
platform to understand a biological system
17
. In particular, systems biology uncovers how
individual components influence observed outputs. Most systems biology modeling is either
data-driven, wherein machine learning or statistical approaches are applied to identify
correlations in the data, or mechanistic, where the known interactions between systems

5
components are represented mathematically as a set of equations. Though both data-driven
statistical approaches and mechanistic techniques are valuable, mechanistic modeling is
particularly valuable because it pairs known detail on the system and biological processes (often
collected from literature) with data, to make predictions rather than simply be descriptive.
Most mechanistic modeling can be categorized as “bottom-up” or “top-down”, broadly
describing the scope of the model. Bottom-up mechanistic modeling focuses specifically on a
small part of the whole system, using detailed equations and rate parameters to predict dynamics.
Because it may be difficult to collect all model parameters, the bottom-up approach is generally
limited in scope to a relatively small number of reactions. For example, my modeling work on
pancreatic beta cells (PBCs) in Appendix 1 uses a bottom-up approach, describing the kinetics of
PBC metabolism using ordinary differential equations
18
. With 65 reactions and approximately
300 kinetic parameters, this is a relatively large equation-based kinetic model. As the model size
grows, so does the number of parameters, and it becomes increasingly difficult to maintain
parameter identifiability. Top-down approaches trade detail for scope, as they allow for much
larger models but lack the detailed kinetic parameters that fully describe the system. For
example, genome-scale metabolic modeling can predict the activity of metabolism networks
containing more than 10,000 reactions. However, this approach sacrifices the molecular detail
that is present with kinetics modeling. In this work, we use genome-scale modeling to predict
macrophage metabolism at the whole-cell level, seeking to describe the metabolic capabilities of
the cell.

6
1.4 Genome-scale metabolic modeling integrates large-scale datasets to predict the
metabolic activity of cells.
Genome-scale metabolic modeling is a computational approach used to simulate and
predict metabolic processes in cells
19
. Development of a genome-scale model (GEM) involves
the reconstruction of a metabolic network at the whole genome level, which is a comprehensive
description of all the metabolic reactions occurring in a given organism. GEMs are constructed
by compiling and integrating information from various sources, including genomic annotations
and biochemical databases. Once constructed, the metabolic model can be used to predict
cellular phenotypes under different conditions by simulating the flow of metabolites through
metabolic pathways. Specifically, each metabolic reaction is represented by a stoichiometric
equation, which describes the conversion of substrates to products. These stoichiometric
equations are typically organized into a matrix called the stoichiometric matrix or S matrix. The
S matrix has rows corresponding to metabolites and columns corresponding to reactions, and
each matrix element represents the stoichiometric coefficient of the corresponding metabolite in
the corresponding reaction. The S matrix therefore allows the cell’s metabolism to be represented
as a series of linear equations, which in turn allow for mathematical predictions of the functional
state of the cell.
The S matrix is also linked with gene-protein-reaction (GPR) rules, a Boolean matrix
specifying the genes needed for the reaction to occur. For example, a simple GPR rule might
state that a reaction can only occur if a specific gene product is present and active. More complex
GPR rules can also account for isoenzymes or alternative pathways. Those GPR rules enable the
integration of -omics data onto a metabolic model. For example, transcriptomics data can be used

7
to constrain the activity of reactions that are known to be catalyzed by enzymes that are
upregulated at the mRNA level
20
. Similarly, proteomics data can be used to constrain the activity
of reactions that are known to be catalyzed by enzymes that are present and active at the protein
level
14,16
. Those distinct -omics data types can be integrated concurrently, allowing the GEMs to
act as data scaffolds that are made context-specific, allowing the investigation of cells under
different conditions.
With a generated (data-constrained) GEM, it is possible to predict metabolic flux, the
flow of material through the network at a given time point. This involves solving the system of
linear equations defined by the stoichiometric matrix and set of constraints. The constraints limit
the range of possible flux values based on known experimental or physiological data, such as
reaction directionality, enzyme expression levels, and thermodynamic feasibility. The most
common technique to predict those metabolic fluxes is flux balance analysis, a form of linear
programming that solves an underdetermined system of equations by maximizing the value of a
cellular objective, such as the production of biomass
21
. Flux sampling has also emerged as a way
to probe the metabolic network by generating a large number of potential flux distributions
22
.
Regardless of technique used, the predictions of flux through the curated metabolic network links
-omics data with phenotype and function. The network can then be applied to predict activity in
new contexts, such as the effect of gene knockouts, nutrient availability, or drug treatments on
cellular metabolism.
1.5 Dissertation Outline
In this work, I have used genome-scale metabolic modeling to better understand
macrophage metabolic activity in CRC. In Chapter 1, I utilize CRC patient transcriptomics data

8
to probe the metabolic differences between M1- and M2-like macrophages. I generated a cohort
of context-specific models, using a range of data integration techniques. These models
characterize the M1- and M2-specific metabolic states. The models show key differences
between the M1 and M2 metabolic networks and capabilities. I then leverage the models to
identify metabolic perturbations that cause the metabolic state of M2 macrophages to more
closely resemble M1 cells. The work therefore delineates cell type-specific metabolism of M1
and M2 cells and identifies novel immunometabolic treatment strategies for CRC patients.
The M1/M2 convention is an oversimplified classification system that does not fully
capture the heterogeneity of macrophages in vivo. Thus, in Chapter 2, I generated a population of
macrophage metabolic models from single-cell RNA sequencing data that characterizes cells in
the tumor microenvironment of ROBO+ and ROBO- CRC pre-clinical mouse models. The work
describes the range of metabolic behavior across a heterogeneous population of macrophages.
Furthermore, I apply the models to identify possible mechanisms by which the downregulation
of CRC ROBO gene (which is correlated with poor patient outcomes) modulates the tumor
microenvironment and influences the metabolism of macrophages. Altogether, this work
identifies clinically relevant biomarkers that can inform future studies.
Cancer cells and macrophages interact in the tumor microenvironment by exchanging
metabolites that can alter the metabolic state of each cell type. Thus, we sought to understand
how a cell’s metabolic function changes when grown together with other types of cells,
compared to when it is grown alone. However, existing mathematical techniques for simulating
metabolic interactions of metabolic models were insufficient for modeling the tumor
microenvironment, as all approaches have utilized flux balance analysis. This analysis applies

9
the explicit assumption that the simulated cells are oriented towards maximal growth, which is
often inaccurate for immune cell metabolism. In Chapter 3, I therefore use genome-scale
modeling with flux sampling approaches to study metabolic interactions of microbial
communities. In doing so, I explore a range of sub-maximal growth rates and alternative optima.
In order to be more accessible to the field of genome-scale modeling as a whole, I focus on
microbial communities as a test case for the method, finding substantial differences in predicted
capability and community-wide metabolic outcomes. Future work can apply our novel approach
to probe metabolic interactions between cells in the tumor microenvironment.
In summary, I use genome-scale metabolic modeling to predict the behavior of
macrophages in colorectal cancer. In particular, I identify differences between the broad M1 and
M2 categories, investigate variation in the metabolic activity within a population of
macrophages, and finally develop a computational approach to explicitly simulate metabolic
interactions in coculture. Altogether, this work captures macrophage metabolic activity at the
whole-cell level, providing a framework to help predict and study novel therapies in colorectal
cancer.

10
Chapter 2

Genome-scale modeling predicts metabolic differences between macrophage subtypes in
colorectal cancer

Portions of this chapter are adapted from:
Patrick Gelbach and Stacey D. Finley.
BiorXiv, 2023; doi.org/10.1101/2023.03.09.532000 (accepted for publication by iScience)

2.1 Abstract
Colorectal cancer (CRC) shows high incidence and mortality, partly due to the tumor
microenvironment, which is viewed as an active promoter of disease progression. Macrophages
are among the most abundant cells in the tumor microenvironment. These immune cells are
generally categorized as M1, with inflammatory and anti-cancer properties, or M2, which
promote tumor proliferation and survival. Although the M1/M2 subclassification scheme is
strongly influenced by metabolism, the metabolic divergence between the subtypes remains
poorly understood. Therefore, we generated a suite of computational models that characterize the
M1- and M2-specific metabolic states. Our models show key differences between the M1 and
M2 metabolic networks and capabilities. We leverage the models to identify metabolic
perturbations that cause the metabolic state of M2 macrophages to more closely resemble M1
cells. Overall, this work increases understanding of macrophage metabolism in CRC and
elucidates strategies to promote the metabolic state of anti-tumor macrophages.

11
2.2 Introduction
Colorectal cancer is the fourth most common cancer in the world, and the second most
common cause of cancer-related death in the United States
1
. Even with the current standard of
care and new therapies, CRC patients have a high rate of relapse, and resistance to therapy is a
key contributor to morbidity and mortality. Part of the difficulty in effectively treating CRC is
the complexity of the tumor microenvironment (TME), which arises from the diverse range of
cell types and extracellular matrix components surrounding the tumor. The TME is composed of
cancer cells, stromal cells such as fibroblasts and immune cells, and extracellular matrix
components such as collagen and proteoglycans
2–4
. The interactions between these different cell
types and matrix components can influence the behavior of cancer cells and affect response to
therapy
5,6
. Moreover, these interactions can promote an immunosuppressive environment and
support drug resistance. Thus, understanding the interactions between the different cell types and
matrix components in the TME is crucial for developing effective therapies for CRC.
One aspect of the TME that is not fully understood is its metabolic profile. Tumor cells
have a distinct metabolic state compared to normal cells, characterized by high rates of glucose
uptake and lactate production. This metabolic shift, known as the Warburg effect, allows cancer
cells to generate energy and biomass at an accelerated rate, which supports tumor growth and
progression
7,8
. The cells surrounding the tumor influence and are influenced by the cancer cells,
and thus experience metabolic changes and the emergence of phenotypically distinct subgroups
within a given cell type
9
. Macrophages are among the most common cells in the TME, and are
responsible for a wide variety of immune activity in the body; therefore, the distinct cell subtypes
within the macrophage population are of particular interest
10,11
.

12
Simplistically, macrophages are classically considered to be polarized into two broad
categories: a pro-inflammatory (M1) state, or a pro-resolving (anti-inflammatory, M2) condition.
The M1 state is responsible for initiating and sustaining immune responses. M1 cells are often
activated in response to foreign infections, causing the secretion of cytokines and other
bactericidal mediators. The M2 state is associated with a reduction in microenvironment
inflammation, as the cells release anti-inflammatory mediators and collagen, which encourage
tissue repair
12,13
. More recent evidence shows that macrophages can exist in a continuum of
states; however, consideration of the pro- and anti-tumor classification is well-supported and
historically accepted, and therefore is deserving of further research
14,15
.
The clear distinction in cellular behavior of macrophages has for a long time been viewed
as strongly related to differences in intracellular metabolism
16–18
. Technological advances in
omics-level profiling provide insights into the metabolic preferences of macrophages.
Metabolomics, the comprehensive and systematic analysis of intracellular metabolites, enables
characterization of the cell’s metabolic status
19,20
. Metabolomics studies show that M1 cells
demonstrate dependence on glycolysis and the catabolism of arginine to nitric oxide. In contrast,
M2 cells are shown to preferentially utilize oxidative phosphorylation and are oriented towards
the production of urea and polyamines, which are used as mediators of wound healing
13,21,22
.
However, most metabolomic studies of macrophage subtypes are limited in their scope,
as they focus on quantifying the levels of intracellular metabolites. Although it is useful to
quantify the metabolite levels, it is difficult to infer cell function and to assess metabolic state of
a cell solely based on the levels of individual metabolites. Rather, the rates of the complex
network of biochemical reactions that the metabolites participate in are highly indicative of the

13
metabolic state of a cell
23
. However, since it is difficult to capture flux measurements at the
whole-cell level, most studies have focused on central metabolism and only a few accessory
pathways
24–27
.
Beyond technical limitations, there are context-dependent effects on macrophage
metabolism that are difficult to capture. For example, although it is known that cancer cells
encourage macrophages to convert from an M1 to an M2 state (also known as tumor associated
macrophages, or TAMs), a quantitative understanding of the effects of cancer cell-induced
metabolic reprogramming of macrophages is relatively unknown
28
. It is not clear what metabolic
alterations exist in cancer-induced macrophages. With a better understanding of the states of
macrophages in the tumor microenvironment, it may be possible to identify strategies to
modulate macrophage metabolism and improve the outlook for CRC patients.
Genome-scale metabolic models (GEMs) are promising tools to address the limitations of
purely experimental metabolomics-based studies. These models consist of two connected
matrices: a stoichiometric (S) matrix showing all the cell’s known metabolites and metabolic
reactions, and a gene-protein-reaction (GPR) rules matrix showing the enzymes and genes
known to be linked to those reactions. The S-matrix allows for the study of cellular metabolism
with linear algebra approaches (such as flux balance analysis)
29,30
. The GPR rules permit multi-
omic data integration, allowing the GEM to act as a scaffold onto which collected data can be
overlayed, thus generating context-specific models
31
. It is therefore possible to predict the
distribution of material (flux) through the metabolic network to quantitatively characterize cell
state and cell phenotype. The predicted flux values are constrained by known biological
properties (such as thermodynamic limits or measured cell activity) or by context-specific

14
confines (such as the availability of extracellular nutrients). Thus, genome-scale modeling is
often called a “constraint-based” analysis of metabolism
32
. The modeling technique emerged in
studies of bacterial and yeast metabolism but has been increasingly utilized in the field of cancer
biology. This is because genome-scale modeling takes advantage of -omics datasets to infer
function and phenotype among all metabolic reactions without a dependence on difficult-to-
obtain kinetic parameters that are required for other modeling techniques
33,34
.
There has been limited work in using genome-scale modeling to understand macrophage
biology and phenotypic divergence. Bordbar et al. studied the host-pathogen interactions of
human alveolar macrophages in tuberculosis, but did not account for variation in M1 and M2
states
35
. In another paper, the same group modeled M1 and M2 distinction and macrophage
activation in a murine leukemia cell line
36
. However, the authors did not account for differences
in structure of the metabolic model between the two macrophage subgroups, instead simulating
the same model with different cellular goals. Similarly, Wang et al. generated a generic model of
human macrophage metabolism, but did not analyze the model’s ability. In this work, we
generate the first example of human-specific models of cancer-associated M1 and M2
macrophage metabolism, based on in vivo -omics data. We analyze the structure of the metabolic
models and predicted fluxes to reveal differences in the metabolic states of M1 and M2
macrophages in CRC. The metabolites and reactions shown in our models to distinguish M1 and
M2 cells match the commonly accepted M1 and M2 metabolic markers, providing confidence
that the models can be used to further investigate macrophage metabolism. Thus, we apply the
models to identify therapeutic targets to induce M2 cells towards an M1-like state, potentially
informing future immunotherapies in colorectal cancer.

15
2.3 Materials and Methods
2.3.1 RNA Sequencing Data
Li et al. collected 1,591 cells from 11 patients with primary stage CRC and profiled the
cells using a single-cell RNA sequencing protocol
37
. Eum et al. processed the data collected by
Li et al., identified CRC-associated macrophages, and categorized the cells as M1 and M2 based
on the presence of accepted cell surface markers and by comparing to reference transcriptomes
38
.
In total, 98 M1 macrophages and 56 M2 macrophages were identified and analyzed with single-
cell RNA sequencing. This sequencing analysis identified 3,216 and 3,187 measured genes in
M1 and M2 macrophages, respectively, that are present in the Recon3D model of human
metabolism
39
. We pooled the measured single-cell data into subtype-specific “pseudo-bulk”
transcriptomics profiles to use for development of the macrophage GEMs
40
.
2.3.2 Data Integration
We integrated the RNA sequencing data into the Recon3D model of human metabolism
using the constraint-based reconstruction and analysis (COBRA) Toolbox (version 3.0,
implemented in MATLAB [Mathworks, Inc.])
41
. Recon3D is among the most recent and
complete models for human metabolism, consisting of 3,288 open reading frames, 13,543
reactions and 4,140 metabolites in 103 distinct pathways in a generic human cell. Several
algorithms exist to integrate transcriptomics data into a generic model of species metabolism,
thus allowing for the generation of context-specific models that can be applied to infer cellular
phenotype and intracellular flux distributions
42
. Each integration approach has its own set of
steps and settings used to determine which reactions should be maintained in or removed from
the base model, given the transcriptomics data. In order to minimize the effect of algorithm

16
selection on cellular predictions, we selected five commonly used algorithms and applied each
one with the aforementioned transcriptomics data. Specifically, we use: (1) integrative metabolic
analysis tool (iMAT), (2) gene inactivity moderated by metabolism and expression (GIMME),
(3) cost optimization reaction dependency assessment (CORDA), (4) integrative network
inference for tissues (INIT), and (5) FASTCORE
43–47
. We describe each, and its relevant
properties and parameters, below.
2.3.2.1 iMAT
This method first divides genes profiled in the transcriptomics data into low-, moderate-,
or high-expression levels. iMAT then maximizes the presence of reactions corresponding to
highly expressed genes and minimizes the presence of reactions linked to low expression genes.
The method thus finds the optimal tradeoff between retaining reactions related to highly
expressed genes and removing reactions related to genes with low expression. We used the top
25% of expressed genes as the cutoff for “high” expression, and the bottom 25% as “low”
expression.
2.3.2.2 GIMME
This method removes “inactive” reactions. These are reactions where the corresponding
RNA transcript level is below a specific lower threshold or reactions that are not required for
user-defined core functionality. GIMME requires an objective function to be maximized, and we
used ATP maintenance. To ensure that the choice of objective function did not largely impact the
generation of model, we also set biomass maintenance as a selected objective. However, there
was no difference in the models generated.
2.3.2.3 CORDA

17
The CORDA method determines the high-, medium-, and low-confidence reactions based
on the transcriptomics data. The method then includes all high-confidence reactions and aims to
maximize inclusion of high confidence reactions while minimizing inclusion of low-confidence
reactions. We define the confidence level based on gene expression: “high” corresponds to the
genes with expression in the top 25%, “medium” confidence reactions as middle 50%, and “low”
as bottom 25% expression levels.
2.3.2.4 INIT
INIT assigns weights to each reaction based on the corresponding gene’s expression
level, then finds the optimal tradeoff between keeping reactions with high weights and removing
reactions with low weights. We calculated weights as:
𝑅𝑒𝑎𝑐𝑡𝑖𝑜𝑛 𝑊𝑒𝑖𝑔ℎ𝑡 =5 ×log 3
𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑙𝑒𝑣𝑒𝑙
𝑐𝑢𝑡𝑜𝑓𝑓 𝑣𝑎𝑙𝑢𝑒 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑡𝑜 𝑡𝑜𝑝 25% 𝑜𝑓 𝑔𝑒𝑛𝑒𝑠
?
2.3.2.5 FASTCORE
This method first defines core reactions: reactions corresponding to genes with high
expression. FASTCORE then searches for a flux consistent network, one that has a nonzero flux
for all of the core reactions and a minimum number of additional reactions. We define genes
with high expression as those in the top 25% expression level of the transcriptomics data.
2.3.2.6 Consistency Between Algorithms
We maintained consistency between algorithms by using the same definition of high and
low gene expression, set of important metabolic tasks relevant to macrophages, and objective
functions. As described above, when there was a threshold required for a gene to be considered
highly expressed, we used the top 25% of the measured data. Similarly, if a cutoff was required

18
for a gene to be designated as low expression, we used the bottom 25% of measured genes. We
ensured inclusion of reactions and metabolites responsible for set of metabolic tasks for which
there is clear evidence in macrophages (Supplementary Table 1). We also ensured the inclusion
of synthetic or pseudo-reactions that represent cellular maintenance functions and are commonly
used as objective functions when simulating the model. Namely, we maintained the biomass
reaction, biomass maintenance reaction, ATP maintenance reaction, and ATP maximization
reactions. Because those reactions represent a lumped biological function and are not directly
measurable in transcriptomics, they would otherwise be removed by the integration algorithms.
2.3.3 Consensus Models Generated via REDGEM Pipeline and Benchmark Analysis
In addition to the individual M1 and M2 models produced by each of the five integration
approaches, we produced a single consensus model for M1 macrophages and a single model for
M2 macrophages using the REDGEM pipeline. REDGEM provides a minimal model from a
user-provided set of reactions of interest
48
. We applied the approach to the list of consensus
model components for each subtype (the genes, reactions, and metabolites found in three or more
of the five derived models), thus obtaining a consolidated model that contained the high-
confidence components. We compare the consensus-derived models of M1 and M2 macrophage
metabolism produced by REDGEM to identify similarities and differences in the genes,
reactions, and subsystems for the two macrophage subtypes. We then analyzed all 12 context-
specific GEMs (10 obtained from integrating transcriptomics data and two consensus models
obtained from REDGEM) using MEMOTE
49
. The MEMOTE test suite analyzes a GEM for
proper annotation and formal correctness, benchmarking the model across four domains: (1)
annotation – ensuring the model is annotated according to community standards; (2) basic tests –

19
checking the correctness of the model, including metabolite formulas, charge, and GPR rules; (3)
biomass – confirming that the model can produce required biomass precursors and thus simulate
cell growth; and (4) stoichiometry – reporting stoichiometric errors and permanently blocked
reactions.
2.3.4 Flux Predictions
2.3.4.1 Flux Balance Analysis
We performed flux balance analysis (FBA) to calculate the steady state reaction fluxes
that account for the stoichiometric and mass balance constraints given by the S-matrix, together
with the flux bounds for each reaction. As the system is underdetermined, an objective function
is specified to predict the optimal set of reaction fluxes required to maximize or minimize the
objective function
50
. Though a single cellular objective (i.e., maximizing biomass or minimizing
ATP usage) is often reasonable when simulating prokaryotic metabolism, it may not be
applicable for higher-order species. In particular, multiple objective simulations may better
represent the metabolic behavior of mammalian cells
51–53
. Thus, we selected objective functions
that collectively comprise the cellular goals of macrophages. For M1 cells, we selected biomass
maintenance, ATP maintenance, and activity of the inducible nitric oxide synthase (iNOS)
enzyme, which is shown to be important for M1 macrophages
54,55
. For M2 cells, we used
biomass maintenance, ATP maintenance, and activity of the arginase 1 (ARG1) enzyme, as it has
been used to identify M2 cells
13,56,57
.
2.3.4.2 Flux Sampling
We performed flux sampling to explore the achievable flux distribution of context-
specific GEMs using the Riemannian Hamiltonian Monte Carlo (RHMC) algorithm
58
. Flux

20
sampling does not require an objective function and can produce many sets of feasible flux
distributions, thus providing confidence values and insight into the range of possible fluxes for
each reaction
59
. In total, we generated 50,000 flux samples per model subtype.
2.3.5 Comparison of Reaction Flux Distributions
With distributions containing a range of flux values for each reaction, we compared the
activity of each shared metabolic reaction present in the M1 and M2 models using the Kullback-
Leibler (KL) divergence
60
. The KL divergence is a statistical metric categorizing the difference
between two distributions. A KL divergence of 0 indicates that the two distributions are
equivalent. Previous work has categorized reaction flux distributions as being in “close
agreement” if the KL divergence is less than 0.05, “medium agreement” if between 0.05 and 0.5,
and “largely divergent” if greater than 0.5
61,62
. Thus, we applied the same cutoffs when
evaluating the KL divergence for the flux distribution for each reaction present in M1 and M2
macrophage GEMs. It is important to note that the KL divergence metric is one-sided. That is,
the KL divergence of M1 versus M2 is not equivalent to the KL divergence of M2 versus M1.
For that reason, we performed the divergence calculation in each direction and then averaged the
two divergence values to arrive at a single distance metric for each reaction. Similarly, we
calculated the average KL divergence metric for each subsystem present in the M1 and M2
models to determine the pathways whose flux values differ between the M1 and M2 models.
2.3.6 PageRank Analysis
We performed a flux-weighted PageRank analysis to determine the relative importance of
the metabolic reactions present in both the M1 and M2 GEMs
63–65
. This approach provides a
graph theory-based measure of connectivity of the metabolic network, scaled by the flux through

21
the reaction. The PageRank algorithm was originally developed to determine the most important
nodes for a set of search engine results, but has since been applied to other graph-based
questions, including understanding the connectivity of metabolic networks. The flux-weighted
PageRank value indicates how significant each metabolic reaction is, allowing for efficient
comparison between two GEMs and identification of reactions that likely drive the observed
metabolic phenotype.
2.3.7 Reaction Knockouts
We simulated a reaction knockout by setting the upper and lower bounds for the flux
through that reaction to zero. We subsequently performed flux sampling to predict the reaction
fluxes in the knockout metabolic model. We were particularly interested in how the reaction
knockout affects the flux distributions for all reactions originally classified as highly divergent
between the unperturbed M1 and M2 models. Thus, we used t-distributed stochastic neighbor
embedding (t-SNE), an unsupervised dimensionality reduction technique, to represent the
distributions for the highly divergent reactions
66
. In doing so, we represented the predicted flux
distributions for the unperturbed and knockout models as points in two-dimensional space. We
calculated the cosine distance between points for the unperturbed M1 model and knockout
models. That distance was normalized to the distance between the unperturbed M1 and M2
models. Finally, the percent change was calculated as:
1−
‖𝑀1−𝑀2
!"
‖
‖𝑀1−𝑀2
#$
‖

2.4 Results
2.4.1 Ensemble modeling of macrophage metabolism

22
We generated in silico models of macrophage metabolic activity by integrating data into
a generic GEM of human metabolism (Recon3D). Using patient-derived data (described in the
Materials and Methods section), we employed five methods (CORDA, GIMME, IMAT, INIT,
and FASTCORE) to integrate the patient-derived transcriptomics data and produce context-
specific metabolic models. Each approach uses distinct algorithms to maintain or remove
metabolic reactions from a generic GEM based on gene expression data. By using five
approaches, we generated a suite of five context-specific metabolic models for each of the
macrophage subtypes (M1 and M2). We maintained consistency in input parameters (the same
base model, data, and identical ranges of the top and bottom 25% of measured genes designated
as “highly expressed” and “lowly expressed”, respectively). However, there was significant
variation in size of the resulting models (Figure 1A). INIT produced the smallest models, while
CORDA and GIMME retained most model components and thus produced large models that
were similar in size to the input model. Furthermore, for a particular data integration algorithm,
the size of the M1 and M2 models were nearly the same (Figure 1B and 1C). This reveals that
the model integration approach, rather than the experimental data, was the primary cause for
divergence in model composition, as shown in the pairwise clustering of M1 and M2 models.

23

Figure 1: Size of context-specific genome-scale models. A. Size of models generated by integrating patient-derived
transcriptomics data from M1 and M2 macrophages using five distinct approaches. B. The number of components (genes,
reactions, and metabolites) and stoichiometric matrix rank for each model generated.

We then sought to analyze consistency of the suite of generated models. We first
evaluated the context-specific models with the MEMOTE test suite, which assesses model
feasibility and correctness (particularly, stoichiometric and thermodynamic consistency and
appropriate annotation). We found no stoichiometric, charge, or thermodynamic errors. No
model had orphan metabolites or dead-end reactions, and there were sufficient GPR rules for
each model reaction. None of the models generated had errors, pointing to the validity of each
integration approach.
We next compared model components (metabolic genes, reactions, and metabolites)
across the five models generated for each subtype. We calculated the number of models that
contained a particular component. That is, we determined the presence of each model gene,
0 2000 4000 6000
0
2000
4000
6000
8000
10000
Metabolites
Reactions
recon3d
GIMME
iMAT
INIT
CORDA
FastCore
GIMME iMAT INIT CORDA FastCore
0
5000
10000
15000
Number of M1 Components
Rank: 5660 2895 964 5658 2122
Reactions
Metabolites
Genes
GIMME iMAT INIT CORDA FastCore
0
5000
10000
15000
Number of M2 Components
Rank: 5671 2965 837 5651 2118
A. B.
C.

24
reaction, and metabolite across the ensembles of models. This is shown in Figure 2A. As
expected, when the ensemble cutoff (the number of models that must contain the component) is
more restrictive, fewer model components meet the threshold. We further investigated the
relationship between the integration algorithm used and presence or absence of a model
component, as shown in the Venn diagrams of Figure 2B. Because INIT tends to produce
smaller models, most model components included by that approach are also found in the other
techniques. Conversely, the models produced by CORDA and GIMME contain genes, reactions,
and metabolites that are not included in models produced by other approaches, since these two
algorithms produce much larger models. Interestingly, those components tend to be shared by the
two techniques, highlighting a similarity in the algorithms’ methods of pruning of the base
model.

25

Figure 2: Comparison of model ensembles. A. Number of genes (top), reactions (middle), and metabolites (bottom) that are
found in the GEMs for various ensemble thresholds. B. Venn diagram showing the number of model components shared between
models generated by each integration algorithm: genes (top), reactions (middle) and metabolites (bottom) for M1 (left) and M2
(right).

2.4.2 Consolidated M1- and M2-specific models
Having demonstrated the quality of individual models, we aimed to arrive at a single
consensus model for each of the M1 and M2 macrophage subtypes, to clearly understand
metabolic differences between the cells. For each subtype, we compiled a list of model
components found in a majority (at least three) of the five generated models. That list of
metabolic components was then used to develop consensus M1- and M2-specific models. We
applied the RedHuman technique to develop the minimal models connecting the model

26
components consistently found in the M1 and M2 model ensembles. The RedHuman pipeline
uses a human base model (Recon3D), thermodynamic information on human metabolic
reactions, and a set of desired model components to generate high confidence reduced or core
models. We therefore generated consensus models characterizing the M1- and M2-specific
metabolism. The two consensus models are of similar size (Figure 3A) and share most model
components, highlighting the overall similarity within the macrophage cell type. However,
differences that arise between the two phenotypes are related to subtype-specific function.
Additionally, we compared those subtype-specific minimal models to the other available
GEM of human macrophage metabolism, published by Wang and coworkers in 2012 as part of
the mCADRE draft model extraction technique
67
. That model is built on the RECON1 base
model, which is substantially less detailed than the RECON3d base model used to build our
models. Furthermore, the mCADRE monocyte-derived macrophage model does not differentiate
between the M1 and M2 subtypes. Despite these differences, all genes, reactions, and
metabolites found in the M1- and M2-specific models developed here were also found in the
model by Wang and coworkers. However, their model was substantially larger than the M1 and
M2 models produced here (10602 reactions versus 7069 [M1] and 7249 [M2]; 5835 metabolites
versus 3717 [M1] and 3857 [M2]; and 2248 genes versus 2012 [M1] and 2038 [M2]). We
believe this indicates that our generated models contain components present in macrophage
metabolism without containing superfluous reactions, thus giving additional confidence in our
approach to identify a minimal metabolic model.
Network composition is known to be a major cause of variation in predicted cell
activity
68
. To assess structural differences between the macrophage subtypes, we analyzed the

27
presence of reactions in specific metabolic pathways in the M1 and M2 models, relative to the
Recon3D base model (Figure 3B). Some metabolic pathways (including lipoate metabolism,
vitamin B12 metabolism, protein formation, xenobiotics metabolism, and biotin metabolism)
were not found to be present in either macrophage subtype. Certain complete pathways
(nucleotide sugar metabolism, heparan sulfate degradation and chondroitin sulfate degradation)
are predicted to be found only in the M2 subtype. Portions of other pathways are only found in
the M2 subtype (nucleotide sugar metabolism, C5-branched dibasic acid metabolism, and dietary
fiber binding). Finally, there are subsystems that are more prevalent in M2, compared to the M1
state, including propanoate metabolism, the urea cycle, and alanine and aspartate metabolism. \
Interestingly, there are no complete pathways found exclusively in the M1 phenotype.
However, several pathways have reactions that are found only in the M1 model. This includes
butanoate metabolism, vitamin E metabolism, thiamine metabolism, vitamin D metabolism, N-
glycan synthesis, ubiquinone synthesis, pyrimidine metabolism, and arachidonic acid
metabolism. Additionally, certain pathways contain more reactions present in M1 than in M2
(such as the xenobiotics pathway, the metabolism of Vitamin D, fatty acid oxidation, and folate
metabolism).

28

Figure 3: Characteristics of the consensus models. A. Sizes of M1- and M2-specific models, including shared (purple) genes,
reactions, and metabolites, and components only found in the M1 (red) or M2 (blue) models. B. Comparison of the pathway
composition for M1 and M2 models, relative to the pathway size in Recon3D. The pathways significantly enriched in M1 and M2
are marked with a red or blue asterisk, respectively. C. Results from FEA for the presence or absence of M1 and M2 metabolic
pathways. Red and blue dotted lines represent significant values of p=0.05 for M1 and M2 models, respectively; the diagonal line
represents the case where M1 and M2 subsystems are equally enriched.

To more robustly quantify differences between the M1 and M2 consensus models, we
performed flux enrichment analysis (FEA)
41,69
. The approach provides a statistical metric for the
overrepresentation of metabolic components in a model relative to a reference state. We
compared each subtypes’ reactions to the Recon3D base model and calculated the enrichment
score and p-value for each metabolic pathway. The results of the approach are shown in Figure
3C, where the adjusted p-value for M1 and M2 pathways are shown on the x- and y-axes,
respectively. Dots to the right of the vertical p=0.05 dashed red line on the x-axis are pathways
considered highly enriched in the M1 model, and dots above the horizontal p=0.05 dashed blue

29
line are highly enriched in the M2 model. The list of pathways is provided in Supplementary
Table 2.
Most metabolic pathways that are enriched compared to the Recon3D base model are
present in both macrophage subtype models (highlighted in purple), comprising 24% of all
metabolic pathways. This implies those metabolic pathways are particularly important to
macrophages but are not subtype-specific. The pathways include glycerophospholipid
metabolism, peptide metabolism, N-glycan metabolism, and pyruvate metabolism, all of which
are traditionally outside of standard metabolomic analyses but may be of particular importance to
macrophage function.
M1-specific enriched pathways (9% of all metabolic pathways) include pyrimidine
metabolism and propanoate metabolism, which have both been heavily implicated with the M1
macrophage immune response
70–73
. Additional pathways include the PPP, which is viewed as
indicative of metabolic reprogramming towards an M1 state, along with ubiquinone metabolism
and the urea cycle
26,74
.
M2-specific significant pathways, which constitute 4% of all pathways consist of
aminosugar metabolism, C5-branched dibasic acid metabolism, eicosanoid metabolism, and
nuclear transport. In particular, the metabolism of eicosapentaenoic acid-derived eicosanoids has
previously been determined to be a major sign of macrophage polarization towards an M2
state
75
.

2.4.3 Analysis of Model Flux Distributions

30
A cell’s distribution of metabolic fluxes is a useful metric for evaluating cellular state and
comparing between distinct phenotypes. We therefore compared the predicted metabolic flux
distributions for the two macrophage subtypes in order to determine reactions and pathways that
are differentially utilized. Namely, we performed flux sampling with the RHMC algorithm,
generating 50,000 flux distributions for each model. We then performed multi-objective FBA to
predict the optimal flux distribution with the chosen objectives. By performing a comparative
analysis on those predicted fluxes for shared reactions, it is possible to characterize the
metabolism of the two subtypes.
With sampling, we found that most metabolic reactions show nearly equivalent mean flux
values in the M1 and M2 subgroups, as shown in the diagonal trend seen in Figure S1A.
Similarly, reactions exhibiting small or wide variance in metabolic flux tend to do so for both
M1 and M2, as shown in the roughly diagonal trend seen in the standard deviation plotted in
Figure S1B. However, the off-diagonal points (where flux values differ substantially for the M1
and M2 case) indicate differential fluxes between the two cell subtypes. When using MOFA
optimization (Figure S1C), we see a near-inversion of the metabolic state, with many reactions’
fluxes showing different directionality and a minimal number along the diagonal. This suggests
that, if we assume maximal orientation of cellular material towards divergent cellular goals
(through selection of objective functions), we will see vastly distinct metabolic states.
To better capture the differences between sampled fluxes, we used the Kullback-Leibler
(KL) divergence metric to compare the flux distributions of metabolic reactions present in both
the M1 and M2 consensus models. The KL divergence metric categorizes the dissimilarity
between two distributions. Thus, we performed a pairwise analysis for each reaction shared

31
between the two models. As shown in Figure 4A, the flux distributions of only 19% of the
reactions present in both the M1 and M2 consensus models are in close agreement, with "low”
divergence (KL divergence value < 0.05). Approximately 20% of the shared reactions have very
different flux distributions or “high” divergence in the M1 and M2 models (KL divergence
value > 0.5) groups. The majority of shared reactions (61%) had “medium” divergence across the
two macrophage subtypes.

Figure 4: Model flux predictions. A. KL divergence values from pairwise comparison of flux distributions for reactions present
in the M1 and M2 consensus models. B. Comparison of the weighted PageRank scores for M1 and M2 consensus models for all
shared metabolic reactions (circles). Red, reactions that were highly important in M1 but not M2; blue, reactions that were highly
important in M2 but not M1. C. Comparison of the metabolite rankings between the M1 and M2 consensus models. Subtype-
specific metabolites: red, M1 and blue, M2.

At the pathway level, there are key differences in the flux distributions between the M1
and M2 consensus models. We calculated the average flux divergence score across the metabolic
subsystems and found five pathways for which the reactions had significantly distinct flux
distributions between the M1 and M2 models: butanoate metabolism, linoleate metabolism,
alkaloid synthesis, nucleotide metabolism, and vitamin E metabolism. Each of those pathways
has previously been shown to be involved in the anti-inflammatory or pro-inflammatory activity
0.0001 0.001 0.01 0.1 1 10 100
0.00
0.25
0.50
0.75
1.00
Averaged (bi-directional) KL Divergence
Cumulative Percentage
of Reactions
1261 reactions 4095 1379
0 20 40 60 80 100
0
20
40
60
80
100
M1 Reaction PageRank Percentile
M2 Reaction PageRank Percentile
0 20 40 60 80 100
0
20
40
60
80
100
M1 Metabolite Ranked Percentile
M2 Metabolite Ranked Percentile
A. B. C.

32
of macrophages
70,76–81
. Thus, this quantitative analysis complements experimental evidence
pointing to differences between macrophage subtypes.
We then calculated the relative importance of each metabolic reaction by pairing a graph
theory-based calculation of network centrality (the PageRank algorithm) with the predicted
metabolic fluxes. The flux-weighted centrality scores were compared between the two subtypes
and are shown in Figure 4B. Thirty-three reactions emerged as only important for M1 cells, and
28 emerged as only important for M2. Most of those were transport reactions, highlighting
variation in preferred metabolic fuel sources. Specifically, import of alanine, L-glutamine, and
His-Glue are more important for M1, while transport of L-leucine, chitobiose, and formate are
more important for M2. Non-transport reactions that were impactful were generally related to
central carbon metabolism and ganglioside metabolism for M1, with malic enzyme and
ganglioside galactotransferase both emerging as important. M2 cells showed strong scores for
Coenzyme-A-related reactions involved in fatty acid metabolism, with the production of both
phytanyl-CoA and hexadecanoyl CoA found to be significant.
As a complement to the analysis of reaction importance, we sought to use a metabolite-
centric approach to elucidate subtype-specific differences. We calculated the flux-sum values for
each metabolite in the model, to understand the relative importance of each metabolite in the
network. The flux-sum value is defined as one-half of the sum of fluxes in and out of a
metabolite pool and is often used to characterize the metabolite’s turnover rate
82
. We compared
the score for each metabolite present in the two cell type-specific metabolic models. This
analysis revealed 19 metabolites whose usage differed substantially in the two subtypes: 9
specific to M1 and 10 specific to M2. Influential M1 metabolites include adenosine and G3P,

33
which have both been connected to the immune response seen in macrophages, as well as several
amino acids (arginyl-valyl-tryptophan and aspartyl-glutamate) and two coenzyme A-activated
acyl groups ((7Z)-hexadecenoly CoA and (6Z,9Z)-octadecadienoyl CoA). M2 metabolites of
importance include cholesterol ester, which has been suggested to be related to M2 polarization,
D-mannose, which is thought to suppress inflammatory (M1) state, and four other coenzyme A-
activated acyl groups (3-oxotridecanoyl CoA, (S)-3-hydroxytetradecanoyl CoA, (S)-3-
hydroxyoctadecanoyl CoA, and nonanoyl CoA)
83–87
. The emergence of distinct CoA-related
metabolites agrees with and builds upon past work emphasizing the divergent role of fatty acid
metabolism in the M1/M2 paradigm
88–91
.
Altogether, by pairing predictions of metabolic flux distributions with network topology,
and by evaluating metabolism from both a reaction- and metabolite-centric view, we produce an
in-depth understanding of the divergent macrophage metabolic phenotypes.
2.4.4 Model validation
To validate the model predictions, we compared model composition and predicted flux
with canonical characteristics of M1 and M2 macrophages, provided in Table 1. We identified
12 metabolic features from the literature regarding commonly accepted differences between the
M1 and M2 phenotypes. The large majority of these features (10 out of 12; 83%) are accurately
captured by our model predictions, providing confidence in the generated model structure and
flux distributions. Notably, many of those metabolic features reported in the literature are from
fluxomics-based in vitro studies, which were not used for model building, highlighting the ability
of the model to predict novel data and types of experimental analyses. Our model fails to show
increased M1 PPP pathway flux and increased M2 glutaminolysis pathway flux; however, we

34
observe increased M1 PPP reaction representation (when comparing model makeup) and
increased M2 flux for individual glutaminolysis reactions, though the pathway-level fluxes were
not significantly distinct.
Additionally, though the general TAM-like phenotype is broadly linked to CRC patient
prognosis, we provide a column explaining the link between our predicted metabolic
characteristics and established clinical outcomes and pathological characteristics. In this way, we
explicitly link model predictions with relevant outcomes
92
.

Experimental
Observation
Model match and notes Effect on Cancer cell and Patient Prognosis
Higher flux
through iNOS
reaction in M1
than M2
54,55,70

• Correlation with favorable patient outcomes
105,106

• Encourage MAPK-mediated ROS-induced killing of
tumor cells
107–109

• Encourage CD8+ T-cell proliferation, thus promoting
cytotoxicity
110,111

• Observed “bystander antitumor effects” shown via iNOS
gene delivery and overexpression
112

Higher flux
through ARG1
reaction in M2
than M1
56,57,70

• Causes suppression of T cell activity
56,113

• Promotion of Warburg-like metabolism in CRC
114,115

• Arginase-1 is correlated with suppression of CD8+
activity
116

More citrate and
succinate
presence in
M1
70,117–119

Higher turnover rate for
citrate and succinate
• Citrate drives inflammatory mediators, icnluding NO,
ROS, and PGE2
70

• Succinate accumulation stabilizes HIF-1alpha and thus
impacts inflammatory response, and drives glyxolysis in
M1 cells
22,70,120

Higher glycolytic
flux in M1
22,70

• Nutrient competition with cancer cells
121,122

• Glycolytic flux is associated with production of increased
proinflammatory/anticancer cytokines
Higher oxidative
phosphorylation
flux in M2
70

• By shifting from a glycolytic state, the TAMs avoid
nutrient competition with cancer cells
121

• Oxphos metabolism in TAMs is believed to promote PD-
L1 expression
122–124

35
Higher PPP flux
in M1
22,70,74

´
PPP reaction presence is
enriched in M1, though flux
is not significantly higher
• PPP generates NADPH, which is a required cofactor for
iNOS and NO metabolism, which in turn prevents M1-to-
M2 transition and enables ROS production (and cancer
killing)
22,125
7/18/23 11:52:00 AM
Higher fatty acid
synthesis in
M1
22,70,74

• Fatty acid synthesis encourages IL-10 expression and
encourages matrix invasion by the cancer cells
126,127

• An increase in fatty acids drives COX2 and prostaglandin
metabolism, thus increasing ROS, NO, and RNS
presence
128

Higher fatty acid
oxidation in
M2
22,70,74,89

• Complementary nutrient sources (Warburg effect in CRC,
FAS in M2) enable maximal survival of both cells
121

• Encourages depletion of extracellular matrix components,
thus enabling tumor migration
• Inhibition of FAO has significantly inhibited tumor
growth and enhanced the efficacy of adopted T-cell
therapy
129

Higher iron
retention in M1,
release in M2
130

Fe3 substantially different,
no difference between Fe2
release
• Ferritin levels correlate with more aggressive cancer and
poor clinical outcome
131

• An increase in iron release induces proliferation and
metastasis, likely through TME iron availability,
angiogenesis, lymphangiogenesis, immunosuppression,
and anti-oxidation
130,132

Higher ROS
metabolism in
M1
108,133,134

• ROS are known to activate MAPK, leading to IL-6, TNF-
a, and IL-1B cytokine secretion, all of which are involved
in tumor killing
70,128,135

Increased
Pyrimidine
synthesis in
M2
136

• Pyrimidine synthesis and release nurtures tumor cells, and
has been shown to inhibit gemcitabine treatment in
pancreatic cancer
137

Higher
glutaminolysis
flux in M2
70,138

´
Though pathway-level
differences are not
significant, higher individual
reaction fluxes for GIDH
and ALT in M2
• Glutamine usage is associated with epigenetic
modification by histone demethylases, driving anti-
immune activity
139

Table 1. Qualitative comparison of model predictions and experimental observations.

2.4.5 Analysis of model sensitivity to perturbation

36
Having constructed and analyzed genome-scale metabolic models for the M1 and M2
macrophage subtypes, we sought to identify metabolic perturbations that could push
macrophages from a TAM-like state towards a pro-immune (and therefore, anti-cancer)
condition. In order to accomplish this, we developed a sampling-based, objective function-
independent algorithm modeled after the minimization of metabolic adjustment (MOMA)
approach. This method identifies the minimal intervention needed to push the sampled flux
distribution for a particular reaction in a candidate constraint-based model towards a desired flux
state. More detail is provided in the Methods and Materials section.
Certain metabolic perturbations are predicted to alter the flux distributions of reactions
that characterize the M2 metabolic phenotype. We first identified the top 10 M2-specific
reactions (via the flux-weighted PageRank analysis) and performed individual and pairwise
enzyme knockouts by systematically inhibiting flux through those reactions. We then sampled
the knockout models and calculated the cosine distance between the sampled flux distribution of
the knockout model and the baseline M2 model flux. This identified the flux distributions for
reactions that are “highly divergent” based on the KL value between the knockout M2 model and
baseline M2 model.
Interestingly, nearly all implemented perturbations caused the knockout M2 model to
take on a phenotype that is distinct from the baseline M2 metabolic state (Figure 5A). This result
suggests validity of using the flux-weighted centrality approach for finding potential metabolic
targets. Furthermore, we observe clear benefit from the multi-target approach, as pairwise
combinations tend to cause greater changes than single knockouts alone (compare off-diagonal
and diagonal values in Figure 5A). The largest percent change for individual enzyme knockouts

37
was achieved with the glycine synthase reaction, causing an 18% difference from the baseline
M2 metabolic state, followed closely by glyceraldehyde-3-phosphage dehydrogenase and the
formation of deoxy-fluvastatin, which each caused a 17% difference from the baseline M2
model
22,93
. The greatest impact of pairwise knockouts was achieved when the phosphate-Na+
transporter (Plt7) and phosphatidylethanolamine N-methyltransferase (PETOHMr_hs) reactions
were shut off in concert, which caused a 30% divergence away from the baseline M2 state.
Notably, that pairwise effect was slightly synergistic, as the combination outcome was greater
than the additive effect of each knockout individually (11% and 17%, respectively). The second-
largest intervention was pairing glycine synthase with the Plt7 reaction, which produced a 29%
difference between the knockout and baseline M2 models.

38

Figure 5: Reaction knockout analysis. A. KL divergence for M2 fluxes in the baseline model and knockout model for all highly
divergent reactions identified by the KL metric shown in Figure 4A. B. Visualization of metabolic flux samples in low-
dimensional space for the baseline M2 model (blue), knockout M2 model (orange), and baseline M1 model (red).

Inhibiting metabolic reactions in the M2-specific model is predicted to move the flux
distribution away from the baseline M2 metabolic state. After performing the enzyme knockouts,
we performed dimensional reduction using t-SNE on the 50,000 sampled flux distributions for
the M2 model for which Plt7 and PETOHMr_hs were inhibited. Figure 5B shows 1,000 of the
sampled flux distributions, for each of the three conditions (baseline M1, baseline M2, and
Plt7/PETOHMr_hs combination knockout M2). Each point in the figure is a flux distribution
vector for all reactions shared between the metabolic models, represented in low-dimensional
space. This analysis shows that the metabolic states of the knockout model are positioned
between the M1 and M2 baseline models, showing the metabolic perturbation elicits a shift in the
metabolic phenotype towards the M1 metabolic state.
ATPS4mi
r0178
DEOXFVShc
r0295
PETOHMr_hs
r0074
GAPD
RE1518M
r0488
PIt7
ATPS4mi
r0178
DEOXFVShc
r0295
PETOHMr_hs
r0074
GAPD
RE1518M
r0488
PIt7
10
20
30
Percent Divergence from M2 Base
40
-100 -50 0 50 100
-100
-50
0
50
100
tsne dimension 2
tsne dimension 1
M1
M2 KO
M2
A. B.

39
Overall, we identify metabolic reactions that define the M2 metabolic state and predict
how targeting those reactions influences the shift towards a more M1-like metabolic phenotype.
2.5 Discussion
Researchers have long acknowledged the importance of the immune system in cancer and
have appreciated the influence of intracellular metabolism on observed cellular activity.
However, cancer immunometabolism, the convergence of immunology and metabolism in
cancer, has only seen intense interest in recent years. It is thought that a proper understanding of
the metabolic mechanisms impacting immune cell behavior may inform promising therapies in
cancer
94,95
. Excitingly, the increased interest in cancer immunometabolism has coincided with a
significant expansion in our technical ability to measure cell content, with large -omics datasets
generated by high-throughput experimental approaches
96
. Those datasets provide substantial
insight into the variation between cells and the effect of the environment on observed
phenotype
97–99
. However, a complete characterization of metabolism can be difficult for many
reasons, including the limited availability of a sufficient number of cells and the dynamic nature
of metabolism. Genome-scale modeling of metabolism has emerged as a possible solution to
comprehensively understand cellular metabolism, allowing integration of -omics datasets to
generate novel biological insight. The models integrate and synthesize data to mechanistically
understand metabolism.
In this work, we generate M1- and M2-specific GEMs of human macrophage
metabolism. The models are the first to study human macrophage subtypes in cancer at the
genome-scale and are built specifically with patient-derived transcriptomics data. The models are
consistent with existing knowledge of cancer-associated macrophages and predict clear

40
differences between the metabolism of the M1 and M2 subtypes, both structurally (the
composition of the metabolic network) and functionally (quantitative predictions of the
utilization of the metabolic reactions). In particular, those differences in flux distribution
between the M1 and M2-like groups are known to affect patient outcomes, particularly through
interactions with other cells in the TME. For example, high iNOS flux (predicted by our model
in M1 cells) both drives cytokine-mediated tumor cell killing and encourages CD8+ T-cell
recruitment, key aspects of a proper immune response in cancer, and therefore of vital clinical
relevance.
In making M1- and M2-specific metabolic models, we combine existing approaches and
algorithms into a coherent methodology that can be applied to other cell types and conditions in
the future. In particular, by generating a set of models using a variety of model pruning
algorithms, we developed an approach that limits bias resulting from the selection of a single
data-integration technique. The models were analyzed as an ensemble, an approach that has
previously been shown to increase model predictive accuracy, but has not been applied to sets of
models generated from distinct -omics data integration techniques
100–102
. The large variation
within the ensemble suggests that future work should identify additional methods to remove
user-imposed bias in model generation, particularly as the availability of -omics data increases.
For both the M1 and M2 subtypes, we consolidated the ensemble of models into a single
consensus model for each subtype. We assessed model composition and combined a variety of
analytical and statistical methods to characterize the divergence and similarities of the two
macrophage subtypes. The approach also allows for rapid assessment of interventions to alter the
predicted metabolic state, allowing the genome-scale models to act as hypothesis-generation

41
tools with powerful predictive capability. The predictions reveal promising strategies that can be
experimentally tested in future work.
With established and validated GEMs of M1 and M2 macrophage metabolism, there are
many newly available directions of research. For example, in this work we operate with the
standard FBA assumption that the system is at a steady state. Future efforts could relax that
constraint, thereby using these models to predict dynamics and the way in which cellular
metabolism changes over time
103
. Second, though the M1-M2 scheme is relatively well validated
and supported in previous studies, it is a substantial oversimplification of the nature of
macrophage phenotypes. Namely, macrophages are extremely plastic, and demonstrate
significant heterogeneity, both across a population and throughout a single cell’s lifespan. Future
work may assess and quantify macrophage metabolic heterogeneity. Finally, these cells do not
exist in isolation, but are influenced by and affect neighboring cells. There has been work to
understand metabolic interactions between GEMs, but it has largely been limited to microbial
interactions. Future studies may apply those techniques to understanding the tumor
microenvironment as well, including GEMs of immune cells such as the ones produced in this
work
104
.
In summary, we utilized genome-scale metabolic modeling to investigate the differences
in M1 and M2 macrophage subtypes in colorectal cancer. We compared model composition and
predicted metabolic activity, furthering our understanding of the subtypes’ metabolic states and
capabilities. Furthermore, we identified potential metabolic targets that might push M2
macrophages toward an anti-cancer condition, potentially improving patient outcomes. Overall,

42
this work is a substantial advance in our understanding of macrophage metabolic state and
activity.
We acknowledge some limitations of our work. We analyzed and simulated the
consensus M1 and M2 models, comparing model components and assessing their network flux
distributions. We found clear and consistent metabolic signatures particular to each phenotype
and find literature support for many of the model predictions. However, because the models are
built directly from patient data, the source or exact cause of those observed signatures cannot
fully be determined. We attempted to limit the effect of patient-to-patient heterogeneity by
merging the measurements into a pseudo-bulk dataset, but it is not entirely clear how much of
the metabolic phenotype we predict is due to differences in the metabolic states of M1 and M2
macrophages, patient-specific differences, or metabolic reprogramming caused by cancer cells
and other cells in the tumor microenvironment. Similarly, due to a paucity of experimental data
characterizing the intracellular metabolism of macrophages (outside of major central metabolic
pathways), it is difficult to make direct comparisons that fully validate our predictions.
Nevertheless, the experimental observations collected in Table 1 provide the most relevant and
informative insight for model validation. Future work can be done to test the model predictions,
starting with in vitro experiments and progressing to in vivo studies.

43

Chapter 3

Single-cell genome-scale modeling of macrophage metabolic activity in the colorectal
cancer microenvironment
3.1 Abstract

Macrophages play an essential role in the tumor microenvironment in colorectal cancer
(CRC). These cells can take on divergent phenotypic states, either limiting or supporting disease
progression (M1 and M2 macrophages, respectively). Studies have demonstrated that CRC cells
have altered metabolism and can influence the metabolism of neighboring cells in the tumor
microenvironment. These metabolic alterations influence cellular growth and contribute to
invasion, metastasis, and drug resistance. Though it is known that macrophage phenotypes
heavily depend on the cells’ intracellular metabolism, few studies have quantitatively
investigated how cancer cells, and their mutational status, influence macrophage metabolism.
Furthermore, metabolic heterogeneity within a population of macrophages is not fully
understood. In this work, we use single-cell transcriptomics and genome-scale modeling to
generate metabolic models for an in silico population of macrophages. We apply the models to
identify variations in the structure and activity of the metabolic network across the population.
Here, we focus on how the ROBO gene in CRC cells, which influences metastasis, affects
macrophage metabolism. We characterize the metabolic variation across the simulated
macrophage population, find critical metabolic pathways and reactions driving phenotypic states,
and identify promising subnetworks contributing to the heightened progression of disease seen in
CRC influenced by ROBO.

44
3.2 Introduction
Macrophages are a vital component of the immune system and make up a substantial part
of the tumor microenvironment in colorectal cancer. They can broadly be categorized into the
pro-immune, pro-inflammatory (anti-cancer) M1 state or the pro-cancer M2 state associated with
increased angiogenesis, tissue remodeling, and immunosuppression
1–4
. The divergent phenotypes
exhibit substantially distinct metabolism
5–8
. Though it is known that macrophages show
substantial heterogeneity and plasticity with their metabolic behavior, the extent to which a
macrophage population exists on a gradient between the extreme M1 and M2 states and varies in
its metabolic activity has not been characterized, particularly within the context of colorectal
cancer.
The importance of the diversity of metabolic states is important to study in the context of
cancer. It is particularly challenging to define population-wide metabolic variation because
macrophages do not exist alone in the tumor microenvironment but are influenced by the
combination of other cell types, secreted metabolites, and inflammatory factors
3,9,10
. The impact
of the colorectal cancer cells on macrophage activity also depends on the particular CRC genetic
makeup and aberrations. One such gene that is known to impact CRC activity is ROBO
11–13
.
ROBO genes encode transmembrane receptors that are essential in axon guidance and cell
migration during development. In colorectal cancer, downregulation of ROBO1 and ROBO2
expression has been associated with increased metastasis and poorer patient outcomes
14–16
.
Recent research has shown that the downregulation of ROBO in CRC cells leads to
alterations in the behavior of macrophages in the TME. Specifically, decreased expression of
ROBO in leads CRC cells to exhibit increased expression of the chemokine CXCL12, which

45
recruits monocytes to the tumor site
11,17
. These monocytes differentiate into pro-tumor
macrophages that support tumor growth and progression. Additionally, the downregulation of
ROBO1 in tumor cells decreases the expression of the ROBO1 ligand SLIT2, which generally
promotes macrophage polarization towards an anti-tumor phenotype
18
. These alterations in
macrophage behavior are thought to be driven by changes in the secretion of cytokines and
chemokines by tumor cells, which in turn influence the phenotype of macrophages in the tumor
microenvironment.
Despite these findings, the impact of ROBO expression in CRC cells on macrophage
metabolism is understudied. Decreased ROBO expression in cancer cells is generally thought to
alter the metabolism of macrophages to support tumor growth and progression. However, there is
a need for a more detailed characterization of the metabolic state of macrophages in CRC cells
lacking ROBO. Given the range of macrophage states shown to occur in CRC, it is particularly
important to understand how ROBO- CRC cells influences heterogeneity of macrophage
metabolic activity
3
. Here, we use single-cell transcriptomics measurements taken from
macrophages isolated from mouse tumors grown from ROBO+ and ROBO- CRC cells. We use
these data together to generate genome-scale metabolic models (GEMs) for a population of in
silico macrophage cells. We analyze those generated metabolic network for each simulated cell,
identifying variations in network structure and metabolic activity. We paired our predictions of
metabolic network flux with a machine learning approach and identified the metabolic reactions
likely leading to the differential metabolic states within the population of macrophages. This
work provides quantitative and mechanistic insights into the metabolic heterogeneity of
macrophage subtypes.

46
3.3 Methods
3. 3.1 Single-cell transcriptomics data used
Single-cell RNA sequencing data was collected for macrophage cells in the
microenvironment of tumors grown by injecting SW480 cells subcutaneously into NSG mice.
The SW480 cells were found in two broad subgroups: CRC cells with the presence or absence of
the ROBO gene. The macrophage cells were categorized into three states based on cell-surface
markers: M1 (tumor-associated macrophage (TAM)-negative), M2 (TAM-positive), and cycling.
In total, 1288 macrophage cells were obtained : 24 ROBO+ M1, 839 ROBO- M1, 253 ROBO+
M2, 56 ROBO- M2, 19 ROBO+ cycling, and 97 ROBO- Cycling. There were 2481 genes in the
RNA sequencing data that were present in the base metabolic model, and 996 genes were
measured on an average (range: 517-1691, median: 996) for each cell.
3.3.2 Generation of Single-cell metabolic models and flux distributions
Genome-scale metabolic modeling involves estimating the flow of material (flux)
through a metabolic network. This type of modeling aims to represent the entire set of metabolic
reactions known to be present in the cell
19–23
. The GEM consists of two matrices. The first is a
stoichiometric (S) matrix, where each row represents a metabolite, and each column represent a
reaction. The second is a gene-protein-reaction (GPR) matrix, which is a Boolean matrix
categorizing the relationship between the metabolic genes, the proteins encoded by those genes,
and the metabolic reactions carried out by the proteins. The entries of the S matrix are the
stoichiometric coefficients of each model reaction, thus allowing the S matrix to describe the
metabolism as a series of linear equations. The GPR matrix enables multi-omics integration of
data into the model, allowing the metabolic model to be context-specific. The resulting context-

47
specific GEM is used to study metabolic differences between cell or tissue types, between
treatments, or between time points
21,24–27
.
In this work, we apply the Recon3D generic model of human metabolism, overlaying
single-cell RNA sequencing data to generate metabolic models of individual macrophage cells.
The integrative metabolic analysis tool (iMAT) was used to generate the context-specific single-
cell models, implemented in MATLAB (Mathworks, Inc.)
29
. The iMAT algorithm maximizes the
presence of reactions linked to the genes with high (top 25%) expression, while minimizing the
presence of reactions corresponding to lowly-expressed (bottom 25%) genes. Genes with RNA
expression in the interquartile range were maintained if necessary for the presence of highly
expressed genes. A gene was similarly permitted but not intentionally included or removed if it
was unmeasured. We manually included the biomass reaction in all models
30
. The generated
models were checked for errors such as stoichiometric or thermodynamic inconsistencies and
"dead-end" metabolites with the MEMOTE test suite to ensure model correctness
31
.
We analyzed the structure of the GEMs, comparing the genes, reactions, metabolites, and
pathways present. In particular, we calculated the Hamming distance between set of reactions for
a pair of GEMs. For each GEM, we made an n-by-1 vector, where n is the number of reactions in
the Recon3D base model. Each entry in this vector was set to 1 if the reaction was present in the
GEM, or 0 if absent
32
. We calculated the Hamming distance for this vector between all possible
pairs of GEMs. We averaged the distance values for each of the six groups (cycling, M1, and M2
cells from ROBO+ tumors and cycling, M1, and M2 from ROBO- tumors) to quantify the
average within-group and between-group heterogeneity in model structure.
3.3.3 Predicted flux distributions

48
We performed flux sampling on each GEM using the Riemannian Hamiltonian Monte
Carlo (RHMC) algorithm, generating 5000 flux distributions for each model
33,34
. After an initial
round of flux sampling for a GEM, we determined the maximal growth rate obtained. We then
performed flux sampling again, this time setting the lower bound of the biomass reaction to be
25% of the model's maximal growth. In this way, we established a basal growth rate for the
predicted flux distributions obtained by sampling for each simulated cell
22,23
. To enable
comparison of the flux distributions, each reaction flux value was normalized by dividing by the
sum of the absolute value of all fluxes in the network for that sample. We also calculated the
mean and standard deviation for each reaction flux for each cell.
3.3.4 Gradient-boosted tree analysis of flux distribution
We applied machine learning to analyze the group-wide differences between model flux
values. We used the sampled flux values as the input to a gradient-boosted tree (GBT) algorithm
(implemented with the sklearn package in Python), with the associated group labels as the
output
35
. Eighty percent of the data were randomly selected for training, with 20% held out as an
independent testing set. The GBT was trained and analyzed, and important features (individual
metabolic reactions) were identified. We calculated the accuracy, the F1 score (the harmonic
mean of precision and recall), and the Matthews Correlation Coefficient (MCC) for each GBT
run using the true positive (TP), true negative (TN), false positive (FP), and false negative (FN)
values. These quantities were calculated using the equations below, as previously described.
𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 =
𝑇𝑃+𝑇𝑁
𝑇𝑃+𝑇𝑁+𝐹𝑃+𝐹𝑁

𝐹1 𝑆𝑐𝑜𝑟𝑒 =
2𝑇𝑃
2𝑇𝑃+𝐹𝑃+𝐹𝑁

49
𝑀𝐶𝐶 =
𝑇𝑃 × 𝑇𝑁−𝐹𝑃×𝐹𝑁
M(𝑇𝑃+𝐹𝑃)(𝑇𝑃+𝐹𝑁)(𝑇𝑁+𝐹𝑃)(𝑇𝑁+𝐹𝑁)

That data splitting, training, testing, and feature extraction approach was repeated 100
times, and we calculated the average metrics across the set of runs. Impactful reactions were
classified according to their metabolic subsystem. The flux distributions of the metabolic
reactions identified as impactful were compared between groups using the Wilcoxon Rank Sum
Test, with p < 0.05 considered significant.
3.4 Results
3.4.1 Generation of Metabolic Models
We generated an in silico cohort of 1288 GEMs, representing single-cell macrophage
metabolism. By utilizing single-cell transcriptomics data (see Methods)GEMs, we captured M1,
M2, and cycling macrophage states in both ROBO+ and ROBO- CRC tumors (Figure 1A). The
GEMs were error-checked with the MEMOTE test suite, and no errors or inconsistencies were
found. The models range in size from 3915 to 6344 reactions, 2722 to 4473 metabolites, and 946
to 2350 genes. However, model size did not correlate with cell type or CRC condition (Figure
1B). Model size also did not directly correlate with the number of measured genes in the single-
cell RNAseq measurement, suggesting that the specific genes and their abundance influence
model composition much more than the number of genes measured in a particular cell, as shown
in Figure S1.
The presence and absence of reactions exhibited bimodality, as ~20% of the reactions in
the Recon3D base model were removed from all generated models with the iMAT approach
(shown in red), and ~10% of all reactions were present in all generated macrophage models

50
(shown in blue) in Figure 1C. Most reactions shared across the generated suite of models
correspond to or support essential macrophage cell functions (such as the generation of ATP or
the ability to synthesize biomass). Many of the reactions absent from all models lacked
supporting data or were specific to other human cell types. Nonetheless, 10353 of the 13543
reactions were present in some, but not all, the models, pointing to the substantial variation in
model structure across the macrophage population.
We then compared the model composition between the six macrophage groups. We
found no statistically significant differences for the number of reactions, metabolites, or genes
(Figure 1D-F). This indicates that the model size is not the primary driver of any observable
metabolic differences between macrophage subgroups.

51

Figure 1: Characteristics of single-cell GEMs. (A) The number of individual GEMs in each of the three macrophage subgroups
and the two CRC ROBO mutation states. (B) Relationship between the number of metabolites and reactions across the full set of
GEMs. Cumulative probability distribution for the number of reactions present, across the full set of GEMs. Number of reactions
(D), metabolites (E), and genes (F) within each group.

3.4.2 Distance-based comparison of metabolic network composition
We next sought to compare model components between the cell subgroups, as
composition of metabolic networks is known to be a significant driver of variation in predicted
cell behavior. In particular, we aimed to identify the genes, reactions, and pathways over- or

52
under-represented in one of the six groups. Here, we assume that the differences in network
topology that emerge between the groups correspond to differences in phenotype or subtype-
specific activity. We first calculated the Hamming distance between the set of reactions for all
pairwise combinations then and averaged the distances for each group. Figure 2A shows the
average distances between cells in each group. We found that within-group heterogeneity (along
the diagonal) is less than between-group heterogeneity, and there is substantial variation within a
group of cells.
Most of the variation between groups in the population was due to six metabolic
subsystems. Figure 2B shows a heatmap indicating what percent of reactions in a pathway is
present for each group. Five of the six metabolic pathways are correlated, as they display
matching trends for all macrophage subgroups: transport (both with the extracellular
environment and into/out of the Golgi apparatus), nucleotide metabolism and salvage, and N-
glycan degradation. Those pathways show exceptionally high expression in the cycling cells and
low expression in the M1 and M2 macrophages from ROBO+ tumors, demonstrating the effects
of both cell subtype and CRC condition. Vitamin K metabolism also emerged as different across
the six groups, showing a higher presence in the ROBO+ state, both for M1 and M2. The results
suggest that the CRC mutation condition drives emergent differences in network structure more
than the distinct subtypes.
The metabolic networks can be analyzed with greater detail by focusing on differences in
individual metabolic reactions. We identified the top 20 divergent reactions in the GEMs (Figure
2C). Interestingly, six of the 20 reactions are related to homoserine, and five are in the APC
(amino acid-polyamine-organocation) superfamily, responsible for importing isoleucine into the

53
cell. This suggests that homoserine metabolism and isoleucine import are primary drivers of
differences in the metabolic network across distinct groups of macrophages. The homoserine-
related reactions tend to be present in ROBO- cells at higher frequency, suggesting the
importance of homoserine in the metabolic state of macrophages due to the CRC mutation.
Isoleucine has previously been implicated in macrophage activity, supporting the prediction of
its importance in these divergent cell subtypes
6,36,37
.

Figure 2: Differentially represented model components..(A) Average Hamming distance between reaction lists for each group.
(B) Model subsystems with representation that varied significantly between groups. (C) Model reactions with representation that
varied significantly between groups.
ROBO+ Cycling
ROBO- Cycling
ROBO+ M1
ROBO- M1
ROBO+ M2
ROBO- M2
ROBO+ Cycling
ROBO- Cycling
ROBO+ M1
ROBO- M1
ROBO+ M2
ROBO- M2
0.155
0.160
0.165
ROBO+ Cycling
ROBO- Cycling
ROBO+ M1
ROBO- M1
ROBO+ M2
ROBO- M2
Acetylation of Homoserine
Alanine-Sodium Symporter
Amino Acid-Polyamine-Organocation (Apc) : L-Ser + Orn
Amino Acid-Polyamine-Organocation (Apc): L-Ile + L-Arg
Amino Acid-Polyamine-Organocation (Apc): L-Ile + L-Cit
Amino Acid-Polyamine-Organocation (Apc): L-Phe + L-Cit
Amino Acid-Polyamine-Organocation (Apc): L-Val + L-His
Carbonyl Reductase (NADPH)
Cytidylate Kinase (CMP), Mitochondrial
Exchange of Acetyl Homoserine
Exchange of L-Homoserine
HMR_9652
L-Methionine Transport in via Sodium Symport
L-Serine via Sodium Symport
L-Tryptophan Transport in via Sodium Symport
Methionine/Leucine Exchange (Met In)
Transport of Acetyl Homoserine, Extracellular
Transport of Acetyl Homoserine, Intracellular
Transport of Glycinevia Sodium Symport
Transport of L-Homoserine, Mitochondrial
0
0.2
0.4
0.6
0.8
1.0
ROBO+ Cycling
ROBO- Cycling
ROBO+ M1
ROBO- M1
ROBO+ M2
ROBO- M2
N-glycan degradation
Nucleotide metabolism
Nucleotide salvage pathway
Transport, extracellular
Transport, golgi apparatus
Vitamin K metabolism
0.10
0.15
0.20
0.25
A. B.
C.

54

3.4.3 Gradient-Boosted Tree Analysis: Identification of important reaction fluxes
We generated context-specific flux distributions using the RHMC sampling approach for
all GEMs. The 5000 flux distributions obtained per simulated cell were averaged and given as an
input to a GBT machine learning approach. We sought to determine whether the metabolic flux
signature can predict the macrophage subtype and the corresponding fluxes that most strongly
contribute to the subtype. We compared reactions that were present in at least 75% of the GEMs
to avoid biasing the analysis by variation in model structure. We achieved 80% accuracy (±3%)
in distinguishing between groups after 100 train-test splits, with average F1 scores of 0.36±0.02
and an MCC value of 0.67±0.04. Each of those metrics is satisfactory, particularly because no
over-sampling, under-sampling, or addition of synthetic data was added to the training protocol
to account for the very unbalanced data (for example, the input matrix had 839 ROBO- M2 cells
compared to 24 ROBO+ M2 cells), as each of those approaches arguably artificially improves
evaluation measurements when it is unclear if type 1 or type 2 error is preferable. Therefore, we
can confidently utilize these techniques to identify the critical metabolic alterations specific to
each macrophage group.
We used the GBT to identify the ten most important metabolic reactions that collectively
impact group membership: Methionine Adenosyltransferase, lysosomal L-Alanine transport,
extracellular transport of Acetyl Homoserine, lysosomal transport of Glycine, intracellular
transport of Acetyl Homoserine, Serine C-Palmitoyltransferase, and four APC transporters (L-
Phenylalanine and L-Threonine, L-Methionine and L- Threonine, L-Alanine and L-Threonine,
and L-Glycine and L-Valine) emerged as influential. Six of those ten impactful reactions are

55
shown in Figure 3.

Figure 3: GBT-identified important reactions. Box plots showing the normalized flux through 6 of the top 10 most impactful
metabolic reactions, separated by group.

Interestingly, most of the variation between groups shows the M1 and M2 cells from
ROBO- tumors separated from the others. The visual separation is supported with pairwise
ANOVA comparisons, with those cell type flux values statistically significantly distinct from all
other groups (shown in supplement). This highlights that the impact of the metabolic state of
macrophages influenced by the loss of ROBO expression in the CRC cells is more significant
than the separation from the broad M1/M2 groupings.
We also identified the reactions whose flux varied the most within each group, shown in
Table 1. We calculated the coefficient of variation for each reaction flux in each cell. The
biomass reaction and reactions involving energy-related nucleosides and nucleotides (dTTP,
-0.00050
-0.00025
0.00000
0.00025
0.00050
Normalized Flux Values
Acetyl Homoserine Transport, Intracellular
-0.00005
0.00000
0.00005
0.00010
0.00015
0.00020
Normalized Flux Values
APC: L-Phe and L-Thr
-0.00010
-0.00005
0.00000
0.00005
0.00010
L-Alanine Transport, Lysosomal
-0.0002
-0.0001
0.0000
0.0001
0.0002
0.0003
APC: L-Met and L-Thr
-0.00050
-0.00025
0.00000
0.00025
0.00050
Glycine Transport, Lysosomal
ROBO+ Cycling
ROBO- Cycling
ROBO+ M1
ROBO- M1
ROBO+ M2
ROBO- M2
-0.00015
-0.00010
-0.00005
0.00000
0.00005
0.00010
0.00015
APC: L-Gly and L-Val

56
DATP, DGTP) emerge as highly variable in all groups. This result makes sense, as growth rate
and energetic demands supporting growth are generally considered a source of phenotypic
heterogeneity. Unexpectedly, all groups showed high variation in thymidine metabolism and
cardiolipin synthesis. Both of those processes have been linked to macrophage pro-immune
activation, and their activity is generally viewed as differentiating the state of the cell into the
pro-immune or pro-resolving phenotypes. Their emergence as having highly variable flux
distributions emphasizes the wide range of possible metabolic states, even within groups
categorized as M1 or M2 based on cell surface markers and traditional gene transcripts.
Table 3.1: Highly variable flux distributions by cell group.
Altogether, we generated flux samples for each generated macrophage model and used
those predictions of metabolic activity to identify the metabolic reactions most likely driving
group divergence and the reactions that exhibit substantial variance within groups.
3.4.4 Importance of homoserine metabolism
We explored the role of homoserine in distinguishing between macrophage groups.
Unexpectedly, when evaluating the composition of the metabolic networks and their sampled
flux distributions, the M1 and M2 cells from ROBO+ tumors appeared more similar, separated
from the other macrophage groups. This indicates that the influence of the CRC ROBO
deficiency on macrophages was greater than the M1-M2 classification in determining metabolic
activity. Additionally, for both M1 and M2 cells, homoserine emerged as the primary metabolite

57
involved in reactions that widely differed between the ROBO+ and ROBO- states, as shown in
Figure 4A. The ROBO- cells had substantially more homoserine uptake into the mitochondria
and substantially more flux through the acetylation reaction of homoserine, depicted in context in
Figure 4B, with the network shaded according to relative reaction flux values. Homoserine and
its related reactions have not been explored for macrophage function or cancer progression.
However, disruption of serine synthesis has been identified as a promising anti-cancer target in
TAMs. Furthermore, homoserine can act as an allosteric inhibitor of glutamate dehydrogenase,
disrupting glutamate metabolism, a biomarker of pro-cancer TAM metabolism
6,8,38
. Our
quantitative analysis of macrophage metabolism identifies homoserine as a factor that
distinguishes macrophage subgroups.

Figure 4: ROBO- and ROBO+ flux differences. (A) The median normalized flux for each reaction across the ROBO- and
ROBO+ M1 cells. (B) The median normalized flux for each reaction across the ROBO- and ROBO+ M2 cells. (C) The median
normalized flux for each reaction across the ROBO- and ROBO+ Cycling cells. (D) Schematic of the homoserine metabolism
pathway, with fluxes corresponding to L-Homoserine import and Homoserine Acetylation bolded.

58
3.5. Discussion
Phenotypic heterogeneity across a population of cells is known to substantially impact the
behavior of the tumor microenvironment and disease progression
39,40
. Cell-to-cell variability,
especially metabolic variability, enables cells in a population to perform a range of functions,
leading to population-wide emergent behavior
41
. Additionally, cellular metabolism is influenced
by other cells present in the local microenvironment. In this work, we generate a population of
genome-scale models of macrophage metabolic behavior from single-cell transcriptomics data,
assessing the population-wide heterogeneity and how the ROBO1 gene in CRC cells influences
macrophage metabolism. Metabolic modeling provides a functional snapshot of the ongoing
biological processes in a cell or organism by capturing complex genotype-phenotype-
biochemical relationships. We applied flux sampling and a machine learning approach to
interrogate the divergence in phenotype, both between classified M1, M2, and cycling
macrophages and between cells taken from the ROBO+ and ROBO- CRC tumor
microenvironment. We identify key metabolic alterations in network structure and predicted
flux, which can collectively act as potential biomarkers or therapeutic targets.
Having generated a large cohort of in silico cells, we first find that group membership
does not correlate with the size of the metabolic network, as each macrophage subtype shows
substantial variation in the model components maintained after pruning the Recon3D generic
human metabolism model with the iMAT approach. Notably, the within-group variation in
model structure is slightly lower than the between-group variation in structure. This suggests that
integration of context-specific transcriptomics data into the generic model of human metabolism
captures known cellular heterogeneity while still enabling the identification of consistent

59
metabolic characteristics particular to each group. For example, at the pathway level, we find
that M1 and M2 cells from ROBO+ tumors exhibit substantially lower N-glycan degradation- an
increase in the activation of the N-glycan receptors is linked to CRC progression
42–44
. Similarly,
nucleoside and nucleotide metabolic subsystems are overrepresented in the ROBO- M1 and M2
cells; those pathways are promising targets to enhance the pro-immune and anti-cancer response
in cancer
45,46
.
Having analyzed each cell's metabolic network and predicted metabolic flux distribution,
we find homoserine metabolism repeatedly emerges as enabling one to distinguish between
macrophage subgroups. Homoserine is necessary for the biosynthesis of serine, which is strongly
associated with increased cell migration and proliferation
47
. The mechanism by which loss of
ROBO in CRC cells impacts macrophages to encourage cancer survival and drive poor patient
outcomes may depend on the homoserine metabolism identified here. Our results can initiate
further studies to explore the role of homoserine metabolism in CRC.L
3.6. Conclusion
In this work, we investigate the metabolic variation of macrophages in the tumor
microenvironment of CRC, specifically in the context of ROBO1 gene mutation. Using single-
cell transcriptomics and genome-scale metabolic modeling, we identify critical metabolic
pathways and reactions driving differences between subgroups of macrophages. In particular, our
analyses identify homoserine metabolism in macrophages associated with ROBO- CRC. Our
findings provide novel insights into the metabolic heterogeneity of macrophages and their impact
on cancer progression.

60
Chapter 4

Flux Sampling in Genome-scale Metabolic Modeling of Microbial Communities

4.1. Abstract

Microbial communities play a crucial role in ecosystem function through metabolic
interactions. Genome-scale modeling is a promising method to understand these interactions.
Flux balance analysis (FBA) is most often used to predict the flux through all reactions in a
genome-scale model. However, the fluxes predicted by FBA depend on a user-defined cellular
objective. Flux sampling is an alternative to FBA, as it provides the range of fluxes possible
within a microbial community. Furthermore, flux sampling may capture additional heterogeneity
across cells, especially when cells exhibit sub-maximal growth rates. In this study, we simulate
the metabolism of microbial communities and compare the metabolic characteristics found with
FBA and flux sampling. With sampling, we find significant differences in the predicted
metabolism, including an increase in cooperative interactions and pathway-specific changes in
predicted flux. Our results suggest the importance of sampling-based and objective function-
independent approaches to evaluate metabolic interactions and emphasize their utility in
quantitatively studying interactions between cells and organisms.
4.2. Introduction
Microbes are essential components of all living ecosystems, and the metabolic
interactions between them are a significant factor in the functioning of these ecosystems.
Microbe-microbe metabolic interactions affect nutrient cycling, energy production, and the
maintenance of microbial diversity
1–3
. Though our understanding of those microbial
communities is aided by metagenomics and in vitro analyses, there is a significant gap in

61
mechanistic understanding of the makeup and interactions between members of microbial
consortia
4,5
.
Genome-scale modeling has emerged as a promising method by which we can probe an
organism's metabolic states, behaviors, and capabilities, either alone or as a community
6–12
.
Genome-scale metabolic modeling is a mathematical approach that uses the known biochemical
reactions of a species to reconstruct a genome-scale metabolic network. Genome-scale models
(GEMs) provide a holistic view of an organism's metabolism, allowing for mathematical
analyses that simulate metabolic fluxes and thus provide insight into metabolic pathways and
physiological processes. The genome-scale model consists primarily of a stoichiometric matrix,
characterizing the interconversion of metabolites by the set of metabolic reactions, linked with a
set of Boolean expressions describing the gene-protein-reaction relationships
40
. Flux balance
analysis is a constraint-based approach for analyzing that metabolic network to predict metabolic
fluxes through the GEM.
Much work has recently been applied to understand the metabolic interactions of a
microbial community in various contexts, including the human gut microbiota and in
environmental bioremediation
14–19
. Given the ubiquity of microbial activity, there is substantial
value in using metabolic modeling to understand these communities' emergent behaviors and
abilities.
Most metabolic modeling of microbial interactions is performed in one of three ways
(Figure 1): (1) compartmentalization, wherein two metabolic models are merged into a single
stoichiometric matrix with a shared compartment representing the extracellular space, (2) lumped
model (also called "enzyme soup") approach, where all metabolites and reactions are pooled into

62
a single model in proportion to the community makeup, and (3) costless secretion, where models
are separately simulated while dynamically and iteratively updating the simulated environment
by adjusting the models' exchange reactions and available nutrients based on metabolites that can
be secreted without decreasing growth (costless metabolites)
19–26
.

Figure 1: Approaches for genome-scale metabolic modeling of communities. Metabolic modeling of microbial communities is
largely performed using (A) Compartmentalization: a single stoichiometric matrix representing the two models joined by a
lumen compartment wherein metabolites can be freely exchanged; (B) Lumped model: a single stoichiometric matrix
representing the union of each individual model’s reactions, thereby ignoring all separation between cells; and (C) Costless
secretion: individual stoichiometric networks for each model, whose exchange reactions are constrained to reflect the shared
extracellular media.
2

Each of these approaches has shown promise, and selection of which approach to use
heavily depends on available data and models and on the intended goal of the analysis. As
currently implemented, each method uses flux balance analysis (FBA), a linear programming
technique that predicts the flow of material through the metabolic network
27–29
. FBA depends on
the maximization of an objective function, and maximizing biomass production is most
commonly used. Optimizing for biomass assumes species are entirely oriented towards maximal
growth, thus ignoring the multiplicity of achievable sub-optimal phenotypes
30
. When simulating

63
the metabolism of a community, this assumption can disregard the variety of metabolic
interactions that the microbes may carry out. Furthermore, the selection and definition of the best
objective function substantially affect model predictive power and generated results
31–34
.
As an alternative to FBA, flux sampling has recently been used to predict flux
distributions in a variety of cases and may provide a more holistic and accurate description of the
cell's flux distribution
35–39
. This is done by randomly generating many flux values for each
reaction in a genome-scale metabolic model, while respecting its defined constraints, such as
mass or energy balance and thermodynamic restrictions. Flux sampling employs Markov chain
Monte Carlo methods to estimate cellular flux and generate many feasible metabolic flux
distributions. Flux sampling estimates the most probable network flux values, enabling statistical
comparisons of the flux distributions. Notably, the approach does not require a selected cellular
objective, thus reducing user-introduced bias on model predictions and exploring the entire
constrained solution space. The approach therefore enables studies of phenotypic heterogeneity,
as a single constrained model can generate a range of flux predictions. However, flux sampling
has not been widely employed in analyses of microbial communities. Furthermore, comparisons
between FBA-based and sampling-based analyses of communities are currently lacking.
In this work, we apply flux sampling to existing analyses of microbial metabolic
interactions, showing the range of potential consortia-wide flux distributions achievable with
genome-scale modeling. We find significant differences in model predictions between FBA and
flux sampling, with substantial heterogeneity across sampled simulations. We see emergent
patterns at sub-maximal growth rates, such as increased cooperation between microbes in anoxic
conditions compared to oxygen-rich environments. In total, we systematically evaluate the effect

64
of flux sampling, and emphasize the utility of objective function-agnostic approaches to evaluate
metabolic interactions.
4.3 Methods
4.3.1 GEMs
Magnusdottir et al. generated the AGORA dataset, a collection of 773 (and later, 7206 in
AGORA2) genome-scale metabolic models comprising the human gut microbiome. These
models were simulated to understand their metabolic behavior when grown in pairwise
combinations, using the approach developed by Kiltgord and Segre
16,42,43
. Notably, the analysis
constrained the models with distinct in silico diets and aerobic states.
We randomly selected 75 of the AGORA models and analyzed all unique pairwise
combinations (2775 in total) and implemented three distinct approaches to study metabolic
interactions between microbes. In this way, we demonstrate the utility of each approach,
compared to flux sampling, while limiting computational intensity.
4.3.2 Flux sampling
We use the Constrained Riemannian Hamiltonian Monte Carlo (RHMC), which has recently
been shown to be substantially more efficient than prior sampling algorithms
41
.
4.3.3 Compartmentalization
The pairwise interaction approach used by Magnusdottier and coworkers is as follows
17
:
Step 1: Select two models.
Step 2: Introduce the lumen compartment, which joins the two models into a merged
model, where the two microbes can secrete and uptake metabolites.
Step 3: Constrain the model by adjusting exchange reaction bounds to reflect the chosen
diet and extracellular conditions.

65
Step 4: Simulate monoculture by shutting off one of the two models by inactivating all
its reactions (setting the reaction upper and lower bound to 0 flux). Then simulate the
active individual model by optimizing for growth.
Step 5: "Shut off" the second individual model by inactivating all its reactions. Then
simulate the active individual model by optimizing for growth.
Step 6: Restore the activity of both individuals in the merged model and optimize each
microbes' objectives separately. This predicts growth while allowing the exchange of
metabolites across the lumen, simulating co-culture.
Step 7: Compare paired growth with the individual growth simulations of steps 4 and 5.
If paired growth was 10% higher or lower than individual growth, the model was
considered to grow faster or slower, respectively, in co-culture than alone.

We replaced the FBA optimization in steps 4, 5, and 6 with flux sampling as an
alternative way to predict cellular flux. We used the RHMC algorithm and generated 1000 flux
distribution samples at each step. We therefore had a range of reaction fluxes (including growth
rates) for both microbes, in mono- and co-culture, with and without oxygen, and with two
different simulated diets (Western and High Fiber). We then categorized all possible
combinations of sampled growth rates, following the classes previously described: parasitism,
commensalism, neutralism, amensalism, competition, or mutualism
17
. For example, if both
models grew more in co-culture than alone, the interaction was classified as mutualism.
Additionally, by ordering the sampled growth rates, we identified distinct interaction
regimes between the two microbes. That is, we found the range of different interaction types as a
function of the different growth rates (and thus, growth demands). We note that the interaction
regimes predicted here are different than the Pareto analysis performed by Magnusdottir et al., as
calculation of the Pareto front relies on biomass optimization with FBA while iteratively
updating and fixing growth rates for each model
16
.
4.3.3 Lumped model

66
Blasco et al. extended the AGORA set of metabolic models by adding degradation
pathways that allow for the simulation of the effect of many human diets on the activity of the
gut flora
26
. After adding those metabolic reactions involved in degradation, they merged all
individual microbe models into a supra-organism model. By pooling all GEMs, they made a
single lumped model comprising all metabolic reactions and metabolites in the population.
This process is often called a "mixed-bag" or "bag-of-genes" approach. This is the
simplest form of genome-scale modeling of bacterial communities, as it does not assume any
spatial or temporal separation between the species and involves the consolidation of ubiquitous
metabolic reactions
44–47
. Nevertheless, the approach has been effective at predicting the
metabolic behavior of consortia while minimizing computation time and reducing model size.
The authors used flux variability analysis (FVA) to identify and correct blocked or low-
confidence reactions and identify the microbial metabolic byproducts produced by the
microbiota's fermentation of lentils. However, the model was not simulated to predict species
growth within the community. We therefore applied the model to predict consortia behavior.
With "mixed-bag", lumped modeling of metabolism, it is common to either merge all individual
model biomass reactions into a supra-organism growth equation or, as chosen by Blasco et al., to
maintain each model's biomass reaction within the pooled network. That allows for the
prediction of each microbe's growth.
We generated flux samples of the lumped model and compared them to the case where each
species' biomass reaction is optimized alone and to the case where the population's overall
growth is maximized. We calculated the “optimal community growth rate” by finding the

67
maximal growth rate that was possible for all models simultaneously and setting all biomass
reactions’ lower bound values to that flux value.
4.3.4 Costless Secretion
Pacheco et al. showed that the secretion of costless metabolites (species that are freely
secreted as the byproduct of a cell's metabolism, without inhibiting fitness) are critical drivers of
the metabolic interactions between cells
48
. The approach is a quasi-dynamic method, as it
maintains the modeling assumption that the system is at a steady state but successively updates
the environment shared by the two simulated cells. The method calculates the growth of each
model at each simulation iteration, finds the secreted metabolites, then updates the simulated
media until the media is stable.
The costless growth approach is as follows:
Setup: Select a simulated minimal media definition (i.e., DMEM, M9, SSM, etc.), and
define the metabolites that comprise that medium. Select N models to be simulated (i.e.,
two models for pairwise interactions, 3 models to simulate a community of 3 microbes,
etc.) Select M metabolites to be individually or provided in addition to the minimal media
(list the carbon sources to be provided, and choose m to be given at a time). Define
whether the model will be simulated in an aerobic or anaerobic environment.
Step 1: Simulate a minimal media condition by setting all exchange reactions' upper
bound values to 0 unless the reaction exchanges metabolites that are contained in the
media.
Step 2: Provide carbon source(s) M by setting the upper bound(s) of exchange reaction(s)
for the corresponding metabolite(s) to be unconstrained.
Step 3: Simulate the models by optimizing for growth.
Step 4: Note the resulting flux values for the models' transport reactions; if a metabolite
is predicted to be exported into the media, then explicitly add that metabolite to the
simulated media (again, by adjusting the models' upper bound for that metabolite's import
reaction).
Step 5: Repeat steps 3-4 until no additional metabolites are secreted, arriving at the
simulation’s final predicted growth rates.
Steps 1-5 can be repeated for a different carbon source (or combination of carbon
sources) to be added to the simulated media.

68
We adjusted step 3, replacing FBA optimization with flux sampling using the RHMC
algorithm, simulating pairwise growth with a single metabolite source. Because the costless
secretion approach repeats the model simulation steps until media convergence, we introduced a
thresholding term to consolidate the results from each simulation round. In particular, we define
the set of secreted metabolites (and thus update the extracellular media) based on whether all,
most, or any of the sampled flux distributions show a metabolite is secreted. For example, if
metabolite M was secreted in 200 of the 1000 generated flux distributions, it would only be
added to the extracellular media in the “any” cutoff simulation for the next round. If secreted in
750 of the 1000 distributions, it would be added to the “any” and “most” analyses. For the “all”
cutoff, that metabolite would only be added to the media for the following iteration if all 1000
flux distributions showed that metabolite being secreted. Thresholding is currently required
because of the computational time needed for flux sampling. Without thresholding at each
simulation, the number of sampled points needed will increase exponentially with each round of
expansions. We use each cutoff to demonstrate and assess the introduced variability, allowing us
to compare the outputs with each set threshold.
4.4 Results
4.4.1 Compartmentalized modeling
Magnusdottir et al. developed AGORA (later, updated as AGORA2), a resource for the
semi-automated generation of genome-scale metabolic models. They applied the set of models to
predict the pairwise interactions between microbes, showing how the individuals' metabolic
potential drives the emergent behavior of the pair. However, their predictions of metabolic
activity assume that each microbe is oriented towards achieving maximal growth. We introduced

69
flux sampling to the pairwise simulation framework, thus permitting any flux distribution from
the confined flux space to be included in the assessment of metabolic interactions. We selected
50 individual models and paired each together, generating 2775 unique pairwise analyses that
spanned the range of microbial taxa in the AGORA dataset. Each paired model was sampled
1000 times, with and without metabolite exchange between the microbes being allowed. As
described in the Methods, the interaction type was calculated for the anaerobic and aerobic states
with two unique simulated diets.
By analyzing the most common interaction for each pair, we calculated the total
percentage of each interaction type, shown in Figure 2A. As expected, slight differences exist
between the optimization and sampling-based analyses. Namely, antagonistic interactions
(competition, amensalism, and parasitism) tend to make up a smaller percentage of the entire set
with sampling instead of optimization (61% compared to 74%). There is an increase of 11% in
positive and net-neutral interactions (commensalism, neutralism, and mutualism) with sampling
compared to optimization-based analysis. Cases of neutralism increased from 6% to 18%, and
frequency of mutualism increased from 7% to 13%. The increase in cooperation is particularly
prevalent with anaerobic analyses, from 30% to 44%. Previous work has highlighted that anoxic
conditions induce mutualism; this effect is notably amplified with sampling compared to
simulations maximizing biomass
23
. When sampling the possible fluxes of anaerobic conditions,
there is a higher frequency of non-inhibitory relationships. In particular, there is a substantial
reduction in parasitism with a nearly equivalent increase in neutralism.

70

Figure 2: Pairwise analyses of the AGORA/AGORA2 set of models. (A) We simulated 2775 pairs of metabolic models, on two
simulated diets with and without the presence of oxygen, and calculated the expected interaction type. Interactions are defined
and colored according to the labels on the far right. Expected interaction type when pairing enterococcus faecalis and prevotella
disiens (B) and bacteriodes celiilosilyticus and pseudomonas montelli (C) and sampling a range of growth rates.
Furthermore, we see an increase in symmetrical interactions (mutualism, neutralism, and
competition, from 25% to 47%), suggesting that without orienting all metabolism towards
optimal growth, a community of bacterial species may be more inclined towards population
stability. This is because as abundances tend to remain steady when primarily exhibiting those
three interaction motifs
49,50
. Importantly, the trends of increased anoxic cooperation and
increased symmetrical interactions are found irrespective of diet constraints. This suggests that

71
the submaximal predicted growth rate that is allowed with sampling, and not the models
themselves or extrinsic factors (such as the nutrients provided), is what is driving the observed
outcomes.
Because flux sampling gives a distribution of growth rates and the corresponding flux
distributions providing for that growth, it is possible to calculate the expected pairwise
interactions likely for each combination of individual growth rates. We ranked the sampled
growth rates for each microbe and calculated the most commonly predicted paired growth rate,
thus giving interaction types for each growth rate. The sampling-based approach highlights the
variety of interactions possible between two microbes, especially given variation in simulated
conditions. Figure 2 shows this analysis for two sets of paired example microbes, represented
similar to chemical phase diagrams. The x- and y-axes represent the individual sampled growth
rates, and their intersection is colored according to the most likely expected metabolic interaction
motif. Figure 2B shows the pairwise interactions of enterococcus faecalis TX2134, a gram
positive nonmotile microbe, and prevotella disiens JCM 6632, a gram negative bacilii-shaped
bacterium. Figure 2B shows the interactions of bacteriodes celiilosilyticus and pseudomonas
montelli, two gram-negative and rod-shaped microbes. We show these calculations for four
distinct extracellular conditions: Western and high fiber diets, with and without oxygen.
When simulating the interactions of the Enterococcus and Prevotella strains in Figure
2B, five distinct types of interactions are possible, depending on the simulated environment and
each species' growth rate. Anaerobic states (columns 1 and 2) show a predominance of
commensalism or mutualism, though parasitism and amensalism are expected when Prevotella is
rapidly proliferating. In the presence of oxygen (columns 3 and 4), there are several diet-

72
independent trends: low growth of both microbes causes commensalism; high Enterococcus and
low Prevotella growth rates cause parasitism; low Enterococcus and high Prevotella growth
rates cause amensalism; and high growth of both causes competition. At intermediate growth
rates, the effect of diet is more apparent, as Western diet constraints drive amensalism and high
fiber constraints push the interaction toward commensalism, parasitism, or amensalism.
Similar insights can be gained when analyzing the interactions between Bacteroides and
Pseudomonas. For example, the anoxic high fiber condition is relatively invariant, as the two
microbes show parasitism at nearly all individual growth rates. Alternatively, there is a large set
of potential outcomes when simulating an anoxic state with a Western diet; the individual
microbe growth rates can elicit widely distinct interaction motifs. It is possible to see a single
microbe "dominate" or drive the observed interaction: in the oxygen-rich simulations, changes in
Pseudomononas growth determine the outcome, largely irrespective of a changing Bacteriodes
growth rate.
Similar analyses can be performed for all combinations of models. In sum, this sampling-
based approach highlights the variety of interactions possible between two simulated microbes,
especially given variety in modeled conditions.
4.4.2 Lumped model
By pooling metabolic reactions, it is possible to generate a single GEM that represents
community metabolic activity. The lumped GEM can then be analyzed using the same
constraint-based approaches typically utilized for single-species models. Though the technique
removes all separation between microbes, it can be a useful approach for assessing the activity
and potential of the community. However, all analyses of such "bag of genes" or "enzyme soup"

73
approaches have explicitly assumed through the assigning of an objective function, that the
community aims to maximize growth. No studies have assessed the effect of flux sampling on
the community metabolic state. We selected the AGREDA pooled model, which combined 538
AGORA models into a single metabolic network. We analyzed the lumped model with three
distinct approaches: (1) iteratively setting each individual's biomass reaction as the objective and
then solving the FBA problem (optimization), (2) performing flux sampling on the network's
flux solution space (flux sampling), and (3) finding the maximal rate at which all microbes can
simultaneously grow, then sampling the solution space when that value is set as the lower bound
for each microbe's growth rate (termed an “optimal community”). These analyses allowed us to
compare the flux distributions achieved through FBA, flux sampling, and flux sampling of the
"best state" of the microbial community.
When comparing flux sampling of the network with FBA, we first assessed the variation
between pathway fluxes to identify large-scale metabolic shifts. Interestingly, flux sampling was
not equally influential across all pathways but disproportionately affected particular subsystems.
Figure 3A shows the median normalized flux value through each pathway predicted by sampling
(y-axis) and the median flux value through the pathway when individually optimizing each of the
531 biomass reactions in the model (x-axis). That suggests the parts of the network that may be
more influential and impactful in community activity when separated from the requirement of
maximizing cellular growth. Notably, thiamine metabolism, terpenoid backbone synthesis,
tannin degradation, pyrimidine synthesis, and NAD metabolism saw substantially higher fluxes
in the sampling approach. A similar plot comparing the sampled community maximum with the
FBA approach is in the supplement, in Figure S1. As an example, we plot the individual fluxes

74
through the NAD metabolism subsystem obtained by the three techniques used to predict
reaction flux (Figure 3B). Maximization of biomass causes consistently low pathway flux, while
unconstrained or optimal community-constrained sampling predicts a wider range of flux values
that are higher compared to the fluxes predicted when biomass production is maximized. The
case with optimal community-constrained sampling produces slightly elevated pathway flux
compared to unconstrained sampling.

Figure 3: Pooled Model Analyses. (A) Median pathway flux values predicted by unconstrained flux sampling compared to
optimization of biomass. Subsystems that have significantly different median fluxes are labeled. (B) Reaction fluxes for the NAD
metabolism pathway predicted with each technique. (C) KL divergence between the distribution of fluxes achieved via
optimization and sampling. (D) Comparison of the flux-sum value for each metabolite for unconstrained flux sampling and
optimization of biomass.
At the reaction level, differences emerge between the three community analysis methods.
We compared the flux distributions for each reaction, calculating the bi-directional KL
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Median pathway flux, via optimization
Median pathway flux, via sampling
Terpenoid backbone synthesis
Thiamine metabolism
Tannin degradation
pyrimidine synthesis NAD metabolism
Optimization
Unconstrained Sampling
Community-constrained Sampling
0.000
0.001
0.002
0.003
0.004
Normalized Pathway Flux
0.01
0.1
1
10
100
1000
Model Reactions
KL Divergence
Low KL
Medium KL
High KL
0.00 0.01 0.02 0.03 0.04 0.05
0.00
0.01
0.02
0.03
0.04
0.05
Metabolite Flux Sum, via optimization
Metabolite Flux Sum, via sampling
NADP
NADPH
H
2
O UDP
Coenzyme A
UDP-glucose
A B D
C

75
divergence values
51
, shown in Figure 3C. We classified the difference in the median fluxes for
each reaction for two analysis methods into low, medium, and high divergence categories. This
calculation revealed that very few (76 of the 5499 reactions, to the left of the leftmost vertical
line) show close alignment between unconstrained flux sampling and optimization of
biomass
37,39
. The predicted flux through a majority of reactions (86%, shown to the right of the
second vertical line) is “widely divergent,” between the two approaches. This points to the
substantial differences between the optimal growth state and the total solution space.
Interestingly, a metabolite-centric view based on metabolite flux-sum analysis shows similar
turnover rates for the metabolites across the two analysis methods (Figure 3D). Metabolites that
vary widely between the two conditions include NADP, NADPH, coenzyme A, UDP, and UDP-
glucose (higher with optimization) and water (higher with sampling).
4.4.3 Costless secretion
Pacheco et al. argued that the secretion of "costless" metabolites (byproducts of the cell's
metabolism that are released without causing a loss of fitness) might be a primary driver of
interspecies interactions within a microbial community
48
. In order to study this metabolic cross-
feeding, they developed a pipeline where two GEMs are constrained to a minimal media
condition, then iteratively simulated, thus updating the media with the costless metabolites until
convergence. By using FBA, the method assumes that cells grow maximally and that all
metabolites are secreted done to enable that maximum growth. It is possible that costless
metabolites predicted to be secreted differ for distinct feasible growth rates. Therefore, while the
FBA-based is valuable, it may not fully describe the simulated system. By allowing submaximal

76
growth rates and alternative maxima through sampling, we demonstrate increased metabolic
latitude for microbial communities.

Figure 4: Costless secretion analysis. (A) Number of iterations required to achieve a stable media, for the aerobic (left) and
anaerobic (right) states for optimization of biomass or different cutoffs for flux sampling (all, most, any), plotted as a percentage
of all simulations. (B) Number of metabolites secreted for optimization of biomass or with distinct cutoffs for flux sampling (all,
most, any) for anaerobic and aerobic conditions. (C) Each simulation was categorized into one of 7 cases (the six shown in the
left panel and the case where no growth was achieved) for the aerobic or anaerobic condition.
A primary output from the costless secretion analysis is the number of iterations of model
simulation until media convergence. We simulated 648 cases (pairwise combinations of 3
microbes, with and without oxygen, with 108 distinct fuel sources provided to supplement the
minimal media). We assessed the number of iterations required to reach a steady media.
Interestingly, for both the normoxic and anoxic conditions, we see an increase in the number of
rounds of model simulation with sampling compared to the base analysis with FBA. This makes

77
sense, as a loosened restriction of growth rate allows for heterogeneous simulation results, which
include a greater possible set of metabolites to be secreted and successive changes in the
simulated media. That trend of more iterations with sampling remains even when we implement
different cutoffs for whether a secreted metabolites is present in all, most, or at least one of the
sets of sampled metabolic flux distributions (Figure 4A). Interestingly, the cutoff selected has
much less of an effect than whether FBA (leftmost column) or flux sampling (right three
columns) is chosen. We predict a much higher number of iterations in the anoxic condition, with
up to 11 iterations of media change, compared to at most 3 rounds in the aerobic state.
We indeed see an increase in the number of metabolites secreted by the microbe pairs
with flux sampling compared to FBA, as shown in Figure 4B. There is an apparent increase in
the number of predicted costless metabolites when the threshold is progressively loosened (from
all to most to any). That is reasonable, as there are outliers or secreted metabolites that are
particular to one or only few sampled flux distributions. We again predict an increase in secreted
metabolites when simulating oxygen-free environments. Specifically, for anerobic conditions,
more unique metabolites are secreted as part of the cells' metabolic flux patterns than in the
oxygen-rich environments for the two most stringent cutoffs (all and most).
Pacheco established distinct interaction types, categorized based on the secretion and
uptake rates of metabolites, using the following naming convention: non-interaction, or N, where
no used media metabolites come from either model, commensalism, or C, characterized by
unidirectional exchange, and mutualism, or M (where metabolites are interchanged between the
two models). Following this letter designation, a numerical value is used to represent the number
of carbon sources added to the environment. Finally, the letters a or b are used to specify the

78
absence and presence of competition, respectively. As an example, N1a would describe a
simulation where a metabolite is taken up by only one cell in the presence of one carbon source.
We used the same naming convention to classify our simulations (Figure 4C). Firstly, with flux
sampling, we notice substantially fewer instances of simulations where neither microbe achieved
growth (204 compared to 114 of the 324 aerobic simulations and 246 compared to 114 of the 324
anaerobic simulations). Though initially counterintuitive (that we would be more likely to
achieve growth without optimizing for it than when attempting to maximize biomass), the result
highlights the benefit of flux sampling. That is, due to the metabolic flexibility simulated with
sampling, it is more likely that a microbe would secrete a metabolite beneficial for the other and
thus enable the other cell to grow. In contrast, when each microbe is "selfishly" oriented towards
its growth at the expense of all other cellular goals (via FBA), that emergent interactive behavior
is less likely. We also note differences between the aerobic and anaerobic conditions, with the
aerobic sampling simulations producing more instances of cooperative mutualism (M1a: 90 with
aerobic sampling vs 5 with anaerobic sampling ), and the anaerobic simulations resulting in more
non-competitive non-interaction (N1a: 91 with anaerobic sampling vs 0 with aerobic sampling).
4.5. Discussion
Phenotypic heterogeneity, even in the monoculture of a genotypically uniform
population, is known to have a substantial effect on observed community outcomes. However,
the effects of this heterogeneity have been understudied, despite the rapid and substantial
increases in modeling efforts at the genome-scale. In addition, microbes have been shown to
exhibit sub-maximal growth, but this has not been sufficiently addressed with GEMs. While
phenotypic heterogeneity and sub-maximal growth dynamics have been studied in individual

79
GEMs of microbial activity , these two phenomena have not been analyzed for models of
microbial interactions
30,52–58
. In this work, we demonstrate how pairing disparate existing
approaches of flux sampling and modeling of communities pushes the field of metabolic
modeling forward. We systematically evaluate the predictive effects of replacing FBA and its
central assumption of maximal growth with flux sampling approaches.
In particular, we assess the effect of exploring the entire flux solution space with three
distinct approaches of microbial community modeling: the compartmentalized approach, the
lumped model or "enzyme soup" approach, and the costless secretion approach. With each
approach, we replicate the major conclusions achieved with optimization of biomass using FBA
For example, we predict higher frequency of cooperation under anaerobic conditions.
Furthermore, applying flux sampling expands our understanding of the systems-level
heterogeneity that gives rise to observed community activity. For the compartmentalized
approach, we show increased tendency toward stable consortia and provide an ability to identify
distinct growth rate-dependent interaction regimes. For the lumped modeling approach, we
predict large differences in the predicted flux for certain pathways and reactions than others, and
in the turnover of specific metabolites. With the costless secretion approach, we predict a
substantially wider range of metabolites secreted, enabling growth on substrates that had not
been predicted when optimizing biomass using FBA.
As previously found, most observable metabolic heterogeneity across a population has
two primary sources: variation in network structure and variation in network usage (divergence
in form and functional utilization)
59
. Ensemble modeling of GEMs has been shown to lead to
increased accuracy and is of particular focus to the field with the emergence of novel tools;

80
however, an equivalent effort has not been put towards understanding heterogeneous states
achieved with a consistent network, despite the existence of flux sampling of GEMs as a tool for
the past 20 years
60,61
. To our knowledge, one paper has used sampling to study cell-cell
metabolic interactions
62
. This gap has been identified by other researchers, and future work can
more earnestly utilize and leverage the technique
63
.
We recognize some limitations of our work. A particular weakness of genome-scale
modeling is the difficulty in assigning constraints for the reaction fluxes. Without appropriate
bounds on metabolic reaction rates, flux sampling may explore biologically unreasonable
metabolic states. The emergence of novel experimental tools is particularly promising to address
this limitation. For example, -omics technologies enable in vitro and in vivo measurements of
growth rates, metabolite secretion, and impact of enzymatic knockouts. Such data can be used to
provide biologically reasonable constraints on reaction fluxes. In addition, we used thresholding
to keep the analyses computationally feasible. However, this potentially limits our results.
Improvements in computational ability, both from advances in computing speed and algorithm
development, will enable us to investigate the full range of biological outcomes possible with
flux sampling without imposing artificial thresholds. Finally, by using flux sampling, we
evaluated microbial fitness and interspecies relationships based on growth rate, while eliminating
the necessity of maximizing biomass. Future work can explore alternative metrics to assess
cellular behavior. This is especially important because genome-scale modeling is increasingly
used for eukaryotic (principally human) cells, where growth rate as a proxy for cell health is less
supported
64–69
. For example, rather than focusing on growth, we could instead study flux through
a specific reaction or pathway known to mediate the behavior of a particular cell type.

81
4.6. Conclusion
In this work, we evaluate the effect of flux sampling on three standard approaches for
modeling the interactions between microbes at the genome scale. The method clearly
distinguishes between optimization-based and sampling-based characterizations of the metabolic
interactions within a community. We demonstrate the utility of flux sampling in quantitatively
studying metabolic interactions in microbial communities.

82
Chapter 5

Conclusion
5.1 Overview

In this work, I utilize genome-scale metabolic modeling to understand the metabolic
behavior of macrophages in CRC. I studied the differences in network structure and metabolic
flux between the broad M1 and M2 categories of macrophages. I generated and metabolic
models that help identify novel treatment strategies to push tumor-associated macrophages
towards an antitumor state. I then expanded the modeling scope, by generating single-cell
metabolic models that collectively describe the population-wide variation among macrophages. I
also examined the effect of flux sampling on metabolic modeling of cell-cell metabolic
interactions, demonstrating an approach that enables genome-scale metabolic modeling of cells
in the tumor microenvironment. Collectively, this work provides mechanistic insight into
macrophage metabolism and generates novel predictions and approaches that can substantially
aid research at the intersection of immunometabolism and precision medicine.
5.2 Summary
I first sought to describe, at a whole-cell level, the metabolism of pro-immune and
immunosuppressive macrophage states. I generated a suite of computational models that
characterize M1- and M2-specific metabolism. I apply a novel approach to produce an ensemble
of models using a variety of transcriptomics integration techniques. I consolidated the models for
each macrophage subtype to generate high-confidence M1 and M2 in silico cells. The models
show key differences between the M1 and M2 metabolic networks and capabilities. I leveraged
the models to identify metabolic perturbations that cause the metabolic state of M2 macrophages

83
to more closely resemble M1 cells. Overall, this work increases understanding of macrophage
metabolism in CRC and elucidates strategies to promote the metabolic state of anti-tumor
macrophages.
Recognizing that the M1/M2 paradigm is incomplete and masks substantial cell-cell
heterogeneity, I then applied the model-generation pipeline to generate 1288 single-cell
macrophage models that span the pro- and anti-cancer gradient while also capturing the effect of
ROBO downregulation in associated cancer cells from the CRC pre-clinical mouse model. I
determined the variation in network composition and predicted cell behavior across macrophage
subgroups. Through this analysis, I identified the metabolism of homoserine as a likely
mechanism by which the loss of ROBO influences macrophage metabolism.
In order to enable detailed modeling of cell-cell interactions in the tumor
microenvironment, I combined existing approaches in a novel way. By pairing flux sampling
with three existing techniques for modeling cells in coculture, I was able to predict metabolic
activity without needing to maximize cellular growth. I focus on microbial communities to make
the method more available to the genome-scale modeling community. Through this work, I show
that an increase in metabolic latitude (i.e., submaximal growth or multiple alternative optima)
enables better agreement with experimentally observed emergent cooperation between
organisms.
5.3 Future Directions
The computational modeling approaches described here collectively impact the fields of
genome-scale metabolic modeling and macrophage biology. However, there are many important
questions and challenges in the field that my work can help address. The most obvious and

84
immediate is applying my described novel method of flux sampling of metabolic interactions to
analyze cells in the tumor microenvironment. Macrophages do not exist in isolation. Rather, they
secrete metabolites and diffusible factors and uptake nutrient sources from a changing
environment that is constantly altered by other cell types (notably CRC cells). Understanding
how these cell-cell interactions influence and is driven by cellular metabolism can be modeled
with the method from chapter 4. This is a promising way to probe metabolic interactions in the
tumor microenvironment.
In chapter 2, I applied a range of data-integration approaches to generate a cohort of
macrophage cells. However, I attempted to maintain consistency between those techniques, for
example, by using the top 25% of expressed genes as “highly expressed” across each integration
method. The parameters for those integration techniques affect the makeup of the generated
models, but the extent to which they influence predictions is not known. In the future, it would
be valuable to study the variation in model output when those integration technique internal
parameters are adjusted. Additionally, though we focused on CRC, the variation in macrophage
metabolism in other cancer types is understudied. It would be interesting to perform this analysis
on a macrophages within other types of tumors.
In chapter 3, I studied the metabolic heterogeneity within a population of macrophages.
In this work, I generated interesting predictions of the range of metabolic behaviors across a
population. However, in addition to exhibiting within-population variation, macrophages also
show plasticity in activity across their lifetimes. I used flux sampling at a steady state for this
work, but future work can study the behavior of cells with that restraint lifted, using unsteady-
state FBA (uFBA) or dynamic FBA (dFBA).

85
References

Chapter 1
1. Karsa, L. v., Lignini, T.A., Patnick, J., Lambert, R., and Sauvaget, C. (2010). The
dimensions of the CRC problem. Best Practice & Research Clinical Gastroenterology 24, 381–
396. 10.1016/j.bpg.2010.06.004.
2. Wagner, J.S., Adson, M.A., Van Heerden, J.A., Adson, M.H., and Ilstrup, D.M. (1984).
The natural history of hepatic metastases from colorectal cancer. A comparison with resective
treatment. Ann Surg 199, 502–508.
3. Yun, C.W., and Lee, S.H. (2018). The Roles of Autophagy in Cancer. Int J Mol Sci 19.
10.3390/ijms19113466.
4. Cassetta, L., Fragkogianni, S., Sims, A.H., Swierczak, A., Forrester, L.M., Zhang, H.,
Soong, D.Y.H., Cotechini, T., Anur, P., Lin, E.Y., et al. (2019). Human Tumor-Associated
Macrophage and Monocyte Transcriptional Landscapes Reveal Cancer-Specific
Reprogramming, Biomarkers, and Therapeutic Targets. Cancer Cell 35, 588-602.e10.
10.1016/j.ccell.2019.02.009.
5. Larionova, I., Cherdyntseva, N., Liu, T., Patysheva, M., Rakina, M., and Kzhyshkowska,
J. (2019). Interaction of tumor-associated macrophages and cancer chemotherapy.
Oncoimmunology 8. 10.1080/2162402X.2019.1596004.
6. Italiani, P., and Boraschi, D. (2014). From Monocytes to M1/M2 Macrophages:
Phenotypical vs. Functional Differentiation. Front. Immunol. 5. 10.3389/fimmu.2014.00514.
7. Biswas, S.K., Allavena, P., and Mantovani, A. (2013). Tumor-associated macrophages:
functional diversity, clinical significance, and open questions. Semin Immunopathol 35, 585–
600. 10.1007/s00281-013-0367-7.
8. Wu, K., Lin, K., Li, X., Yuan, X., Xu, P., Ni, P., and Xu, D. (2020). Redefining Tumor-
Associated Macrophage Subpopulations and Functions in the Tumor Microenvironment. Front
Immunol 11. 10.3389/fimmu.2020.01731.
9. Edin, S., Wikberg, M.L., Dahlin, A.M., Rutegård, J., Öberg, Å., Oldenborg, P.-A., and
Palmqvist, R. (2012). The Distribution of Macrophages with a M1 or M2 Phenotype in Relation
to Prognosis and the Molecular Characteristics of Colorectal Cancer. PLOS ONE 7, e47045.
10.1371/journal.pone.0047045.
10. Viola, A., Munari, F., Sánchez-Rodríguez, R., Scolaro, T., and Castegna, A. (2019). The
Metabolic Signature of Macrophage Responses. Front. Immunol. 10.
10.3389/fimmu.2019.01462.
11. Biswas, S.K., and Mantovani, A. (2012). Orchestration of Metabolism by Macrophages.
Cell Metabolism 15, 432–437. 10.1016/j.cmet.2011.11.013.
12. Anders, C.B., Lawton, T.M.W., Smith, H., Garret, J., and Ammons, M.C.B. (2020).
Metabolic Immunomodulation, Transcriptional Regulation, and Signal Protein Expression
Define the Metabotype and Effector Functions of Five Polarized Macrophage Phenotypes.
bioRxiv, 2020.03.10.985788. 10.1101/2020.03.10.985788.
13. Galván-Peña, S., and O’Neill, L.A.J. (2014). Metabolic Reprograming in Macrophage
Polarization. Front. Immunol. 5. 10.3389/fimmu.2014.00420.

86
14. Hyduke, D.R., Lewis, N.E., and Palsson, B.Ø. (2013). Analysis of omics data with
genome-scale models of metabolism. Mol Biosyst 9, 167–174. 10.1039/c2mb25453k.
15. Tebani, A., Afonso, C., Marret, S., and Bekri, S. (2016). Omics-Based Strategies in
Precision Medicine: Toward a Paradigm Shift in Inborn Errors of Metabolism Investigations.
International Journal of Molecular Sciences 17, 1555. 10.3390/ijms17091555.
16. Dahal, S., Yurkovich, J.T., Xu, H., Palsson, B.O., and Yang, L. (2020). Synthesizing
Systems Biology Knowledge from Omics Using Genome-Scale Models. PROTEOMICS 20,
1900282. https://doi.org/10.1002/pmic.201900282.
17. Kitano, H. (2002). Computational systems biology. Nature 420, 206–210.
10.1038/nature01254.
18. Gelbach, P.E., Zheng, D., Fraser, S.E., White, K.L., Graham, N.A., and Finley, S.D.
(2022). Kinetic and data-driven modeling of pancreatic β-cell central carbon metabolism and
insulin secretion. PLOS Computational Biology 18, e1010555. 10.1371/journal.pcbi.1010555.
19. Passi, A., Tibocha-Bonilla, J.D., Kumar, M., Tec-Campos, D., Zengler, K., and Zuniga,
C. (2021). Genome-Scale Metabolic Modeling Enables In-Depth Understanding of Big Data.
Metabolites 12, 14. 10.3390/metabo12010014.
20. Kim, M.K., and Lun, D.S. (2014). Methods for integration of transcriptomic data in
genome-scale metabolic models. Computational and Structural Biotechnology Journal 11, 59–65.
10.1016/j.csbj.2014.08.009.
21. Orth, J.D., Thiele, I., and Palsson, B.Ø. (2010). What is flux balance analysis? Nature
Biotechnology 28, 245–248. 10.1038/nbt.1614.
22. Herrmann, H.A., Dyson, B.C., Vass, L., Johnson, G.N., and Schwartz, J.-M. (2019). Flux
sampling is a powerful tool to study metabolism under changing environmental conditions. npj
Syst Biol Appl 5, 1–8. 10.1038/s41540-019-0109-0.

87
Chapter 2
1. Long, A.G., Lundsmith, E.T., and Hamilton, K.E. (2017). Inflammation and Colorectal
Cancer. Curr Colorectal Cancer Rep 13, 341–351. 10.1007/s11888-017-0373-6.
2. Arneth, B. (2020). Tumor Microenvironment. Medicina 56, 15.
10.3390/medicina56010015.
3. Song, M., Li, D., Makaryan, S.Z., and Finley, S.D. (2021). Quantitative modeling to
understand cell signaling in the tumor microenvironment. Current Opinion in Systems Biology
27, 100345. 10.1016/j.coisb.2021.05.006.
4. Whiteside, T.L. (2008). The tumor microenvironment and its role in promoting tumor
growth. Oncogene 27, 5904–5912. 10.1038/onc.2008.271.
5. Wu, T., and Dai, Y. (2017). Tumor microenvironment and therapeutic response. Cancer
Letters 387, 61–68. 10.1016/j.canlet.2016.01.043.
6. Roma-Rodrigues, C., Mendes, R., Baptista, P.V., and Fernandes, A.R. (2019). Targeting
Tumor Microenvironment for Cancer Therapy. International Journal of Molecular Sciences 20,
840. 10.3390/ijms20040840.
7. Vander Heiden, M.G., Cantley, L.C., and Thompson, C.B. (2009). Understanding the
Warburg Effect: The Metabolic Requirements of Cell Proliferation. Science 324, 1029–1033.
10.1126/science.1160809.
8. Cairns, R.A., Harris, I.S., and Mak, T.W. (2011). Regulation of cancer cell metabolism.
Nat Rev Cancer 11, 85–95. 10.1038/nrc2981.
9. Justus, C.R., Sanderlin, E.J., and Yang, L.V. (2015). Molecular Connections between
Cancer Cell Metabolism and the Tumor Microenvironment. International Journal of Molecular
Sciences 16, 11055–11086. 10.3390/ijms160511055.
10. Qian, B.-Z., and Pollard, J.W. (2010). Macrophage Diversity Enhances Tumor
Progression and Metastasis. Cell 141, 39–51. 10.1016/j.cell.2010.03.014.
11. Biswas, S.K., Allavena, P., and Mantovani, A. (2013). Tumor-associated macrophages:
functional diversity, clinical significance, and open questions. Semin Immunopathol 35, 585–
600. 10.1007/s00281-013-0367-7.
12. Orecchioni, M., Ghosheh, Y., Pramod, A.B., and Ley, K. (2019). Macrophage
Polarization: Different Gene Signatures in M1(LPS+) vs. Classically and M2(LPS–) vs.
Alternatively Activated Macrophages. Frontiers in Immunology 10.
13. Boutilier, A.J., and Elsawa, S.F. (2021). Macrophage Polarization States in the Tumor
Microenvironment. Int J Mol Sci 22, 6995. 10.3390/ijms22136995.
14. Sica, A., and Mantovani, A. (2012). Macrophage plasticity and polarization: in vivo
veritas. J Clin Invest 122, 787–795. 10.1172/JCI59643.
15. Palma, A., Jarrah, A.S., Tieri, P., Cesareni, G., and Castiglione, F. (2018). Gene
Regulatory Network Modeling of Macrophage Differentiation Corroborates the Continuum
Hypothesis of Polarization States. Frontiers in Physiology 9.
16. Biswas, S.K., and Mantovani, A. (2012). Orchestration of Metabolism by Macrophages.
Cell Metabolism 15, 432–437. 10.1016/j.cmet.2011.11.013.
17. Wang, Y., Li, N., Zhang, X., and Horng, T. (2021). Mitochondrial metabolism regulates
macrophage biology. Journal of Biological Chemistry 297. 10.1016/j.jbc.2021.100904.

88
18. Jha, A.K., Huang, S.C.-C., Sergushichev, A., Lampropoulou, V., Ivanova, Y.,
Loginicheva, E., Chmielewski, K., Stewart, K.M., Ashall, J., Everts, B., et al. (2015). Network
Integration of Parallel Metabolic and Transcriptional Data Reveals Metabolic Modules that
Regulate Macrophage Polarization. Immunity 42, 419–430. 10.1016/j.immuni.2015.02.005.
19. Zhang, A., Sun, H., Wang, P., Han, Y., and Wang, X. (2011). Modern analytical
techniques in metabolomics analysis. Analyst 137, 293–300. 10.1039/C1AN15605E.
20. Dettmer, K., Aronov, P.A., and Hammock, B.D. (2007). Mass spectrometry-based
metabolomics. Mass Spectrometry Reviews 26, 51–78. 10.1002/mas.20108.
21. Zhu, L., Zhao, Q., Yang, T., Ding, W., and Zhao, Y. (2015). Cellular Metabolism and
Macrophage Functional Polarization. International Reviews of Immunology 34, 82–100.
10.3109/08830185.2014.969421.
22. Galván-Peña, S., and O’Neill, L.A.J. (2014). Metabolic Reprograming in Macrophage
Polarization. Frontiers in Immunology 5.
23. Nielsen, J. (2003). It Is All about Metabolic Fluxes. J Bacteriol 185, 7031–7035.
10.1128/JB.185.24.7031-7035.2003.
24. Verberk, S.G.S., de Goede, K.E., Gorki, F.S., van Dierendonck, X.A.M.H., Argüello,
R.J., and Van den Bossche, J. (2022). An integrated toolbox to profile macrophage
immunometabolism. Cell Rep Methods 2, 100192. 10.1016/j.crmeth.2022.100192.
25. Bailey, J.D., Diotallevi, M., Nicol, T., McNeill, E., Shaw, A., Chuaiphichai, S., Hale, A.,
Starr, A., Nandi, M., Stylianou, E., et al. (2019). Nitric Oxide Modulates Metabolic Remodeling
in Inflammatory Macrophages through TCA Cycle Regulation and Itaconate Accumulation. Cell
Rep 28, 218-230.e7. 10.1016/j.celrep.2019.06.018.
26. Baardman, J., Verberk, S.G.S., Prange, K.H.M., van Weeghel, M., van der Velden, S.,
Ryan, D.G., Wüst, R.C.I., Neele, A.E., Speijer, D., Denis, S.W., et al. (2018). A Defective
Pentose Phosphate Pathway Reduces Inflammatory Macrophage Responses during
Hypercholesterolemia. Cell Rep 25, 2044-2052.e5. 10.1016/j.celrep.2018.10.092.
27. Van den Bossche, J., O’Neill, L.A., and Menon, D. (2017). Macrophage
Immunometabolism: Where Are We (Going)? Trends Immunol 38, 395–406.
10.1016/j.it.2017.03.001.
28. Zhou, J., Tang, Z., Gao, S., Li, C., Feng, Y., and Zhou, X. (2020). Tumor-Associated
Macrophages: Recent Insights and Therapies. Frontiers in Oncology 10.
29. Orth, J.D., Thiele, I., and Palsson, B.Ø. (2010). What is flux balance analysis? Nature
Biotechnology 28, 245–248. 10.1038/nbt.1614.
30. Orman, M.A., Berthiaume, F., Androulakis, I.P., and Ierapetritou, M.G. (2011).
Advanced Stoichiometric Analysis of Metabolic Networks of Mammalian Systems. Crit Rev
Biomed Eng 39, 511–534.
31. Kim, M.K., and Lun, D.S. (2014). Methods for integration of transcriptomic data in
genome-scale metabolic models. Computational and Structural Biotechnology Journal 11, 59–65.
10.1016/j.csbj.2014.08.009.
32. Bordbar, A., Monk, J.M., King, Z.A., and Palsson, B.O. (2014). Constraint-based models
predict metabolic and associated cellular functions. Nat Rev Genet 15, 107–120.
10.1038/nrg3643.

89
33. Yizhak, K., Chaneton, B., Gottlieb, E., and Ruppin, E. (2015). Modeling cancer
metabolism on a genome scale. Mol Syst Biol 11, 817. 10.15252/msb.20145307.
34. Nilsson, A., and Nielsen, J. (2017). Genome scale metabolic modeling of cancer. Metab
Eng 43, 103–112. 10.1016/j.ymben.2016.10.022.
35. Bordbar, A., Lewis, N.E., Schellenberger, J., Palsson, B.Ø., and Jamshidi, N. (2010).
Insight into human alveolar macrophage and M. tuberculosis interactions via metabolic
reconstructions. Mol Syst Biol 6, 422. 10.1038/msb.2010.68.
36. Bordbar, A., Mo, M.L., Nakayasu, E.S., Schrimpe-Rutledge, A.C., Kim, Y.-M., Metz,
T.O., Jones, M.B., Frank, B.C., Smith, R.D., Peterson, S.N., et al. (2012). Model-driven multi-
omic data analysis elucidates metabolic immunomodulators of macrophage activation. Mol Syst
Biol 8, 558. 10.1038/msb.2012.21.
37. Li, H., Courtois, E.T., Sengupta, D., Tan, Y., Chen, K.H., Goh, J.J.L., Kong, S.L., Chua,
C., Hon, L.K., Tan, W.S., et al. (2017). Reference component analysis of single-cell
transcriptomes elucidates cellular heterogeneity in human colorectal tumors. Nat Genet 49, 708–
718. 10.1038/ng.3818.
38. Eum, H.H., Kwon, M., Ryu, D., Jo, A., Chung, W., Kim, N., Hong, Y., Son, D.-S., Kim,
S.T., Lee, J., et al. (2020). Tumor-promoting macrophages prevail in malignant ascites of
advanced gastric cancer. Experimental & Molecular Medicine 52, 1976–1988. 10.1038/s12276-
020-00538-y.
39. Brunk, E., Sahoo, S., Zielinski, D.C., Altunkaya, A., Dräger, A., Mih, N., Gatto, F.,
Nilsson, A., Preciat Gonzalez, G.A., Aurich, M.K., et al. (2018). Recon3D enables a three-
dimensional view of gene variation in human metabolism. Nat Biotechnol 36, 272–281.
10.1038/nbt.4072.
40. Squair, J.W., Gautier, M., Kathe, C., Anderson, M.A., James, N.D., Hutson, T.H.,
Hudelle, R., Qaiser, T., Matson, K.J.E., Barraud, Q., et al. (2021). Confronting false discoveries
in single-cell differential expression. Nat Commun 12, 5692. 10.1038/s41467-021-25960-2.
41. Heirendt, L., Arreckx, S., Pfau, T., Mendoza, S.N., Richelle, A., Heinken, A.,
Haraldsdóttir, H.S., Wachowiak, J., Keating, S.M., Vlasov, V., et al. (2019). Creation and
analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0. Nature
Protocols 14, 639–702. 10.1038/s41596-018-0098-2.
42. Blazier, A.S., and Papin, J.A. (2012). Integration of expression data in genome-scale
metabolic network reconstructions. Front. Physiol. 3. 10.3389/fphys.2012.00299.
43. Zur, H., Ruppin, E., and Shlomi, T. (2010). iMAT: an integrative metabolic analysis tool.
Bioinformatics 26, 3140–3142. 10.1093/bioinformatics/btq602.
44. Becker, S.A., and Palsson, B.O. (2008). Context-Specific Metabolic Networks Are
Consistent with Experiments. PLOS Computational Biology 4, e1000082.
10.1371/journal.pcbi.1000082.
45. Schultz, A., and Qutub, A.A. (2016). Reconstruction of Tissue-Specific Metabolic
Networks Using CORDA. PLoS Comput Biol 12, e1004808. 10.1371/journal.pcbi.1004808.
46. Agren, R., Bordel, S., Mardinoglu, A., Pornputtapong, N., Nookaew, I., and Nielsen, J.
(2012). Reconstruction of Genome-Scale Active Metabolic Networks for 69 Human Cell Types
and 16 Cancer Types Using INIT. PLOS Computational Biology 8, e1002518.
10.1371/journal.pcbi.1002518.

90
47. Vlassis, N., Pacheco, M.P., and Sauter, T. (2014). Fast Reconstruction of Compact
Context-Specific Metabolic Network Models. PLOS Computational Biology 10, e1003424.
10.1371/journal.pcbi.1003424.
48. Ataman, M., Gardiol, D.F.H., Fengos, G., and Hatzimanikatis, V. (2017). redGEM:
Systematic reduction and analysis of genome-scale metabolic reconstructions for development of
consistent core metabolic models. PLOS Computational Biology 13, e1005444.
10.1371/journal.pcbi.1005444.
49. Lieven, C., Beber, M.E., Olivier, B.G., Bergmann, F.T., Ataman, M., Babaei, P., Bartell,
J.A., Blank, L.M., Chauhan, S., Correia, K., et al. (2020). MEMOTE for standardized genome-
scale metabolic model testing. Nat Biotechnol 38, 272–276. 10.1038/s41587-020-0446-y.
50. Feist, A.M., and Palsson, B.O. (2010). The Biomass Objective Function. Curr Opin
Microbiol 13, 344–349. 10.1016/j.mib.2010.03.003.
51. Zhao, Q., Stettner, A.I., Reznik, E., Paschalidis, I.Ch., and Segrè, D. (2016). Mapping the
landscape of metabolic goals of a cell. Genome Biology 17, 109. 10.1186/s13059-016-0968-2.
52. García Sánchez, C.E., and Torres Sáez, R.G. (2014). Comparison and analysis of
objective functions in flux balance analysis. Biotechnology Progress 30, 985–991.
10.1002/btpr.1949.
53. Griesemer, M., and Navid, A. (2021). MOFA: Multi-Objective Flux Analysis for the
COBRA Toolbox. 2021.05.20.445041. 10.1101/2021.05.20.445041.
54. Kashfi, K., Kannikal, J., and Nath, N. (2021). Macrophage Reprogramming and Cancer
Therapeutics: Role of iNOS-Derived NO. Cells 10, 3194. 10.3390/cells10113194.
55. McNeill, E., Crabtree, M.J., Sahgal, N., Patel, J., Chuaiphichai, S., Iqbal, A.J., Hale,
A.B., Greaves, D.R., and Channon, K.M. (2015). Regulation of iNOS function and cellular redox
state by macrophage Gch1 reveals specific requirements for tetrahydrobiopterin in NRF2
activation. Free Radic Biol Med 79, 206–216. 10.1016/j.freeradbiomed.2014.10.575.
56. Arlauckas, S.P., Garren, S.B., Garris, C.S., Kohler, R.H., Oh, J., Pittet, M.J., and
Weissleder, R. (2018). Arg1 expression defines immunosuppressive subsets of tumor-associated
macrophages. Theranostics 8, 5842–5854. 10.7150/thno.26888.
57. Sharda, D.R., Yu, S., Ray, M., Squadrito, M.L., De Palma, M., Wynn, T.A., Morris,
S.M., Jr., and Hankey, P.A. (2011). Regulation of Macrophage Arginase Expression and Tumor
Growth by the Ron Receptor Tyrosine Kinase. The Journal of Immunology 187, 2181–2192.
10.4049/jimmunol.1003460.
58. Kook, Y., Lee, Y.T., Shen, R., and Vempala, S.S. (2022). Sampling with Riemannian
Hamiltonian Monte Carlo in a Constrained Space.
59. Bordel, S., Agren, R., and Nielsen, J. (2010). Sampling the Solution Space in Genome-
Scale Metabolic Networks Reveals Transcriptional Regulation in Key Enzymes. PLOS
Computational Biology 6, e1000859. 10.1371/journal.pcbi.1000859.
60. Kullback, S., and Leibler, R.A. (1951). On Information and Sufficiency. The Annals of
Mathematical Statistics 22, 79–86. 10.1214/aoms/1177729694.
61. Martino, D.D., Mori, M., and Parisi, V. (2015). Uniform Sampling of Steady States in
Metabolic Networks: Heterogeneous Scales and Rounding. PLOS ONE 10, e0122670.
10.1371/journal.pone.0122670.

91
62. Fallahi, S., Skaug, H.J., and Alendal, G. (2020). A comparison of Monte Carlo sampling
methods for metabolic network models. PLOS ONE 15, e0235393.
10.1371/journal.pone.0235393.
63. Brin, S., and Page, L. (1998). The anatomy of a large-scale hypertextual Web search
engine. Computer Networks and ISDN Systems 30, 107–117. 10.1016/S0169-7552(98)00110-X.
64. Frainay, C., Aros, S., Chazalviel, M., Garcia, T., Vinson, F., Weiss, N., Colsch, B., Sedel,
F., Thabut, D., Junot, C., et al. (2019). MetaboRank: network-based recommendation system to
interpret and enrich metabolomics results. Bioinformatics 35, 274–283.
10.1093/bioinformatics/bty577.
65. Page, L., Brin, S., Motwani, R., and Winograd, T. (1999). The PageRank Citation
Ranking: Bringing Order to the Web. http://ilpubs.stanford.edu:8090/422/.
66. Maaten, L. van der, and Hinton, G. (2008). Visualizing Data using t-SNE. Journal of
Machine Learning Research 9, 2579–2605.
67. Wang, Y., Eddy, J.A., and Price, N.D. (2012). Reconstruction of genome-scale metabolic
models for 126 human tissues using mCADRE. BMC Systems Biology 6, 153. 10.1186/1752-
0509-6-153.
68. Cabbia, A., Hilbers, P.A.J., and van Riel, N.A.W. (2020). A Distance-Based Framework
for the Characterization of Metabolic Heterogeneity in Large Sets of Genome-Scale Metabolic
Models. Patterns (N Y) 1, 100080. 10.1016/j.patter.2020.100080.
69. Subramanian, A., Tamayo, P., Mootha, V.K., Mukherjee, S., Ebert, B.L., Gillette, M.A.,
Paulovich, A., Pomeroy, S.L., Golub, T.R., Lander, E.S., et al. (2005). Gene set enrichment
analysis: A knowledge-based approach for interpreting genome-wide expression profiles.
Proceedings of the National Academy of Sciences 102, 15545–15550.
10.1073/pnas.0506580102.
70. Viola, A., Munari, F., Sánchez-Rodríguez, R., Scolaro, T., and Castegna, A. (2019). The
Metabolic Signature of Macrophage Responses. Front. Immunol. 10.
10.3389/fimmu.2019.01462.
71. Rattigan, K.M., Pountain, A.W., Regnault, C., Achcar, F., Vincent, I.M., Goodyear, C.S.,
and Barrett, M.P. (2018). Metabolomic profiling of macrophages determines the discrete
metabolomic signature and metabolomic interactome triggered by polarising immune stimuli.
PLoS One 13, e0194126. 10.1371/journal.pone.0194126.
72. Abuawad, A., Mbadugha, C., Ghaemmaghami, A.M., and Kim, D.-H. (2020). Metabolic
characterisation of THP-1 macrophage polarisation using LC–MS-based metabolite profiling.
Metabolomics 16, 33. 10.1007/s11306-020-01656-4.
73. Sung, J., and Cheong, J. (2022). Intercellular communications and metabolic
reprogramming as new predictive markers for immunotherapy responses in gastric cancer.
Cancer Commun (Lond) 42, 572–575. 10.1002/cac2.12285.
74. Liu, Y., Xu, R., Gu, H., Zhang, E., Qu, J., Cao, W., Huang, X., Yan, H., He, J., and Cai,
Z. (2021). Metabolic reprogramming in macrophage responses. Biomarker Research 9, 1.
10.1186/s40364-020-00251-y.
75. Cui, J., Shan, K., Yang, Q., Chen, W., Feng, N., and Chen, Y.Q. (2022). Eicosanoid
production by macrophages during inflammation depends on the M1/M2 phenotype.
Prostaglandins Other Lipid Mediat 160, 106635. 10.1016/j.prostaglandins.2022.106635.

92
76. Schulthess, J., Pandey, S., Capitani, M., Rue-Albrecht, K.C., Arnold, I., Franchini, F.,
Chomka, A., Ilott, N.E., Johnston, D.G.W., Pires, E., et al. (2019). The Short Chain Fatty Acid
Butyrate Imprints an Antimicrobial Program in Macrophages. Immunity 50, 432-445.e7.
10.1016/j.immuni.2018.12.018.
77. Ji, J., Shu, D., Zheng, M., Wang, J., Luo, C., Wang, Y., Guo, F., Zou, X., Lv, X., Li, Y.,
et al. (2016). Microbial metabolite butyrate facilitates M2 macrophage polarization and function.
Sci Rep 6, 24838. 10.1038/srep24838.
78. Batista-Gonzalez, A., Vidal, R., Criollo, A., and Carreño, L.J. (2020). New Insights on
the Role of Lipid Metabolism in the Metabolic Reprogramming of Macrophages. Frontiers in
Immunology 10.
79. Johnson, A.R., Qin, Y., Cozzo, A.J., Freemerman, A.J., Huang, M.J., Zhao, L., Sampey,
B.P., Milner, J.J., Beck, M.A., Damania, B., et al. (2016). Metabolic reprogramming through
fatty acid transport protein 1 (FATP1) regulates macrophage inflammatory potential and adipose
inflammation. Molecular Metabolism 5, 506–526. 10.1016/j.molmet.2016.04.005.
80. L’homme, L., Esser, N., Riva, L., Scheen, A., Paquot, N., Piette, J., and Legrand-Poels,
S. (2013). Unsaturated fatty acids prevent activation of NLRP3 inflammasome in human
monocytes/macrophages [S]. Journal of Lipid Research 54, 2998–3008. 10.1194/jlr.M037861.
81. Wallert, M., Schmölz, L., Galli, F., Birringer, M., and Lorkowski, S. (2014). Regulatory
metabolites of vitamin E and their putative relevance for atherogenesis. Redox Biology 2, 495–
503. 10.1016/j.redox.2014.02.002.
82. Chung, B.K.S., and Lee, D.-Y. (2009). Flux-sum analysis: a metabolite-centric approach
for understanding the metabolic network. BMC Systems Biology 3, 117. 10.1186/1752-0509-3-
117.
83. Santana, K.G., Righetti, R.F., Breda, C.N. de S., Domínguez-Amorocho, O.A., Ramalho,
T., Dantas, F.E.B., Nunes, V.S., Tibério, I. de F.L.C., Soriano, F.G., Câmara, N.O.S., et al.
(2021). Cholesterol-Ester Transfer Protein Alters M1 and M2 Macrophage Polarization and
Worsens Experimental Elastase-Induced Pulmonary Emphysema. Frontiers in Immunology 12.
84. Torretta, S., Scagliola, A., Ricci, L., Mainini, F., Di Marco, S., Cuccovillo, I., Kajaste-
Rudnitski, A., Sumpton, D., Ryan, K.M., and Cardaci, S. (2020). D-mannose suppresses
macrophage IL-1β production. Nat Commun 11, 6343. 10.1038/s41467-020-20164-6.
85. Haskó, G., and Pacher, P. (2012). Regulation of Macrophage Function by Adenosine.
Arterioscler Thromb Vasc Biol 32, 865–869. 10.1161/ATVBAHA.111.226852.
86. Csóka, B., Selmeczy, Z., Koscsó, B., Németh, Z.H., Pacher, P., Murray, P.J., Kepka-
Lenhart, D., Morris, S.M., Gause, W.C., Leibovich, S.J., et al. (2012). Adenosine promotes
alternative macrophage activation via A2A and A2B receptors. FASEB J 26, 376–386.
10.1096/fj.11-190934.
87. Ma, J., Wei, K., Liu, J., Tang, K., Zhang, H., Zhu, L., Chen, J., Li, F., Xu, P., Chen, J., et
al. (2020). Glycogen metabolism regulates macrophage-mediated acute inflammatory responses.
Nat Commun 11, 1769. 10.1038/s41467-020-15636-8.
88. Namgaladze, D., and Brüne, B. (2016). Macrophage fatty acid oxidation and its roles in
macrophage polarization and fatty acid-induced inflammation. Biochimica et Biophysica Acta
(BBA) - Molecular and Cell Biology of Lipids 1861, 1796–1807. 10.1016/j.bbalip.2016.09.002.

93
89. Nomura, M., Liu, J., Rovira, I.I., Gonzalez-Hurtado, E., Lee, J., Wolfgang, M.J., and
Finkel, T. (2016). Fatty acid oxidation in macrophage polarization. Nat Immunol 17, 216–217.
10.1038/ni.3366.
90. Morgan, P.K., Huynh, K., Pernes, G., Miotto, P.M., Mellett, N.A., Giles, C., Meikle, P.J.,
Murphy, A.J., and Lancaster, G.I. (2021). Macrophage polarization state affects lipid
composition and the channeling of exogenous fatty acids into endogenous lipid pools. J Biol
Chem 297, 101341. 10.1016/j.jbc.2021.101341.
91. Rosa Neto, J.C., Calder, P.C., Curi, R., Newsholme, P., Sethi, J.K., and Silveira, L.S.
(2021). The Immunometabolic Roles of Various Fatty Acids in Macrophages and Lymphocytes.
Int J Mol Sci 22, 8460. 10.3390/ijms22168460.
92. Jayasingam, S.D., Citartan, M., Thang, T.H., Mat Zin, A.A., Ang, K.C., and Ch’ng, E.S.
(2020). Evaluating the Polarization of Tumor-Associated Macrophages Into M1 and M2
Phenotypes in Human Cancer Tissue: Technicalities and Challenges in Routine Clinical Practice.
Front Oncol 9, 1512. 10.3389/fonc.2019.01512.
93. Kieler, M., Hofmann, M., and Schabbauer, G. (2021). More than just protein building
blocks: how amino acids and related metabolic pathways fuel macrophage polarization. The
FEBS Journal 288, 3694–3714. 10.1111/febs.15715.
94. Traba, J., Sack, M.N., Waldmann, T.A., and Anton, O.M. (2021). Immunometabolism at
the Nexus of Cancer Therapeutic Efficacy and Resistance. Frontiers in Immunology 12.
95. Roy, D.G., Kaymak, I., Williams, K.S., Ma, E.H., and Jones, R.G. (2021).
Immunometabolism in the Tumor Microenvironment. Annual Review of Cancer Biology 5, 137–
159. 10.1146/annurev-cancerbio-030518-055817.
96. Purohit, V., Wagner, A., Yosef, N., and Kuchroo, V.K. (2022). Systems-based
approaches to study immunometabolism. Cell Mol Immunol 19, 409–420. 10.1038/s41423-021-
00783-9.
97. Cotten, C., and Reed, J.L. (2013). Mechanistic analysis of multi-omics datasets to
generate kinetic parameters for constraint-based metabolic models. BMC Bioinformatics 14, 32.
10.1186/1471-2105-14-32.
98. Lewis, J.E., and Kemp, M.L. (2021). Integration of machine learning and genome-scale
metabolic modeling identifies multi-omics biomarkers for radiation resistance. Nat Commun 12,
2700. 10.1038/s41467-021-22989-1.
99. Tebani, A., Afonso, C., Marret, S., and Bekri, S. (2016). Omics-Based Strategies in
Precision Medicine: Toward a Paradigm Shift in Inborn Errors of Metabolism Investigations.
International Journal of Molecular Sciences 17, 1555. 10.3390/ijms17091555.
100. Bernstein, D.B., Sulheim, S., Almaas, E., and Segrè, D. (2021). Addressing uncertainty in
genome-scale metabolic model reconstruction and analysis. Genome Biology 22, 64.
10.1186/s13059-021-02289-z.
101. Medlock, G.L., Moutinho, T.J., and Papin, J.A. (2020). Medusa: Software to build and
analyze ensembles of genome-scale metabolic network reconstructions. PLOS Computational
Biology 16, e1007847. 10.1371/journal.pcbi.1007847.
102. Biggs, M.B., and Papin, J.A. (2017). Managing uncertainty in metabolic network
structure and improving predictions using EnsembleFBA. PLOS Computational Biology 13,
e1005413. 10.1371/journal.pcbi.1005413.

94
103. Wang, J., Delfarah, A., Gelbach, P.E., Fong, E., Macklin, P., Mumenthaler, S.M.,
Graham, N.A., and Finley, S.D. (2022). Elucidating tumor-stromal metabolic crosstalk in
colorectal cancer through integration of constraint-based models and LC-MS metabolomics.
Metab Eng 69, 175–187. 10.1016/j.ymben.2021.11.006.
104. Frades, I., Foguet, C., Cascante, M., and Araúzo-Bravo, M.J. (2021). Genome Scale
Modeling to Study the Metabolic Competition between Cells in the Tumor Microenvironment.
Cancers (Basel) 13, 4609. 10.3390/cancers13184609.
105. Kennel, K.B., and Greten, F.R. (2021). Immune cell - produced ROS and their impact on
tumor growth and metastasis. Redox Biol 42, 101891. 10.1016/j.redox.2021.101891.
106. Poh, A.R., and Ernst, M. (2018). Targeting Macrophages in Cancer: From Bench to
Bedside. Frontiers in Oncology 8.
107. Liou, G.-Y., and Storz, P. (2010). Reactive oxygen species in cancer. Free Radic Res 44,
10.3109/10715761003667554. 10.3109/10715761003667554.
108. Canton, M., Sánchez-Rodríguez, R., Spera, I., Venegas, F.C., Favia, M., Viola, A., and
Castegna, A. (2021). Reactive Oxygen Species in Macrophages: Sources and Targets. Frontiers
in Immunology 12.
109. Liang, W., He, X., Bi, J., Hu, T., and Sun, Y. (2021). Role of reactive oxygen species in
tumors based on the ‘seed and soil’ theory: A complex interaction (Review). Oncology Reports
46, 1–15. 10.3892/or.2021.8159.
110. Vermare, A., Guérin, M.V., Peranzoni, E., and Bercovici, N. (2022). Dynamic CD8+ T
Cell Cooperation with Macrophages and Monocytes for Successful Cancer Immunotherapy.
Cancers (Basel) 14, 3546. 10.3390/cancers14143546.
111. Navasardyan, I., and Bonavida, B. (2021). Regulation of T Cells in Cancer by Nitric
Oxide. Cells 10, 2655. 10.3390/cells10102655.
112. Vannini, F., Kashfi, K., and Nath, N. (2015). The dual role of iNOS in cancer. Redox
Biology 6, 334–343. 10.1016/j.redox.2015.08.009.
113. Pesce, J.T., Ramalingam, T.R., Mentink-Kane, M.M., Wilson, M.S., Kasmi, K.C.E.,
Smith, A.M., Thompson, R.W., Cheever, A.W., Murray, P.J., and Wynn, T.A. (2009). Arginase-
1–Expressing Macrophages Suppress Th2 Cytokine–Driven Inflammation and Fibrosis. PLOS
Pathogens 5, e1000371. 10.1371/journal.ppat.1000371.
114. Scheurlen, K.M., Billeter, A.T., O’Brien, S.J., and Galandiuk, S. (2020). Metabolic
dysfunction and early‐onset colorectal cancer – how macrophages build the bridge. Cancer Med
9, 6679–6693. 10.1002/cam4.3315.
115. Chen, J., Cao, X., Li, B., Zhao, Z., Chen, S., Lai, S.W.T., Muend, S.A., Nossa, G.K.,
Wang, L., Guo, W., et al. (2021). Warburg Effect Is a Cancer Immune Evasion Mechanism
Against Macrophage Immunosurveillance. Front Immunol 11, 621757.
10.3389/fimmu.2020.621757.
116. Pham, T.N.D., Spaulding, C., Shields, M.A., Metropulos, A.E., Shah, D.N., Khalafalla,
M.G., Principe, D.R., Bentrem, D.J., and Munshi, H.G. Inhibition of MNKs promotes
macrophage immunosuppressive phenotype to limit CD8+ T cell antitumor immunity. JCI
Insight 7, e152731. 10.1172/jci.insight.152731.
117. Guay, C., Joly, E., Pepin, E., Barbeau, A., Hentsch, L., Pineda, M., Madiraju, S.R.M.,
Brunengraber, H., and Prentki, M. (2013). A role for cytosolic isocitrate dehydrogenase as a

95
negative regulator of glucose signaling for insulin secretion in pancreatic ß-cells. PLoS One 8,
e77097. 10.1371/journal.pone.0077097.
118. Harber, K.J., de Goede, K.E., Verberk, S.G.S., Meinster, E., de Vries, H.E., van Weeghel,
M., de Winther, M.P.J., and Van den Bossche, J. (2020). Succinate Is an Inflammation-Induced
Immunoregulatory Metabolite in Macrophages. Metabolites 10, 372. 10.3390/metabo10090372.
119. Tannahill, G.M., Curtis, A.M., Adamik, J., Palsson-McDermott, E.M., McGettrick, A.F.,
Goel, G., Frezza, C., Bernard, N.J., Kelly, B., Foley, N.H., et al. (2013). Succinate is an
inflammatory signal that induces IL-1β through HIF-1α. Nature 496, 238–242.
10.1038/nature11986.
120. Weiss, J.M. (2020). The promise and peril of targeting cell metabolism for cancer
therapy. Cancer Immunol Immunother 69, 255–261. 10.1007/s00262-019-02432-7.
121. Vitale, I., Manic, G., Coussens, L.M., Kroemer, G., and Galluzzi, L. (2019).
Macrophages and Metabolism in the Tumor Microenvironment. Cell Metabolism 30, 36–50.
10.1016/j.cmet.2019.06.001.
122. Chang, C.-H., Qiu, J., O’Sullivan, D., Buck, M.D., Noguchi, T., Curtis, J.D., Chen, Q.,
Gindin, M., Gubin, M.M., van der Windt, G.J.W., et al. (2015). Metabolic Competition in the
Tumor Microenvironment Is a Driver of Cancer Progression. Cell 162, 1229–1241.
10.1016/j.cell.2015.08.016.
123. Hartley, G.P., Chow, L., Ammons, D.T., Wheat, W.H., and Dow, S.W. (2018).
Programmed Cell Death Ligand 1 (PD-L1) Signaling Regulates Macrophage Proliferation and
Activation. Cancer Immunology Research 6, 1260–1273. 10.1158/2326-6066.CIR-17-0537.
124. Han, Y., Liu, D., and Li, L. (2020). PD-1/PD-L1 pathway: current researches in cancer.
Am J Cancer Res 10, 727–742.
125. Geeraerts, X., Bolli, E., Fendt, S.-M., and Van Ginderachter, J.A. (2017). Macrophage
Metabolism As Therapeutic Target for Cancer, Atherosclerosis, and Obesity. Front Immunol 8.
10.3389/fimmu.2017.00289.
126. Park, J., Lee, S.E., Hur, J., Hong, E.B., Choi, J.-I., Yang, J.-M., Kim, J.-Y., Kim, Y.-C.,
Cho, H.-J., Peters, J.M., et al. (2015). M-CSF from Cancer Cells Induces Fatty Acid Synthase
and PPARβ/δ Activation in Tumor Myeloid Cells, Leading to Tumor Progression. Cell Reports
10, 1614–1625. 10.1016/j.celrep.2015.02.024.
127. Siddiqui, S., and Glauben, R. (2022). Fatty Acid Metabolism in Myeloid-Derived
Suppressor Cells and Tumor-Associated Macrophages: Key Factor in Cancer Immune Evasion.
Cancers 14, 250. 10.3390/cancers14010250.
128. Netea-Maier, R.T., Smit, J.W.A., and Netea, M.G. (2018). Metabolic changes in tumor
cells and tumor-associated macrophages: A mutual relationship. Cancer Letters 413, 102–109.
10.1016/j.canlet.2017.10.037.
129. Hossain, F., Al-Khami, A.A., Wyczechowska, D., Hernandez, C., Zheng, L., Reiss, K.,
Valle, L.D., Trillo-Tinoco, J., Maj, T., Zou, W., et al. (2015). Inhibition of Fatty Acid Oxidation
Modulates Immunosuppressive Functions of Myeloid-Derived Suppressor Cells and Enhances
Cancer Therapies. Cancer Immunology Research 3, 1236–1247. 10.1158/2326-6066.CIR-15-
0036.

96
130. Gaetano, C., Massimo, L., and Alberto, M. (2010). Control of iron homeostasis as a key
component of macrophage polarization. Haematologica 95, 1801–1803.
10.3324/haematol.2010.030239.
131. Alkhateeb, A.A., and Connor, J.R. (2013). The significance of ferritin in cancer: Anti-
oxidation, inflammation and tumorigenesis. Biochimica et Biophysica Acta (BBA) - Reviews on
Cancer 1836, 245–254. 10.1016/j.bbcan.2013.07.002.
132. Liang, W., and Ferrara, N. (2021). Iron Metabolism in the Tumor Microenvironment:
Contributions of Innate Immune Cells. Frontiers in Immunology 11.
133. Zhang, Y., Choksi, S., Chen, K., Pobezinskaya, Y., Linnoila, I., and Liu, Z.-G. (2013).
ROS play a critical role in the differentiation of alternatively activated macrophages and the
occurrence of tumor-associated macrophages. Cell Res 23, 898–914. 10.1038/cr.2013.75.
134. Roux, C., Jafari, S.M., Shinde, R., Duncan, G., Cescon, D.W., Silvester, J., Chu, M.F.,
Hodgson, K., Berger, T., Wakeham, A., et al. (2019). Reactive oxygen species modulate
macrophage immunosuppressive phenotype through the up-regulation of PD-L1. Proceedings of
the National Academy of Sciences 116, 4326–4335. 10.1073/pnas.1819473116.
135. Griess, B., Mir, S., Datta, K., and Teoh-Fitzgerald, M. (2020). Scavenging reactive
oxygen species selectively inhibits M2 macrophage polarization and their pro-tumorigenic
function in part, via Stat3 suppression. Free Radic Biol Med 147, 48–60.
10.1016/j.freeradbiomed.2019.12.018.
136. Boyer, S., Lee, H.-J., Steele, N., Zhang, L., Sajjakulnukit, P., Andren, A., Ward, M.H.,
Singh, R., Basrur, V., Zhang, Y., et al. (2022). Multiomic characterization of pancreatic cancer-
associated macrophage polarization reveals deregulated metabolic programs driven by the GM-
CSF–PI3K pathway. eLife 11, e73796. 10.7554/eLife.73796.
137. Halbrook, C.J., Pontious, C., Kovalenko, I., Lapienyte, L., Dreyer, S., Lee, H.-J.,
Thurston, G., Zhang, Y., Lazarus, J., Sajjakulnukit, P., et al. (2019). Macrophage-Released
Pyrimidines Inhibit Gemcitabine Therapy in Pancreatic Cancer. Cell Metab 29, 1390-1399.e6.
10.1016/j.cmet.2019.02.001.
138. Ren, W., Xia, Y., Chen, S., Wu, G., Bazer, F.W., Zhou, B., Tan, B., Zhu, G., Deng, J.,
and Yin, Y. (2019). Glutamine Metabolism in Macrophages: A Novel Target for Obesity/Type 2
Diabetes. Adv Nutr 10, 321–330. 10.1093/advances/nmy084.
139. Claiborne, M.D., and Leone, R. (2022). Differential glutamine metabolism in the tumor
microenvironment – studies in diversity and heterogeneity: A mini-review. Frontiers in
Oncology 12.

97
Chapter 3
1. Qian, B.-Z., and Pollard, J.W. (2010). Macrophage Diversity Enhances Tumor
Progression and Metastasis. Cell 141, 39–51. 10.1016/j.cell.2010.03.014.
2. Biswas, S.K., Allavena, P., and Mantovani, A. (2013). Tumor-associated macrophages:
functional diversity, clinical significance, and open questions. Semin Immunopathol 35, 585–
600. 10.1007/s00281-013-0367-7.
3. Boutilier, A.J., and Elsawa, S.F. (2021). Macrophage Polarization States in the Tumor
Microenvironment. Int J Mol Sci 22, 6995. 10.3390/ijms22136995.
4. Mosser, D.M., and Edwards, J.P. (2008). Exploring the full spectrum of macrophage
activation. Nat Rev Immunol 8, 958–969. 10.1038/nri2448.
5. Anders, C.B., Lawton, T.M.W., Smith, H., Garret, J., and Ammons, M.C.B. (2020).
Metabolic Immunomodulation, Transcriptional Regulation, and Signal Protein Expression
Define the Metabotype and Effector Functions of Five Polarized Macrophage Phenotypes.
bioRxiv, 2020.03.10.985788. 10.1101/2020.03.10.985788.
6. Galván-Peña, S., and O’Neill, L.A.J. (2014). Metabolic Reprograming in Macrophage
Polarization. Front. Immunol. 5. 10.3389/fimmu.2014.00420.
7. Biswas, S.K., and Mantovani, A. (2012). Orchestration of Metabolism by Macrophages.
Cell Metabolism 15, 432–437. 10.1016/j.cmet.2011.11.013.
8. Italiani, P., and Boraschi, D. (2014). From Monocytes to M1/M2 Macrophages:
Phenotypical vs. Functional Differentiation. Front. Immunol. 5. 10.3389/fimmu.2014.00514.
9. Arneth, B. (2020). Tumor Microenvironment. Medicina 56, 15.
10.3390/medicina56010015.
10. Chang, C.-H., Qiu, J., O’Sullivan, D., Buck, M.D., Noguchi, T., Curtis, J.D., Chen, Q.,
Gindin, M., Gubin, M.M., van der Windt, G.J.W., et al. (2015). Metabolic Competition in the
Tumor Microenvironment Is a Driver of Cancer Progression. Cell 162, 1229–1241.
10.1016/j.cell.2015.08.016.
11. Gara, R.K., Kumari, S., Ganju, A., Yallapu, M.M., Jaggi, M., and Chauhan, S.C. (2015).
Slit/Robo pathway: a promising therapeutic target for cancer. Drug Discovery Today 20, 156–
164. 10.1016/j.drudis.2014.09.008.
12. Huang, T., Kang, W., Cheng, A.S.L., Yu, J., and To, K.F. (2015). The emerging role of
Slit-Robo pathway in gastric and other gastro intestinal cancers. BMC Cancer 15, 950.
10.1186/s12885-015-1984-4.
13. Mi Je, E., Gwak, M., Oh, H., Ryoung Choi, M., Jin Choi, Y., Lee, S.H., and Jin Yoo, N.
(2013). Frameshift mutations of axon guidance genes ROBO1 and ROBO2 in gastric and
colorectal cancers with microsatellite instability. Pathology 45, 645–650.
10.1097/PAT.0000000000000007.
14. Zhang, Q.-Q., Zhou, D., Lei, Y., Zheng, L., Chen, S.-X., Gou, H.-J., Gu, Q.-L., He, X.-
D., Lan, T., Qi, C.-L., et al. (2014). Slit2/Robo1 signaling promotes intestinal tumorigenesis
through Src-mediated activation of the Wnt/β-catenin pathway. Oncotarget 6, 3123–3135.
15. Zhou, W.-J., Geng, Z.H., Chi, S., Zhang, W., Niu, X.-F., Lan, S.-J., Ma, L., Yang, X.,
Wang, L.-J., Ding, Y.-Q., et al. (2011). Slit-Robo signaling induces malignant transformation
through Hakai-mediated E-cadherin degradation during colorectal epithelial cell carcinogenesis.
Cell Res 21, 609–626. 10.1038/cr.2011.17.

98
16. Wang, B., Xiao, Y., Ding, B.B., Zhang, N., Yuan, X. bin, Gui, L., Qian, K.X., Duan, S.,
Chen, Z., Rao, Y., et al. (2003). Induction of tumor angiogenesis by Slit-Robo signaling and
inhibition of cancer growth by blocking Robo activity. Cancer Cell 4, 19–29. 10.1016/s1535-
6108(03)00164-8.
17. Prasad, A., Qamri, Z., Wu, J., and Ganju, R.K. (2007). Slit-2/Robo-1 modulates the
CXCL12/CXCR4-induced chemotaxis of T cells. Journal of Leukocyte Biology 82, 465–476.
10.1189/jlb.1106678.
18. Kaul, K., Benej, M., Mishra, S., Ahirwar, D.K., Yadav, M., Stanford, K.I., Jacob, N.K.,
Denko, N.C., and Ganju, R.K. (2021). Slit2-Mediated Metabolic Reprogramming in Bone
Marrow-Derived Macrophages Enhances Antitumor Immunity. Front Immunol 12, 753477.
10.3389/fimmu.2021.753477.
19. Ankrah, N.Y.D., Bernstein, D.B., Biggs, M., Carey, M., Engevik, M., García-Jiménez,
B., Lakshmanan, M., Pacheco, A.R., Sulheim, S., and Medlock, G.L. (2021). Enhancing
Microbiome Research through Genome-Scale Metabolic Modeling. mSystems 6, e00599-21.
10.1128/mSystems.00599-21.
20. Orth, J.D., Thiele, I., and Palsson, B.Ø. (2010). What is flux balance analysis? Nature
Biotechnology 28, 245–248. 10.1038/nbt.1614.
21. Dahal, S., Yurkovich, J.T., Xu, H., Palsson, B.O., and Yang, L. (2020). Synthesizing
Systems Biology Knowledge from Omics Using Genome-Scale Models. PROTEOMICS 20,
1900282. https://doi.org/10.1002/pmic.201900282.
22. Oberhardt, M.A., Palsson, B.Ø., and Papin, J.A. (2009). Applications of genome-scale
metabolic reconstructions. Molecular Systems Biology 5, 320. 10.1038/msb.2009.77.
23. Øyås, O., and Stelling, J. (2018). Genome-scale metabolic networks in time and space.
Current Opinion in Systems Biology 8, 51–58. 10.1016/j.coisb.2017.12.003.
24. Hyduke, D.R., Lewis, N.E., and Palsson, B.Ø. (2013). Analysis of omics data with
genome-scale models of metabolism. Mol Biosyst 9, 167–174. 10.1039/c2mb25453k.
25. Ramon, C., Gollub, M.G., and Stelling, J. (2018). Integrating –omics data into genome-
scale metabolic network models: principles and challenges. Essays in Biochemistry 62, 563–574.
10.1042/EBC20180011.
26. Blazier, A.S., and Papin, J.A. (2012). Integration of expression data in genome-scale
metabolic network reconstructions. Front. Physiol. 3. 10.3389/fphys.2012.00299.
27. Hadadi, N., Pandey, V., Chiappino-Pepe, A., Morales, M., Gallart-Ayala, H., Mehl, F.,
Ivanisevic, J., Sentchilo, V., and Meer, J.R. van der (2020). Mechanistic insights into bacterial
metabolic reprogramming from omics-integrated genome-scale models. npj Systems Biology and
Applications 6, 1–11. 10.1038/s41540-019-0121-4.
28. Brunk, E., Sahoo, S., Zielinski, D.C., Altunkaya, A., Dräger, A., Mih, N., Gatto, F.,
Nilsson, A., Preciat Gonzalez, G.A., Aurich, M.K., et al. (2018). Recon3D enables a three-
dimensional view of gene variation in human metabolism. Nat Biotechnol 36, 272–281.
10.1038/nbt.4072.
29. Zur, H., Ruppin, E., and Shlomi, T. (2010). iMAT: an integrative metabolic analysis tool.
Bioinformatics 26, 3140–3142. 10.1093/bioinformatics/btq602.
30. Feist, A.M., and Palsson, B.O. (2010). The Biomass Objective Function. Curr Opin
Microbiol 13, 344–349. 10.1016/j.mib.2010.03.003.

99
31. Lieven, C., Beber, M.E., Olivier, B.G., Bergmann, F.T., Ataman, M., Babaei, P., Bartell,
J.A., Blank, L.M., Chauhan, S., Correia, K., et al. (2020). MEMOTE for standardized genome-
scale metabolic model testing. Nat Biotechnol 38, 272–276. 10.1038/s41587-020-0446-y.
32. Cabbia, A., Hilbers, P.A.J., and van Riel, N.A.W. (2020). A Distance-Based Framework
for the Characterization of Metabolic Heterogeneity in Large Sets of Genome-Scale Metabolic
Models. Patterns (N Y) 1, 100080. 10.1016/j.patter.2020.100080.
33. Herrmann, H.A., Dyson, B.C., Vass, L., Johnson, G.N., and Schwartz, J.-M. (2019). Flux
sampling is a powerful tool to study metabolism under changing environmental conditions. npj
Syst Biol Appl 5, 1–8. 10.1038/s41540-019-0109-0.
34. Kook, Y., Lee, Y.T., Shen, R., and Vempala, S.S. (2022). Sampling with Riemannian
Hamiltonian Monte Carlo in a Constrained Space.
35. Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel,
M., Prettenhofer, P., Weiss, R., Dubourg, V., et al. (2011). Scikit-learn: Machine Learning in
Python. Journal of Machine Learning Research 12, 2825–2830.
36. Kieler, M., Hofmann, M., and Schabbauer, G. (2021). More than just protein building
blocks: how amino acids and related metabolic pathways fuel macrophage polarization. The
FEBS Journal 288, 3694–3714. 10.1111/febs.15715.
37. Cai, Z., Li, W., Brenner, M., Bahiraii, S., Heiss, E.H., and Weckwerth, W. (2022).
Branched-chain ketoacids derived from cancer cells modulate macrophage polarization and
metabolic reprogramming. Front Immunol 13, 966158. 10.3389/fimmu.2022.966158.
38. Kotre, A.M., Sullivan, S.J., and Savageau, M.A. (1973). Metabolic Regulation by
Homoserine in Escherichia coli B/r. J Bacteriol 116, 663–672.
39. Laviron, M., Petit, M., Weber-Delacroix, E., Combes, A.J., Arkal, A.R., Barthélémy, S.,
Courau, T., Hume, D.A., Combadière, C., Krummel, M.F., et al. (2022). Tumor-associated
macrophage heterogeneity is driven by tissue territories in breast cancer. Cell Reports 39.
10.1016/j.celrep.2022.110865.
40. Zhang, Y., Zhao, Y., Li, Q., and Wang, Y. (2021). Macrophages, as a Promising Strategy
to Targeted Treatment for Colorectal Cancer Metastasis in Tumor Immune Microenvironment.
Front Immunol 12, 685978. 10.3389/fimmu.2021.685978.
41. Li, S., Yu, J., Huber, A., Kryczek, I., Wang, Z., Jiang, L., Li, X., Du, W., Li, G., Wei, S.,
et al. (2022). Metabolism drives macrophage heterogeneity in the tumor microenvironment. Cell
Rep 39, 110609. 10.1016/j.celrep.2022.110609.
42. de Freitas Junior, J.C.M., and Morgado-Díaz, J.A. (2015). The role of N-glycans in
colorectal cancer progression: potential biomarkers and therapeutic applications. Oncotarget 7,
19395–19413. 10.18632/oncotarget.6283.
43. Doherty, M., Theodoratou, E., Walsh, I., Adamczyk, B., Stöckmann, H., Agakov, F.,
Timofeeva, M., Trbojević-Akmačić, I., Vučković, F., Duffy, F., et al. (2018). Plasma N-glycans
in colorectal cancer risk. Sci Rep 8, 8655. 10.1038/s41598-018-26805-7.
44. Zhao, Q., Zhan, T., Deng, Z., Li, Q., Liu, Y., Yang, S., Ji, D., and Li, Y. (2018). Glycan
analysis of colorectal cancer samples reveals stage-dependent changes in CEA glycosylation
patterns. Clinical Proteomics 15, 9. 10.1186/s12014-018-9182-4.

100
45. Viola, A., Munari, F., Sánchez-Rodríguez, R., Scolaro, T., and Castegna, A. (2019). The
Metabolic Signature of Macrophage Responses. Front. Immunol. 10.
10.3389/fimmu.2019.01462.
46. Sun, J.-X., Xu, X.-H., and Jin, L. (2022). Effects of Metabolism on Macrophage
Polarization Under Different Disease Backgrounds. Front Immunol 13, 880286.
10.3389/fimmu.2022.880286.
47. Amelio, I., Cutruzzolá, F., Antonov, A., Agostini, M., and Melino, G. (2014). Serine and
glycine metabolism in cancer. Trends Biochem Sci 39, 191–198. 10.1016/j.tibs.2014.02.004.

101
Chapter 4
1. Ponomarova, O., and Patil, K.R. (2015). Metabolic interactions in microbial
communities: untangling the Gordian knot. Current Opinion in Microbiology 27, 37–44.
10.1016/j.mib.2015.06.014.
2. Douglas, A.E. (2020). The microbial exometabolome: ecological resource and architect
of microbial communities. Philos Trans R Soc Lond B Biol Sci 375, 20190250.
10.1098/rstb.2019.0250.
3. Melkonian, C., Seidl, M.F., Hooft, J.J.J. van der, and Vos, M.G.J. de (2022). Metabolic
interactions shape a community’s phenotype. Trends in Microbiology 30, 609–611.
10.1016/j.tim.2022.05.001.
4. Zhou, Z., Tran, P.Q., Breister, A.M., Liu, Y., Kieft, K., Cowley, E.S., Karaoz, U., and
Anantharaman, K. (2022). METABOLIC: high-throughput profiling of microbial genomes for
functional traits, metabolism, biogeochemistry, and community-scale functional networks.
Microbiome 10, 33. 10.1186/s40168-021-01213-8.
5. Embree, M., Liu, J.K., Al-Bassam, M.M., and Zengler, K. (2015). Networks of energetic
and metabolic interactions define dynamics in microbial communities. Proceedings of the
National Academy of Sciences 112, 15450–15455. 10.1073/pnas.1506034112.
6. Khandelwal, R.A., Olivier, B.G., Röling, W.F.M., Teusink, B., and Bruggeman, F.J.
(2013). Community Flux Balance Analysis for Microbial Consortia at Balanced Growth. PLoS
One 8, e64567. 10.1371/journal.pone.0064567.
7. Tzamali, E., Poirazi, P., Tollis, I.G., and Reczko, M. (2011). A computational exploration
of bacterial metabolic diversity identifying metabolic interactions and growth-efficient strain
communities. BMC Syst Biol 5, 167. 10.1186/1752-0509-5-167.
8. Gu, C., Kim, G.B., Kim, W.J., Kim, H.U., and Lee, S.Y. (2019). Current status and
applications of genome-scale metabolic models. Genome Biology 20, 121. 10.1186/s13059-019-
1730-3.
9. Sertbas, M., and Ulgen, K.O. (2020). Genome-Scale Metabolic Modeling for Unraveling
Molecular Mechanisms of High Threat Pathogens. Frontiers in Cell and Developmental Biology
8.
10. Zhang, C., Qi, J., and Cao, Y. (2014). Synergistic Effect of Yeast-Bacterial Co-Culture
on Bioremediation of Oil-Contaminated Soil. Bioremediation Journal 18, 136–146.
10.1080/10889868.2013.847402.
11. Thommes, M., Wang, T., Zhao, Q., Paschalidis, I.C., and Segrè, D. (2019). Designing
Metabolic Division of Labor in Microbial Communities. mSystems 4, e00263-18.
10.1128/mSystems.00263-18.
12. Reed, J.L. (2017). Genome-Scale Metabolic Modeling and Its Application to Microbial
Communities (National Academies Press (US)).
13. Cuevas, D.A., Edirisinghe, J., Henry, C.S., Overbeek, R., O’Connell, T.G., and Edwards,
R.A. (2016). From DNA to FBA: How to Build Your Own Genome-Scale Metabolic Model.
Frontiers in Microbiology 7.
14. Proffitt, C., Bidkhori, G., Lee, S., Tebani, A., Mardinoglu, A., Uhlen, M., Moyes, D.L.,
and Shoaie, S. (2022). Genome-scale metabolic modelling of the human gut microbiome reveals

102
changes in the glyoxylate and dicarboxylate metabolism in metabolic disorders. iScience 25,
104513. 10.1016/j.isci.2022.104513.
15. Ankrah, N.Y.D., Bernstein, D.B., Biggs, M., Carey, M., Engevik, M., García-Jiménez,
B., Lakshmanan, M., Pacheco, A.R., Sulheim, S., and Medlock, G.L. (2021). Enhancing
Microbiome Research through Genome-Scale Metabolic Modeling. mSystems 6, e00599-21.
10.1128/mSystems.00599-21.
16. Zorrilla, F., Buric, F., Patil, K.R., and Zelezniak, A. (2021). metaGEM: reconstruction of
genome scale metabolic models directly from metagenomes. Nucleic Acids Research 49, e126.
10.1093/nar/gkab815.
17. Magnúsdóttir, S., Heinken, A., Kutt, L., Ravcheev, D.A., Bauer, E., Noronha, A.,
Greenhalgh, K., Jäger, C., Baginska, J., Wilmes, P., et al. (2017). Generation of genome-scale
metabolic reconstructions for 773 members of the human gut microbiota. Nat Biotechnol 35, 81–
89. 10.1038/nbt.3703.
18. Ang, K.S., Lakshmanan, M., Lee, N.-R., and Lee, D.-Y. (2018). Metabolic Modeling of
Microbial Community Interactions for Health, Environmental and Biotechnological
Applications. Curr Genomics 19, 712–722. 10.2174/1389202919666180911144055.
19. Sonawane, J.M., Mahadevan, R., Pandey, A., and Greener, J. (2022). Recent progress in
microbial fuel cells using substrates from diverse sources. Heliyon 8, e12353.
10.1016/j.heliyon.2022.e12353.
20. Frioux, C., Singh, D., Korcsmaros, T., and Hildebrand, F. (2020). From bag-of-genes to
bag-of-genomes: metabolic modelling of communities in the era of metagenome-assembled
genomes. Comput Struct Biotechnol J 18, 1722–1734. 10.1016/j.csbj.2020.06.028.
21. R. Dillard, L., D. Payne, D., and A. Papin, J. (2021). Mechanistic models of microbial
community metabolism. Molecular Omics 17, 365–375. 10.1039/D0MO00154F.
22. Roume, H., Heintz-Buschart, A., Muller, E.E.L., May, P., Satagopam, V.P., Laczny,
C.C., Narayanasamy, S., Lebrun, L.A., Hoopmann, M.R., Schupp, J.M., et al. (2015).
Comparative integrated omics: identification of key functionalities in microbial community-wide
metabolic networks. npj Biofilms Microbiomes 1, 1–11. 10.1038/npjbiofilms.2015.7.
23. Faria, J.P., Khazaei, T., Edirisinghe, J.N., Weisenhorn, P., Seaver, S.D., Conrad, N.,
Harris, N., DeJongh, M., and Henry, C.S. (2016). Constructing and Analyzing Metabolic Flux
Models of Microbial Communities. Springer Protocols Handbooks Hydrocarbon and Lipid
Microbiology Protocols. 10.1007/8623_2016_215.
24. Heinken, A., and Thiele, I. (2015). Anoxic Conditions Promote Species-Specific
Mutualism between Gut Microbes In Silico. Applied and Environmental Microbiology 81, 4049–
4061. 10.1128/AEM.00101-15.
25. Stolyar, S., Van Dien, S., Hillesland, K.L., Pinel, N., Lie, T.J., Leigh, J.A., and Stahl,
D.A. (2007). Metabolic modeling of a mutualistic microbial community. Molecular Systems
Biology 3, 92. 10.1038/msb4100131.
26. Wintermute, E.H., and Silver, P.A. (2010). Emergent cooperation in microbial
metabolism. Molecular Systems Biology 6, 407. 10.1038/msb.2010.66.
27. Blasco, T., Pérez-Burillo, S., Balzerani, F., Hinojosa-Nogueira, D., Lerma-Aguilera, A.,
Pastoriza, S., Cendoya, X., Rubio, Á., Gosalbes, M.J., Jiménez-Hernández, N., et al. (2021). An

103
extended reconstruction of human gut microbiota metabolism of dietary compounds. Nat
Commun 12, 4728. 10.1038/s41467-021-25056-x.
28. Orth, J.D., Thiele, I., and Palsson, B.Ø. (2010). What is flux balance analysis? Nature
Biotechnology 28, 245–248. 10.1038/nbt.1614.
29. Celiker, H., and Gore, J. (2012). Competition between species can stabilize public-goods
cooperation within a species. Mol Syst Biol 8, 621. 10.1038/msb.2012.54.
30. Raman, K., and Chandra, N. (2009). Flux balance analysis of biological systems:
applications and challenges. Briefings in Bioinformatics 10, 435–449. 10.1093/bib/bbp011.
31. Diener, C., and Gibbons, S.M. (2023). More is Different: Metabolic Modeling of Diverse
Microbial Communities. mSystems, e01270-22. 10.1128/msystems.01270-22.
32. García Sánchez, C.E., and Torres Sáez, R.G. (2014). Comparison and analysis of
objective functions in flux balance analysis. Biotechnology Progress 30, 985–991.
10.1002/btpr.1949.
33. Schnitzer, B., Österberg, L., and Cvijovic, M. (2022). The choice of the objective
function in flux balance analysis is crucial for predicting replicative lifespans in yeast. PLOS
ONE 17, e0276112. 10.1371/journal.pone.0276112.
34. Lachance, J.-C., Lloyd, C.J., Monk, J.M., Yang, L., Sastry, A.V., Seif, Y., Palsson, B.O.,
Rodrigue, S., Feist, A.M., King, Z.A., et al. (2019). BOFdat: Generating biomass objective
functions for genome-scale metabolic models from experimental data. PLOS Computational
Biology 15, e1006971. 10.1371/journal.pcbi.1006971.
35. Feist, A.M., and Palsson, B.O. (2010). The Biomass Objective Function. Curr Opin
Microbiol 13, 344–349. 10.1016/j.mib.2010.03.003.
36. Herrmann, H.A., Dyson, B.C., Vass, L., Johnson, G.N., and Schwartz, J.-M. (2019). Flux
sampling is a powerful tool to study metabolism under changing environmental conditions. npj
Syst Biol Appl 5, 1–8. 10.1038/s41540-019-0109-0.
37. Bordel, S., Agren, R., and Nielsen, J. (2010). Sampling the Solution Space in Genome-
Scale Metabolic Networks Reveals Transcriptional Regulation in Key Enzymes. PLOS
Computational Biology 6, e1000859. 10.1371/journal.pcbi.1000859.
38. Fallahi, S., Skaug, H.J., and Alendal, G. (2020). A comparison of Monte Carlo sampling
methods for metabolic network models. PLOS ONE 15, e0235393.
10.1371/journal.pone.0235393.
39. Scott, W.T., Smid, E.J., Block, D.E., and Notebaart, R.A. (2021). Metabolic flux
sampling predicts strain-dependent differences related to aroma production among commercial
wine yeasts. Microbial Cell Factories 20, 204. 10.1186/s12934-021-01694-0.
40. Martino, D.D., Mori, M., and Parisi, V. (2015). Uniform Sampling of Steady States in
Metabolic Networks: Heterogeneous Scales and Rounding. PLOS ONE 10, e0122670.
10.1371/journal.pone.0122670.
41. Heinken, A., Hertel, J., Acharya, G., Ravcheev, D.A., Nyga, M., Okpala, O.E., Hogan,
M., Magnúsdóttir, S., Martinelli, F., Nap, B., et al. (2023). Genome-scale metabolic
reconstruction of 7,302 human microorganisms for personalized medicine. Nat Biotechnol, 1–12.
10.1038/s41587-022-01628-0.
42. Klitgord, N., and Segrè, D. (2010). Environments that induce synthetic microbial
ecosystems. PLoS Comput Biol 6, e1001002. 10.1371/journal.pcbi.1001002.

104
43. Kook, Y., Lee, Y.T., Shen, R., and Vempala, S.S. (2022). Sampling with Riemannian
Hamiltonian Monte Carlo in a Constrained Space.
44. Eng, A., and Borenstein, E. (2016). An algorithm for designing minimal microbial
communities with desired metabolic capacities. Bioinformatics 32, 2008–2016.
10.1093/bioinformatics/btw107.
45. Frioux, C., Fremy, E., Trottier, C., and Siegel, A. (2018). Scalable and exhaustive
screening of metabolic functions carried out by microbial consortia. Bioinformatics 34, i934–
i943. 10.1093/bioinformatics/bty588.
46. Greenblum, S., Turnbaugh, P.J., and Borenstein, E. (2012). Metagenomic systems
biology of the human gut microbiome reveals topological shifts associated with obesity and
inflammatory bowel disease. Proc Natl Acad Sci U S A 109, 594–599.
10.1073/pnas.1116053109.
47. Ofaim, S., Ofek-Lalzar, M., Sela, N., Jinag, J., Kashi, Y., Minz, D., and Freilich, S.
(2017). Analysis of Microbial Functions in the Rhizosphere Using a Metabolic-Network Based
Framework for Metagenomics Interpretation. Front Microbiol 8, 1606.
10.3389/fmicb.2017.01606.
48. Pacheco, A.R., Moel, M., and Segrè, D. (2019). Costless metabolic secretions as drivers
of interspecies interactions in microbial ecosystems. Nat Commun 10, 103. 10.1038/s41467-018-
07946-9.
49. Blanchard, A.E., and Lu, T. (2015). Bacterial social interactions drive the emergence of
differential spatial colony structures. BMC Systems Biology 9, 59. 10.1186/s12918-015-0188-5.
50. Boza, G., Barabás, G., Scheuring, I., and Zachar, I. (2023). Eco-evolutionary modelling
of microbial syntrophy indicates the robustness of cross-feeding over cross-facilitation. Sci Rep
13, 907. 10.1038/s41598-023-27421-w.
51. Kullback, S., and Leibler, R.A. (1951). On Information and Sufficiency. The Annals of
Mathematical Statistics 22, 79–86. 10.1214/aoms/1177729694.
52. Chung, C.H., and Chandrasekaran, S. (2022). A flux-based machine learning model to
simulate the impact of pathogen metabolic heterogeneity on drug interactions. PNAS Nexus 1,
pgac132. 10.1093/pnasnexus/pgac132.
53. Damiani, C., Maspero, D., Filippo, M.D., Colombo, R., Pescini, D., Graudenzi, A.,
Westerhoff, H.V., Alberghina, L., Vanoni, M., and Mauri, G. (2019). Integration of single-cell
RNA-seq data into population models to characterize cancer metabolism. PLOS Computational
Biology 15, e1006733. 10.1371/journal.pcbi.1006733.
54. Zampieri, G., Vijayakumar, S., Yaneske, E., and Angione, C. (2019). Machine and deep
learning meet genome-scale metabolic modeling. PLOS Computational Biology 15, e1007084.
10.1371/journal.pcbi.1007084.
55. Øyås, O., and Stelling, J. (2018). Genome-scale metabolic networks in time and space.
Current Opinion in Systems Biology 8, 51–58. 10.1016/j.coisb.2017.12.003.
56. Jouhten, P., Wiebe, M., and Penttilä, M. (2012). Dynamic flux balance analysis of the
metabolism of Saccharomyces cerevisiae during the shift from fully respirative or
respirofermentative metabolic states to anaerobiosis. The FEBS Journal 279, 3338–3354.
10.1111/j.1742-4658.2012.08649.x.

105
57. Diener, C., Gibbons, S.M., and Resendis-Antonio, O. (2020). MICOM: Metagenome-
Scale Modeling To Infer Metabolic Interactions in the Gut Microbiota. mSystems 5, e00606-19.
10.1128/mSystems.00606-19.
58. Panikov, N.S. (2021). Genome-Scale Reconstruction of Microbial Dynamic Phenotype:
Successes and Challenges. Microorganisms 9, 2352. 10.3390/microorganisms9112352.
59. Cabbia, A., Hilbers, P.A.J., and van Riel, N.A.W. (2020). A Distance-Based Framework
for the Characterization of Metabolic Heterogeneity in Large Sets of Genome-Scale Metabolic
Models. Patterns (N Y) 1, 100080. 10.1016/j.patter.2020.100080.
60. Medlock, G.L., Moutinho, T.J., and Papin, J.A. (2020). Medusa: Software to build and
analyze ensembles of genome-scale metabolic network reconstructions. PLOS Computational
Biology 16, e1007847. 10.1371/journal.pcbi.1007847.
61. Biggs, M.B., and Papin, J.A. (2017). Managing uncertainty in metabolic network
structure and improving predictions using EnsembleFBA. PLOS Computational Biology 13,
e1005413. 10.1371/journal.pcbi.1005413.
62. Benito-Vaquerizo, S., Diender, M., Parera Olm, I., Martins dos Santos, V.A.P., Schaap,
P.J., Sousa, D.Z., and Suarez-Diez, M. (2020). Modeling a co-culture of Clostridium
autoethanogenum and Clostridium kluyveri to increase syngas conversion to medium-chain
fatty-acids. Comput Struct Biotechnol J 18, 3255–3266. 10.1016/j.csbj.2020.10.003.
63. Scott, W.T., Benito-Vaquerizo, S., Zimmerman, J., Bajić, D., Heinken, A., Suarez-Diez,
M., and Schaap, P.J. (2023). A structured evaluation of genome-scale constraint-based modeling
tools for microbial consortia. 2023.02.08.527721. 10.1101/2023.02.08.527721.
64. Wang, H., Robinson, J.L., Kocabas, P., Gustafsson, J., Anton, M., Cholley, P.-E., Huang,
S., Gobom, J., Svensson, T., Uhlen, M., et al. (2021). Genome-scale metabolic network
reconstruction of model animals as a platform for translational research. Proceedings of the
National Academy of Sciences 118, e2102344118. 10.1073/pnas.2102344118.
65. Nilsson, A., and Nielsen, J. (2017). Genome scale metabolic modeling of cancer. Metab
Eng 43, 103–112. 10.1016/j.ymben.2016.10.022.
66. Wang, J., Delfarah, A., Gelbach, P.E., Fong, E., Macklin, P., Mumenthaler, S.M.,
Graham, N.A., and Finley, S.D. (2022). Elucidating tumor-stromal metabolic crosstalk in
colorectal cancer through integration of constraint-based models and LC-MS metabolomics.
Metab Eng 69, 175–187. 10.1016/j.ymben.2021.11.006.
67. Gelbach, P.E., and Finley, S.D. (2023). Ensemble-based genome-scale modeling predicts
metabolic differences between macrophage subtypes in colorectal cancer. 2023.03.09.532000.
10.1101/2023.03.09.532000.
68. Frades, I., Foguet, C., Cascante, M., and Araúzo-Bravo, M.J. (2021). Genome Scale
Modeling to Study the Metabolic Competition between Cells in the Tumor Microenvironment.
Cancers (Basel) 13, 4609. 10.3390/cancers13184609.
69. Brunk, E., Sahoo, S., Zielinski, D.C., Altunkaya, A., Dräger, A., Mih, N., Gatto, F.,
Nilsson, A., Preciat Gonzalez, G.A., Aurich, M.K., et al. (2018). Recon3D enables a three-
dimensional view of gene variation in human metabolism. Nat Biotechnol 36, 272–281.
10.1038/nbt.4072.

106
Appendix 1:
Kinetic and data-driven modeling of pancreatic beta cell central carbon metabolism and
insulin secretion

RESEARCHARTICLE
Kineticanddata-drivenmodelingof
pancreatic β-cellcentralcarbonmetabolism
andinsulinsecretion
PatrickE.GelbachID
1
,DongqingZheng
2
,ScottE.Fraser
3
,KateL.WhiteID
4
,Nicholas
A.GrahamID
2
,StaceyD.FinleyID
1,2,5
*
1 DepartmentofBiomedicalEngineering,USC,LosAngeles,California,UnitedStatesofAmerica,2 Mork
FamilyDepartmentofChemicalEngineeringandMaterialsScience,USC,LosAngeles,California,United
StatesofAmerica,3 TranslationalImagingCenter,UniversityofSouthernCalifornia,LosAngeles,California,
UnitedStatesofAmerica,4 DepartmentsofBiologicalSciencesandChemistry,BridgeInstitute,USC
MichelsonCenter,USC,LosAngeles,California,UnitedStatesofAmerica,5 DepartmentofQuantitativeand
ComputationalBiology,USC,LosAngeles,California,UnitedStatesofAmerica
*sfinley@usc.edu
Abstract
Pancreatic β-cellsrespondtoincreasedextracellularglucoselevelsbyinitiatingametabolic
shift.Thatchangeinmetabolismispartoftheprocessofglucose-stimulatedinsulinsecre-
tionandisofparticularinterestinthecontextofdiabetes.However,wedonotfullyunder-
standhowthecoordinatedchangesinmetabolicpathwaysandmetaboliteproducts
influenceinsulinsecretion.Inthiswork,weapplysystemsbiologyapproachestodevelopa
detailedkineticmodeloftheintracellularcentralcarbonmetabolicpathwaysinpancreatic β-
cellsuponstimulationwithhighlevelsofglucose.Themodeliscalibratedtopublishedmeta-
bolomicsdatasetsfortheINS1823/13cellline,accuratelycapturingthemeasuredmetabo-
litefold-changes.Wefirstemployedthecalibratedmechanisticmodeltoestimatethe
stimulatedcell’sfluxome.Wethenusedthepredictednetworkfluxesinadata-driven
approachtobuildapartialleastsquaresregressionmodel.Bydevelopingthecombined
kineticanddata-drivenmodelingframework,wegaininsightsintothelinkbetween β-cell
metabolismandglucose-stimulatedinsulinsecretion.Thecombinedmodelingframework
wasusedtopredicttheeffectsofcommonanti-diabeticpharmacologicalinterventionson
metabolitelevels,fluxthroughthemetabolicnetwork,andinsulinsecretion.Oursimulations
revealtargetsthatcanbemodulatedtoenhanceinsulinsecretion.Themodelisapromising
tooltocontextualizeandextendtheusefulnessofmetabolomicsdataandtopredictdynam-
icsandmetabolitelevelsthataredifficulttomeasure in vitro.Inaddition,themodeling
frameworkcanbeappliedtoidentify,explain,andassessnovelandclinically-relevantinter-
ventionsthatmaybeparticularlyvaluableindiabetestreatment.
Authorsummary
Diabetesisamongthemostcommonchronicillnesses,occurringwhenthe β-cellsinthe
pancreasareunabletoproduceenoughinsulintoproperlymanagethebody’sbloodsugar
PLOS COMPUTATIONAL BIOLOGY
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 1/30
a1111111111
a1111111111
a1111111111
a1111111111
a1111111111
OPEN ACCESS
Citation:GelbachPE,ZhengD,FraserSE,White
KL,GrahamNA,FinleySD(2022)Kineticanddata-
drivenmodelingofpancreatic β-cellcentralcarbon
metabolismandinsulinsecretion.PLoSComput
Biol18(10):e1010555.https://doi.org/10.1371/
journal.pcbi.1010555
Editor:VassilyHatzimanikatis,EcolePolytechnique
Fe ´de ´raledeLausanne,SWITZERLAND
Received:October11,2021
Accepted:September8,2022
Published:October17,2022
PeerReviewHistory:PLOSrecognizesthe
benefitsoftransparencyinthepeerreview
process;therefore,weenablethepublicationof
allofthecontentofpeerreviewandauthor
responsesalongsidefinal,publishedarticles.The
editorialhistoryofthisarticleisavailablehere:
https://doi.org/10.1371/journal.pcbi.1010555
Copyright: ©2022Gelbachetal.Thisisanopen
accessarticledistributedunderthetermsofthe
CreativeCommonsAttributionLicense,which
permitsunrestricteduse,distribution,and
reproductioninanymedium,providedtheoriginal
authorandsourcearecredited.
DataAvailabilityStatement:Allrelevantdataare
withinthemanuscriptanditsSupporting
Informationfiles.Modelscriptsareavailableat:

107

levels. β-cellsmetabolizenutrientstoproduceenergyneededforinsulinsecretionin
responsetohighglucose,andthereisapotentialtoharness β-cellmetabolismfortreating
diabetes.However, β-cellmetabolismisnotfullycharacterized.Wehavedevelopeda
computationalmodelingframeworktobetterunderstandtherelationshipbetweencellu-
larmetabolismandinsulinproductioninthepancreatic β-cell.Withthismodelingframe-
work,weareabletosimulatemetabolicperturbations,suchastheknockdownofthe
activityofametabolicenzyme,andpredicttheeffectonthemetabolicnetworkandon
insulinproduction.Thisworkcanthereforebeappliedtoinvestigate,inatime-andcost-
efficientmanner, β-cellmetabolismandpredicteffectivetherapiesthattargetthecell’s
metabolicnetwork.
1.Introduction
Pancreatic β-cells,thepredominantcelltypeinthepancreaticisletsofLangerhans,respondto
andtightlyregulatethebody’sbloodglucoselevelsthroughinsulinsecretion.Theprocessof
glucose-stimulatedinsulinsecretion(GSIS)isheavilydependentonthecells’intracellular
metabolism[1,2].Uponstimulationwithhighglucoselevels,glucoseistransportedintothe
cell,causinganincreaseinglycolysisandoxidativephosphorylation,whichleadtoanincrease
inthecellularATP/ADPratio[3].IncreasedATPcausestheclosureofpotassium(K
+
)chan-
nelsandtheopeningofcalcium(Ca
2+
)channels,whichpromotethereleaseofinsulin.In
ordertoaccomplishthiscascadeofevents,the β-cellhasseveralkeyglucose-sensingmetabolic
stepsthatarewidelyconsideredtobevitaltoinsulinsecretion,includingaspecializedglucose
transporterandtheglucokinasereaction[4,5].However,therearemanyadditionalpathways,
metabolites,andreactionsthatarepurportedtobeimpactfulininsulinsecretion,depending
onthecontext[6–10].Additionally,thewaycoordinatedchangesinmetabolicpathwaysand
resultingmetabolitepoolsinfluenceinsulinsecretionisnotfullyunderstood.Fortheserea-
sons,thereisaneedtostudypancreatic β-cellmetabolismatasystems-level,identifyinghow
setsofmetabolicpathwaysworktogethertocausetheobservedbiologicalpropertiesofinsu-
lin-secretingpancreatic β-cells.
Giventhatappropriatesecretionofinsulinisvitaltothesuccessfulmaintenanceofblood
glucosehomeostasis,animpairedmetabolicstateofthe β-celliscloselylinkedtodiseasepro-
gression[11].LoweredinsulinsecretioniscorrelatedwiththeemergenceandseverityofType
2diabetes[12,13].Thereissignificantvalueindevelopingadeeperunderstandingof β-cell
metabolicactivitytodetermineunderlyingbiologicalprocessesdrivingdiseaseprogression
andtofindnovelpotentialmechanismstotreatthedisease.Massspectrometry-basedmetabo-
lomics,whichenablesquantitativemeasurementsofcellularmetabolites,hasemergedasaway
toanalyzethecell’smetabolicconditionandtherebyelucidatemetabolicprocesses,inboth
healthyanddiseasedconditions.Becausemeasurementsofmetabolitepoolsizesalonedonot
giveholisticinsightintocellularbehavior,theirutilitymaybeextendedbyintegratingthedata
intoframeworksthatpredicttransientdynamics,thuslinkingexperimentalmeasurements
withphenotypicunderstanding[14].Computationalmodelingofmetabolismisonesuch
techniquethatcanleveragemetabolomicsdatatopredictdynamicbehavior.Especially
becausetheGSISsystemisinherentlytime-dependent,itisvaluabletousenonlinearordinary
differentialequation(ODE)models,trainedandrefinedwithmetabolomicsdata,tofurther
ourunderstandingofthemechanismsdrivinginsulinsecretion.
Severalmathematicalmodelshavebeendevelopedtounderstandtherelationshipbetween
β-cellmetabolismandinsulinproduction.Toppetal.developedasimplethree-equation
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 2/30
https://github.com/FinleyLabUSC/
PancreaticBetaCellMetabolism.
Funding:SDF,NAG,KW,andSEFreceivedsupport
fromtheUSCPancreaticBetaCellConsortium.
SDFreceivedsupportfromtheNIHNational
CancerInstitute(1U01CA232137).Thefundershad
noroleinstudydesign,datacollectionand
analysis,decisiontopublish,orpreparationofthe
manuscript.
Competinginterests:Theauthorshavedeclared
thatnocompetinginterestsexist.

108

modeldescribingtherelationshipsbetweenglucose,insulin,and β-cellmass[15].Modeling
workbyBertrametel.focusedprimarilyonATPsynthesisfrompyruvate[16].Magnusand
Keizerstudiedtheunderlyingmechanismsdrivingcalciumcyclingin β-cells,whileYugiand
Tomitafocusedonmitochondrialmetabolicactivity[17–19].Fridylandfocusedonthelink
betweencellularmetabolismandenergeticprocessessuchasthemaintenanceofamitochon-
drialmembranepotential[20].Jiangetal.builtuponmanyoftheseworkstodevelopadetailed
kineticmodelofglucose-stimulatedmetabolismin β-cells[21].However,theJiangmodel
lackedseveralglycolyticmetabolitesandpathwaysthatmaycontributetotheactivityofpan-
creatic β-cells,anditdidnotlinkinsulinsecretiontothemodeledmetabolicprocesses.Thus,
whilecomputationalmodelinghasbeenused,thereisacurrentneedforgreaterunderstand-
ingofcorecentralcarbonmetabolicpathwaysandhowtheirdynamicscorrelatetoinsulin
secretion.
Toaddressthisgapinknowledge,wedevelopakineticmodelofpancreatic β-cellintracel-
lularmetabolism,includingkey β-cell-specificmetabolicpathways.Werefineandtrainthe
modelwithpublished in vitrometabolomicsdataandassesstheimpactofmetabolicperturba-
tionsontheentirenetwork.Wealsopairpredictionsfromthekineticmodelwithlinear
regressionanalysistolinkmetabolicprocesseswithinsulinsecretion.Ourintegrativemodel-
ingapproachisthereforeavaluabletooltounderstandthedynamicsofGSISandmayinform
futureresearchaimedattreating β-celldysfunction.
2.Materialsandmethods
2.1Modelstructureandmetabolicpathways
WeconstructedakineticmodelofthecentralcarbonmetabolismoftheINS1832/13pancre-
atic β-celllinebybuildinguponpreviouslypublishedmodelsofintracellularmetabolism(Fig
1)[21–23].Themodelconsistsof56metabolitesand65enzyme-catalyzedmetabolicreactions
insixprimarymetabolicpathways:glycolysis,glutaminolysis,thepentosephosphatepathway
(PPP),thetricarboxylicacid(TCA)cycle,thepolyolpathway,andelectrontransportchain
(ETC).Thesereactionsoccurintwocellularsub-compartments(cytosolandmitochondria).
Byincludingthesecentralcarbonmetabolicpathways,themodelissignificantlymoredetailed
andexpansivethanotherpublishedmodelsofpancreatic β-cellmetabolism.Themodelisrep-
resentedasaseriesofnonlinearODEs,characterizedwithMichaelis-Mentenorbi-bireaction
kinetics,thatdescribehowtheconcentrationsofintracellularmetabolitesevolveovertimeina
pancreatic β-cell[24,25].Thus,thereisasingleODEforeachmetaboliteincludedinthe
model.Metabolitesthatarefoundinbothcytosolandmitochondriahaveseparateequations,
allowingforthecomparisonofconcentrationsbetweenthetwocellularsub-compartments.
TheODEsareimplementedinMATLABandsolvedwiththebuilt-in ode15sdifferentialequa-
tionsolver[26]
Glycolysispathway. Pancreatic β-cellsrespondtohighbloodglucoselevelsbymetaboliz-
ingtheextracellularglucose,triggeringanincreaseinATPproduction,whichdrivestheclo-
sureofK
+
channelsandtheopeningofCa
2+
channels,leadingtothesecretionofinsulin[27].
Theglycolyticpathwayisthereforetheprimarypathwaymodulatinginsulinsecretion,asitini-
tiatesthestepsallowingforinsulinrelease.ThepathwaybeginswiththeGLUT2glucosetrans-
porter,which,duetoanestimatedhighMichaelisconstant(K
m
)value,actsasaglucosesensor
[28].Specifically,therateofglucoseuptakebytheGLUT2enzymeisproportionaltoextracel-
lularglucoselevels,thusmodulatingtheglycolyticfluxinsideofthecellandtheamountof
insulinreleased[20]. β-cellsalsoexpresstheglucokinase(gk)enzyme(calledhexokinasetype
IV),whichfurtherscontributestothecells’sensitivitytoglucoseandactsastherate-control-
lingstepinGSIS[29].Thecellsshowlowexpressionofthelactatedehydrogenase(ldh)enzyme
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 3/30

109

andcompensatefortheneedtomanageNADandNADHlevelsbyincreasingtheactivityof
mitochondrialhydrogenshuttles,whichareincludedinthismodel[30].Wealsoinclude
downstreamglycolyticintermediates,suchas2-phosphoglycericacid(2PG),whichhavenot
previouslybeenincorporatedintokineticmodelsofpancreatic β-cellmetabolism.Intotal,gly-
colysisisrepresentedinthecytosolwith12metabolites(2PG,3PG,BPG,DHAP,F6P,FBP,
G3P,G6P,GLC,LAC,PEP,PYR)and13reactions(aldo,eno,gapdh,gk,glut,hpi,ldh,mct,
pfk1,pgam,pgk,pyk,andtpi).Theglucosetransportreaction(glut)andlactatetransportreac-
tion(ldh)aremetabolicsourcesorsinksforthemodel,connectingtheintracellularmetabo-
liteswiththeextracellularcondition.
Fig1. Metabolicnetwork.Thenetworkofpancreaticbetacellcentralmetabolismconsistsof56metabolitesconnectedvia65enzyme-
catalyzedreactions,makingupglycolysis,glutaminolysis,PPP,TCACycle,polyolpathway,theelectrontransportchain,andshuttlesbetween
thecytoplasmandmitochondria(denotedbytheshadedrectangle).Forclarity,somemetabolitesareshownasmultiplenodeswithina
subcompartment(forexample,mitochondrialAKGisshownastwonodes,thoughtheyrepresentthesamemetabolicspecies).Aspartof
modeltraining,weperformedasensitivityanalysis,andthereactionswhoseV
max
valuesweresignificantlyimpactfularecoloredgreen.We
comparedmodelpredictionsofmetabolitelevelsafter60minutesofstimulationwith2.8mMglucose,relativetometabolitelevelsfollowing
60minutesofstimulationwith16.7mM,toqualitativeshiftsinmetabolismasreportedintheliterature,providedinthesupplemental
material(S1Table).Theexperimentalobservationsareindicatedbythelefthalfofthemetabolitenodes,andthemodelpredictionsareshown
ontheright.Themodelcandifferentiatebetweenmetabolitelocation(cytosolversusmitochondria),whilethemassspectrometryapproaches
canonlymeasurethetotal(pooled)amountofametabolite;wehaveoutlinedthosemetabolitesinorange.Thefullsetofabbreviationsand
reactionequationsisgiveninS1Text.
https://doi.org/10.1371/journal.pcbi.1010555.g001
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 4/30

110

Pentose-phosphatepathway. TherelationshipbetweenthePPPandinsulinreleaseisnot
fullycharacterized,asitisrelativelyinactiveinpancreatic β-cells[31].However,thePPPcon-
tributestothegenerationofNADPH,whichisbelievedtoinfluenceormodulateinsulinsecre-
tion[32].Furthermore,PPPmetaboliteshavebeenobservedtoincreaseinabundance
followingglucosestimulation[33–35].Wehavethereforeincludedthepathwayinthemodel,
withsevenmetabolites(6PG,E4P,PRPP,R5P,Ru5P,S7P,andX5P)involvedinsevenmeta-
bolicreactions(6pgdh,g6pd,prpps,rpi,ta,tk1,andtk2).
Tricarboxylicacidcycle. TCAintermediateshavebeenlinkedwithGSIS,asamajorityof
glucoseisconvertedintopyruvate,whichisthenutilizedintheTCAcycle.Inparticular,meta-
boliccouplingfactors(MCFs)suchasglutamateareknowntobelinkedwithandamplify
insulinsecretion[36–39].Inaddition,insulinsecretionislikelydependentoncofactorssuch
asNADorNADP,whichareproducedthroughtheTCAcycle[40–42].TheTCAcycleinthis
modeliscomposedof20metabolitesacrosstwocompartments.Thirteenarefoundinthe
mitochondria(ACCoA,ALA,AKG,ASP,CIT,FUM,GLU,ICIT,MAL,OAA,PYR,SCOA,
andSUC)andsevenarefoundinthecytosol(AKG,ASP,CIT,GLN,GLU,MAL,andOAA).
Twenty-fivemetabolicreactionscarryouttheimportandinterconversionofthosemetabolites
(acon,akgd,akgmal,asct2,aspglu,citmal,cly,cs,fum,gls,gluh,got1,got2,gpt,idh,malpi,
mdh1,mdh2,me1,mmalic,pc,pdh,pyrh,scoas,andsdh).Theglutaminetransportreaction
(asct2)isametabolicsourceforthemodel,connectingtheintracellularmetaboliteswiththe
extracellularcondition.
Polyolpathway. Thepolyolpathway(alsocalledthealdosereductasepathway)consistsof
theproductionofsorbitolfromglucoseinthealdosereductasereaction,andthesubsequent
conversionofsorbitoltofructoseinthesorbitoldehydrogenasereaction[43].Thus,thepath-
wayconsistsoftwometabolites(SORandFRU)andthreereactions(aldr,sodh,fruT).The
polyolpathwayisrelativelyinactiveinmostphysiologicalconditionsduetothealdosereduc-
tasereaction’shighK
m
valueandlowaffinityforglucose[44].However,thispathwayactsasa
mechanismfortheprocessingandeliminationofglucoseinhyperglycemicconditions,in
ordertoprotectagainstglucosetoxicity[45,46].Thepathwayisthereforeofinterestwithin
thecontextof β-cellstimulationwithhighglucoselevels,thoughithasneverbeenincludedin
existingmodelsof β-cells.Additionally,thereissubstantialvalueinstudyingthepolyolpath-
waywithinthecontextoftheentiremetabolicnetworkbeingmodeled,asthePPPreduces
NADPHthatisoxidizedbythepolyolpathway,leadingtoapotentialmetaboliccyclethatmay
impactinsulinsecretion[33].
Electrontransportchain. Inpancreatic β-cells,pyruvateisoxidizedintheTCAcycle,
generatingNADHandFADH.Thosereducingequivalentsarethentransferredthroughaset
ofelectroncarriers(theelectrontransportchain,orETC),leadingtothehyperpolarizationof
themitochondrialmembrane.Thishyperpolarizationchangesthecell’sATP/ADPratioand
directlyinfluencesthereleaseofinsulin.Thepathwayisthereforeofparticularinterestfor
understanding β-cellmetabolism.TheETCinthekineticmodeliscomposedofsixmetabolites
(NADH,NAD,Cyt_c3,Cyt_c2,ATP,andADP),andfourreactions(complex1,complex3,com-
plex4,complex5).
Additionalmodelmetabolitesandreactions. Besidesglycolysis,thePPP,TCA
cycle,polyolpathwayandETC,thereareotherknownreactionsandmetabolites
involvedin β-cellmetabolismthatwehaveincludedinthemodel.Namely,the gssgrreac-
tioninterconvertsGSSGandGSH, gpxconvertsGSHtoGSSG, oxtransportsextracellular
oxygen(o2
e
)intothecell(o2
i
), dhasesinterconvertsNADandNADH, akconvertsAMP
andADPintoandfrom2ATPmolecules,and atpaseand oxphosinterconvertADPandPi
withATP.
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 5/30

111

2.2Modelequationsandparameters
Weprovideadifferential-equationbasedmodelofpancreaticbetacellmetabolism;assuch,it
calculatesthesimulatedchangeinmetabolitelevelsintime,andthereforepredictsthedynam-
icsofintracellularmetabolitesandtheactivityofmetabolicreactionsdrivingthosemetabolite
changes.Thereactionsinthemetabolicpathwaysincludedinthemodelaresimulatedwith
enzymaticreactionrateexpressions,andthemajorityofthemodelreactionratelawsandover-
allmodelstructurearederivedfromRoyandFinley’smodelofpancreaticductaladenocarci-
noma[22]. β-cell-specificenzymeisoforms,suchasglucokinaseandtheglucosetransporter,
aretakenfromthepublishedmodelsofpancreatic β-cellsfromJiangandFridyland[20,21].
RateequationsforthepolyolpathwayaretakenfromCortassaetal.,whichsimulatescardiac
cellmetabolism[23].EquationsfortheETCwerealsotakenfromthemodelpublishedby
Jiang.Intotal,themodelcontains385parameters,including96reactionvelocities(V
max
val-
ues).Wenotethattherearemorereactionvelocitiesthanmodeledreactionsbecausesome
reactionsarereversibleandthushavebothaforwardandreverseV
max
value.Tomakethe
modelspecificto β-cellmetabolism,wefittheV
max
valuestopublishedmetabolomicsdata
obtainedfromthepancreatic β-celllineINS1832/13,asthereactionvelocitiesoftencandistin-
guishmetabolismbetweendistinctcelltypes.
Wecalculatedtheleftnullspaceofthegeneratedmodel’sstoichiometricmatrix(S2Table)
andthereforedeterminedthemodel’sconservedmetabolitepools.Thefollowingpairsof
metaboliteswerefoundtobeconservedmoieties:NADP-NADPH,GSH-GSSG,o2
e
-o2
i
,and
mGDP-mGTP.Furthermore,assessingthemodelstoichiometricmatrixshowsthatthemodel
isindeedmassbalanced,andthatallsinksandsourcesareaccountedfor.
2.3Initialconditions
Whereavailable,initialconditionsweretakenfrompublishedstudiesthatquantifiedintracel-
lularmetaboliteconcentrationsin β-cells[21].Theinitialvaluesforthemetabolitesforwhich
therewasnoavailabledataweresetusingLatinHypercubeSampling[47].Wespecifiedcon-
centrationrangesbasedonpublishedmeasurementsofmetabolitesinothercelltypesand
sampled50setsofinitialconditions[48,49].Themodelwasfitfivetimeswitheachsetofini-
tialconditions,andweassessedthemodelagreementtodata;theinitialconditionsetthat
allowedforthebestmatchtodatawasusedforthesubsequentfitting.Thisprocesslimitedthe
numberoffittedmodelparameterstoonlytheV
max
valuesselectedwithsubsequentsensitivity
analyses(describedinsection2.5),therebyavoidingoverfitting.
2.4Dataextraction
Therehavebeenarangeofpublishedmassspectrometry-basedexperimentsaimedatunder-
standingthemetabolicalterationsthatoccurinINS1832/13pancreatic β-cellsfollowingstim-
ulationwithextracellularglucose.Wecompiledthosestudiesandextractedthemetabolite
fold-changesusingtheinternet-basedwebplotdigitizertool[26].Thefold-changeininsulin
secretionamountwassimilarlycalculatedwhenavailable.
InthestudypublishedbySpegeletal., β-cellsweretreatedwith2.8mMglucosefortwo
hoursandthen16.7mMglucosefor3,6,10,and15minutes[50].Metabolitefold-change
amountswerecalculatedforthe16.7mMglucoseconditionrelativetothe2.8mMglucose
conditionfor14metabolites:2PG,3PG,AKG,ALA,ASP,CIT,FUM,G3P,LAC,MAL,PEP,
PYR,R5P,andSUC.Insulinwasalsomeasuredforthesameexperimentalconditions.We
selectedthe3-and10-minutetimepointsastrainingdataforuseinmodelfitting.The6-and
15-minutetimepointswerewithheldfrommodelparameterestimationinordertobeusedfor
validation.Someofthemeasuredmetabolitesarefoundinboththecytosolandmitochondria;
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 6/30

112

however,theycannotbedistinguishedviametabolomicanalysis.Therefore,wefitthemea-
suredfold-changeofthetotalmetabolitepool.Wethendeterminedthecytosolicandmito-
chondrialpoolsseparatelybyaccountingfortherelativevolumesofthosecomponents,with
thecytosolassumedtobethreetimeslargerthanthemitochondria.Thus,wecanalgebraically
solvefortheindividualcytosolicandmitochondrialconcentrations.
IntheworkpublishedbyMalmgrenetal., β-cellsweretreatedwith2.8mMor16.7mM
glucosefor60minutes[51].Fold-changeswerecalculatedforinsulinand14metabolites:
AKG,ALA,ASP,CIT,FUM,G3P,G6P,GLC,GLU,ICIT,LAC,MAL,PYR,andSUC.Allof
thesemeasurementswereusedastrainingdata.
Additionally,Spegeletal.,ina2015paper,measuredmetabolitefoldchangesrelativetothe
0-minutetimepoint,aftertreatingwith16.7mMglucose[52].Becausethoseprovidedatarela-
tivetotheinitialconditions,weusedthemeasurementstoconstrainthemodelandensureit
reachesasteadystate.Dataforthefollowingmetaboliteswereusedformodeltraining:2PG,
3PG,AKG,ALA,CIT,F6P,FUM,G6P,ICIT,LAC,MAL,PEP,R5P,andSUC.
OurtrainingdatawasthereforeacombinationoftheSpegeletal.(3-and10-minute)data,
Malmgren(60-minute)etaldata.,andtheSpegeletal.(6-and15-minute)datarelativetothe
initialtimepoint[50–52].Altogether,therewereatotalof70individualdatapointsinthe
trainingset.Thevalidationdatawascomprisedofthe6-and15-minutetimepointspublished
bySpegelandcoauthors,comprisingatotalof28distinctdatapoints.Inadditiontothose
quantitativedatapoints,datafromelevenotherpublishedpaperswereusedasqualitativevali-
dationofpredictedfold-changedirectionformetabolitesinthemodelupontreatmentwith
above-basalglucoselevels[33–35,50–59],showninFigAinS1SupportingInformation.All
experimentaldatausedisprovidedinS2Table.
2.5Parameterestimation
Inordertoproperlyfitthekineticmodel,wefirstperformedanaprioriparameteridentifiability
analysis.Specifically,wevariedeachmodelreactionratetodeterminewhichparameterpairs
maybemathematicallycorrelatedtoeachotherandthereforestructurallynon-identifiable[60,
61].Wefound11forwardorreversereactionvelocities(V
f
orV
r
parameters)thatwerecorre-
latedtooneanother,andthereforedefinedthosereactionvelocitiesusingequilibriumcon-
stants.Thatis,wesetthereversereactionvelocity,V
R
,tobeexpressedintermsoftheforward
reactionvelocityandtheequilibriumconstant,K,sothatV
r
=V
f
/K.Becauseofthenonlinear
anddynamicnatureofthemodel,itispossibleforanytwomodelparameterstobecorrelated,
andthereforebestructurallyunidentifiable;however,forourmodel,theonlyparametersfound
tobecorrelatedtoeachotherwereV
f
/V
r
pairsforthesamereaction.Withthisprocess,we
thereforehad85V
max
parametersavailableformodelfittingandsubsequentanalyses.
Next,weidentifiedtheparametersthatshouldbefittothetrainingdata.TheextendedFou-
rierAmplitudeSensitivityTest(eFAST),avariance-basedglobalsensitivityanalysismethod,
wasperformedbysimulatingthesameinvitroexperimentalmethodsusedtocollectthemeta-
bolomicdata[62].TheeFASTmethodvariesmodelinputs(the85V
max
parameters)two
ordersofmagnitudeaboveandbelowtheirbaselinevaluesinordertounderstandthesensitiv-
ityofthemodeloutputs(themetabolitefold-changes).Wecanthereforeidentifythemost
influentialmodelparameterstofittoexperimentaldata,sothatthemodelcanaccurately
matchthedatawithoutoverfitting.BasedontheeFASTresults,weidentified33influential
modelparametersbyselectingtheparametersthathadsensitivityindicesabove0.85.Byonly
fittingthe33mostimpactfulparameterstothe70trainingdatapoints,wecouldaccurately
capturetheobserveddynamicsandadequatelyconstraintheparameterset,whileavoiding
overfitting.
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 7/30

113

Parameterestimationwasthenperformedviaparticleswarmoptimization(PSO)withthe
ParameterEstimationToolbox(PESTO)inMATLAB(Mathworks,Inc.),minimizingthe
weightedsumofsquaredresiduals(WSSR)[63,64].Inordertofitthedata,wecomputation-
allysimulatedtheexperimentalprotocolsforeachdatasetdescribedinSection2.4.PSOisa
stochasticglobaloptimizationtoolthatiterativelyupdatessetsofrandomlyseededparticles
(parametersets)toconvergeuponasingleparametersetthatminimizestheWSSR.The
WSSRerrorcalculationissimilartothesumofsquaredresiduals(SSR),buteachdatapointis
weightedbyitsassociatedstandarddeviationandmagnitude.Weighingbythestandarddevia-
tionensuresthatthefittingalgorithmprioritizeshigh-confidencedatapoints,whileweighing
theerrorfunctionbythedatapoint’smagnitudepreventsprioritizingthehighfoldchange
measurementsattheexpenseofthesmallfoldchanges.InthePSOprotocol,eachparameteris
allowedtovary100timesaboveandbelowitsinitialestimate,andeachfittingruncarriesout
2,000steps;thislimitsthecomputationalcostwhileexploringthetotalparameterspace.One
hundredfittingrunswereperformedwithPSO,andthebestparametersetswereselected(a
totalof8bestfits)basedontheWSSR.Thesebestfittedparametervalueswereusedforallsub-
sequentanalysesandfigures.Thisfittingapproachenabledustofittheentiretrainingdataset
(70distinctdatapoints,asmentionedinsection2.4)andderiveconsistentandhighconfi-
denceparametersets.Acommonfeatureofsystemsbiologymodelsisvariabilityintheesti-
matedparametervaluesduetothecomplexityofthemodel,withmultipleparametersets
beingequallycapableofdescribingthesystemandcapturingtheobserveddata.However,per-
formingthePSOmultipletimesfrominitialstateshavingdifferentinitialconcentrationsaims
toensuretheparameterestimationhasreachedaglobalminimumfortheerrorfunction.
Inordertojustifytheassumptionthatthekineticparametersdeemednon-impactfulbythe
sensitivityanalysiswerenotdrivingthefittedmodel’sresponse,weperformedadditional
modelfitswiththeentiresetof85parameters,andfoundthemodelperformancedidnot
changesubstantially.However,wecouldnotensureparameteridentifiability,andcouldnot
obtainaconsistentsetofparametervalues.Therefore,weperformedmodelsimulationsusing
thebestfittedparametersfromfittingthe32parametersshowntobeinfluentialbasedonthe
eFASTresults.Weusethosebest-fitparametersetsforallsubsequentanalyses.
Thefittedmodelwasthereforeabletopredictmetaboliteconcentrations(inmM)andreac-
tionfluxes(inmM/min)foreachmodeledspeciesandreaction,respectively.Inparticular,we
simulatethemetabolitefoldchangesbetweenhigh(16.7mM)andlow(2.8mM)glucosecondi-
tions(Figs1and2),andmetabolitelevelsandredactionfluxesuponstimulationwithhigh
extracellularglucosealone(Figs3and4).
2.6Partialleastsquaresregression
Usingthetrainedkineticmodel,wepredictedthefluxthrougheachofthe65metabolicreac-
tionsovertimein1-minuteintervals.Wethenfoundtheaveragefluxthrougheachreaction
overthetimeperiodforwhichwehadmetabolomicsdata(3,6,10,15,or60minutes).Thus,
wepredictedasingletime-averagedfluxvalueforaparticularlengthofglucosestimulation.
Thepredictedfluxvaluesareinputstoaregressionanalysis,andthecorrespondingfold-
changeamountsforinsulinsecretionforINS1832/13cellsstimulatedwith16.7mMglucose
relativetoinsulinsecretionfollowing2.8mMglucosefromthepublishedstudiesareoutputs
oftheregressionanalysis.
Weperformedpartialleastsquaresregression(PLSR),amultivariatedimensionalityreduc-
tiontechniquethatseekstodetermineamathematicalcorrelationbetweenachoseninputvec-
torwithanoutputmeasurementofinterest[65].PLSRproducesthecomponents,weighted
linearcombinationsoftheinputs,thatcorrelatewiththeoutput,andweusedtheSIMPLS
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 8/30

114

algorithmtocompletethisanalysis[66].Theinputmatrixwas5rowsby65columns,withthe
columnsrepresentingthepredictedaveragefluxforeachmodelreaction,andtherowsrepre-
sentingthefivetimepointsofinterest.Theoutputmatrixwas5rowsby1column,corre-
spondingtoexperimentallymeasuredinsulinsecretionfold-changeatthefivetimepoints.By
performingpartialleastsquaresregression,wespecifytherelationshipbetweenflowofmate-
rialthroughthemetabolicnetworkandinsulinreleasedbythe β-cell.The6-and10-minute
Fig2. Modelfittorelative16.7/2.8mMglucoseexperimentaldata.WetrainedthemodeltomassspectrometrydatapublishedbySpegeletal.and
Malmgrenetal.,forthe3-,10-,and60-minutetimepoints(graybarswithblackoutline)for17distinctmetabolites[51,52].Modelpredictions(blue
bars)matchexperimentalmeasurements;theerrorbarsrepresentthestandarddeviationofmodelpredictionsacrosstheeightbest-fitparametersets.
Theexperimentaldataforthe6-and15-minutetimepoints(graybarswithredoutline)werewithheldasvalidationdatatotesttherobustnessofmodel
predictions.Predictedfold-changesformetabolitesfoundinboththecytosolandmitochondriaaresummedtogetherasatotalmetabolitepool,inorder
tocomparetotheexperimentaldata.
https://doi.org/10.1371/journal.pcbi.1010555.g002
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 9/30

115

timepointswerewithheldtobeusedasvalidationdata,whilethe3-,15-,and60-minutetime
pointswereusedtobuildthePLSRmodel.Thisprocesswasperformedusingeachoftheeight
best-fitparametersets.Thus,allpredictionsfromPLSRanalysisareshowingtheaveraged
resultsacrosstheeightPLSRmodels.WeevaluatedthePLSRmodelfitnesswiththeR
2
and
Q
2
Yvalues,whichrangefrom0to1.TheR
2
valueindicatesmodelagreementtothetraining
data,termed“goodnessoffit”,andtheQ
2
Yvalueassessestheabilityofthemodeltopredict
datanotusedfortraining,i.e.,“goodnessofprediction”[67].
Fig3. Modelfittoexperimentaldatarelativetoinitialstate.WetrainedthemodeltomassspectrometrydatapublishedbySpegeletal.for14metabolites(at
16.7mMglucose),relativetotheinitial0-minutecondition[52].Theexperimentaldata(blacktrianglesformeasurementaverage,barsrepresentingdatastandard
deviation)areatthe6-and15-minutetimepoints.Themodelsimulations(bluedotsforaverageprediction,bluebarsshowingstandarddeviation)demonstratethat
themodelreachesasteadystatecondition,within200minutesformostmetabolites.Predictedtimecoursesforallmetabolitespredictedbythemodelareshownin
FigDinS1SupportingInformation.
https://doi.org/10.1371/journal.pcbi.1010555.g003
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 10/30

116

WeusetwoquantitiescalculatedinthePLSRanalysistogainbiologicalinsightintohow
intracellularmetabolisminfluencesinsulinsecretion.ThePLSRanalysisestimatesthevariable
importanceofprojection(VIP)scoreforeachreactionflux.TheVIPscorequantifiesthecon-
tributionofeachinputvaluetothemodelpredictions.Here,theVIPscoreidentifiesthemeta-
bolicreactionsthataremoststronglycorrelatedtoinsulinsecretion.Generally,VIPscores
greaterthanoneindicateinfluentialinputs[68].Inaddition,byassessingthePLSRmodel
weights,wedeterminedtheeffectthatalteringfluxthroughthemetabolicnetworkwouldhave
oninsulinsecretion.Forexample,anegativeweightindicatesthatincreasingfluxthroughthat
reactionwoulddecreaseinsulinsecretion.TheVIPscoreandweightsareunitlessquantities.
WealsoperformedPLSRanalysistodeterminehowintermediatetimepointsinfluence
insulinsecretion,tounderstandthetime-dependentnatureofthelinkbetweenmetabolism
Fig4. Predictedsteady-statereactionfluxes.Weappliedthemodeltopredictthefluxthrougheachreaction
followingstimulationwith16.7mMextracellularglucose.Resultsarepresentedasthefluxthrougheachmodelreaction
whenthesystemhasreachedsteadystate,usingParameterSet1inS5Table.Fluxvaluesareshownasapercentageof
theglucosetransportreactionflux.Wenotethatforclarity,somemetabolitesareshownasmultiplenodeswithina
subcompartment(forexample,mitochondrialAKGisshownastwonodes,thoughtheyrepresentthesamemetabolic
species).
https://doi.org/10.1371/journal.pcbi.1010555.g004
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 11/30

117

andinsulinatahigherresolution.Inordertoaccomplishthisgoal,weagainusedthemeta-
bolicnetwork’sfluxomepredictedbythefittedkineticmodelofmetabolismasaninputtoa
PLSRmodel;butthistime,at1-minuteintervalsforasingletimecourse.Forexample,the
kineticmodelpredictedthefluxesthrougheachreactionforthefirstthreeminutesofsimula-
tionandusedthissetofthreepredictedfluxesasinputstoaPLSRmodel.Thefold-changein
thesecretedinsulincalculatedfromtheexperimentaldatawasusedasthePLSRoutput.
BecausethePLSRapproachrequiresmultipledatapointsforbothitsinputandoutput,we
assumedalinearincreaseinsecretedinsulinperminute,thusgivingthesamenumberofout-
puts(fold-changeofinsulinsecretioncalculatedperminutefromtheexperimentaldata)as
inputs(predictedreactionfluxesforeachminute).Weperformedthisanalysistodetermine
thetime-dependentrelationshipsbetweenreactionfluxesandinsulinsecretionover3,6,10,
and15minutes.Asdescribedabove,weusedtheVIPscoresandweightsfromthePLSRmod-
elstoidentifythemostimportantreactionfluxesforeachone-minuteintervalwithineach
timecourse.
2.7Kineticmodelperturbations
Variationofeachmodelparameter. Thekineticnetworkcanbeusedtopredictthe
effectsofmetabolicperturbationsonmetabolitelevelsandthefluxesthroughthemetabolic
reactions,therebygivingapredictionofthesystems-levelresponseofthecell.Usingthefitted
kineticmodel,wesimulatedmetabolicperturbations,whereweincreasedanddecreasedthe
rateofeachmodelreactionbyafactoroftwoandassessedtheimpactofthatperturbationon
allmodeledmetabolites,comparedtotheunperturbedbaselinecondition.
Implementationofpharmacologicalinterventions. Weselectedthreeanti-diabetic
pharmacologicalinterventionstosimulateinthemodel.Twoperturbationsarebasedonexist-
ingagents:metformin,whichisthemostcommondrugtakenbydiabeticpatientsbutwhose
impacton β-cellsisnotfullyunderstood,andagrimony,amedicinalplantbelievedtoactasan
antioxidantinthe β-cell.Lastly,wesimulatedtheupregulationoftheadenylatekinase(ak)
reaction,whichreversiblycatalyzesATPandAMPfromtwoADPmolecules,asthatinterven-
tionwaspredictedtobethemostbeneficialforincreasinginsulinsecretionaccordingtothe
PLSRmodel.
Metforminprimarilyactsontheperipheraltissuesandorgansbyreducinghepaticglucose
productionandincreasingskeletalmuscleglucoseuptake.Together,theseeffectsreduce
hyperglycemiaandeffectivelytreatdiabetes[69].Itisunclearhoworifmetforminaffectspan-
creatic β-cellsinvivo.Lamontagneetal.proposedthatmetformindrove“metabolicdecelera-
tion”,whereintheINS1 β-cellexperiencesadecreaseinglucose-inducedinsulinsecretion,
therebyprotectingthecellsfromhyper-responsivenessorhyperglycemicglucotoxicityand
lipotoxicity[70].Othershaveshownthatmetforminprotectsagainst β-cellexhaustionby
reducingthebody’sbloodglucoselevels[26,71,72].Totestthishypothesis,wedecreasedglu-
cosetransportintothecellbyreducingtheV
max
valuefortheglutreactionby80%.Wethen
calculatedtheeffectonmetabolites,metabolicfluxes,andinsulinsecretion,andcompared
modelpredictionstoreportedmetabolomicsdatawhenpossible.
Agrimony(Agrimoniaeupatoria)isamedicinalplantusedaroundtheworldtotreatdiabe-
tes,especiallyintraditionalEasternmedicinepractices[26,73].Ithasbeenshowntoaffect
insulinsecretoryactivity,bothinpatientsandinapancreatic β-celllineinvitro[74].Itis
believedthatagrimonyactsasanantioxidantinthe β-cell[75].Itiswellknownthatoxidative
stress,inducedbyreactiveoxygenspecies(ROS)andreactivenitrogenspecies(RNS),impairs
β-cellactivityandisacontributingfactorobservedindiabetesprogression[76–78].ThePPP
isbelievedtoimpacttheoxidativestressresponse,asitisaoneoftheprimaryNADPH-
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 12/30

118

generatingpathways.ThegenerationofNADPHinhigh-glucoseconditionsisshownto
reducecellinflammation[26,79].Furthermore,anincreaseinPPPfluxshiftsthecellmetabo-
lismawayfromROS-generatingpathways,limitingfurtherstressonthecells[80].Tosimulate
theactionofagrimony,weperturbedtheglucose-6-phosphatedehydrogenase(g6pd)reaction
withafive-foldincreaseofitsV
max
value,tosimulateoverexpression,asg6pdistheprimary
upstreamcontrollerofPPPactivity[81,82,87].
Finally,basedonresultsfromPLSRmodeling,wesimulatedtheeffectsofperturbingtheak
reaction.Weimplementedafive-foldreductioninV
max
valueandassessedtheeffectonthe
metabolicnetworkasawhole.
3.Results
Wedevelopedakineticmodelcapableofsimulatingthedynamicsofintracellularmetabolism
ofthepancreatic β-cell.Themodelincludeskeymetabolitesandreactionsinvolvedinglycoly-
sis,glutaminolysis,PPP,TCAcycle,andpolyolpathways,withcytosolicandmitochondrial
compartments.Themodelconsistsof58metabolitesand65metabolicreactionsandwas
trainedtopublishedmassspectrometry-basedmetabolomicsdatasets.Thefittedmodelpre-
dictionswereusedtocreateaPLSRmodeltostudytherelationshipbetweenfluxthroughthe
metabolicnetworkandsecretedinsulin.Wethenassessedtheimpactofvariousmetabolicper-
turbationsonmodelpredictions.
3.1Modelfittingtotrainingandvalidationmetabolomicsdata
Wedevelopedthemodelstructuretocomprisepancreatic β-cellcentralcarbonmetabolism,
includingisoformsandpathwaysuniquetothe β-cell.Afterperformingaparameteridentifia-
bilityanalysistoexcludetheforwardandreversereactionvelocitiesthatwerecorrelatedto
eachother,weperformedaglobalsensitivityanalysisusingtheeFASTmethod,identifyingthe
influentialmodelparameterstofittoexperimentaldata(FigBinS1SupportingInforma-
tion).Finally,weusedpublishedmetabolomicsdataandperformedPSOinordertofindopti-
malparametervalues.Weselectedtheeightbest-fitparametersetsbasedontheerrorbetween
modelpredictionsandexperimentaldata.Theestimatedvaluesforsomeparameterswerecon-
sistent,with10ofthe32parametersvaryinglessthan10%acrosstheeightbestfits(FigCin
S1SupportingInformation).Interestingly,theV
max
valuesforseveralreactionsexhibitbimo-
dalityacrosstheeightfittedparametersets,showingmultipleregimesthatareequallycapable
ofexplainingthedata.
Thetrainedmodelwasabletocloselymatchthequantitativefold-changevaluesmeasured
experimentallyfor17metabolitesusedforparameterestimation(Fig2).Furthermore,the
modelmatchedthefold-changedatafortimepointsthathadbeenwithheldasvalidationdata,
pointingtotheabilitytosuccessfullypredictdatanotusedformodeltraining.Thisfurther
establishesthemodel’sabilitytomatchexperimentaldata.Wealsocomparedmodelpredic-
tionstothequalitativedirectionofthechangeinmetabolitelevelsuponstimulationwithhigh
glucose,basedonliteraturereview.Theseobservedchangesareindicatedinthecoloringofthe
nodesinFig1andthesquaresinFigAinS1SupportingInformation.Additionally,weper-
formedastatisticalanalysisonthemodelfits,comparingeachmodelpredictionwithitscorre-
spondingexperimentaldatawithat-test.Onlysixofthe99t-tests(3-minuteCITand
60-minuteMALforthehigh-glucoserelativetolow-glucosecomparisons,andthe6-and
15-minute2PG,15-minuteALA,and15-minuteCITforthemetabolitecomparisonsrelative
totheirinitialconditions)foundastatisticallysignificantdifferencebetweenthepredictions
anddata.Thisanalysisindicatesthatthemodelpredictionsmatchdatawell.Theresultsfrom
thisstatisticalanalysisaregiveninthesupplementasS3Table.
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 13/30

119

Besidesthe17uniquemetabolitesusedformodelfitting,themodelalsopredictsthefold-
changesof31distinctmetabolites.Mostmetabolites(88%)qualitativelymatchtheexperimen-
talfold-changedirection,evenmetabolitesthatwerenotusedintraining.
Themodelisalsocapableofcapturingthedynamicsofbiomarkersknowntobeimportant
inGSIS.Forexample,themodelsshowa6.2-foldincreaseintheNADPH/NADPratioafter
stimulationwithhighglucoseforsixminutes,ascomparedtoan8-foldincreasereportedby
Spegel2013.Thisratioisconsideredametaboliccouplingfactorforinsulinandisthereforean
importantmetricforconfidenceinthemodel[83–85].Thisdemonstratesthatthemodelpre-
dictionsarecloselyalignedwithdatanotusedformodeltraining.
Inadditiontoconfirmingthatthemodeliscapableofrecreatingobservedmetabolitelevels
formultipleglucosestimulationlevels,wealsowantedtoensurethatcouldcaptureasteady
statecondition.Wethereforesimulatedthemodelwith16.7mMextracellularglucosefor72
hourstodemonstratethatthepredictedmetabolitesdonotsteadilyincrease,butapproachan
equilibriumcondition.Weprovidethefirst600minutesinFig3andshowthatthemodel
metabolitesevolvetowardsasteadystatewhileagreeingwellwiththeexperimentaldata
(showninblack).
Wealsoappliedthemodeltopredictthefluxdistributionsofthecell(Fig4),corresponding
tothesteadystateconditionsattainedbythemetabolitesinFig3.Becausethemetabolitelevels
areatsteadystate,thesumoffluxesintoeachnodeofthenetworkequalsthefluxesleavingthe
node,andthetotalfluxintothesystemwillequalthesumoffluxesoutofthenetwork(Fig4).
ThemodelpredictsfluxesinunitsofmM/min,andwepresentthefluxvaluesrelativetoglu-
coseimportintothecell,thusassigningtheglucosetransportreactionfluxavalueof100and
allowingallotherreactionfluxestobeseenasapercentageofthatimportflux.Thisgives
insightintohowglucoseisutilizedinthemetabolicnetwork.
Thoughthereisapaucityofexperimentaldatawithwhichtocomparethefluxpredictions,
Clineetal.,Shietal.,andBermanetal.havequantitativelymeasuredtheactivityofvarious
metabolicreactionsinINS1cells[86–88].Althoughwecannotmakeaclose,directcompari-
songivendifferencesinincubationandtreatmentofthecells,themodelpredictedfluxesshow
aclosecorrespondencewiththeexperimentallymeasuredreactionfluxes(FigEinS1Sup-
portingInformation).Fouroutofthefivepredictedfluxesarewithintheerroroftheexperi-
mentaldata,whichwerenotusedformodeltraining.Therefore,withbothpredictionsof
metaboliteconcentrationsandreactionfluxes,themodelcanprovideasystems-levelunder-
standingoftheeffectofglucosestimulation.
3.2Partialleastsquaresregressionmodeling
WedevelopedaPLSRmodelcorrelatingthereactionfluxespredictedbyourcalibratedmodel
toreportedinsulinsecretion.Foreachoftheeightbest-fitparametersets,wepredictedthe
fluxthrougheachreactionforthetimeperiodusedintheexperimentalstudies.Wethenper-
formedPLSRanalysiswiththepredictedfluxesasinputsandthemeasuredfold-changein
insulinsecretionasoutputs.Becauseeachparametersetproducedadistinctsetofreaction
fluxes,wegeneratedandanalyzedeightseparatePLSRmodels.WefoundthatPLSRmodels
withthreePLSRcomponentsbestrepresentedthedata,capturingthemajorityofthevariation
intheoutputs(Fig5A).
ThePLSRmodelsagreedwellwiththeexperimentaldata(Fig5B),bothforthedatausedin
traininganddatawithheldforvalidation.TheaverageR
2
valueacrossthemodelswas0.95,
andtheQ
2
Ywas0.74.WenotethatthelowQ
2
Yvalueislikelyduetothelownumberoftime
pointsusedtodevelopthemodel,astheQ
2
Yperformancemetricassesseshowthemodel
wouldperformiftrainedonasubsetoftheavailabledataandaskedtopredictthewithheld
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 14/30

120

data(leave-one-outcrossvalidation).ForaPLSRmodelwithasmallnumberofrowsinthe
inputmatrix,leavinganydatapointoutcansubstantiallychangethemodel’spredictive
power.Thus,thesomewhatlowQ
2
Yvalueistobeexpected.Overall,thisdata-drivenregres-
sionanalysisapproachreliablypredictstherelationshipbetweentheflowofmaterialthrough
thenetworkandtheinsulinproduced.
WeusedthePLSRmodelstoestimatetheVIPscores,identifyingthemostimportantreac-
tionfluxesthatdriveinsulinsecretion(Fig5C).ThereactionswithVIPscoresgreaterthan
onearecoloredred,andthepredictionsareconsistentacrosstheeightmodels.
Interestingly,severalreactionfluxeswithaVIPscoreabovethatthresholdareeither
involvedinglycolysis(pykandpgam),thesynthesisofenergy(oxtransferandak)orthecon-
versionofTCAcyclemetabolites(got2,fum, pdh,malpi,andacon).ThePLSRmodelweights
forreactionswithVIPscoresabove1(Fig5D)provideinformationonwhetherareactionis
positivelyornegativelycorrelatedtoinsulinsecretion,andthestrengthofthatcorrelation. Ak,
got2,pgk,fum,andaconarenegativelycorrelatedinthemodel,suggestingthatknockingdown
thereactionwilldriveanincreaseininsulinsecretion.Thepyk, pdh,oxtransfer,acon,and
malpireactionswerepositivelycorrelatedwithreleasedinsulin.
WealsodevelopedPLSRmodelsat1-minutetimeintervalsforeachshorttimecourseindi-
vidually(3,6,10,and15-minutes).Weagainassessedtheimportanceofeachmetabolicreac-
tiononinsulinproducedperminuteinagiventimeperiod.Theseresultsareshownin(Fig6).
ThoughthereactionswithhighVIPscores(pyk, ak,got2,fum,oxtransfer,and acon)are
Fig5. Partialleastsquaresregressionanalysis.ThePLSRmodelcorrelatesthepredictedfluxthrougheachreactionwithmeasuredinsulinsecretionamount
ateachtimepointofinterest.ResultsshownaretheaveragepredictionacrossthePLSRmodelfromeachoftheeightbest-fitparametersets.(A)ThreePLSR
componentswereused,astheycollectivelyaccountedformostofthevariance.(B)Modelpredictionsagreedwithreportedinsulinamount,bothfortime
pointsusedforPLSRmodelbuilding(3,10,and60minutes,bluecircles),andforthoseheldoutasvalidation(6and15minutes,orangecircles).Resultsare
shownasfold-changeininsulinsecretedfor2.8mMglucosecomparedto16.7mM.ThePLSRmodelshadanaverageR
2
valueof0.95andQ
2
Yvalueof0.74.
(C)WeassessedtheVIPscoresforeachmetabolicreactionflux,showninincreasingorder.ReactionswithVIPscoresgreaterthanoneareshownwithred
bars.(D)WeanalyzedthePLSRmodelweightsassociatedwitheachreactionfluxthatweredeterminedtobeimpactful.Theweightshowshowachangeinflux
valuewillaffectinsulinsecretion.Apositiveweightindicatesthatincreasingthefluxvaluewillincreaseinsulinsecretion.
https://doi.org/10.1371/journal.pcbi.1010555.g005
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 15/30

121

consistentbetweenthetotaltreatmenttime(Fig5C)andtheshorttimecourses,theoxygen
transferreactionemergesasimportantintheshortterm.Interestingly,thoughthesamefive
reactionsareconsistentintheshort-termtime,theVIPscoresdifferacrossthedifferenttime
points.Got2growsincreasinglymoreimpactfulovertime,whilefumismostinfluentialduring
theinitialtimepoints.Overall,thekineticandPLSRmodelsallowustopredicttargetsfor
modulatingintracellularmetabolismandinsulinsecretion.
3.3EffectsofvaryingeachmodelV
max
value
BycombiningthekineticandPLSRmodels,welinkedintracellularmetabolismandinsulin
secretion.Usingtheintegratedmodelingframework,wepredicthowperturbingmetabolic
reactionsaffectsinsulinsecretionandthewholemetabolicnetwork.Weknockeddownand
increasedtheV
max
valueofeachmetabolicreactionbyafactoroftwoandassessedtheimpact
oneachmetaboliteandoninsulinsecretion.Thepredictedfold-changesinthemetabolitelev-
elscomparedtothebaselinemodelwithnoperturbationareshowninFig7,forallparameter
valuesthatelicitachangeinanyprediction.
Asexpected,increasingaV
max
valueledtotheoppositeeffectasdecreasingthevaluefor
mostreactions,buttheamountbywhichthoseopposingperturbationsaffectcellularmetabo-
lismisnotequalforeveryreactionvelocity.Forexample,increasingthepyruvatedehydroge-
nase(pdh)reactioncausessubstantialdecreasesinTCAcycleintermediates,butdecreasing
theratedoesnotleadtoacomparablechangeinmetaboliteamounts.Similartrendscanbe
seenwithchangingpyruvatecarboxylase(pc),thecytosolicmalicenzyme(cmalic),and
Fig6. Short-termtimecoursePLSRmodels.PLSRmodelsweregeneratedforeachshortertimecourseofinterest(3,
6,10,and15minutes),correlatingtheaveragefluxthrougheachreactionwiththeinsulinproduced.Thepredicted
VIPscoresareshownforeachtimecourse.
https://doi.org/10.1371/journal.pcbi.1010555.g006
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 16/30

122

glucose-6-phosphatedehydrogenase(g6pd),wherethedirectionoftheperturbationsubstan-
tiallyanddifferentiallyimpactsthemetabolitelevelsinonedirectionmorethantheother.Per-
turbingsomemetabolicreactionsisonlyimpactfulinonedirection;forexample,increasing
fluxthroughtheglucosetransportreactionwillleadtoanincreaseinS7P,butdecreasingthat
reactionwillhavenoimpactonthemetabolitelevels.
Consideringallofthemetabolitesinthemodel,wepredictthatdownstreamglycolytic
metabolites(1,3-BPG,2PG,3PG,andPEP)areparticularlysusceptibletoperturbationsinthe
restofthenetwork,irrespectiveofthedirectionofthatperturbation.Similarly,mitochondrial
aspartateandglutamatearesensitivetochangesinthenetwork,likelyduetotheirubiquityin
themetabolicprocesses.Inaddition,perturbingtheglut,pdh,pyk,andpcreactionselicitwide-
spreadchangesinmetabolitelevels,suggestingthatthereactionsareprimarycontrolpointsin
thenetworkthatcouldcauseadrasticshiftinmetabolismiftargeted.Interestingly,perturbing
theglucosetransporter(glut)impactsthelevelsofcertainTCAcyclemetabolites(mitochon-
drialfumarate,malate,oxaloacetate,andaspartate;cytosolicoxaloacetate,malate, α-ketogluta-
rate,andcitrate)whethertheenzymeV
max
valueisincreasedordecreased.Thisindicatesthat
theinfluxofglucoseintothecellexerttightcontrolovermetabolicchanges,aswouldbe
expected.
Fig7. Effectsofmetabolicperturbations.Wedecreased(left)andincreased(right)eachreactionVmax value(y-axis)byafactoroftwoandassessedthe
impactonallmetabolitesandinsulin(x-axis).Metabolitesandparametersthatdidnotchangeorcauseanychanges,respectively,wereexcludedfromthe
figureforbetterreadability.Thecolorbarindicatestheeffectoftheperturbationrelativetothebasemodelwithnoperturbation.Parametervalueswhichwere
foundtobeinfluentialinthePLSRanalysisaremarkedwithastar.
https://doi.org/10.1371/journal.pcbi.1010555.g007
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 17/30

123

Theregressionanalysisgivescomplementaryinformationtothekineticmodeling,asit
showsthemetabolicreactionsthatarerelatedtoinsulin.TheVIPscoresshowwhichreaction
fluxescorrelatetoinsulinsecretion,whiletheweightsshowwhetherthosefluxesarepositively
ornegativelycorrelated.Weincreasedanddecreasedeachmetabolicreactionfluxbyafactorof
two,andassessedtheresultingpredictedchangeininsulinsecretion.Theseresultsareshownin
therightmostrowofFig7.AsindicatedbytheVIPscoresandweightsfromthePLSRmodel
(Fig5),increasingthepykandpdhreactionfluxesarepredictedtoincreaseinsulinsecretion.
Increasingtheakorgot2reactionfluxesleadstoadecreaseininsulinproduced.Interestingly,
reactionswithlowerVIPscoresarealsopredictedtoaffectinsulinsecretion,includingtheglut,
g6pd,andpc,sinceadjustingtheV
max
valueforthesereactionsaffectsinsulinsecretion.
3.4Effectsofmetforminonpancreatic β-cellmetabolism
Metforminwasinitiallydiscoveredasanantimalarialagent,buthasbecometheleadingdiabe-
tesdruginusebecauseofitsabilitytolowerbloodglucoselevelsinthebody[89].Metformin
primarilyactsontheperipheraltissuesandorgans,reducinghepaticglucoseproductionand
increasingskeletalmuscleglucoseuptake.Thoughitisunclearhoworifthedrugaffectspan-
creatic β-cells,oneproposedhypothesisisthatitreducesthecells’uptakeofglucose,thereby
actingasaprotectivemechanismtoavoidoveractivityandcellularexhaustion[26,70,72].We
testedtheeffectsofmetforminwithourintegratedmodelingframeworkbydecreasingthe
V
max
valueoftheglutreactionby80%.Weanalyzedtheimpactonthepredictedinsulin
amountandthemetabolicnetwork(i.e.,metabolitesandreactionfluxes).
ThePLSRmodelrankedthefluxthroughtheglucosetransporterasarelativelyuninfluen-
tialreaction,withanaverageVIPscoreof0.3.Thus,itisnotunexpectedthatdecreasingthe
V
max
oftheglutreactiondoesnotchangethepredictedinsulinsecretion.Thisisconsistent
withthefield’sconsensusthattheavailabilityofglucose,andnotitstransportrate,isbelieved
tobethedrivingfactormodulatinginsulinsecretion.Thisisbecausetheglucosetransporter
hasahighK
m
value,whichcausesitsobserved“glucosesensing”ability[1,90].
Wethenassessedtheimpactofthesimulatedperturbationoftheglutreactiononthekinetic
model(Fig8).Thepredictedmetabolitefold-changearegiveninS4Table.Asexpected,wesee
adecreaseinintracellularglucoselevels.Similarly,upstreamglycolyticmetabolitesarepredicted
todecrease,asdomostPPPandTCAcycleintermediates.Fluxthroughthereactionsinvolving
thosemetabolitelevelsisalsosubstantiallydecreased,comparedtotheunperturbedsystem.
Duetothesimulatedmetforminperturbation,thefum,akgmal,andrpireactionsproceedinthe
oppositedirectioncomparedtothebasemodel.Interestingly,thelevelsofdownstreamglyco-
lyticmetabolites(1,3-BPG,3PG,2PG,andPEP)arepredictedtoincreaseduetothesimulated
perturbation.Thisindicatesthatmetforminleadstoanaccumulationorpoolingofthose
metabolites.Thisaccumulationisfurtherconfirmedbythepredictionthatfluxthroughthegly-
colyticreactionsinvolvingthesespecies(pgk,pgam,eno,andpyk)decreases.
Thesimulatedperturbationofglucosetransportalsoaffectedsomenucleotides,asweseea
reductionincellularADPandAMPlevels.However,ATP,NAD,NADH,NADP,and
NADPHlevelsaremostlyunchanged.ThepredicteddecreaseinADPandAMPlevelsis
drivenbyadecreaseintheak,ox,anddhasesreactions,andanincreaseintheatpasereaction.
Thus,themodelpredictsthatthelevelsofthehigh-energymetabolitearerobusttoperturba-
tionsinglucoseuptake.
3.5Predictedeffectsofagrimonyonpancreatic β-cellmetabolism
Agrimoniaeupatoria(alsocalledchurchsteeples,intheRosaceaefamily)isatraditional
medicinalherbusedtotreatdiabetes,asithasbeenshowntopromoteinsulinsecretion[74].
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 18/30

124

Acommonproposedmechanismbywhichagrimonyinducesincreasedinsulinreleaseis
throughantioxidantactivities.Itiswellunderstoodthatdiabetesandmanyotherchronicill-
nessesaremediatedthroughchronicinflammation,oftendrivenbyreactiveoxygenornitro-
genspecies,whichareaffectedbyantioxidants[91–94].IthasbeenshownthatthePPPserves
toreduceinflammatoryspecies,asthepathwaydrivestheproductionofNADPHinthecell,
whichexertsaprotectiveandanti-inflammatoryinfluenceonthe β-cell[40–42,79].Tosimu-
latetheactionofagrimony,weperturbedtheglucose-6-phosphatedehydrogenase(g6pd)reac-
tionbyincreasingitsflux,tosimulateoverexpression,as g6pdistheprimaryupstream
controllerofPPPactivity.
ThePLSRmodelpredictedrelativelyminorincreasesintheinsulinsecretionofthecell(Fig
9),reportedbyalowVIPscore.ThoughthemetabolitesandmetabolicfluxesinthePPPare
predictedtomarkedlyincreasecomparedtothebaselinemodelcondition,theperturbation
causedrelativelyfewotherchangesinthekineticmetabolicnetwork:themodelpredictsno
changeinthemetabolitelevelsormetabolicreactionfluxesinglycolysis,theTCAcycle,orthe
polyolpathway(Fig9andS4Table).
Fig8. Effectofmetformintreatment.Weimplementedmetforminasan80%knockdownoftheglucosetransport(glut2)reactionandassessed
theeffectonthenetwork,comparingmetabolitelevels,reactionfluxes,andinsulinsecretiontotheunperturbedcondition.
https://doi.org/10.1371/journal.pcbi.1010555.g008
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 19/30

125

Additionally,themodelpredictsthatincreasingfluxthroughtheg6pdreactiondoesnot
substantiallyaffectthelevelsofenergyprecursors,ADP,ATP,NADP,NADH,andNAD.
NADPHistheonlyenergyprecursorpredictedtoincreaseinresponsetoincreasingflux
throughtheg6pdreaction.Thisindicatesthateffectofg6pdperturbationishighlyspecific.
Glutathione(GSH)levelsinthecellarealsopredictedtobeaffectedbythesimulatedtargeting
ofg6pd,asNADPHisusedtoproducedGSHintheglutathionereductase(gssgr)reaction.
3.6Predictedeffectsofperturbingtheakreaction
TheVIPscoresandweightscalculatedinthePLSRanalysisindicatethemostimpactfulreac-
tionfluxesinvolvedinpancreatic β-cellmetabolismandsuggestthedirectioninwhichchang-
ingtheassociatedV
max
valueswouldshiftinsulinsecretion.OfthereactionswithVIPscores
greaterthanone,theakreaction,whichconvertsATPandAMPintotwomoleculesofADP,
waspredictedtobeamongthemostimpactfulreactionscorrelatedwithinsulin.Theakreac-
tionistheprimarymechanismbywhichcellsmaintainadeninenucleotidehomeostasis,andit
affectstheAMP-activatedproteinkinase(AMPK)signalingcascade.TheroleofAMPKin
Fig9. Effectofagrimonytreatment.Weimplementedagrimonyasa5-foldincreaseintheg6pdreaction,andassessedtheeffectonthenetwork,
comparingmetabolitelevels,reactionfluxes,andinsulinsecretiontotheunperturbedcondition.
https://doi.org/10.1371/journal.pcbi.1010555.g009
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 20/30

126

insulinreleaseisdisputed,asithasbeendescribedbothasapositiveandanegativeregulator
ofinsulinsecretion[95].However,mostpublishedworkaffirmsalinkbetweenakandthe
ATP-mediatedpotassiumchannels,makingthereactionofparticularinterestin β-cells.Thus,
wereducedtheV
max
valuefortheakreactionandassessedtheeffectontheentiremetabolic
network.
InourPLSRmodel,theakreactionfluxisstronglynegativelycorrelatedtothesecretionof
insulin,asithasahighVIPscoreandnegativeweight.Ourintegratedmodelingapproachpre-
dictsthatafive-folddecreaseintheV
max
valuefortheakreactionleadstoa1.38-foldincrease
ininsulinsecretioncomparedtothebaselinemodel.However,decreasingitsV
max
isnotpre-
dictedtosignificantlyaffectmetabolitesinthekineticnetwork(FigFinS1SupportingInfor-
mationandS4Table).Thismayidentifyakasacandidatetreatmenttargetfordiabetes,asit
couldbeusedtoincreaseinsulinsecretion,withoutdisruptingthehomeostasisofthe β-cell.
4.Discussion
4.1Utilityofourpredictivemodelingframework
Computationalmodelingisatoolbywhichwecansynthesizedisparateinformationanddata
togeneratenovelpredictions.Inparticular,modelingallowsustotakeasystems-levelviewof
howindividualpartsofametabolicnetwork(i.e.,reactionsandmetabolites)worktogetherto
generateobservedbehavior.Here,wehavedevelopedapredictivekineticmodelthatisableto
capturethedynamicsofmetabolisminpancreatic β-cells.Themodelconsistsofglycolysis,
glutaminolysis,thePPP,theTCAcycle,polyolpathway,andelectrontransportchain,building
uponpreviouslypublishedmodelingefforts.Themodelhasbeentrainedtoandvalidatedwith
publishedqualitativeandquantitativemetabolomicsdatafromtheINS1832/13celllinecol-
lectedinvitro.Thecalibratedkineticmodelpredictsmetaboliteconcentrationsandreaction
fluxes.Itisimportanttonotethatthecomputationalmodelcandifferentiatebetweenthelevels
ofmetabolitesthatarefoundinboththecytosolandmitochondria,whereasthemassspec-
trometrypipelinepoolsthemtogetherandcannoteasilydiscriminatebetweenmetabolitesin
differentcellularsub-compartments.Thisisafurtherbenefitofthekineticmodelingapproach,
asitcaninvestigatetheproportionofametabolitepoolinaparticularcompartment.
Wepairedthekineticmodelwithregressionanalysis.Integratingakineticmodelwitha
PLSRmodelallowsustofurtheranalyzesystems-leveldynamicsofthecentralcarbonmeta-
bolicnetworkin β-cellsandrelatethepredictedmetabolitelevelsandreactionfluxestoacellu-
lar-levelresponse(insulinsecretion).Thoughpairingkineticmodelingwithdata-driven
modelingisasomewhatunderutilizedapproach,itcanbeusedtoextendthepredictivecapa-
bilitiesofkineticmodeling,therebygainingnovelinsights.
TheinfluentialreactionspredictedbycombiningkineticandPLSRmodelsagreewith
experimentalobservations.Ourapproachpredictedthatreactionsinvolvedinenergysynthesis
andTCAcycleactivitystronglycontributetoinsulinsecretion.Bothofthosecellularprocesses
havebeenpreviouslyimplicatedwithinsulinproduction[26,96,97].Theakreactionwaspre-
dictedtobeamongthemostimpactfulmetabolicreactionaffectinginsulinsecretionandto
haveanegativecorrelationwithinsulinrelease.Ithaspreviouslybeenshownthatakisanega-
tiveregulatorofinsulinsecretion;forexample,knockingoutaksubstantiallyaffectedthestim-
ulatoryactivityoftheK
ATP
channelsthatdriveinsulinsecretion[98–100].TCAcyclereactions
(namely,got2,fum,andacon)alsoemergedasimpactful.Bothmitochondrialandcytosolic
TCAcyclesignalinghasbeenimplicatedwithinsulinsecretion.Got2hasnotbeenstudiedin
depthinthiscontext,but,interestingly,thatreactionissubstantiallyreducedinthe β-cellsof
neonatalmice.Thispotentiallysuggestsalinkbetweengot2andinsulinsecretion,asneonatal
micefailtoshowproperglucoseresponsiveness[101,102].Fumarasewaspredictedtobe
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 21/30

127

negativelyrelatedtoinsulinsecretion;micewithfumarase-deficient β-cellsdevelopeddiabetes,
suggestingthatproperregulationofthe β-cellGSISsystemisdependentonproperfunctionof
thefumreaction[11,103].Similarly,aconwascorrelatedtoinsulinsecretion.Thoughthe
mechanismsareunclear,apossibleexplanationisthataconactivityisinfluencedbynitric
oxide(NO)damagetothe β-cell,whichisalsoheavilyinvolvedintheinsulinsecretoryactivity
of β-cells[104].Wealsopredicttheimportanceofthepyruvatekinaseenzymeinglycolysis.
ThisenzymehasakeyregulatoryroleinGSIS,asitisbelievedtocontributetotheregulation
ofthesignalstrengthofinsulinsecretionandtheATP/ADPratiointhecell.[105,106].
Agoalofourmodelingworkistoestablishaquantitativeframeworkthatcanbeusedto
identifynovelmechanismstotreattype2diabetes,whichinvolves β-celldysfunction[107,
108].Asasteptowardsthisgoal,weperturbedeachmodelreactionandexploredindetailthe
effectofpharmacologicinterventions,bothonmetabolitelevelsandfluxesandoninsulin
secretion.Wethususedthemodelforhypothesisgenerationandtesting.Additionally,our
modelingframeworkcanidentifythetime-dependentnatureofinsulinsecretion,asshownby
comparingtheoverallPLSRmodel(generatedwithallfivetimepoints)withtheshort-term
PLSRmodelsgenerated.Wepredictthattheoxygentransferreactionisimportantonlyinthe
shorttimecourse.Becausepancreatic β-cellsutilizemitochondrialmetabolism,thecellsdem-
onstrateahighoxygenconsumptionrate.Itisnotablethatthemetabolicreactionemergesas
impactful,asthishighlightsthetime-dependentanddynamicnatureof β-cellactivityandsug-
gestsitmaybeworthwhiletoinvestigatetheimpactofperturbingtheoxygentransportreac-
tionsinvivo.
Excitingly,ourmodelpredictionsoftheeffectsofmetabolicperturbationsinducedbyphar-
macologicagentsagreewithliteratureevidence.Hasanetal.suppressedpyruvatecarboxylase
(pc)reactionactivityinINS1cellsandobservedthatlactateandpyruvatelevelsincreased,and
thatmalateandcitratelevelsdecreased;ourkineticmodelagreeswiththoseexperimentalmea-
surements,asseeninFig6[109].Guayetal.showedthatknockdownofthemalicenzyme
causedadecreaseinglucoseoxidation(thestepsconvertingglucosetopyruvate).Ourmodel
alsopredictsadecreaseinglycolyticintermediates(1,3BPG,2PG,3PG,andPEP)uponsup-
pressionofmalicenzyme[110].WedofindthatthoughMacDonaldetal.showtheidhknock-
downchangingNADPH/NADPratio,ourmodeldoesnotpredictachangeinmetabolite
levelswhenidhisdecreased[111].Overall,ourmodelpredictionsarewellsupportedbyexper-
imentalresults,lendinggreatconfidencetothemodel.
Lamontagneetal.treatedINS1cellswithmetforminatvaryingextracellularglucoselevels
[70].TheyshowedthatmetformincausedadecreaseinGSISatintermediateglucosecondi-
tions,whichsupportsthePLSRmodel’sprediction,astheglucosetransporterhasanegative,
albeitsmall,weight,indicatinganegativecorrelationwithinsulin.Lamontagneandcoworkers
alsomeasuredmetabolitelevelsfollowingmetformintreatment,proposingthatthetreatment
increasedcellularglutamatelevels,didnotaffecttheconcentrationsofmetabolitessuchas
G3P,GSH,GSSG,NAD,orNADH,andattenuatedtheeffectofhighglucoselevelsonTCA
cyclemetabolites.Eachofthoseexperimentalmeasurementsisalsoseeninourmodelpredic-
tions,suggestingtheimplementedmechanism(reducingglucosetransport)isapromising
hypothesis.
Ourmodelunexpectedlypredictedthatalteringtheg6pdreaction(simulatingagrimony
supplementation)ledtoanincreaseinreducedglutathione(GSH)levelsinthecell.Glutathi-
oneisamongthemostwell-studiednaturalantioxidants,capableofpreventingcelldamage
incurredbyreactiveoxygenandnitrogenspecies[112–115].Thisemergentandunanticipated
predictionfromourmodelsupportsthepotentialutilityofagrimonysupplementationamong
diabetespatients.Itisalsointerestingthatthemodelwasabletoprovideconfirmationtoa
hypothesisregardingthemechanismofactionofagrimony;namely,wepredictthatagrimony
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 22/30

128

targetsthe g6pdreactioninthePPP.Increasedfluxthroughthisreactioncancauseincreased
levelsofantioxidants,whichreducecellularinflammationandenablethe β-celltoproperly
function[31,116–119].
Increasingtherateofthe akreactionispredictedtodecreaseinsulinsecretionwithoutsub-
stantiallychangingthemetabolicnetworkdynamics.Thismaybeduetoitsinvolvementinthe
AMP-activatedproteinkinasesignalingpathway,whichwasnotincludedinourmodeling
effortbuthasbeenshowntoinfluenceinsulinsecretion.Targetingthe akreactionmaybeof
particularclinicalinterest,asitcanincreaseinsulinproductionandreducethehyperglycemic
pressuresexperiencedbypatientswithoutaffectingthesurvivalofthe β-cell.Anexperimental
drug,bis(adenosine)-5’-pentaphosphate,whichtargetsthe akreaction,haspreviouslybeen
studiedasavasoconstrictor[26].Ourworksuggeststhatitmaybeofuseindiabetes,repur-
posedtoincreaseinsulinsecretion.Futureworkcanassessitsviabilityasananti-diabetictreat-
mentstrategy.
4.2StudyLimitations
Themodelcapturesthedynamicsofpancreatic β-cellmetabolismandcanbeappliedtostudy
clinicallyrelevantinterventions.However,weacknowledgesomeaspectsofthecomputational
modelthatcanbeimproveduponfuturework.Themodeldoesnotaccountforheterogeneity
withinapopulationofcellsanddoesnotconsiderthemetabolicorparacrineinteractions
between β-cellandtheotherisletcells,suchas α-or δ-cells.As β-cellscanexhibitadifferent
metabolismdependingoninteractionswithothercells,thiswouldbearelevantdirectionfor
futuremodelexpansion.Themodelisbuiltbaseduponpriormodelingeffortsfrom β-cells
andothercelltypes.WeusedexperimentaldatafromtheINS1832/13celllinetomakethe
reactionvelocitiesspecifictothepancreatic β-cell;however,theformoftherateequationscan
alsoberefinedbasedon β-cell-specificdataastheybecomeavailable.Wefocusedoncentral
carbonmetabolism,butthereareadditionalpathwaysthatcouldbeincluded.Forexample,the
degradationoffreefattyacidsisthoughttoimpairinsulinsecretionin β-cell,andmaybeof
particularinterestindiabetes;thisisanavenueforfutureresearch.Morebroadly,futureitera-
tionsofthisworkmayaddresstheselimitations.
5.Conclusions
Wepresentanovelkineticmodelthatcaneffectivelybeusedtostudythedynamicsofcentral
carbonmetabolisminpancreatic β-cells.Themodelgoesbeyondexistingmodelsandconsists
ofkeypathwaysandmetabolitesknowntobeimportantinGSIS.Themodelhasbeentrained
andvalidatedwithpublisheddatafromtheINS1cellline.Themodelsimulatestheeffectsof
metabolicperturbations,predictingthemetabolitelevelsandfluxdistributionsuponknock-
downorupregulationofspecificenzymaticreactions.Wepairthekineticmodelwithadata-
drivenmodelingapproach,therebylinkingintracellularmetabolismtoinsulinsecretion.The
modelisapromisingsteptowardseffectivelyusing in silicotechniquestogeneratenovel
insightsintopancreatic β-cells.Thus,ourworkcomplementsexperimentalstudiesandcanbe
usedtoidentifynoveltreatmentstrategiesfordiabetes.
Supportinginformation
S1Table.Experimentaldatausedformodeltraining.
(XLSX)
S2Table.Stoichiometricmatrix.
(XLSX)
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 23/30

129

S3Table.Multiple t-testscomparingpredictionswithexperimentaldata.
(XLSX)
S4Table. In silicometabolitefoldchangesfollowingmetabolicperturbations.
(XLSX)
S5Table.Modelparametervalues,units,andsources.
(XLSX)
S1SupportingInformation.Supplementaryfigures.
(PDF)
S1Text.Modelequations.
(DOCX)
Acknowledgments
TheauthorsthankmembersoftheFinleyresearchgroupandthePancreaticBetaCellConsor-
tium(especiallytheMetabolomicssub-group)forhelpfuldiscussions.Computationforthe
workdescribedinthispaperwassupportedbytheUniversityofSouthernCaliforniaCenter
forAdvancedResearchComputing(https://www.carc.usc.edu/).
AuthorContributions
Conceptualization:ScottE.Fraser,StaceyD.Finley.
Datacuration:DongqingZheng,KateL.White,NicholasA.Graham.
Formalanalysis:PatrickE.Gelbach.
Investigation:PatrickE.Gelbach.
Projectadministration:StaceyD.Finley.
Resources:StaceyD.Finley.
Writing–originaldraft:PatrickE.Gelbach,StaceyD.Finley.
Writing–review&editing:PatrickE.Gelbach,DongqingZheng,ScottE.Fraser,KateL.
White,NicholasA.Graham,StaceyD.Finley.
References
1. MacDonaldPE,JosephJW,RorsmanP.Glucose-sensingmechanismsinpancreatic β-cells.Philos
TransRSocBBiolSci.2005Dec29;360(1464):2211–25.
2. SchuitFC,HuypensP,HeimbergH,PipeleersDG.GlucoseSensinginPancreatic β-Cells:AModel
fortheStudyofOtherGlucose-RegulatedCellsinGut,Pancreas,andHypothalamus.Diabetes.2001
Jan1;50(1):1–11.
3. DetimaryP,VandenBergheG,HenquinJC.ConcentrationDependenceandTimeCourseofthe
EffectsofGlucoseonAdenineandGuanineNucleotidesinMousePancreaticIslets.JBiolChem.
1996Aug;271(34):20559–65.https://doi.org/10.1074/jbc.271.34.20559PMID:8702800
4. RutterGA,GeorgiadouE,Martinez-SanchezA,PullenTJ.Metabolicandfunctionalspecialisationsof
thepancreaticbetacell:genedisallowance,mitochondrialmetabolismandintercellularconnectivity.
Diabetologia.2020Oct1;63(10):1990–8.https://doi.org/10.1007/s00125-020-05205-5PMID:
32894309
5. MeglassonMD,MatschinskyFM.Newperspectivesonpancreaticisletglucokinase.AmJPhysiol-
EndocrinolMetab.1984Jan1;246(1):E1–13.https://doi.org/10.1152/ajpendo.1984.246.1.E1PMID:
6364828
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 24/30

130

6. Spe ´gelP,MulderH.MetabolomicsAnalysisofNutrientMetabolismin β-Cells.JMolBiol.2020Mar6;
432(5):1429–45.https://doi.org/10.1016/j.jmb.2019.07.020PMID:31325441
7. AronoffSL,BerkowitzK,ShreinerB,WantL.GlucoseMetabolismandRegulation:BeyondInsulinand
Glucagon.DiabetesSpectr.2004Jul1;17(3):183–90.
8. NichollsDG.ThePancreatic β-Cell:ABioenergeticPerspective.PhysiolRev.2016Oct1;96
(4):1385–447.https://doi.org/10.1152/physrev.00009.2016PMID:27582250
9. MulderH.Metaboliccouplinginpancreaticbetacells:lipolysisrevisited.Diabetologia.2016Dec1;59
(12):2510–3.https://doi.org/10.1007/s00125-016-4111-4PMID:27660005
10. WorthamM,SanderM.Mechanismsof β-cellfunctionaladaptationtochangesinworkload.Diabetes
ObesMetab.2016Sep;18(Suppl1):78–86.https://doi.org/10.1111/dom.12729PMID:27615135
11. HaythorneE,RohmM,vandeBuntM,BreretonMF,TarasovAI,BlackerTS,etal.Diabetescauses
markedinhibitionofmitochondrialmetabolisminpancreatic β-cells.NatCommun.2019Jun6;10
(1):2474.https://doi.org/10.1038/s41467-019-10189-xPMID:31171772
12. ClarkA,JonesLC,deKoningE,HansenBC,MatthewsDR.Decreasedinsulinsecretionintype2dia-
betes:aproblemofcellularmassorfunction?Diabetes.2001Feb;50Suppl 1:S169–171.https://doi.
org/10.2337/diabetes.50.2007.s169PMID:11272183
13. HolmanRR,ClarkA,RorsmanP. β-cellsecretorydysfunction:akeycauseoftype2diabetes.Lancet
DiabetesEndocrinol.2020May1;8(5):370.https://doi.org/10.1016/S2213-8587(20)30119-4PMID:
32333873
14. VolkovaS,MatosMRA,MattanovichM,Marı ´ndeMasI.MetabolicModellingasaFrameworkfor
MetabolomicsDataIntegrationandAnalysis.Metabolites.2020Jul24;10(8):E303.https://doi.org/10.
3390/metabo10080303PMID:32722118
15. ToppB,PromislowK,DevriesG,MiuraRM,FinegoodDT.AModelof β-CellMass,Insulin,andGlu-
coseKinetics:PathwaystoDiabetes.JTheorBiol.2000Oct21;206(4):605–19.
16. BertramR,GramPedersenM,LucianiDS,ShermanA.AsimplifiedmodelformitochondrialATPpro-
duction.JTheorBiol.2006Dec21;243(4):575–86.https://doi.org/10.1016/j.jtbi.2006.07.019PMID:
16945388
17. MagnusG,KeizerJ.Minimalmodelofbeta-cellmitochondrialCa2+handling.AmJPhysiol.1997
Aug;273(2Pt1):C717–733.https://doi.org/10.1152/ajpcell.1997.273.2.C717PMID:9277370
18. MagnusG,KeizerJ.Modelofbeta-cellmitochondrialcalciumhandlingandelectricalactivity.I.Cyto-
plasmicvariables.AmJPhysiol.1998Apr;274(4):C1158–1173.https://doi.org/10.1152/ajpcell.1998.
274.4.C1158PMID:9575813
19. YugiK,TomitaM.Ageneralcomputationalmodelofmitochondrialmetabolisminawholeorganelle
scale.BioinformaOxfEngl.2004Jul22;20(11):1795–6.
20. FridlyandLE,PhilipsonLH.Glucosesensinginthepancreaticbetacell:acomputationalsystemsanal-
ysis.TheorBiolMedModel.2010May24;7:15.https://doi.org/10.1186/1742-4682-7-15PMID:
20497556
21. JiangN,CoxRD,HancockJM.Akineticcoremodeloftheglucose-stimulatedinsulinsecretionnet-
workofpancreatic βcells.MammGenome.2007Jul1;18(6):508–20.
22. RoyM,FinleySD.ComputationalModelPredictstheEffectsofTargetingCellularMetabolisminPan-
creaticCancer.FrontPhysiol[Internet].2017[cited2021Aug9];0.Availablefrom:https://www.
frontiersin.org/articles/10.3389/fphys.2017.00217/full.https://doi.org/10.3389/fphys.2017.00217
PMID:28446878
23. CortassaS,CaceresV,BellLN,O’RourkeB,PaolocciN,AonMA.FromMetabolomicstoFluxomics:
AComputationalProceduretoTranslateMetaboliteProfilesintoMetabolicFluxes.BiophysJ.2015
Jan6;108(1):163–72.https://doi.org/10.1016/j.bpj.2014.11.1857PMID:25564863
24. Cornish-BowdenA.OnehundredyearsofMichaelis–Mentenkinetics.PerspectSci.2015Mar1;4:3–
9.
25. UlusuNN.EvolutionofEnzymeKineticMechanisms.JMolEvol.2015;80(5–6):251–7.https://doi.org/
10.1007/s00239-015-9681-0PMID:25987355
26. CurveFittingToolbox[Internet].[cited2021Aug9].Availablefrom:https://www.mathworks.com/
products/curvefitting.html.
27. GermanMS.Glucosesensinginpancreaticisletbetacells:thekeyroleofglucokinaseandtheglyco-
lyticintermediates.ProcNatlAcadSci.1993Mar1;90(5):1781–5.https://doi.org/10.1073/pnas.90.5.
1781PMID:8446591
28. EfratS,TalM,LodishHF.Thepancreaticbeta-cellglucosesensor.TrendsBiochemSci.1994Dec;
19(12):535–8.https://doi.org/10.1016/0968-0004(94)90056-6PMID:7846765
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 25/30

131

29. MatschinskyFM,WilsonDF.TheCentralRoleofGlucokinaseinGlucoseHomeostasis:APerspective
50YearsAfterDemonstratingthePresenceoftheEnzymeinIsletsofLangerhans.FrontPhysiol
[Internet].2019[cited2021Aug9];0.Availablefrom:https://www.frontiersin.org/articles/10.3389/
fphys.2019.00148/full.https://doi.org/10.3389/fphys.2019.00148PMID:30949058
30. BrunT,MaechlerP.Beta-cellmitochondrialcarriersandthediabetogenicstressresponse.Biochim
BiophysActaBBA—MolCellRes.2016Oct1;1863(10):2540–9.https://doi.org/10.1016/j.bbamcr.
2016.03.012PMID:26979549
31. GeT,YangJ,ZhouS,WangY,LiY,TongX.TheRoleofthePentosePhosphatePathwayinDiabetes
andCancer.FrontEndocrinol.2020Jun9;11:365.https://doi.org/10.3389/fendo.2020.00365PMID:
32582032
32. KalwatMA,CobbMH.MechanismsoftheAmplifyingPathwayofInsulinSecretioninthe βCell.Phar-
macolTher.2017Nov;179:17–30.https://doi.org/10.1016/j.pharmthera.2017.05.003PMID:
28527919
33. HuangM,JosephJW.Metabolomicanalysisofpancreatic β-cellinsulinreleaseinresponsetoglu-
cose.Islets.2012May1;4(3):210–22.https://doi.org/10.4161/isl.20141PMID:22847496
34. LorenzMA,ElAzzounyMA,KennedyRT,BurantCF.Metabolomeresponsetoglucoseinthe β-cell
lineINS-1832/13.JBiolChem.2013Apr12;288(15):10923–35.https://doi.org/10.1074/jbc.M112.
414961PMID:23426361
35. GoehringI,SauterNS,CatchpoleG,AssmannA,ShuL,ZienKS,etal.Identificationofanintracellular
metabolicsignatureimpairingbetacellfunctionintheratbetacelllineINS-1Eandhumanislets.Dia-
betologia.2011Jul28;54(10):2584.https://doi.org/10.1007/s00125-011-2249-7PMID:21796486
36. JitrapakdeeS,WutthisathapornchaiA,WallaceJC,MacDonaldMJ.Regulationofinsulinsecretion:
roleofmitochondrialsignalling.Diabetologia.2010Jun;53(6):1019–32.https://doi.org/10.1007/
s00125-010-1685-0PMID:20225132
37. NewgardCB,McGarryJD.Metaboliccouplingfactorsinpancreaticbeta-cellsignaltransduction.
AnnuRevBiochem.1995;64:689–719.https://doi.org/10.1146/annurev.bi.64.070195.003353PMID:
7574498
38. NewgardCB,LuD,JensenMV,SchisslerJ,BoucherA,BurgessS,etal.Stimulus/SecretionCoupling
FactorsinGlucose-StimulatedInsulinSecretion:InsightsGainedFromaMultidisciplinaryApproach.
Diabetes.2002Dec1;51(suppl3):S389–93.https://doi.org/10.2337/diabetes.51.2007.s389PMID:
12475781
39. PrentkiM,MatschinskyFM,MadirajuSRM.MetabolicSignalinginFuel-InducedInsulinSecretion.
CellMetab.2013Aug6;18(2):162–85.https://doi.org/10.1016/j.cmet.2013.05.018PMID:23791483
40. GrayJP,AlavianKN,JonasEA,HeartEA.NADkinaseregulatesthesizeoftheNADPHpoolandinsu-
linsecretioninpancreatic β-cells.AmJPhysiol-EndocrinolMetab.2012Jul15;303(2):E191–9.
https://doi.org/10.1152/ajpendo.00465.2011PMID:22550069
41. LuoX,LiR,YanLJ.RolesofPyruvate,NADH,andMitochondrialComplexIinRedoxBalanceand
Imbalancein βCellFunctionandDysfunction.JDiabetesRes.2015Oct19;2015:e512618.
42. XiaoW,WangRS,HandyDE,LoscalzoJ.NAD(H)andNADP(H)RedoxCouplesandCellularEnergy
Metabolism.AntioxidRedoxSignal.2018Jan20;28(3):251–72.https://doi.org/10.1089/ars.2017.
7216PMID:28648096
43. Nishimura-YabeC.[Aldosereductaseinthepolyolpathway:apotentialtargetforthetherapeuticinter-
ventionofdiabeticcomplications].NihonYakurigakuZasshiFoliaPharmacolJpn.1998Mar1;111
(3):137–45.
44. GabbayKH,TzeWJ.InhibitionofGlucose-InducedReleaseofInsulinbyAldoseReductaseInhibitors.
ProcNatlAcadSci.1972Jun1;69(6):1435–9.https://doi.org/10.1073/pnas.69.6.1435PMID:
4402538
45. RobertsonRP.ChronicOxidativeStressasaCentralMechanismforGlucoseToxicityinPancreatic
IsletBetaCellsinDiabetes*.JBiolChem.2004Oct8;279(41):42351–4.https://doi.org/10.1074/jbc.
R400019200PMID:15258147
46. TangW,MartinKA,HwaJ.AldoseReductase,OxidativeStress,andDiabeticMellitus.FrontPharma-
col[Internet].2012[cited2021Aug9];0.Availablefrom:https://www.frontiersin.org/articles/10.3389/
fphar.2012.00087/full.https://doi.org/10.3389/fphar.2012.00087PMID:22582044
47. McKayMD,BeckmanRJ,ConoverWJ.AComparisonofThreeMethodsforSelectingValuesofInput
VariablesintheAnalysisofOutputfromaComputerCode.Technometrics.1979;21(2):239–45.
48. NazaretC,HeiskeM,ThurleyK,MazatJP.Mitochondrialenergeticmetabolism:Asimplifiedmodelof
TCAcyclewithATPproduction.JTheorBiol.2009Jun7;258(3):455–64.https://doi.org/10.1016/j.jtbi.
2008.09.037PMID:19007794
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 26/30

132

49. NielsenK,S ørensenPG,HynneF,BusseHG.Sustainedoscillationsinglycolysis:anexperimental
andtheoreticalstudyofchaoticandcomplexperiodicbehaviorandofquenchingofsimpleoscillations.
BiophysChem.1998May5;72(1):49–62.https://doi.org/10.1016/s0301-4622(98)00122-7PMID:
17029704
50. Spe ´gelP,SharoykoVV,GoehringI,DanielssonAPH,MalmgrenS,NagornyCLF,etal.Time-resolved
metabolomicsanalysisof β-cellsimplicatesthepentosephosphatepathwayinthecontrolofinsulin
release.BiochemJ.2013Mar15;450(3):595–605.https://doi.org/10.1042/BJ20121349PMID:
23282133
51. MalmgrenS,Spe ´gelP,DanielssonAPH,NagornyCL,AnderssonLE,NitertMD,etal.Coordinate
ChangesinHistoneModifications,mRNALevels,andMetaboliteProfilesinClonalINS-1832/13 β-
CellsAccompanyFunctionalAdaptationstoLipotoxicity*.JBiolChem.2013Apr26;288(17):11973–
87.https://doi.org/10.1074/jbc.M112.422527PMID:23476019
52. Spe ´gelP,AnderssonLE,StormP,SharoykoV,Go ¨hringI,RosengrenAH,etal.UniqueandShared
MetabolicRegulationinClonal β-CellsandPrimaryIsletsDerivedFromRatRevealedbyMetabolo-
micsAnalysis.Endocrinology.2015Jun1;156(6):1995–2005.https://doi.org/10.1210/en.2014-1391
PMID:25774549
53. Spe ´gelP,MalmgrenS,SharoykoVV,NewsholmeP,KoeckT,MulderH.Metabolomicanalyses
revealprofounddifferencesinglycolyticandtricarboxylicacidcyclemetabolisminglucose-responsive
and-unresponsiveclonal β-celllines.BiochemJ.2011Apr1;435(1):277–84.https://doi.org/10.1042/
BJ20100655PMID:21208194
54. HuangM,JosephJW.AssessmentoftheMetabolicPathwaysAssociatedWithGlucose-Stimulated
BiphasicInsulinSecretion.Endocrinology.2014May1;155(5):1653–66.https://doi.org/10.1210/en.
2013-1805PMID:24564396
55. El-AzzounyM,EvansCR,TreutelaarMK,KennedyRT,BurantCF.Increasedglucosemetabolism
andglycerolipidformationbyfattyacidsandGPR40receptorsignalingunderliesthefattyacidpotenti-
ationofinsulinsecretion.JBiolChem.2014May9;289(19):13575–88.https://doi.org/10.1074/jbc.
M113.531970PMID:24675078
56. GuayC,JolyE,PepinE,BarbeauA,HentschL,PinedaM,etal.Aroleforcytosolicisocitratedehydro-
genaseasanegativeregulatorofglucosesignalingforinsulinsecretioninpancreaticß-cells.PloS
One.2013;8(10):e77097.https://doi.org/10.1371/journal.pone.0077097PMID:24130841
57. MugaboY,ZhaoS,LamontagneJ,Al-MassA,PeyotML,CorkeyBE,etal.Metabolicfateofglucose
andcandidatesignalingandexcess-fueldetoxificationpathwaysinpancreatic β-cells.JBiolChem.
2017May5;292(18):7407–22.https://doi.org/10.1074/jbc.M116.763060PMID:28280244
58. AnderssonLE,ShcherbinaL,Al-MajdoubM,VishnuN,ArroyoCB,CarraraJA,etal.Glutamine-Elic-
itedSecretionofGlucagon-LikePeptide1IsGovernedbyanActivatedGlutamateDehydrogenase.
Diabetes.2018Mar1;67(3):372–84.https://doi.org/10.2337/db16-1441PMID:29229616
59. StamenkovicJA,AnderssonLE,AdriaenssensAE,BaggeA,SharoykoVV,GribbleF,etal.Inhibition
ofthemalate-aspartateshuttleinmousepancreaticisletsabolishesglucagonsecretionwithoutaffect-
inginsulinsecretion.BiochemJ.2015May15;468(1):49–63.https://doi.org/10.1042/BJ20140697
PMID:25731850
60. LiP,VuQD.Identificationofparametercorrelationsforparameterestimationindynamicbiological
models.BMCSystBiol.2013Sep22;7(1):91.https://doi.org/10.1186/1752-0509-7-91PMID:
24053643
61. BerthoumieuxS,BrilliM,KahnD,deJongH,CinquemaniE.Ontheidentifiabilityofmetabolicnetwork
models.JMathBiol.2013Dec1;67(6):1795–832.https://doi.org/10.1007/s00285-012-0614-xPMID:
23229063
62. SaltelliA,TarantolaS,ChanKPS.AQuantitativeModel-IndependentMethodforGlobalSensitivity
AnalysisofModelOutput.Technometrics.1999Feb1;41(1):39–56.
63. KennedyJ,EberhartR.Particleswarmoptimization.In:ProceedingsofICNN’95—InternationalCon-
ferenceonNeuralNetworks.1995.p.1942–8vol.4.
64. StaporP,WeindlD,BallnusB,HugS,LoosC,FiedlerA,etal.PESTO:ParameterEStimationTOol-
box.Bioinformatics.2018Feb15;34(4):705–7.https://doi.org/10.1093/bioinformatics/btx676PMID:
29069312
65. HellandIS.Sometheoreticalaspectsofpartialleastsquaresregression.ChemomIntellLabSyst.
2001Oct28;58(2):97–107.
66. deJongS.SIMPLS:Analternativeapproachtopartialleastsquaresregression.ChemomIntellLab
Syst.1993Mar1;18(3):251–63.
67. AkterS,D’AmbraJ,RayP.AnevaluationofPLSbasedcomplexmodels:therolesofpoweranalysis,
predictiverelevanceandGoFindex.2011;9.
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 27/30

133

68. AkarachantachoteN,ChadchamS,SaithanuK.CUTOFFTHRESHOLDOFVARIABLEIMPOR-
TANCEINPROJECTIONFORVARIABLESELECTION.IntJPureAplliedMath[Internet].2014Jul
17[cited2021Aug9];94(3).Availablefrom:http://www.ijpam.eu/contents/2014-94-3/2/.
69. RenaG,HardieDG,PearsonER.Themechanismsofactionofmetformin.Diabetologia.2017;60
(9):1577–85.https://doi.org/10.1007/s00125-017-4342-zPMID:28776086
70. LamontagneJ,Al-MassA,NolanCJ,CorkeyBE,MadirajuSRM,JolyE,etal.Identificationofthesig-
nalsforglucose-inducedinsulinsecretioninINS1(832/13) β-cellsusingmetformin-inducedmetabolic
decelerationasamodel.JBiolChem.2017Nov24;292(47):19458–68.https://doi.org/10.1074/jbc.
M117.808105PMID:28972173
71. TajimaK,ShirakawaJ,OkuyamaT,KyoharaM,YamazakiS,TogashiY,etal.Effectsofmetforminon
compensatorypancreatic β-cellhyperplasiainmicefedahigh-fatdiet.AmJPhysiol-Endocrinol
Metab.2017Sep1;313(3):E367–80.https://doi.org/10.1152/ajpendo.00447.2016PMID:28512156
72. GelinL,LiJ,CorbinKL,JahanI,NunemakerCS.MetforminInhibitsMouseIsletInsulinSecretionand
AltersIntracellularCalciuminaConcentration-DependentandDuration-DependentMannernearthe
CirculatingRange.JDiabetesRes.2018Mar18;2018:e9163052.
73. LiWL,ZhengHC,BukuruJ,DeKimpeN.NaturalmedicinesusedinthetraditionalChinesemedical
systemfortherapyofdiabetesmellitus.JEthnopharmacol.2004May1;92(1):1–21.https://doi.org/10.
1016/j.jep.2003.12.031PMID:15099842
74. GrayAM,FlattPR.Actionsofthetraditionalanti-diabeticplant,Agrimonyeupatoria(agrimony):effects
onhyperglycaemia,cellularglucosemetabolismandinsulinsecretion.BrJNutr.1998Jul;80(1):109–
14.https://doi.org/10.1017/s0007114598001834PMID:9797650
75. SantosTN,CostaG,FerreiraJP,LiberalJ,FranciscoV,ParanhosA,etal.Antioxidant,Anti-Inflamma-
tory,andAnalgesicActivitiesofAgrimoniaeupatoriaL.Infusion.Evid-BasedComplementAlternMed
ECAM.2017;2017:8309894.
76. SakaiK,MatsumotoK,NishikawaT,SuefujiM,NakamaruK,HirashimaY,etal.Mitochondrialreac-
tiveoxygenspeciesreduceinsulinsecretionbypancreatic β-cells.BiochemBiophysResCommun.
2003Jan3;300(1):216–22.
77. TiganisT.Reactiveoxygenspeciesandinsulinresistance:thegood,thebadandtheugly.Trends
PharmacolSci.2011Feb1;32(2):82–9.https://doi.org/10.1016/j.tips.2010.11.006PMID:21159388
78. MatsuokaT,KajimotoY,WatadaH,KanetoH,KishimotoM,UmayaharaY,etal.Glycation-depen-
dent,reactiveoxygenspecies-mediatedsuppressionoftheinsulingenepromoteractivityinHITcells.
JClinInvest.1997Jan1;99(1):144–50.https://doi.org/10.1172/JCI119126PMID:9011569
79. McCartyMF,Barroso-ArandaJ,ContrerasF.NADPHoxidasemediatesglucolipotoxicity-induced
betacelldysfunction—clinicalimplications.MedHypotheses.2010Mar;74(3):596–600.https://doi.
org/10.1016/j.mehy.2008.09.062PMID:19576699
80. NewsholmeP,KeaneKN,CarlessiR,CruzatV.Oxidativestresspathwaysinpancreatic β-cellsand
insulin-sensitivecellsandtissues:importancetocellmetabolism,function,anddysfunction.AmJPhy-
siol-CellPhysiol.2019Sep1;317(3):C420–33.
81. GlucoseTiwariM.6phosphatasedehydrogenase(G6PD)andneurodegenerativedisorders:Mapping
diagnosticandtherapeuticopportunities.GenesDis.2017Sep23;4(4):196–203.
82. YangHC,SternA,ChiuDTY.G6PD:Ahubformetabolicreprogrammingandredoxsignalingincan-
cer.BiomedJ.2021Jun1;44(3):285–92.https://doi.org/10.1016/j.bj.2020.08.001PMID:33097441
83. Bena ´kova ´ S
ˇ
,Holendova ´ B,Plecita ´-Hlavata ´ L.RedoxHomeostasisinPancreatic β-Cells:FromDevel-
opmenttoFailure.Antioxidants.2021Mar27;10(4):526.https://doi.org/10.3390/antiox10040526
PMID:33801681
84. Jez ˇekP,Dlaskova ´ A,Plecita ´-Hlavata ´ L.RedoxHomeostasisinPancreatic βCells.OxidMedCell
Longev.2012;2012:932838.https://doi.org/10.1155/2012/932838PMID:23304259
85. RomaLP,JonasJC.NutrientMetabolism,SubcellularRedoxState,andOxidativeStressinPancre-
aticIsletsand β-Cells.JMolBiol.2020Mar6;432(5):1461–93.https://doi.org/10.1016/j.jmb.2019.10.
012PMID:31634466
86. BermanHK,NewgardCB.FundamentalMetabolicDifferencesbetweenHepatocytesandIslet β-cells
RevealedbyGlucokinaseOverexpression.Biochemistry.1998Mar1;37(13):4543–52.
87. ShiJ,McLamoreES,JarochD,ClaussenJC,RickusJL,PorterfieldDM.Oscillatoryglucosefluxin
INS1pancreatic βcells:Aself-referencingmicrobiosensorstudy.AnalBiochem.2011Apr15;411
(2):185–93.https://doi.org/10.1016/j.ab.2010.12.019PMID:21167120
88. ClineGW,LePineRL,PapasKK,KibbeyRG,ShulmanGI.13CNMRIsotopomerAnalysisofAna-
pleroticPathwaysinINS-1Cells*.JBiolChem.2004Oct22;279(43):44370–5.https://doi.org/10.
1074/jbc.M311842200PMID:15304488
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 28/30

134

68. AkarachantachoteN,ChadchamS,SaithanuK.CUTOFFTHRESHOLDOFVARIABLEIMPOR-
TANCEINPROJECTIONFORVARIABLESELECTION.IntJPureAplliedMath[Internet].2014Jul
17[cited2021Aug9];94(3).Availablefrom:http://www.ijpam.eu/contents/2014-94-3/2/.
69. RenaG,HardieDG,PearsonER.Themechanismsofactionofmetformin.Diabetologia.2017;60
(9):1577–85.https://doi.org/10.1007/s00125-017-4342-zPMID:28776086
70. LamontagneJ,Al-MassA,NolanCJ,CorkeyBE,MadirajuSRM,JolyE,etal.Identificationofthesig-
nalsforglucose-inducedinsulinsecretioninINS1(832/13) β-cellsusingmetformin-inducedmetabolic
decelerationasamodel.JBiolChem.2017Nov24;292(47):19458–68.https://doi.org/10.1074/jbc.
M117.808105PMID:28972173
71. TajimaK,ShirakawaJ,OkuyamaT,KyoharaM,YamazakiS,TogashiY,etal.Effectsofmetforminon
compensatorypancreatic β-cellhyperplasiainmicefedahigh-fatdiet.AmJPhysiol-Endocrinol
Metab.2017Sep1;313(3):E367–80.https://doi.org/10.1152/ajpendo.00447.2016PMID:28512156
72. GelinL,LiJ,CorbinKL,JahanI,NunemakerCS.MetforminInhibitsMouseIsletInsulinSecretionand
AltersIntracellularCalciuminaConcentration-DependentandDuration-DependentMannernearthe
CirculatingRange.JDiabetesRes.2018Mar18;2018:e9163052.
73. LiWL,ZhengHC,BukuruJ,DeKimpeN.NaturalmedicinesusedinthetraditionalChinesemedical
systemfortherapyofdiabetesmellitus.JEthnopharmacol.2004May1;92(1):1–21.https://doi.org/10.
1016/j.jep.2003.12.031PMID:15099842
74. GrayAM,FlattPR.Actionsofthetraditionalanti-diabeticplant,Agrimonyeupatoria(agrimony):effects
onhyperglycaemia,cellularglucosemetabolismandinsulinsecretion.BrJNutr.1998Jul;80(1):109–
14.https://doi.org/10.1017/s0007114598001834PMID:9797650
75. SantosTN,CostaG,FerreiraJP,LiberalJ,FranciscoV,ParanhosA,etal.Antioxidant,Anti-Inflamma-
tory,andAnalgesicActivitiesofAgrimoniaeupatoriaL.Infusion.Evid-BasedComplementAlternMed
ECAM.2017;2017:8309894.
76. SakaiK,MatsumotoK,NishikawaT,SuefujiM,NakamaruK,HirashimaY,etal.Mitochondrialreac-
tiveoxygenspeciesreduceinsulinsecretionbypancreatic β-cells.BiochemBiophysResCommun.
2003Jan3;300(1):216–22.
77. TiganisT.Reactiveoxygenspeciesandinsulinresistance:thegood,thebadandtheugly.Trends
PharmacolSci.2011Feb1;32(2):82–9.https://doi.org/10.1016/j.tips.2010.11.006PMID:21159388
78. MatsuokaT,KajimotoY,WatadaH,KanetoH,KishimotoM,UmayaharaY,etal.Glycation-depen-
dent,reactiveoxygenspecies-mediatedsuppressionoftheinsulingenepromoteractivityinHITcells.
JClinInvest.1997Jan1;99(1):144–50.https://doi.org/10.1172/JCI119126PMID:9011569
79. McCartyMF,Barroso-ArandaJ,ContrerasF.NADPHoxidasemediatesglucolipotoxicity-induced
betacelldysfunction—clinicalimplications.MedHypotheses.2010Mar;74(3):596–600.https://doi.
org/10.1016/j.mehy.2008.09.062PMID:19576699
80. NewsholmeP,KeaneKN,CarlessiR,CruzatV.Oxidativestresspathwaysinpancreatic β-cellsand
insulin-sensitivecellsandtissues:importancetocellmetabolism,function,anddysfunction.AmJPhy-
siol-CellPhysiol.2019Sep1;317(3):C420–33.
81. GlucoseTiwariM.6phosphatasedehydrogenase(G6PD)andneurodegenerativedisorders:Mapping
diagnosticandtherapeuticopportunities.GenesDis.2017Sep23;4(4):196–203.
82. YangHC,SternA,ChiuDTY.G6PD:Ahubformetabolicreprogrammingandredoxsignalingincan-
cer.BiomedJ.2021Jun1;44(3):285–92.https://doi.org/10.1016/j.bj.2020.08.001PMID:33097441
83. Bena ´kova ´ S
ˇ
,Holendova ´ B,Plecita ´-Hlavata ´ L.RedoxHomeostasisinPancreatic β-Cells:FromDevel-
opmenttoFailure.Antioxidants.2021Mar27;10(4):526.https://doi.org/10.3390/antiox10040526
PMID:33801681
84. Jez ˇekP,Dlaskova ´ A,Plecita ´-Hlavata ´ L.RedoxHomeostasisinPancreatic βCells.OxidMedCell
Longev.2012;2012:932838.https://doi.org/10.1155/2012/932838PMID:23304259
85. RomaLP,JonasJC.NutrientMetabolism,SubcellularRedoxState,andOxidativeStressinPancre-
aticIsletsand β-Cells.JMolBiol.2020Mar6;432(5):1461–93.https://doi.org/10.1016/j.jmb.2019.10.
012PMID:31634466
86. BermanHK,NewgardCB.FundamentalMetabolicDifferencesbetweenHepatocytesandIslet β-cells
RevealedbyGlucokinaseOverexpression.Biochemistry.1998Mar1;37(13):4543–52.
87. ShiJ,McLamoreES,JarochD,ClaussenJC,RickusJL,PorterfieldDM.Oscillatoryglucosefluxin
INS1pancreatic βcells:Aself-referencingmicrobiosensorstudy.AnalBiochem.2011Apr15;411
(2):185–93.https://doi.org/10.1016/j.ab.2010.12.019PMID:21167120
88. ClineGW,LePineRL,PapasKK,KibbeyRG,ShulmanGI.13CNMRIsotopomerAnalysisofAna-
pleroticPathwaysinINS-1Cells*.JBiolChem.2004Oct22;279(43):44370–5.https://doi.org/10.
1074/jbc.M311842200PMID:15304488
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 28/30

135

89. BaileyCJ.Metformin:historicaloverview.Diabetologia.2017Sep;60(9):1566–76.https://doi.org/10.
1007/s00125-017-4318-zPMID:28776081
90. ThorensB.GLUT2,glucosesensingandglucosehomeostasis.Diabetologia.2015Feb1;58(2):221–
32.https://doi.org/10.1007/s00125-014-3451-1PMID:25421524
91. WellenKE,HotamisligilGS.Inflammation,stress,anddiabetes.JClinInvest.2005May2;115
(5):1111–9.https://doi.org/10.1172/JCI25102PMID:15864338
92. TsalamandrisS,AntonopoulosAS,OikonomouE,PapamikroulisGA,VogiatziG,PapaioannouS,
etal.TheRoleofInflammationinDiabetes:CurrentConceptsandFuturePerspectives.EurCardiol
Rev.2019Apr;14(1):50–9.
93. BajajS,KhanA.Antioxidantsanddiabetes.IndianJEndocrinolMetab.2012Dec;16(Suppl2):S267–
71.https://doi.org/10.4103/2230-8210.104057PMID:23565396
94. KanetoH,KajimotoY,MiyagawaJ,MatsuokaT,FujitaniY,UmayaharaY,etal.Beneficialeffectsof
antioxidantsindiabetes:possibleprotectionofpancreaticbeta-cellsagainstglucosetoxicity.Diabetes.
1999Dec;48(12):2398–406.https://doi.org/10.2337/diabetes.48.12.2398PMID:10580429
95. FuA,EberhardCE,ScreatonRA.RoleofAMPKinpancreaticbetacellfunction.MolCellEndocrinol.
2013Feb25;366(2):127–34.https://doi.org/10.1016/j.mce.2012.06.020PMID:22766107
96. FuZ,GilbertER,LiuD.RegulationofInsulinSynthesisandSecretionandPancreaticBeta-CellDys-
functioninDiabetes.CurrDiabetesRev.2013Jan1;9(1):25–53.PMID:22974359
97. JosephJW,JensenMV,IlkayevaO,PalmieriF,Ala ´rconC,RhodesCJ,etal.Themitochondrialcit-
rate/isocitratecarrierplaysaregulatoryroleinglucose-stimulatedinsulinsecretion.JBiolChem.2006
Nov24;281(47):35624–32.https://doi.org/10.1074/jbc.M602606200PMID:17001083
98. OlsonLK,SchroederW,RobertsonRP,GoldbergND,WalsethTF.SuppressionofAdenylateKinase
CatalyzedPhosphotransferPrecedesandIsAssociatedwithGlucose-inducedInsulinSecretionin
IntactHIT-T15Cells*.JBiolChem.1996Jul12;271(28):16544–52.https://doi.org/10.1074/jbc.271.
28.16544PMID:8663240
99. SchulzeDU,Du ¨ferM,WieringaB,Krippeit-DrewsP,DrewsG.Anadenylatekinaseisinvolvedin
KATPchannelregulationofmousepancreaticbetacells.Diabetologia.2007Oct1;50(10):2126–34.
https://doi.org/10.1007/s00125-007-0742-9PMID:17704905
100. StanojevicV,HabenerJF,HolzGG,LeechCA.CytosolicadenylatekinasesregulateK-ATPchannel
activityinhuman β-cells.BiochemBiophysResCommun.2008Apr11;368(3):614–9.
101. JermendyA,ToschiE,AyeT,KohA,Aguayo-MazzucatoC,SharmaA,etal.Ratneonatalbetacells
lackthespecialisedmetabolicphenotypeofmaturebetacells.Diabetologia.2011Mar;54(3):594–
604.https://doi.org/10.1007/s00125-010-2036-xPMID:21240476
102. AsplundK.EffectsofGlucoseonInsulinBiosynthesisinFoetalandNewbornRats.HormMetabRes.
1973;5(06):410–5.https://doi.org/10.1055/s-0028-1093914PMID:4588114
103. AdamJ,RamracheyaR,ChibalinaMV,TernetteN,HamiltonA,TarasovAI,etal.FumarateHydratase
DeletioninPancreatic βCellsLeadstoProgressiveDiabetes.CellRep.2017Sep26;20(13):3135–
48.https://doi.org/10.1016/j.celrep.2017.08.093PMID:28954230
104. Theharmonyofthespheres:induciblenitricoxidesynthaseandrelatedgenesinpancreaticbeta
cells.:16.
105. SrinivasanM,ChoiCS,GhoshalP,PlissL,PandyaJD,HillD,etal. β-Cell-specificpyruvatedehydro-
genasedeficiencyimpairsglucose-stimulatedinsulinsecretion.AmJPhysiol—EndocrinolMetab.
2010Dec;299(6):E910–7.https://doi.org/10.1152/ajpendo.00339.2010PMID:20841503
106. SugdenMC,BulmerK,AugustineD,HolnessMJ.SelectiveModificationofPyruvateDehydrogenase
KinaseIsoformExpressioninRatPancreaticIsletsElicitedbyStarvationandActivationofPeroxisome
Proliferator–ActivatedReceptor- α:ImplicationsforGlucose-StimulatedInsulinSecretion.Diabetes.
2001Dec1;50(12):2729–36.
107. BillingsLK,FlorezJC.Thegeneticsoftype2diabetes:whathavewelearnedfromGWAS?AnnNY
AcadSci.2010Nov;1212:59–77.https://doi.org/10.1111/j.1749-6632.2010.05838.xPMID:21091714
108. EizirikDL,PasqualiL,CnopM.Pancreatic β-cellsintype1andtype2diabetesmellitus:differentpath-
waystofailure.NatRevEndocrinol.2020Jul;16(7):349–62.https://doi.org/10.1038/s41574-020-
0355-7PMID:32398822
109. HasanNM,LongacreMJ,StokerSW,BoonsaenT,JitrapakdeeS,KendrickMA,etal.ImpairedAna-
plerosisandInsulinSecretioninInsulinomaCellsCausedbySmallInterferingRNA-mediatedSup-
pressionofPyruvateCarboxylase*.JBiolChem.2008Oct17;283(42):28048–59.https://doi.org/10.
1074/jbc.M804170200PMID:18697738
110. GuayC,MadirajuSRM,AumaisA,JolyE
´
,PrentkiM.ARoleforATP-CitrateLyase,MalicEnzyme,
andPyruvate/CitrateCyclinginGlucose-inducedInsulinSecretion*.JBiolChem.2007Dec7;282
(49):35657–65.https://doi.org/10.1074/jbc.M707294200PMID:17928289
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 29/30

136

111. MacDonaldMJ,BrownLJ,LongacreMJ,StokerSW,KendrickMA,HasanNM.Knockdownofboth
mitochondrialisocitratedehydrogenaseenzymesinpancreaticbetacellsinhibitsinsulinsecretion.
BiochimBiophysActa.2013Nov;1830(11):5104–11.https://doi.org/10.1016/j.bbagen.2013.07.013
PMID:23876293
112. EguchiN,VaziriND,DafoeDC,IchiiH.TheRoleofOxidativeStressinPancreatic βCellDysfunction
inDiabetes.IntJMolSci.2021Jan;22(4):1509.https://doi.org/10.3390/ijms22041509PMID:
33546200
113. RobertsonRP,HarmonJS.Pancreaticislet β-cellandoxidativestress:Theimportanceofglutathione
peroxidase.FEBSLett.2007Jul31;581(19):3743–8.
114. ZhangJ,AnH,NiK,ChenB,LiH,LiY,etal.Glutathionepreventschronicoscillatingglucoseintake-
induced β-celldedifferentiationandfailure.CellDeathDis.2019Apr11;10(4):1–13.https://doi.org/10.
1038/s41419-019-1552-yPMID:30975975
115. LacrazG,FigeacF,MovassatJ,KassisN,CoulaudJ,GalinierA,etal.Diabetic β-CellsCanAchieve
Self-ProtectionagainstOxidativeStressthroughanAdaptiveUp-RegulationofTheirAntioxidant
Defenses.PLOSONE.2009Aug5;4(8):e6500.
116. ZhangZ,LiewCW,HandyDE,ZhangY,LeopoldJA,HuJ,etal.Highglucoseinhibitsglucose-6-phos-
phatedehydrogenase,leadingtoincreasedoxidativestressand β-cellapoptosis.FASEBJ.2010
May;24(5):1497–505.
117. SalveminiF,Franze ´ A,IervolinoA,FilosaS,SalzanoS,UrsiniMV.Enhancedglutathionelevelsand
oxidoresistancemediatedbyincreasedglucose-6-phosphatedehydrogenaseexpression.JBiol
Chem.1999Jan29;274(5):2750–7.https://doi.org/10.1074/jbc.274.5.2750PMID:9915806
118. PandolfiPP,SonatiF,RiviR,MasonP,GrosveldF,LuzzattoL.Targeteddisruptionofthehousekeep-
inggeneencodingglucose6-phosphatedehydrogenase(G6PD):G6PDisdispensableforpentose
synthesisbutessentialfordefenseagainstoxidativestress.EMBOJ.1995Nov1;14(21):5209–15.
https://doi.org/10.1002/j.1460-2075.1995.tb00205.xPMID:7489710
119. MullarkyE,CantleyLC.DivertingGlycolysistoCombatOxidativeStress.In:NakaoK,MinatoN,
UemotoS,editors.InnovativeMedicine:BasicResearchandDevelopment[Internet]. Tokyo:
Springer;2015[cited2021Aug9].Availablefrom:http://www.ncbi.nlm.nih.gov/books/NBK500351/.
PLOS COMPUTATIONAL BIOLOGY Computationalmodelingofpancreatic β-cellmetabolism
PLOSComputationalBiology|https://doi.org/10.1371/journal.pcbi.1010555 October17,2022 30/30

137

Appendix 2:
Supplementary Information for Chapter 2
Table S1: Essential Metabolic Tasks
Oxidative phosphorylation via NADHcoenzyme Q oxidoreductase (COMPLEX I)
Oxidative phosphorylation via succinatecoenzyme Q oxidoreductase (COMPLEX II)
Krebs cycle oxidative decarboxylation of pyruvate
Krebs cycle NADH generation
ATP regeneration from glucose (normoxic conditions) glycolysis + krebs cycle
ATP generation from glucose (hypoxic conditions) glycolysis
Reactive oxygen species detoxification (H2O2 to H2O)
Presence of the thioredoxin system through the thioredoxin reductase activity
Inosine monophosphate synthesis (IMP)
Cytidine triphosphate synthesis (CTP)
Guanosine triphosphate synthesis (GTP)
Uridine triphosphate synthesis (UTP)
Deoxyadenosine triphosphate synthesis (dATP)
Deoxycytidine triphosphate synthesis (dCTP)
Deoxyguanosine triphosphate synthesis (dGTP)
Deoxyuridine triphosphate synthesis (dUTP)
Deoxythymidine triphosphate synthesis (dTTP)
AMP salvage from adenine
IMP salvage from hypoxanthine
GMP salvage from guanine
3Phospho5adenylyl sulfate synthesis
Degradation of adenine to urate
Degradation of guanine to urate
Degradation of uracil
Gluconeogenesis from pyruvate
Gluconeogenesis from Lactate
Gluconeogenesis from Glycerol
Gluconeogenesis from Alanine
Gluconeogenesis from Glutamine
Glucose to lactate conversion
Malate to pyruvate conversion

138
Synthesis of fructose6phosphate from erythrose4phosphate (HMP shunt)
Synthesis of ribose5phosphate
Glycogen biosynthesis
Glycogen degradation
Fructose to glucose conversion (via fructose6phosphate)
UDPglucose synthesis
UDPgalactose synthesis
UDPglucuronate synthesis
GDPLfucose synthesis
Mannose degradation (to fructose6phosphate)
GDPmannose synthesis
UDPNacetyl Dgalactosamine synthesis
CMPNacetylneuraminate synthesis
NAcetylglucosamine synthesis
Glucuronate synthesis (via udpglucose)
(R)3Hydroxybutanoate synthesis
Synthesis of inositol
Inositol as input for glucuronatexylulose pathway
Synthesis of phosphatidylinositol from inositol
Conversion of 1phosphatidyl1Dmyoinositol 4,5bisphosphate to 1Dmyoinositol
1,4,5trisphosphate
Link between glyoxylate metabolism and pentose phosphate pathway (Xylulose to glycolate)
Synthesis of methylglyoxal
Alanine synthesis
Alanine degradation
Arginine synthesis
Arginine degradation
Synthesis of arginine from glutamine
Synthesis of nitric oxide from arginine
Synthesis of aspartate from glutamine
Synthesis of creatine from arginine
Asparagine synthesis
Asparagine degradation
Aspartate synthesis
Aspartate degradation
Conversion of aspartate to arginine

139
Conversion of asparate to asparagine
betaAlanine synthesis
betaAlanine degradation
Cysteine synthesis (need serine and methionine)
Cysteine degradation
Glutamate synthesis
Glutamate degradation
Conversion of glutamate to glutamine
Conversion of glutamate to proline
Glutamine synthesis
Glutamine degradation
Glutaminolysis (glutamine to lactate)
Glycine synthesis
Glycine degradation
Histidine degradation
Homocysteine synthesis (need methionine)
Isoleucine degradation
Leucine degradation
Lysine degradation
Methionine degradation
SadenosylLmethionine synthesis
Ornithine degradation
Synthesis of ornithine from glutamine
Synthesis of spermidine from ornithine
Serine synthesis
Serine degradation
Phenylalanine degradation
Proline synthesis
Proline degradation
Threonine degradation
Tryptophan degradation
Tyrosine degradation
Valine degradation
Valine to succinylcoA
HydroxymethylglutarylCoA synthesis
Cholesterol synthesis

140
Acetoacetate synthesis
Mevalonate synthesis
Phosphatidylcholine synthesis
Phosphatidylethanolamine synthesis
Phosphatidylserine synthesis
Phosphatidylinositol synthesis
Cardiolipin synthesis
Triacylglycerol synthesis
Sphingomyelin synthesis
Ceramide synthesis
Palmitate synthesis
Palmitate degradation
Palmitolate synthesis
Palmitolate degradation
cisvaccenic acid synthesis
cisvaccenic acid degradation
Elaidate synthesis
Elaidate degradation
Linolenate degradation
Linoleate degradation
gammaLinolenate synthesis
gammaLinolenate degradation
Arachidonate synthesis
Arachidonate degradation
Synthesis of malonylcoa
Synthesis of palmitoylCoA
Synthesis of galactosyl glucosyl ceramide (link with ganglioside metabolism)
Synthesis of glucocerebroside
Synthesis of globoside (link with globoside metabolism)
NAD synthesis from nicotinamide
FAD synthesis
Synthesis of coenzyme A
Synthesis of ubiquinone from tyrosine
Heme synthesis

141
Table S2: FEA results

Not significant Significant in M1
only
Significant in
M2 only
Significant in M1 and M2
Alanine and aspartate
metabolism
Folate metabolism Aminosugar
metabolism
Androgen and estrogen synthesis
and metabolism
Alkaloid synthesis Glutamate metabolism C5-branched
dibasic acid
metabolism
Arachidonic acid metabolism
Arginine and proline
metabolism
Glutathione
metabolism
Eicosanoid
metabolism
Bile acid synthesis
Beta-Alanine metabolism Glycosphingolipid
metabolism
Transport,
nuclear
Blood group synthesis
Butanoate metabolism Glyoxylate and
dicarboxylate
metabolism

Chondroitin sulfate degradation
Cholesterol metabolism Pentose phosphate
pathway

Chondroitin synthesis
CoA catabolism Propanoate
metabolism

Citric acid cycle
CoA synthesis Purine synthesis

Cytochrome metabolism
D-alanine metabolism Pyrimidine synthesis

Drug metabolism
Fructose and mannose
metabolism
Tetrahydrobiopterin
metabolism

Fatty acid synthesis
Galactose metabolism Transport, lysosomal

Glycerophospholipid metabolism
Glycine, serine, alanine, and
threonine metabolism
Ubiquinone synthesis

Glycolysis/gluconeogenesis
Heme degradation Urea cycle

Heparan sulfate degradation
Heme synthesis Vitamin A metabolism

Histidine metabolism
Hippurate metabolism Fatty acid oxidation

Keratan sulfate degradation
Hyaluronan metabolism

Keratan sulfate synthesis
Inositol phosphate
metabolism

Linoleate metabolism
Leukotriene metabolism

N-glycan metabolism
Lysine metabolism

N-glycan synthesis
Methionine and cysteine
metabolism

Nucleotide interconversion
Miscellaneous

Peptide metabolism
N-glycan degradation

Phosphatidylinositol phosphate
metabolism

142
NAD metabolism

Purine catabolism
Nucleotide metabolism

Pyruvate metabolism
Nucleotide salvage pathway

Sphingolipid metabolism
Nucleotide sugar
metabolism

Steroid metabolism
O-glycan metabolism

Transport, endoplasmic reticular
Oxidative phosphorylation

Transport, mitochondrial
Phenylalanine metabolism

Vitamin D metabolism
Pyrimidine catabolism

Dietary fiber binding
R group synthesis

ROS detoxification

Squalene and cholesterol
synthesis

Starch and sucrose
metabolism

Taurine and hypotaurine
metabolism

Thiamine metabolism

Transport, extracellular

Transport, golgi apparatus

Transport, peroxisomal

Triacylglycerol synthesis

Tryptophan metabolism

Tyrosine metabolism

Valine, leucine, and
isoleucine metabolism

Vitamin B2 metabolism

Vitamin B6 metabolism

Vitamin C metabolism

Vitamin E metabolism

143

Figure S1: MOFA results
A

144
B

145
C.

146
S4: Star Methods

REAGENT or RESOURCE SOURCE IDENTIFIER
Deposited data used
Colorectal Cancer-associated Macrophages
Transcriptomics Data
Li et al., 2017
37
EGAS00001001945
Software and algorithms used
Recon3D Human Metabolic Model Brunk et al., 2018
39
10.1038/nbt.4072
Cobra Toolbbox Heirendt et al., 2019
41
10.1038/s41596-018-0098-2
MATLAB Mathworks https://www.mathworks.com/
GUROBI solver Gurobi https://www.gurobi.com/
iMAT Zur et al., 2010
43
10.1093/bioinformatics/btq602
GIMME Becker and Palsson, 2008
44
10.1371/journal.pcbi.1000082
CORDA Schultz and Qutub, 2016
45
10.1371/journal.pcbi.1004808
FastCore Vlassis et al., 2014
47
10.1371/journal.pcbi.1003424
INIT Agren et al., 2012
46
10.1371/journal.pcbi.1002518
REDGEM Ataman et al., 2017
48
10.1371/journal.pcbi.1005444
MEMOTE Lieven et al., 2020
49
10.1038/s41587-020-0446-y
MOFA Griesemer and Navid, 2021
53
10.1101/2021.05.20.445041
RHMC Kook et al., 2022
58
http://arxiv.org/abs/2202.01908
Graphpad Prism Graphpad Software, Inc. https://www.graphpad.com/

147

Appendix 3:
Supplementary Information, Chapter 3

Acetyl-Homoserine Transport

Tukey's multiple comparisons test Mean Diff. 95.00% CI of diff. Below
threshold?
Summary Adjusted P Value
ROBO+ Cycling vs. ROBO- Cycling 0.00007107 -2.958e-005 to 0.0001717 No ns 0.332
ROBO+ Cycling vs. ROBO+ M1 -0.00002134 -0.0001368 to 9.410e-005 No ns 0.995
ROBO+ Cycling vs. ROBO- M1 -0.0001158 -0.0002142 to -1.733e-005 Yes * 0.0107
ROBO+ Cycling vs. ROBO+ M2 0.000121 2.251e-005 to 0.0002194 Yes ** 0.0064
ROBO+ Cycling vs. ROBO- M2 -0.0002326 -0.0003353 to -0.0001300 Yes **** <0.0001
ROBO- Cycling vs. ROBO+ M1 -0.00009241 -0.0001836 to -1.239e-006 Yes * 0.0448
ROBO- Cycling vs. ROBO- M1 -0.0001868 -0.0002359 to -0.0001378 Yes **** <0.0001
ROBO- Cycling vs. ROBO+ M2 0.00004989 8.057e-007 to 9.896e-005 Yes * 0.0438
ROBO- Cycling vs. ROBO- M2 -0.0003037 -0.0003642 to -0.0002432 Yes **** <0.0001
ROBO+ M1 vs. ROBO- M1 -0.00009443 -0.0001832 to -5.700e-006 Yes * 0.0294
ROBO+ M1 vs. ROBO+ M2 0.0001423 5.356e-005 to 0.0002310 Yes **** <0.0001
ROBO+ M1 vs. ROBO- M2 -0.0002113 -0.0003047 to -0.0001179 Yes **** <0.0001
ROBO- M1 vs. ROBO+ M2 0.0002367 0.0002037 to 0.0002698 Yes **** <0.0001
ROBO- M1 vs. ROBO- M2 -0.0001169 -0.0001736 to -6.013e-005 Yes **** <0.0001
ROBO+ M2 vs. ROBO- M2 -0.0003536 -0.0004103 to -0.0002969 Yes **** <0.0001

Test details Mean 1 Mean 2 Mean Diff. SE of diff. N1
ROBO+ Cycling vs. ROBO- Cycling 0.0001758 0.0001048 0.00007107 0.00003517 19
ROBO+ Cycling vs. ROBO+ M1 0.0001758 0.0001972 -0.00002134 0.00004034 19
ROBO+ Cycling vs. ROBO- M1 0.0001758 0.0002916 -0.0001158 0.0000344 19
ROBO+ Cycling vs. ROBO+ M2 0.0001758 0.00005489 0.000121 0.0000344 19
ROBO+ Cycling vs. ROBO- M2 0.0001758 0.0004085 -0.0002326 0.00003586 19
ROBO- Cycling vs. ROBO+ M1 0.0001048 0.0001972 -0.00009241 0.00003186 97
ROBO- Cycling vs. ROBO- M1 0.0001048 0.0002916 -0.0001868 0.00001715 97
ROBO- Cycling vs. ROBO+ M2 0.0001048 0.00005489 0.00004989 0.00001715 97
ROBO- Cycling vs. ROBO- M2 0.0001048 0.0004085 -0.0003037 0.00002113 97
ROBO+ M1 vs. ROBO- M1 0.0001972 0.0002916 -0.00009443 0.000031 24
ROBO+ M1 vs. ROBO+ M2 0.0001972 0.00005489 0.0001423 0.000031 24
ROBO+ M1 vs. ROBO- M2 0.0001972 0.0004085 -0.0002113 0.00003262 24
ROBO- M1 vs. ROBO+ M2 0.0002916 0.00005489 0.0002367 0.00001155 680

148
ROBO- M1 vs. ROBO- M2 0.0002916 0.0004085 -0.0001169 0.00001982 680
ROBO+ M2 vs. ROBO- M2 0.00005489 0.0004085 -0.0003536 0.00001982 253
L-Alanine Transport

Tukey’s multiple comparisons test Mean Diff. 95.00% CI of diff. Below
threshold?
Summary Adjusted P Value
ROBO+ Cycling vs. ROBO- Cycling 0.000003168 -1.078e-005 to 1.711e-005 No ns 0.987
ROBO+ Cycling vs. ROBO+ M1 -
0.000006338
-2.231e-005 to 9.630e-006 No ns 0.8661
ROBO+ Cycling vs. ROBO- M1 -0.00000329 -1.693e-005 to 1.035e-005 No ns 0.983
ROBO+ Cycling vs. ROBO+ M2 -
0.000002489
-1.613e-005 to 1.115e-005 No ns 0.9953
ROBO+ Cycling vs. ROBO- M2 0.000002215 -1.220e-005 to 1.663e-005 No ns 0.9979
ROBO- Cycling vs. ROBO+ M1 -
0.000009506
-2.214e-005 to 3.132e-006 No ns 0.2623
ROBO- Cycling vs. ROBO- M1 -
0.000006458
-1.325e-005 to 3.302e-007 No ns 0.0728
ROBO- Cycling vs. ROBO+ M2 -
0.000005657
-1.245e-005 to 1.132e-006 No ns 0.1637
ROBO- Cycling vs. ROBO- M2 -9.525E-07 -9.957e-006 to 8.052e-006 No ns 0.9997
ROBO+ M1 vs. ROBO- M1 0.000003048 -9.254e-006 to 1.535e-005 No ns 0.9808
ROBO+ M1 vs. ROBO+ M2 0.000003849 -8.452e-006 to 1.615e-005 No ns 0.9475
ROBO+ M1 vs. ROBO- M2 0.000008553 -4.600e-006 to 2.171e-005 No ns 0.4276
ROBO- M1 vs. ROBO+ M2 8.017E-07 -3.769e-006 to 5.372e-006 No ns 0.9961
ROBO- M1 vs. ROBO- M2 0.000005506 -3.019e-006 to 1.403e-005 No ns 0.4357
ROBO+ M2 vs. ROBO- M2 0.000004704 -3.821e-006 to 1.323e-005 No ns 0.6127

Test details Mean 1 Mean 2 Mean Diff. SE of diff. N1
ROBO+ Cycling vs. ROBO- Cycling 0.000006263 0.000003095 0.000003168 0.000004872 19
ROBO+ Cycling vs. ROBO+ M1 0.000006263 0.0000126 -
0.000006338
0.000005579 19
ROBO+ Cycling vs. ROBO- M1 0.000006263 0.000009554 -0.00000329 0.000004766 19
ROBO+ Cycling vs. ROBO+ M2 0.000006263 0.000008752 -
0.000002489
0.000004766 19
ROBO+ Cycling vs. ROBO- M2 0.000006263 0.000004048 0.000002215 0.000005036 19
ROBO- Cycling vs. ROBO+ M1 0.000003095 0.0000126 -
0.000009506
0.000004416 97
ROBO- Cycling vs. ROBO- M1 0.000003095 0.000009554 -
0.000006458
0.000002372 97
ROBO- Cycling vs. ROBO+ M2 0.000003095 0.000008752 -
0.000005657
0.000002372 97
ROBO- Cycling vs. ROBO- M2 0.000003095 0.000004048 -9.525E-07 0.000003146 97
ROBO+ M1 vs. ROBO- M1 0.0000126 0.000009554 0.000003048 0.000004298 24

149
ROBO+ M1 vs. ROBO+ M2 0.0000126 0.000008752 0.000003849 0.000004298 24
ROBO+ M1 vs. ROBO- M2 0.0000126 0.000004048 0.000008553 0.000004596 24
ROBO- M1 vs. ROBO+ M2 0.000009554 0.000008752 8.017E-07 0.000001597 680
ROBO- M1 vs. ROBO- M2 0.000009554 0.000004048 0.000005506 0.000002979 680
ROBO+ M2 vs. ROBO- M2 0.000008752 0.000004048 0.000004704 0.000002979 253

Glycine Import

Tukey's multiple comparisons test Mean Diff. 95.00% CI of diff. Below
threshold?
Summary Adjusted P Value
ROBO+ Cycling vs. ROBO- Cycling 0.00003188 -6.481e-005 to 0.0001286 No ns 0.9349
ROBO+ Cycling vs. ROBO+ M1 -0.00004043 -0.0001511 to 7.027e-005 No ns 0.9023
ROBO+ Cycling vs. ROBO- M1 -0.0001746 -0.0002691 to -7.999e-005 Yes **** <0.0001
ROBO+ Cycling vs. ROBO+ M2 0.00007276 -2.182e-005 to 0.0001673 No ns 0.2389
ROBO+ Cycling vs. ROBO- M2 -0.0003273 -0.0004273 to -0.0002274 Yes **** <0.0001
ROBO- Cycling vs. ROBO+ M1 -0.00007231 -0.0001599 to 1.531e-005 No ns 0.172
ROBO- Cycling vs. ROBO- M1 -0.0002064 -0.0002535 to -0.0001594 Yes **** <0.0001
ROBO- Cycling vs. ROBO+ M2 0.00004088 -6.188e-006 to 8.794e-005 No ns 0.1305
ROBO- Cycling vs. ROBO- M2 -0.0003592 -0.0004216 to -0.0002968 Yes **** <0.0001
ROBO+ M1 vs. ROBO- M1 -0.0001341 -0.0002194 to -4.885e-005 Yes *** 0.0001
ROBO+ M1 vs. ROBO+ M2 0.0001132 2.790e-005 to 0.0001985 Yes ** 0.0023
ROBO+ M1 vs. ROBO- M2 -0.0002869 -0.0003781 to -0.0001957 Yes **** <0.0001
ROBO- M1 vs. ROBO+ M2 0.0002473 0.0002156 to 0.0002790 Yes **** <0.0001
ROBO- M1 vs. ROBO- M2 -0.0001528 -0.0002119 to -9.366e-005 Yes **** <0.0001
ROBO+ M2 vs. ROBO- M2 -0.0004001 -0.0004592 to -0.0003410 Yes **** <0.0001

Test details Mean 1 Mean 2 Mean Diff. SE of diff. N1
ROBO+ Cycling vs. ROBO- Cycling 0.0001169 0.00008506 0.00003188 0.00003378 19
ROBO+ Cycling vs. ROBO+ M1 0.0001169 0.0001574 -0.00004043 0.00003868 19
ROBO+ Cycling vs. ROBO- M1 0.0001169 0.0002915 -0.0001746 0.00003304 19
ROBO+ Cycling vs. ROBO+ M2 0.0001169 0.00004419 0.00007276 0.00003304 19
ROBO+ Cycling vs. ROBO- M2 0.0001169 0.0004443 -0.0003273 0.00003492 19
ROBO- Cycling vs. ROBO+ M1 0.00008506 0.0001574 -0.00007231 0.00003061 97
ROBO- Cycling vs. ROBO- M1 0.00008506 0.0002915 -0.0002064 0.00001644 97
ROBO- Cycling vs. ROBO+ M2 0.00008506 0.00004419 0.00004088 0.00001644 97
ROBO- Cycling vs. ROBO- M2 0.00008506 0.0004443 -0.0003592 0.00002181 97
ROBO+ M1 vs. ROBO- M1 0.0001574 0.0002915 -0.0001341 0.0000298 24

150
ROBO+ M1 vs. ROBO+ M2 0.0001574 0.00004419 0.0001132 0.0000298 24
ROBO+ M1 vs. ROBO- M2 0.0001574 0.0004443 -0.0002869 0.00003186 24
ROBO- M1 vs. ROBO+ M2 0.0002915 0.00004419 0.0002473 0.00001107 680
ROBO- M1 vs. ROBO- M2 0.0002915 0.0004443 -0.0001528 0.00002065 680
ROBO+ M2 vs. ROBO- M2 0.00004419 0.0004443 -0.0004001 0.00002065 253
APC: L-Thr and L-Phe

Tukey's multiple comparisons test Mean Diff. 95.00% CI of diff. Below
threshold?
Summary Adjusted P Value
ROBO+ Cycling vs. ROBO- Cycling -0.00000966 -3.136e-005 to 1.204e-005 No ns 0.7992
ROBO+ Cycling vs. ROBO+ M1 -0.00001041 -3.526e-005 to 1.444e-005 No ns 0.8375
ROBO+ Cycling vs. ROBO- M1 0.000004543 -1.669e-005 to 2.577e-005 No ns 0.9901
ROBO+ Cycling vs. ROBO+ M2 -0.00001124 -3.247e-005 to 9.985e-006 No ns 0.6541
ROBO+ Cycling vs. ROBO- M2 0.00001857 -3.862e-006 to 4.100e-005 No ns 0.1694
ROBO- Cycling vs. ROBO+ M1 -7.467E-07 -2.041e-005 to 1.892e-005 No ns >0.9999
ROBO- Cycling vs. ROBO- M1 0.0000142 3.638e-006 to 2.477e-005 Yes ** 0.0019
ROBO- Cycling vs. ROBO+ M2 -
0.000001585
-1.215e-005 to 8.980e-006 No ns 0.9981
ROBO- Cycling vs. ROBO- M2 0.00002823 1.422e-005 to 4.224e-005 Yes **** <0.0001
ROBO+ M1 vs. ROBO- M1 0.00001495 -4.194e-006 to 3.409e-005 No ns 0.2238
ROBO+ M1 vs. ROBO+ M2 -
0.000000838
-1.998e-005 to 1.831e-005 No ns >0.9999
ROBO+ M1 vs. ROBO- M2 0.00002898 8.506e-006 to 4.945e-005 Yes *** 0.0008
ROBO- M1 vs. ROBO+ M2 -0.00001579 -2.290e-005 to -8.675e-006 Yes **** <0.0001
ROBO- M1 vs. ROBO- M2 0.00001403 7.602e-007 to 2.729e-005 Yes * 0.0312
ROBO+ M2 vs. ROBO- M2 0.00002981 1.655e-005 to 4.308e-005 Yes **** <0.0001

Test details Mean 1 Mean 2 Mean Diff. SE of diff. N1
ROBO+ Cycling vs. ROBO- Cycling 0.00006127 0.00007093 -0.00000966 0.000007583 19
ROBO+ Cycling vs. ROBO+ M1 0.00006127 0.00007167 -0.00001041 0.000008682 19
ROBO+ Cycling vs. ROBO- M1 0.00006127 0.00005673 0.000004543 0.000007417 19
ROBO+ Cycling vs. ROBO+ M2 0.00006127 0.00007251 -0.00001124 0.000007417 19
ROBO+ Cycling vs. ROBO- M2 0.00006127 0.0000427 0.00001857 0.000007838 19
ROBO- Cycling vs. ROBO+ M1 0.00007093 0.00007167 -7.467E-07 0.000006871 97
ROBO- Cycling vs. ROBO- M1 0.00007093 0.00005673 0.0000142 0.000003691 97
ROBO- Cycling vs. ROBO+ M2 0.00007093 0.00007251 -
0.000001585
0.000003691 97
ROBO- Cycling vs. ROBO- M2 0.00007093 0.0000427 0.00002823 0.000004896 97
ROBO+ M1 vs. ROBO- M1 0.00007167 0.00005673 0.00001495 0.000006688 24

151
ROBO+ M1 vs. ROBO+ M2 0.00007167 0.00007251 -
0.000000838
0.000006688 24
ROBO+ M1 vs. ROBO- M2 0.00007167 0.0000427 0.00002898 0.000007152 24
ROBO- M1 vs. ROBO+ M2 0.00005673 0.00007251 -0.00001579 0.000002485 680
ROBO- M1 vs. ROBO- M2 0.00005673 0.0000427 0.00001403 0.000004635 680
ROBO+ M2 vs. ROBO- M2 0.00007251 0.0000427 0.00002981 0.000004635 253
APC: L-Met and L-Thr

Tukey's multiple comparisons test Mean Diff. 95.00% CI of diff. Below
threshold?
Summary Adjusted P Value
ROBO+ Cycling vs. ROBO- Cycling -
0.000007663
-3.309e-005 to 1.777e-005 No ns 0.9551
ROBO+ Cycling vs. ROBO+ M1 0.000002323 -2.680e-005 to 3.144e-005 No ns >0.9999
ROBO+ Cycling vs. ROBO- M1 0.00001945 -5.431e-006 to 4.432e-005 No ns 0.2228
ROBO+ Cycling vs. ROBO+ M2 -
0.000008005
-3.288e-005 to 1.687e-005 No ns 0.941
ROBO+ Cycling vs. ROBO- M2 0.00003348 7.192e-006 to 5.977e-005 Yes ** 0.004
ROBO- Cycling vs. ROBO+ M1 0.000009985 -1.306e-005 to 3.303e-005 No ns 0.8169
ROBO- Cycling vs. ROBO- M1 0.00002711 1.473e-005 to 3.949e-005 Yes **** <0.0001
ROBO- Cycling vs. ROBO+ M2 -
0.000000342
-1.272e-005 to 1.204e-005 No ns >0.9999
ROBO- Cycling vs. ROBO- M2 0.00004114 2.472e-005 to 5.756e-005 Yes **** <0.0001
ROBO+ M1 vs. ROBO- M1 0.00001712 -5.310e-006 to 3.956e-005 No ns 0.2469
ROBO+ M1 vs. ROBO+ M2 -0.00001033 -3.276e-005 to 1.211e-005 No ns 0.7752
ROBO+ M1 vs. ROBO- M2 0.00003116 7.169e-006 to 5.514e-005 Yes ** 0.0031
ROBO- M1 vs. ROBO+ M2 -0.00002745 -3.579e-005 to -1.912e-005 Yes **** <0.0001
ROBO- M1 vs. ROBO- M2 0.00001403 -1.514e-006 to 2.958e-005 No ns 0.1035
ROBO+ M2 vs. ROBO- M2 0.00004148 2.594e-005 to 5.703e-005 Yes **** <0.0001

Test details Mean 1 Mean 2 Mean Diff. SE of diff. N1
ROBO+ Cycling vs. ROBO- Cycling -0.00001414 -0.000006474 -
0.000007663
0.000008886 19
ROBO+ Cycling vs. ROBO+ M1 -0.00001414 -0.00001646 0.000002323 0.00001017 19
ROBO+ Cycling vs. ROBO- M1 -0.00001414 -0.00003358 0.00001945 0.000008692 19
ROBO+ Cycling vs. ROBO+ M2 -0.00001414 -0.000006132 -
0.000008005
0.000008692 19
ROBO+ Cycling vs. ROBO- M2 -0.00001414 -0.00004762 0.00003348 0.000009184 19
ROBO- Cycling vs. ROBO+ M1 -
0.000006474
-0.00001646 0.000009985 0.000008052 97
ROBO- Cycling vs. ROBO- M1 -
0.000006474
-0.00003358 0.00002711 0.000004325 97

152
ROBO- Cycling vs. ROBO+ M2 -
0.000006474
-0.000006132 -
0.000000342
0.000004325 97
ROBO- Cycling vs. ROBO- M2 -
0.000006474
-0.00004762 0.00004114 0.000005737 97
ROBO+ M1 vs. ROBO- M1 -0.00001646 -0.00003358 0.00001712 0.000007838 24
ROBO+ M1 vs. ROBO+ M2 -0.00001646 -0.000006132 -0.00001033 0.000007838 24
ROBO+ M1 vs. ROBO- M2 -0.00001646 -0.00004762 0.00003116 0.000008381 24
ROBO- M1 vs. ROBO+ M2 -0.00003358 -0.000006132 -0.00002745 0.000002912 680
ROBO- M1 vs. ROBO- M2 -0.00003358 -0.00004762 0.00001403 0.000005432 680
ROBO+ M2 vs. ROBO- M2 -
0.000006132
-0.00004762 0.00004148 0.000005432 253

APC: L-Gly and L-Val

Tukey's multiple comparisons test Mean Diff. 95.00% CI of diff. Below
threshold?
Summary Adjusted P Value
ROBO+ Cycling vs. ROBO- Cycling -0.0000046 -2.899e-005 to 1.979e-005 No ns 0.9945
ROBO+ Cycling vs. ROBO+ M1 0.000006336 -2.159e-005 to 3.426e-005 No ns 0.9871
ROBO+ Cycling vs. ROBO- M1 0.00001644 -7.413e-006 to 4.030e-005 No ns 0.3597
ROBO+ Cycling vs. ROBO+ M2 -0.00001142 -3.528e-005 to 1.243e-005 No ns 0.7448
ROBO+ Cycling vs. ROBO- M2 0.00003917 1.397e-005 to 6.438e-005 Yes *** 0.0002
ROBO- Cycling vs. ROBO+ M1 0.00001094 -1.116e-005 to 3.304e-005 No ns 0.7171
ROBO- Cycling vs. ROBO- M1 0.00002104 9.171e-006 to 3.291e-005 Yes **** <0.0001
ROBO- Cycling vs. ROBO+ M2 -
0.000006821
-1.869e-005 to 5.050e-006 No ns 0.5694
ROBO- Cycling vs. ROBO- M2 0.00004377 2.803e-005 to 5.952e-005 Yes **** <0.0001
ROBO+ M1 vs. ROBO- M1 0.00001011 -1.140e-005 to 3.162e-005 No ns 0.7598
ROBO+ M1 vs. ROBO+ M2 -0.00001776 -3.927e-005 to 3.755e-006 No ns 0.1718
ROBO+ M1 vs. ROBO- M2 0.00003284 9.835e-006 to 5.584e-005 Yes *** 0.0007
ROBO- M1 vs. ROBO+ M2 -0.00002786 -3.586e-005 to -1.987e-005 Yes **** <0.0001
ROBO- M1 vs. ROBO- M2 0.00002273 7.822e-006 to 3.764e-005 Yes *** 0.0002
ROBO+ M2 vs. ROBO- M2 0.00005059 3.569e-005 to 6.550e-005 Yes **** <0.0001

Test details Mean 1 Mean 2 Mean Diff. SE of diff. N1
ROBO+ Cycling vs. ROBO- Cycling -
0.000005427
-8.268E-07 -0.0000046 0.000008521 19
ROBO+ Cycling vs. ROBO+ M1 -
0.000005427
-0.00001176 0.000006336 0.000009756 19
ROBO+ Cycling vs. ROBO- M1 -
0.000005427
-0.00002187 0.00001644 0.000008335 19
ROBO+ Cycling vs. ROBO+ M2 -
0.000005427
0.000005994 -0.00001142 0.000008335 19

153
ROBO+ Cycling vs. ROBO- M2 -
0.000005427
-0.0000446 0.00003917 0.000008807 19
ROBO- Cycling vs. ROBO+ M1 -8.268E-07 -0.00001176 0.00001094 0.000007722 97
ROBO- Cycling vs. ROBO- M1 -8.268E-07 -0.00002187 0.00002104 0.000004148 97
ROBO- Cycling vs. ROBO+ M2 -8.268E-07 0.000005994 -
0.000006821
0.000004148 97
ROBO- Cycling vs. ROBO- M2 -8.268E-07 -0.0000446 0.00004377 0.000005501 97
ROBO+ M1 vs. ROBO- M1 -0.00001176 -0.00002187 0.00001011 0.000007516 24
ROBO+ M1 vs. ROBO+ M2 -0.00001176 0.000005994 -0.00001776 0.000007516 24
ROBO+ M1 vs. ROBO- M2 -0.00001176 -0.0000446 0.00003284 0.000008036 24
ROBO- M1 vs. ROBO+ M2 -0.00002187 0.000005994 -0.00002786 0.000002792 680
ROBO- M1 vs. ROBO- M2 -0.00002187 -0.0000446 0.00002273 0.000005209 680
ROBO+ M2 vs. ROBO- M2 0.000005994 -0.0000446 0.00005059 0.000005209 253

154
Appendix 4
Supplementary Information for Chapter 4

Figure S1

Figure S1: Community-constrained sampling compared to FBA optimization. (A) Median pathway flux values predicted by
community-constrained flux sampling compared to optimization of biomass. Subsystems that have significantly different median
fluxes are labeled. (B) Comparison of the flux-sum value for each metabolite for community-constrained flux sampling and
optimization of biomass.

10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Median pathway flux, via optimization
Median pathway flux, via sampling
tRNA Charging
Terpenoid backbone synthesis
Thiamine metabolism
Tannin degradation
pyrimidine synthesis
NAD metabolism
0.00 0.01 0.02 0.03 0.04 0.05
0.00
0.01
0.02
0.03
0.04
0.05
Metabolite Flux Sum, via optimization
Metabolite Flux Sum, via sampling
NADP
NADPH
H
2
O UDP
Coenzyme A
UDP-glucose
A. B.

Abstract (if available)

Abstract Macrophages are immune cells that play a critical role in the body’s response to illness, particularly colorectal cancer (CRC). Macrophages show high versatility, as they can adapt to different microenvironments and conditions. Their plasticity makes them challenging to categorize definitively; however, broad groupings have emerged based on differences in observed behavior. Cell behavior is increasingly understood to be driven by the metabolic state of the cell; macrophage metabolism in CRC therefore warrants further study.

Traditionally, activated macrophages are classified into two general phenotypes, an "M1" pro-inflammatory condition, and an "M2" immunosuppressive state. The M1/M2 paradigm is relatively understudied, particularly in cancer. In the first section of this work, I use computational modeling to understand the subtype-specific metabolic differences between the pro- and anti-immune macrophage states. Cancer cells show distinct behavior depending on their genetic state- certain mutations can cause the cancer cell to be more aggressive, thereby leading to worse patient outcomes. Those cancer cell mutations also cause the associated macrophages to act differently. One CRC mutation that is understudied but is known to drive poor patient prognosis is the loss of the ROBO gene. In this second portion of this work, I study the metabolic differences between macrophages surrounding CRC cells with and without the ROBO mutation to identify potential therapeutic interventions. Finally, I develop a novel computational approach to study the metabolic interactions between cells, enabling future work to study the way macrophages interact with CRC cells and other cell types in the tumor microenvironment. Altogether, this work captures macrophage metabolic activity, providing a framework to help predict and study novel therapies in colorectal cancer

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Development of a colorectal cancer-on-chip to investigate the tumor microenvironment's role in cancer progression

PDF

Microenvironmental and biomechanical regulation of mitochondrial membrane potential in cancer cells

PDF

Insights from a computational approach to natural killer cell activation

PDF

Mechanistic model of chimeric antigen receptor T cell activation

PDF

Mechanistic modeling of angiogenic factors network and cancer therapy

PDF

Understanding anti-angiogenic signaling and treatment for cancer through mechanistic modeling

PDF

Systems approaches to understanding metabolic vulnerabilities in cancer cells

PDF

Roles of circadian clock genes in cancer

PDF

Mechanistic investigation of pro-angiogenic signaling and endothelial sprouting mediated by FGF and VEGF

PDF

Investigating the complexity of the tumor microenvironment's role in drug response

PDF

Tumor-immune agent-based modeling: drawing insights from learned spaces

PDF

System biology approaches to cancer and diabetes metabolism

PDF

Machine learning and image processing of fluorescence lifetime imaging microscopy enables tracking and analysis of subcellular metabolism

PDF

Ancestral inference and cancer stem cell dynamics in colorectal tumors

PDF

Cisplatin activates mitochondrial oxphos leading to acute treatment resistance in bladder cancer

PDF

Investigating hematopoietic stem cells via multiscale modeling, single-cell genomics, and gene regulatory network inference

PDF

Model-based approaches to objective inference during steady-state and adaptive locomotor control

PDF

Engineering chimeric antigen receptor-directed immune cells for enhanced antitumor efficacy in solid tumors

PDF

Modeling dyadic synchrony with heterogeneous data: validation in infant-mother and infant-robot interactions

PDF

Development of a toolbox for global functional brain imaging of wake and sleep states in zebrafish

Asset Metadata

Creator Gelbach, Patrick Eamon (author)

Core Title Genome-scale modeling of macrophage activity in the colorectal cancer microenvironment

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Degree Conferral Date 2023-08

Publication Date 07/18/2023

Defense Date 04/21/2023

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag cancer,computational modeling,macrophage,metabolism,OAI-PMH Harvest,systems biology

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Finley, Stacey (committee chair), Fraser, Scott (committee member), Graham, Nicholas (committee member), Mumenthaler, Shannon (committee member)

Creator Email patrickgelbach@gmail.com,pgelbach@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113281402

Unique identifier UC113281402

Identifier etd-GelbachPat-12106.pdf (filename)

Legacy Identifier etd-GelbachPat-12106

Document Type Dissertation

Format theses (aat)

Rights Gelbach, Patrick Eamon

Internet Media Type application/pdf

Type texts

Source 20230719-usctheses-batch-1070 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu