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Microbial interaction networks: from single cells to collective behavior

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Microbial interaction networks: from single cells to collective behavior

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Content Microbial Interaction Networks: From Single Cells to
Collective Behavior

by
Xiaokan Guo

Department of Physics and Astronomy
University of Southern California

This dissertation is submitted in partial fulfilment of the
requirements for the degree of Doctor of Philosophy

Doctorates conferred by the faculty of the USC graduate school

December 2018

I

Contents
Acknowledgement ............................................................................................................. V
List of Figures .................................................................................................................... VI
List of Tables ...................................................................................................................... IX
Abstract .............................................................................................................................. X
Chapter 1: Introduction ...................................................................................................... 1
1.1 High-order interaction within multispecies microbial community ........................... 1
1.2 Cellular heterogeneity and cell-cell interaction at single-cell level .......................... 2
1.3 Collective behavior of bacteria ................................................................................. 4
1.4 Summary of my work ................................................................................................ 5
Chapter 2: The contribution of high-order metabolic interactions to the global activity of
a four-species microbial community .................................................................................. 7
2.1 Interactions between species set the overall metabolic rate of a four species
microbial community. ..................................................................................................... 7
2.2 Measuring the interaction between two species ..................................................... 8
2.3 A predictive model incorporating higher-order multispecies interactions ............. 11
2.4 Multispecies interactions in spatially fragmented microbial systems .................... 14
2.5 Discussion ............................................................................................................... 16
2.6 Materials and Methods ........................................................................................... 18
Chapter 3: Single-cell variability of growth interactions within a two-species bacterial
community ....................................................................................................................... 20
3.1 Single-cell growth measurements in the microwell array ...................................... 20
3.2 From single-cell growth to growth dynamics at bulk population level ................... 21
3.3 Interaction of two species at single-cell level ......................................................... 23

II

3.4 Discussion ............................................................................................................... 26
3.5 Materials and Methods ........................................................................................... 28
3.5.1 Microwell device fabrication ............................................................................ 28
3.5.2 Loading microwells with cells ........................................................................... 29
3.5.3 Cell culture and growth measurements ........................................................... 30
3.5.4 Bulk growth measurements ............................................................................. 31
3.5.5 Image analysis .................................................................................................. 31
3.5.6 Calculation of the doubling time from growth in microwells ........................... 31
3.5.7 Simulation of the bulk growth curves .............................................................. 32
Chapter 4: Single-cell properties and collective behavior of Enterobacter wild isolates . 33
4.1 Enterobacter Wild Isolates Form Swarm Bands of Varying Propagation Speeds .... 33
4.2 Band Speed is not Correlated Any Individual Strain Properties .............................. 35
4.3 Band Speed and Strain Properties are Perturbed by Exclusion of Methionine from
Media ............................................................................................................................ 37
4.4 Run Speed and Tumbling Frequency in Combination are Most Connected to Band
Speed ............................................................................................................................ 39
4.5 Discussion ............................................................................................................... 41
4.6 Materials and Methods ........................................................................................... 44
4.6.1 Migration Screening ......................................................................................... 44
4.6.2 Band Visualization ............................................................................................ 45
4.6.3 Tracking Single-Cell Trajectories ....................................................................... 46
4.6.4 Trajectory Feature Detection ........................................................................... 46
4.6.5 Growth Curves .................................................................................................. 48
4.6.6 Multiple linear regression ................................................................................ 48

III

4.6.7 16S Tree Construction ...................................................................................... 49
4.6.8 Statistical Methods ........................................................................................... 50
Chapter 5: Critical transition in collective behavior for a two-species microbial
community ....................................................................................................................... 51
5.1 Co-migration of Enterobacter strains in semisolid medium ................................... 51
5.2 Tracking bacterial band under the microscope ...................................................... 54
5.3 Fluorescence microscopy reveals the composition of the migrating band ............ 55
5.4 Simulations reproduce the speed switch ................................................................ 59
5.5 Discussion ............................................................................................................... 61
5.6 Materials and Methods ........................................................................................... 63
5.6.1 Strains and sample preparation ....................................................................... 63
5.6.2 Band formation and imaging in rectangular plate ........................................... 63
5.6.3 Microscopy in 3D-printed device and data processing .................................... 64
5.6.4 Mathematical model ........................................................................................ 65
Chapter 6: Conclusion ...................................................................................................... 68
6.1 The contribution of high-order interactions to a microbial community ................. 68
6.2 How single-cell interactions relate to population-level interactions ...................... 68
6.3 How single-cell properties set the collective behavior of bacteria ......................... 69
6.4 The mode of emergent behavior of mixed systems ............................................... 69
6.5 Future directions ..................................................................................................... 70
Appendix ........................................................................................................................... 71
A.1.1 Cell Isolation and Growth .................................................................................... 71
A.1.2 Measuring Interactions ........................................................................................ 72
A.1.3 Calculating interaction coefficients ..................................................................... 73

IV

A.1.4 16s rRNA Sequences ............................................................................................ 78
A.2.1 Time of first division in the microwell ................................................................. 81
A.2.2 Plasmids of E. coli and E. cloacae ........................................................................ 81
A.2.3 Distribution of droplet volume ............................................................................ 82
A.2.4 Chip-to-chip variability ........................................................................................ 83
A.2.5 Growth curves in microwells for coculture of E. coli and E. cloacae ................... 84
A.2.6. Spatial correlations of doubling times ................................................................ 85
A.3.1. Swarm Band Detection and Speed Quantification. ............................................ 85
A.3.2 Trajectory Feature Detection. Related to Fig. 4.2. ............................................... 86
A.3.3 Run Speed and Run Time Distributions for Each Strain. ...................................... 87
A.3.4. Pairwise Comparisons of Strain Properties with Band Speed. ............................ 88
A.4.1 Plasmids of EcSlow and EcFast ............................................................................ 91
A.4.2 Influence of model parameters on the band speed ............................................ 91
A.4.3 Growth curves ..................................................................................................... 92
A.4.4 Cell distribution of mixture of EcSlow and EcFast ............................................... 93
A.4.5 Simulations of band propagation of EcSlow and EcFast by themselves .............. 94
References ........................................................................................................................ 95

V

Acknowledgement

I would like to express sincere gratitude to my advisor Dr. James Boedicker, for his
guidance, patience, encouragement, and insight throughout my research projects. I
would also like to thank my committee members: Paul Bogdan, Ian Ehrenreich, Moh El-
Naggar, and Stephan Haas.
I am very thankful to my labmates, especially Prithvi Chellamuthu, Sean Lim, Pavan Silva,
and Frances Tran, for their valuable help during my research.
Finally, I am deeply grateful to my family and friends for inspiring me in completing my
Ph.D.

VI

List of Figures
Figure 2.1 Metabolic activity of a 4-species community. ................................................... 8
Figure 2.2 Pairwise interactions within the microbial community. .................................. 11
Figure 2.3 Accounting for higher-order interactions. ....................................................... 13
Figure 2.4 Simulations for a spatially fragmented multispecies microbial community. ... 14
Figure 3.1 Monocultures of E. coli and E. cloacae grown in microwells. .......................... 20
Figure 3.2 Simulation from single-cell doubling time to bulk growth shows high
consistency with measurement. ....................................................................................... 22
Figure 3.3.1 Mixed culture of E. coli and E. cloacae growing in the same microwell. ...... 24
Figure 3.3.2 Correlation between doubling times of the two species in mixed microwells.
.......................................................................................................................................... 25
Figure 3.5 Fabrication, seeding procedures, and microscopic images of the microwell
device. .............................................................................................................................. 30
Figure 4.1 Propagation of the Bacterial Swarm Band formed by Strains of the
Enterobacter cloacae complex in Semisolid (0.26% agar) Migration Media. ................... 34
Figure 4.2 Strain Properties and their Correlations with Band Speed. ............................. 36
Figure 4.3 Removal of Methionine from Migration Media Altered Both Strain Properties
and Band Speed. ............................................................................................................... 38
Figure 4.4.1 Multiple Linear Regression Reveals Band Speed is Connected with Run
Speed and Tumbling Frequency. ...................................................................................... 40
Figure 4.4.2 Related Enterobacter Strains Have Distinct Combinations in Strain
Properties and Band Speeds. ............................................................................................ 41
Figure 5.1.1 Enterobacter strains form traveling band with different speeds in semisolid
medium. ........................................................................................................................... 51
Figure 5.1.2 Influence of composition of the original mixture on the speed switch. ....... 53
Figure 5.2 Tracking bacterial band in 3D-printed device under the microscope. ............. 54
Figure 5.3.1 Composition of the dual-strain migrating band formed by an original 1:1
mixture of EcSlow and EcFast. .......................................................................................... 56

VII

Figure 5.3.2 Relationship between the band speed and composition reveals a critical
fraction for the timing of speed switch. ........................................................................... 58
Figure 5.4 Simulation results of the dual-strain migration in soft agar. ........................... 59
Figure A.1.1 Optical densities (OD 600) of cell cultures growing in 10% LB. .................... 71
Figure A.1.2 Different volumes of cell cultures from 10 to 80 μL were diluted to 180 μL
with 10% LB media. .......................................................................................................... 72
Figure A.1.3.1 Metabolic rates for species ratios from 1:7 to 7:1 for all 6 2-species
combinations. ................................................................................................................... 73
Figure A.1.3.2 Comparison of predictions to experimental measurements of total activity
of the 4-species community over a wide range of species ratios. .................................... 74
Figure A.1.3.3 The contribution of each interaction term in Equation in the 4-species
community for different species ratios. ........................................................................... 74
Figure A.1.3.4 Parameters extracted from 4-species experiment data only. ................... 75
Figure A.1.3.5 Pairwise parameters extracted from 4-species experiment data only
assuming no high-order interaction. ................................................................................ 76
Figure A.1.3.6 Plate reader data. ...................................................................................... 77
Figure A.1.3.7 Simulations for spatially fragmented multispecies microbial community.78
Figure A.2.1 Distribution of time when the first division occurs in the microwell for the
growth curves shown in Fig. 3.1. ...................................................................................... 81
Figure A.2.2 Plasmids used for expression of fluorescent proteins. ................................. 82
Figure A.2.3 Droplet volume and the influence on doubling time. .................................. 82
Figure A.2.4 The mean doubling times from two independent coculture experiments are
compared. ........................................................................................................................ 83
Figure A.2.5 Growth curves and distribution of doubling times of E. coli and E. cloacae
growing in the same microwell. ....................................................................................... 84
Figure A.2.6 Doubling times of E. coli in microwells near the middle and edge (within 10
rows of microwells from the edge) of the device. ............................................................ 85
Figure A.3.1 Swarm Band Detection and Speed Quantification. Related to Fig. 4.1. ....... 85
Figure A.3.2 Trajectory Feature Detection. Related to Fig. 4.2. ....................................... 86

VIII

Figure A.3.3 Run Speed and Run Time Distributions for Each Strain. ............................... 87
Figure A.3.4 Pairwise Comparisons of Strain Properties with Band Speed. Related to Fig.
4.4. .................................................................................................................................... 88
Figure A.4.1 Plasmids used for expression of fluorescent proteins. ................................. 91
Figure A.4.2 Simulations with 50% and 200% of original parameter values are repeated
to show the influence of model parameters on the band speed. .................................... 91
Figure A.4.3 Growth curves of EcSlow and EcFast. Error bar indicates standard error. ... 92
Figure A.4.4 Intensity and cell distribution of the traveling bacterial band along the
direction of propagation. .................................................................................................. 93
Figure A.4.5 Simulation results for monocultures of EcSlow and EcFast. ........................ 94

IX

List of Tables
Table 1 Parameter values used in simulations. ................................................................ 67
Table 2 Bacterial strains used in this study, related to Experimental Procedures. .......... 89
Table 3 Trajectory statistics, related to Experimental Procedures. .................................. 90

X

Abstract
The activity of a biological community is the outcome of complex processes involving
interactions between community members. It is often unclear how to accurately
incorporate these interactions into predictive models. Previous work has shown a range
of positive and negative interactions between species resulting from the exchange of
metabolites, molecular signals, and even cell-cell contact. Even though cell-cell
interaction networks have been examined in many high diversity microbial communities
using macroscale approaches, microscale studies of multispecies communities are lacking
and it remains unclear how macroscale trends scale down to small groups of cells. Current
models to predict macroscale trends do not account for the heterogeneity of activity in
individual cells, and the potential for variability in cell-cell interactions has not been
explored. Interactions between cells not only influence the behavior of individuals, but
may also result in spontaneous group behavior. Collective behavior, as a complex
outcome of interactions between individual members of a population, is observed in
many biological systems coordinating cellular activity over multiple time and length scales.
The main goal of this work was to connect single-cell behaviors to activities at bulk
population level.
To explore our ability to predict the behavior of complex networks of microbes we
analyzed the cell-cell interaction and collective behavior of multiple bacterial systems. In
a 4 species microbial community, we examined pairwise interactions as well as high-order
interactions between community members, and found that pairwise interactions were
sufficient to predict the overall metabolic rate of the community. In another project we
focused on the single-cell variability of such interactions finding diverse relationships
between individual cells that traditional bulk measurement would not reveal. To connect
individual and group behavior, we quantitatively studied the correlation between single-
cell characteristics and collective behavior at population level. Finally, we found a critical
transition in collective behavior within a two-species community, emphasizing the
complexity of hybrid collective behavior of mixed populations. As a whole, these project
have revealed connections between single-cell activity and population-level behaviors

XI

that should deepen understanding of complex cellular networks and help to identify
strategies for the control and accurate prediction of microbial community function.
Here we quantify the contribution of interactions between more than two species to the
overall metabolic rate of a mixture of four freshwater bacteria. In isolated small
microcolonies, high-order interactions could play a dominant role in setting ecosystem
outputs. Besides, our single-cell view of interactions implies the importance of cellular
heterogeneity in regulating cell-cell interaction networks. The device we report here
enables future studies of variability of single-cell activity. We also reveal that single-cell
properties are strongly correlated with collective behavior. In synthetic biological systems,
it may be possible to achieve desired collective behavior by combining properties found
in the wild. Furthermore, the non-linear scaling and critical behavior we observe in the
hybrid collective behavior of mixed strains can play a vital role in stabilizing networks in
disturbed conditions.

1

Chapter 1: Introduction
Interactions, either between individuals or between populations, play a critical role in
regulating cellular networks. Interactions not only regulate functional traits of the
community, but can also result in coordinated behavior of community members.
Understanding cellular interaction networks at quantitative level is the key to predict and
control the activity of natural or synthetic communities. However, developing predictive
models that accurately account for cell-cell interactions remains a challenge. Whether
interaction among small groups of cells differs from bulk-population level interaction is
also unclear. In addition, the connection between single-cell behavior and group behavior
is not fully elucidated. To better understand interactions within complex networks, we
quantify the interactions at both single-cell and population level and connect individual
behaviors with group behavior. Here, we combined simulations with experiments to study
cell-cell interaction in cellular networks. Instead of large datasets, we used simpler but
still complex multispecies networks to examine interactions and correlations between
individual cells and largescale dynamics of the system. Our work should serve as a
stepping stone for understanding cellular networks in more complex systems.
1.1 High-order interaction within multispecies microbial community
We are surrounded by complex communities of microbes, many that play a fundamental
role in our everyday lives. Microbial ecosystems in nature are typically composed of
hundreds or thousands of microbial species, heterogeneously distributed in space and
time. Working together, these networks of microorganisms are critical in environmental
remediation, food production, wastewater treatment, and human health and disease and
there is great interest designing synthetic microbial ecosystems for new biotechnologies.
Given the diversity of microbial ecosystems (1), there are many potential types of
interactions between species, including all combination of positive, negative, and neutral
interactions (2) resulting from coupled metabolism and signal exchange within diverse
microbial communities. Developing a quantitative understanding of how ecosystems of
microbes interact will be essential to predicting how microbial networks respond to

2

environmental or biological changes and aid in designing synthetic communities with
tailored functionality (3).
To quantify how interactions between species impact overall community function,
previous experimental work has systematically measured pairwise interactions between
species, such as crossfeeding between E. coli auxotrophs (4, 5) or natural isolates (6, 7).
Other work has inferred interactions between species from measurements of the
population dynamics within a complex community (8-11). These previous studies focused
on pairwise interactions and the ability of pairwise interaction models to predict network
function (2, 12). Given the increase in data for biological interactions, there is great
emphasis on the development of predictive models of biological networks, including
constraint based, Boolean, and directed network models (13-18).
It is currently unclear how to accurately account for cell-cell interactions within models
of microbial ecosystems and whether pairwise interactions are generally sufficient.
Foster and Bell measured total productivity of subsets of microbial microcosms with up
to 72 species, and no evidence for positive high-order interactions was observed (19). In
other biological contexts, measurements of interactions in neural or cytokine networks
revealed pairwise interactions were dominant, although a few high-order combinations
significantly altered patterns of cytokine activity (20, 21). The impact of high-order
interactions, between 3 or more components, have not been quantified in microbial
ecosystems.
1.2 Cellular heterogeneity and cell-cell interaction at single-cell level
Cellular heterogeneity exists between individual cells, even within populations that
consist of a single type of cell. Measurements of such heterogeneity have revealed
discrepancy between single-cell behavior and cell population averages (22-26). Ensemble
measurements obtained by traditional methods give no insight into such cellular
individuality. Studying bacteria at the single-cell level, which requires new experimental
tools, enables a more predictive understanding of how cells act in a variety of contexts,
including systems that are not well mixed (27).

3

Over the past decade, many technologies have been developed for analysis of single-cell
behavior (28-32), including 3D printing (33), surface acoustic waves (34), and optical
trapping (35). Many microfluidic techniques have proven to be useful for studying
bacterial cells at the single-cell level (36-39). Microfluidic techniques have enabled study
of gene regulation and signaling at the single-cell level (40-42) , single-cell manipulation
(43, 44), and measurement of variability in the growth kinetics of individual cells (45). The
high-throughput nature of many microfluidic devices enables simultaneous capture of the
full range of cell individuality within a population (46, 47). However, many microfluidic
devices are only capable of low-resolution images of single cells, which limits accurate
measurements of single-cell physiology. The device implemented here is based on a
technique to create arrays of aqueous droplets 10-100 micrometers in diameter and only
a few micrometers in height (48). As opposed to other micro droplet approaches (49-52),
the use of thin droplets directly on top of a glass coverslip is amenable to imaging at 100X
magnification and reduces imaging problems associated with curved interfaces.
It is known that most bacteria live in well-organized multispecies communities rather than
exist as independent cells (53). Communication between community members and other
cell-cell interactions regulate cellular activities such as metabolism, growth, and
adaptation to changes in the environment (54-56). Understanding cell-cell interactions
helps to predict the largescale behavior of microbial populations. Previous work has
applied Lotka-Volterra equations to ecological time-series data from a complex microbial
community to quantify pairwise interactions (12). Beyond pairwise interactions, the
importance of high-order or non-additive interactions on global activity and the diversity
of microbial communities has been recently investigated (57-59). The variability of such
interactions due to single-cell heterogeneity has not been reported, despite the known
importance of single-cell variability in contexts with only one species (60-62).
In natural microbial ecosystems, cells are often dispersed into small groups (27, 63). It is
still unknown how this fragmentation impacts the regulation and function of real systems.
Although numerous studies based on traditional bulk experiments have explored pairwise
interactions within microbial communities (6, 19), no studies to date have probed the

4

variability of these interactions within small groups of cells. Whether the strength of cell-
cell interactions are variable within individual cells, and whether this variability translates
to differences in the emergent behaviors of populations is unexplored.
1.3 Collective behavior of bacteria
Collective behavior is a complex consequence of interactions between individual
members that constitute the population. Individuals of the group communicate with
neighbors to adapt to the environmental change, resulting in global coherence. Although
arising from collection of group members, collective behavior is usually very different
from and more complex than the sum of individual behaviors. For centuries, this self-
organized phenomenon has been observed in a wide variety of biological systems at
different scales, including bird flocks (64), fish schools (65, 66), and honey bees (67, 68).
Because of the heterogeneous distribution of biological systems in the nature, the global
behavior usually involves mutual interaction between members of ecological community,
and hardly maintain undisturbed. However, due to the complexity and uncontrollability,
collective behavior of mixed systems is not fully elucidated.
Collective motion is not only observed in animals or insects, but also in microorganisms.
Swarming, as a good example of collective behavior in bacteria, is the form of flagella-
mediated migration that bacteria use to move over solid surfaces or semisolid medium
(69-72). Unlike swimming as individual cell, bacteria swarm in cell groups with bundled
flagella, which requires cell-cell interactions (73, 74). Furthermore, many studies have
shown certain chemotactic strains inoculated in semisolid medium concentrate into
visible traveling band that progresses outwards (75-77). The bacterial band is a high
concentration region that cells are bound together by secreting and sensing
chemoattractant. The successive consumption of nutrients and oxygen in the soft agar
medium results in an attractant gradient that drives the band propagate towards less
explored area. Previously, this self-organized chemotactic process, as an example of
collective behavior and intercellular interaction, was mainly observed in Escherichia coli
and Salmonella (69, 76-78).

5

Linking collective behaviors of bacterial populations to the rules followed by constituent
cells is an important challenge in biology (79-81). Many studies on the mechanisms of
band formation also attribute the band’s behavior, a macroscopic property, to the
motility dynamics of single cells (82-84). Several studies have examined how individual
motion of cells relates to properties of the collective (85, 86). However, there have been
limited experimental studies investigating differences in collective behavior between
closely related strains of bacteria (87).
Genetic variations between strains have been previously shown to impact macroscopic
behavior by acting on several motility subsystems (88, 89). To move, bacteria rely on a
series of “runs” (unidirectional swimming) and “tumbles” (sharp reorientations) to
translocate themselves in space using helical, whip-like structures called flagella (83, 90,
91). Food consumption and signal production generate molecular gradients in
environments that were initially uniform. Cells detect these gradients and perform a
biased random walk in the direction of a gradient (92). In this way, cell movement and
activity potentially drive populations to chemotactically self-organize in space (93, 94).
Thus, natural genetic variation among wild-type strains in their growing and swimming
faculties may result in varying degrees of macroscopic migratory behavior. However,
studies are often limited to single species in Enterobactericae, such as Escherichia coli or
Salmonella typhimurium,, for which most experiments and theoretical models on
collective motility behavior have been performed for (69, 75-77, 84, 95, 96). Examination
of natural, subtle variation in both collective and single-cell properties should yield new
insights as to how these two scales of behavior are interrelated.
1.4 Summary of my work
In Chapter 2, I examine the interaction network of a four-species microbial community
using a fluorogenic indicator. I study the contribution of pairwise and higher interactions
within the model community, and predict the impact of such interactions on community-
level activity using a theoretical model. Overall activity is well described by pairwise model.
Theoretical results still highlight the importance of specifically high-order interactions in
spatially heterogeneous populations of cells.

6

In Chapter 3, I use a microfluidic device to measure the growth kinetics of two species,
Escherichia coli and Enterobacter cloacae, both in isolation and when combined. I reveal
variability in the growth of a coculture of bacteria and quantify the extent to which the
growth of each species is correlated.
In Chapter 4, I focus on connecting single-cell characteristics with the collective behavior
of wild isolates of the Enterobactericae family. Analyzing single-cell trajectories, I reveal
run speeds and tumbling frequency together set the property of the collective behavior.
In Chapter 5, I discuss a two-state transition we observe in group behavior of a microbial
community with diverse composition. I show that the hybrid collective behavior of
microorganisms is more complex than we expect, and may involve interactions between
different species and environments.
In Chapter 6, I conclude the most important questions I answered during my PhD studies.
I also talk about future directions based on my research.

7

Chapter 2: The contribution of high-order metabolic interactions
to the global activity of a four-species microbial community
This work appears essentially as published in 2016 in Plos Computational Biology.
10.1371/journal.pcbi.1005079
2.1 Interactions between species set the overall metabolic rate of a four species
microbial community.

The four strains that comprise the community were all isolated from freshwater
environments, including three isolates from the Los Angeles area and the previously
isolated Shewanella oneidensis MR-1 (97). Strains were collected near the water surface
and isolated on low strength LB plates. 16S rRNA sequencing has identified the strains as
being closely related to Escherichia coli K-12, Aeromonas veronii, and Aeromonas
hydrophila, see Supplemental Materials for details. Throughout the paper these strains
will be referred as So, Ec, Av, and Ah respectively, as shown in Fig. 2.1A. We aim to
elucidate the general properties of the interaction network within a microbial community
by exhaustively measuring the output of all subsets of the community under a specific set
of conditions. These four species were chosen based on viability under the same culturing
conditions, no particular metabolic capabilities or potential for interactions were
assumed.
To quantify the contribution of interactions between the species on metabolic rate, we
first measured the metabolic rate of the four strains in isolation. Strains were grown in 5
mL scale cultures of low strength LB. After growth to an OD 600 around 0.2, strains were
transferred to a 96 wellplate. The metabolic rate was quantified using a fluorogenic assay
for the presence of metabolic intermediates, the AlamarBlue assay containing the redox
activity indicator compound resazurin (98-100). Resazurin based assays have been used
to quantify metabolism in a variety of bacterial and eukaryotic cells (101), making it a
useful, universal indicator for metabolism in multispecies bacterial communities. From

8

these measurements the relative metabolic rates of the four species were determined, as
shown in Fig. 2.1B.
To determine the influence of multispecies interactions on ecosystem outputs, we
compared the overall metabolic rate of a 4-species microbial community to the metabolic
rate of each strain in isolation. If the species did not interact, the overall metabolic rate
of 4 strains together would simply be the average metabolic rate. However when mixing
the 4 species together the overall metabolic rate was 31% larger than the prediction made
assuming no interactions, as shown in Fig. 2.1B. This demonstrates that interactions
between species significantly modulate the metabolic rate of one or more strains within
the community. To further dissect the distribution of interactions within our community,
we measured interactions between all combinations of species.

Figure 2.1 Metabolic activity of a 4-species community.
(A) The community contains four freshwater isolates, Escherichia coli (Ec), Aeromonas
veronii (Av), Aeromonas hydrophila (Ah), and Shewanella oneidensis (So). Species were
grown separately and combined to measure the impact of multispecies interactions on
the metabolic rate. (B) The overall metabolic rate of all four strains together was
greater than the prediction made from measurements of the metabolic rate of
individual strains, demonstrating that multispecies interactions contributed to the
overall metabolic rate. Error bars show standard error. Metabolic rate has been
normalized such that the 4-strain measurement has a value of 1.
2.2 Measuring the interaction between two species
Pairwise interactions models are common to predict the activity of microbial networks.
We measured the metabolic activity of two-species mixed cultures to determine if

9

pairwise models could account for interactions within our microbial community (Fig. 2.2).
The strains were grown separately, mixed together for 30 minutes, and then metabolic
activity was measured using the fluorogenic indicator. The ratio of the two species was
varied between 1:7 and 7:1 to quantify how interactions between species depended upon
the ratio of species. The metabolic rate was found to be linearly proportional to the
number of cells measured, as shown in Figure A.1.2. Metabolic activity of each species
alone was measured to determine the baseline metabolic rate. The three sets of
measurements for species Ec and Av shown in Fig. 2.2A were taken on three different
days, demonstrating the reproducibility of interactions.
To analyze how interactions between species determined the overall metabolic rate, we
implemented a model in which the overall metabolic rate is modulated by an interaction
parameter, as shown in Eq. 2.1,
R(X,Y) = R(X)·N x/N total+ R(Y)·N y/N total+ i xy·p(N x, N y, N total), (Equation 2.1)
in which R(X), R(Y) and R(X,Y) are the average metabolic rates of species X, Y, and X and Y
together respectively, i xy is the pairwise interaction parameter that accounts for the
increase or decrease of overall metabolic activity, N x, N y, and N total are numbers of cells of
species x, y, and the total number of cells in the single species control measurement, and
p(N x, N y,) scales the interaction parameter based on the number of interacting cell. These
General Lotka-Volterra models have been used previously (2). The interaction
coefficients can be positive or negative, such that the sum of the interactions did not
result in non-physical negative metabolic rate. The metabolic rate (R) is proportional to
the slope of fluorescence vs. time curve in experiments. We assume that p(N x, N y,) should
be a function of N x, N y, and N total, as shown in Eq. 2.2,
p(N x, N y, N total) = (N x / N total) · (N y / (N total), (Equation 2.2)
in which p is the product of ratios of species X and Y in the mixture. With the existence of
p in the Eq. 2.1, the interaction term is largest when equal numbers of species are present
and will decay to zero as one of the populations dominates. Note that because we
measure the overall metabolic output of combinations of species, the experiments cannot

10

separate the individual impact of species X and Y and the impact of species Y on X. Our
interaction term accounts for the overall change in activity due to species-species
interactions.
The metabolic rate data was fit to determine the value of the interaction parameter, i xy.
As shown in Fig. 2.2A, the metabolic rate was measured by a pair of species over a range
of ratios between the two species. As shown in Fig. 2.2A, modeling pairwise interactions
using Eq. 2.1 agreed well with metabolic measurements of mixtures of Ec and Av over a
range of species compositions.
The data in Fig. 2.2A suggested that interactions for mixtures of species could be captured
in a single interaction parameter. Figure A.1.3.1 shows the data for all species
combinations, and most pairwise combinations are in close agreement with the
prediction using a single interaction parameter. To determine whether the interaction
strength was valid for all combination of the 4 species, in Fig. 2.2B we plotted the ratio of
prediction to measurement vs. species ratio for all 6 species combinations. We extended
the species ratio to 0.625%, 1.25%, 6.25%, 93.75%, 98.75% and 99.375% for 3
combinations of species and found that the model fit data well even at these more
extreme ratios of species.
We define the normalized interactions strength as the interaction term divided by the
total metabolic rate when the species ratios are equal, which represents the maximum of
the interaction term. In Fig. 2.2C, we show the range of normalized interactions strengths
in our system for all 6 pairwise combinations of Ec, Av, Ah and So at species ratio 1:1. The
interaction coefficients were fit using all the data between species ratios of 0.625 to
99.375%. In our experiment, the first order normalized interaction strengths were all
positive with values between 0.05 and 0.3.

11

Figure 2.2 Pairwise interactions within the microbial community.
(A) We measured metabolic rates at seven different ratios from 1/8 to 7/8 for Ec and
Av. Interaction coefficient was extracted from the data. The prediction line uses this
interaction coefficient. (B) All pairwise combinations of the four strains were assayed.
Predictions using solved interaction coefficients were compared to experimental
measurements. The normalized strengths of interaction for all 6 pairwise combinations
are shown in (C) for species ratio 1:1. Red numbers show confidence intervals at
confidence level 95%. Error bars show standard errors of at least three measurements.
2.3 A predictive model incorporating higher-order multispecies interactions
Next, the model was expanded to incorporate higher-order interactions between 3 or
more species. The overall metabolic rate of the community is now,
𝑅
"#"$%
=∑ 𝑅
(
𝑝
(
*
+, -
+∑ ∑ 𝑖
+(
*
(0+
𝑝
+(
*
+, -
+∑ ∑ ∑ 𝑖
+(1
*
10(0+
*
(0+
𝑝
+(1
*
+, -
+
𝑖
+(12
𝑝
+(12
, (Equation 2.3)

12

in which M is the total number of species in the community, i wx accounts for pairwise
interaction between two species, i wxy accounts for interactions between three species,
and i wxyz accounts for interactions between four species. This equation could be adapted
to incorporate more higher-order terms. Building from the results of pairwise
interactions, we approximate that higher-order interactions also dependent on the ratio
of species. Similar to Eq. 2.2, the scale factor p can be calculated from the following
general form,
𝑝 =∏
5
6
5
7879:
*
+, -
, (Equation 2.4)
where N total is the total number of cells in the community. Analogous to finding the
pairwise coefficients, measurements of the metabolic activity of three species
combinations and Eq. 2.3 and 2.4 together with the pairwise interaction coefficients
already measured were used to calculate the 4 second order coefficients. A single third
order coefficient was calculated from experimental measurements of the 4 species
community. The strengths of second and third order interaction terms in three- and four-
species communities respectively are listed in Fig. 2.3A.
Fig. 2.3B shows in a four-species community, the proportions of all interaction terms in
predicted overall metabolic rate for five different species ratios. The average
contributions of 0
th
, 1
st
, 2
nd
, and 3
rd
order interaction terms, shown as red lines, sharply
decrease. The contribution of each term is calculated as the strength of interaction,
defined as the sum of all interactions of a specific order divided by the total metabolic
rate. For example the strength of the 2
nd
order interactions would be,
𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =∑ ∑ ∑ 𝑖
+(1
5
6
5
F
5
G
5
7879:
H
*
10(0+
*
(0+
*
+, -
. (Equation 2.5)

13

Figure 2.3 Accounting for higher-order interactions.
(A) The proportions of 2
nd
and 3
rd
order interaction terms in 3 and 4 species microbial
communities respectively. Interaction coefficients were calculated using Eq. 2.3 and 2.4
and experimental measurements of metabolic activity within subsets of the community.
The 95% confidence interval is shown. (B) Proportions of different interaction terms in
the 4-species community for different species ratios (Ec:Av:Ah:So). (C) Using all
interaction coefficients derived from our data, we compared the experimental
measurements of total activity of the 4-species community with even composition and
with one member in excess. Predictions made assuming no interactions (0
th
order
model), 2-species interactions (1
st
order model), and 2 and 3-species interactions (2
nd

order model), and 2, 3, and 4-species interactions (3
rd
order model). Error bars indicates
standard deviations. Red lines indicate average values. The strength of interaction is
normalized by dividing by the total metabolic rate.
After extracting all interaction coefficients within the 4 species community, we compared
the predictive ability of models incorporating different levels of interactions. Fig. 2.3C
compares measurements of the 4-species at different ratios of cells to versions of the
model incorporating subsequently higher-order interaction terms. The 0
th
order model
gives us a metabolic rate that is under predicted, and adding first order coefficients
greatly improves the accuracy of the prediction. Incorporating 3- and 4-species
coefficients gives an accurate prediction, but is not an improvement over the 1
st
-order
model. In the Supplemental Information Figure A.1.3.2 and A.1.3.3 we compare
measurements to theory for a wider range of community composition. On average the
ratio of prediction to measurements is 0.82±0.06 for the 0
th
order model, 0.98±0.11 for
the 1
st
order model, 1.07±0.13 for the 2
nd
order model, and 1.02±0.13 for the full 3
rd
order

14

model. The interaction network was built from the bottom up, fitting for low order
coefficients from measurements of the minimum number of combined strains. We also
analyzed the data by fitting to only the four-species data, as shown in Figures A.1.3.4 and
A.1.3.5, both using a pairwise only model and the model incorporating high-order
interactions described in Eq. 2.3. Fitting only the four-species data resulted in an
interaction network that did not accurately describe the activity of pairwise combinations
of species.
2.4 Multispecies interactions in spatially fragmented microbial systems

Figure 2.4 Simulations for a spatially fragmented multispecies microbial community.
(A) The community is divided into microcolonies of variable size. (B) Relative
contributions of different levels of interaction to the overall metabolic rate for the
experimentally measured community. (C) Simulation results shown how the total
metabolic activity of the system depends on the number of cells per microcolony and
the community composition. The total metabolic rate has been normalized to 1. (D)
Distributions of the metabolic rate of individual cells for microcolony sizes of 1, 3, 20

15

and 200. Metabolic activity was calculated using Eq. 2.3, with basal metabolic rates of
0.16, 0.66, 0.57, 0.34 for Ec, Av, Ah, and So respectively. The fraction of Ah is 0.5 in (D).
Given the importance of interactions in setting overall activity levels of multispecies
microbial communities, simulations were used to explore the experimentally measured
interaction network in the context of a spatially structured population, as depicted in Fig.
2.4A. Some natural microbial ecosystems have disperse, patchy distribution of cells (27,
63), potentially giving rise to many local neighborhoods of cells with a range of activity
levels. If specific combinations are significant contributors to the overall activity level of
the community, the size of these microcolonies and the evenness of the population could
have significant consequences on the overall community activity. Agent-based models
using Eq. 2.3 and 2.4 were used to explore the consequence of multispecies interactions
in the limit of spatially isolated or non-interacting microcolonies.
A community incorporating 2-species, 3-species and 4-species interactions was simulated
that contained the experimentally determined interactions parameters from Fig. 2.2 and
Fig. 2.3. Fig. 2.4B shows the relative contribution of pairwise and higher-order
interactions to the overall metabolic rate. The system contains 8,400 cells, unevenly
distributed with a variable number of Ah cells and equal numbers of cell Av, So, and Ec
making up the remainder of the population. The cells are randomly distributed into
microcolonies such that each one has an equal number of cells. After distributing the cells,
the activity of each group of cells is calculated using Eq. 2.3 and assuming that interactions
are local, i.e. restricted to neighbors within the same colony. The total activity of the
community is the sum of the activity of all the cells in each micro-colony.
As shown in Fig. 2.4C, the overall metabolic rate of the community is sensitive to how the
species are distributed in space. Community activity increases with colony size as larger
colonies allow the positive pairwise and three-species interactions. An even population
distribution, not dominated by Ah, also leads to an increased metabolic rate as the
positive interactions between the four strains are more likely to be sampled in each
microcolony.

16

Group size also impacts the distribution of local activity levels. Fig. 2.4D shows the activity
of each microcolony in populations containing 50% of species Ah for microcolony sizes of
1, 3, 20, and 200 cells. We observe that for 1-cell microcolonies activity is low, as groups
that are too small omit even 1
st
-order interactions. For small groups containing multiple
cell types, the activity of individual cells broadens as a result of the variability of the
composition of each microcolony. As microcolony size continues to expand, the average
composition becomes more predictable, sampling all possible interactions, and single-cell
activity levels are uniform. The distribution of activity levels in even this simple interaction
network demonstrates how both the global species composition and the microscale
distribution of cells can strongly influence local activity profiles. Local “hotspots” may be
present in such populations, but only when populations are fragmented into small groups.
2.5 Discussion
Here we measured the metabolic interactions within a four species community of
microbes, to quantify the influence of pairwise and higher-order interactions on the
overall metabolic rate of the community. In previous studies, pairwise interactions have
been measured, including a large screen of Streptomyces species (7). Similar to these
previous studies, we found a range of interactions between the species, ranging from no
interaction to strongly positive. Interestingly, no negative pairwise interactions were
found in within the small set of species tried here, despite previous work finding that
many pairwise interactions were negative (19). One possible explanation is the use of
dilute LB media, a complex media that may contain compounds that negatively impact
the growth of some strains. Interactions with So were performed at 37 °C, which is higher
than its optimal growth temperature of 30 °C (102). The temperature stress on So may
be related its positive pairwise interactions with the other community members.
Interactions between some species likely depend on cellular state and growth phase, and
here we grew each species to exponential phase. We also examined metabolic rates after
only 30 minutes of coculture, a time scale over which changes in species ratios are small,
see Figure A.1.1 for growth rates. Our measurements capture changes in metabolic rate
that occur on short timescales, and may not indicate the long term behavior of such

17

systems, such as alteration of the growth environment by different types of cells. In
multispecies communities long-term adaption can also change interaction networks,
leading to unexpected and sometimes uncertain outcomes (103-105).
Quantitative measurements of higher-order interactions between these four species
revealed that pairwise interactions dominated and were sufficient to predict community
overall activity. When not taking any interactions into account, the predictions of the
overall metabolic rate were off by more than 18%. Fig. 2.3C shows that a pairwise model
predicted the overall metabolic rate of the four species community within 2%, whereas
adding the 3-species and 4-species coefficients, within the error of the measurement, did
not improve predictions. However, this by no means denies the possible influences of
higher-order interactions in other communities. The distribution of the magnitude of
these high-order interactions within other, more complex communities would be valuable
in determining how sensitive a community would be to changes in the community
diversity. It is possible that even rare combinations of species may have evolved to
strongly interact in natural microbial ecosystems. For a community with 100 species,
there are in total >160,000 3-species combinations. The difficulty in measuring these
interactions increases as communities become more complex, and it is unclear if strong
interactions would be seen in even higher-order combinations of species. More work is
needed to explore how much is gained by quantifying high order interactions in more
complex settings.
Extending these findings to predict the activity within more complex multispecies
microbial ecosystems will require a combination of predictive theoretical models and
perhaps new experimental tools to quantify interactions. With the rapid development of
nanofabrication technology, microfluidic devices are widely used for single-cell analysis
(36, 38), allowing us to study multispecies interactions at the microsystem level such as
suggested in Fig. 2.4 and elsewhere (40, 42). We implemented a model in Fig. 2.4 to
explore how the species evenness and the interaction network set the overall ecosystem
outputs. For systems in which species are fragmented into small microcolonies, high-
order interactions and microcolony size could play a dominant role in setting ecosystem

18

outputs, especially in networks with strong high-order interactions such as for a toy
network shown in Figure A.1.3.7. Small groups also displayed a broader range of local
activity levels. Given that a patchy distribution of cells has been observed in many natural
communities (106-110), such “hotspot” microcolonies may be important drivers of
function of some real microbial communities containing high-order interactions between
species. Our results point for a need of new experimental methods to identify such species
combinations in real systems.
2.6 Materials and Methods
In experiments, all strains were taken from frozen glycerol stocks and grown overnight in
10% LB media (BD). The next day, we pipetted 5 to 150 μL from the suspension cultures
into 3mL 10% LB media and grew them again for 3 to 4 hours such that all cultures
simultaneously grew to a final optical density at 600 nm near 0.2. Ec, Av, and As were
grown at 37 °C in 10% LB media, while So was grown at 30 °C. Cells were cultured at 5 mL
scale and shaken at 200 rpm.
For measurements of metabolic activity, 100 μL of 10% LB media and 80 μL culture were
pipetted into the wells of a 96-well microplate. The 80 μL suspension cultures could be
single-species or multiple-species mixed to different ratios. The microplate was incubated
at 37°C for 30 minutes to allow microbial communities to interact. Finally, we pipetted 20
μL of the metabolic indicator AlamarBlue (Thermo Scientific) into each well and measured
the fluorescence change using a well-plate reader. Fluorescence was measured at
excitation and emission wavelengths of 560 to 590 nm, and a media-only control was used
to account for background fluorescence. Figure A.1.3.6 shows that during the
measurement, the OD 600 of cultures increased, as expected given the doubling times
reported in Figure A.1.1.
For two-species combinations, we measured different ratios from 1:7 to 7:1. For three-
species combinations, we measured 6:1:1, 1:6:1, 1:1:6, 4:2:2, 2:4:2, 2:2:4, 2:3:3, 3:2:3,
3:3:2. For four-species combinations, we measured 1:2:2:3, 1:2:3:2, 1:3:2:2, 2:1:2:3,
2:1:3:2, 3:1:2:2, 2:2:1:3, 2:3:1:2, 3:2:1:2, 2:2:3:1, 2:3:2:1, 3:2:2:1, 2:2:2:2, 1:1:1:5, 1:1:5:1,

19

1:5:1:1, 5:1:1:1. All combinations were repeated three times. Interactions coefficients in
Eq. 2.3 were solved using Solver in excel (GRG Nonlinear solving method) to minimize the
sum of differences between predictions and measurements of all ratios. In higher-order
models, we applied the same method to solve for higher-order interaction coefficients,
using lower-order interaction coefficients solved previously in experiments involving
fewer species.

20

Chapter 3: Single-cell variability of growth interactions within a
two-species bacterial community
This work is currently under review at Physical Biology. This work was done in
collaboration with Pavan Silva.
3.1 Single-cell growth measurements in the microwell array
To probe the single-cell heterogeneity, growth was monitored in devices loaded with
single species to both validate the microwell assay and establish the baseline for growth
of each strain in isolation (see Materials and Methods for details). Cultures of
fluorescently labeled bacteria were loaded into the microwell chip as depicted in Fig. 3.1A.

Figure 3.1 Monocultures of E. coli and E. cloacae grown in microwells.

21

(A) RFP-labeled E. coli and YFP-labeled E. cloacae were loaded into separate microwell
devices. (B) Fluorescence images showing the growth of E. coli or E. cloacae cells in an
example microwell from each device. (C,D) Growth curves are recorded for each
microwell, 80 growth curves from wells containing E. coli and 114 growth curves from
wells containing E. cloacae. Log indicates the natural log of the number of cells. (E,F) A
doubling time was calculated for each growth curve. The distribution of doubling times
for each well is shown.
Cell growth was monitored using fluorescent microscopy. Fig. 3.1B shows the growth of
fluorescence-labeled cells in an example microwell over time. Fig. 3.1C and D show the
growth curves of E. coli and E. cloacae within each microwell. The curves saturate at an
average cell number of 10. Microwell dimensions are 60 μm by 60 μm by 5 μm and the
droplets typically filled the majority of the microwell. See Fig. A.2.3 for droplet volumes
and the effect on doubling time. At the average volume of 8 pL, a single cell in a droplet
has a density of 7 x 10
7
cell mL
-1
, and cell growth slows as the density approaches 4 x 10
8

cell mL
-1
(similar to bulk measurements of growth). See Materials and Methods for
calculation of doubling times from microwell data. Fig. 3.1E and F show the distributions
of doubling times from individual microwells. The mean doubling times are 76.5 minutes
and 153.9 minutes for E. coli and E. cloacae respectively. See Fig. A.2.4 for chip-to-chip
variability.
3.2 From single-cell growth to growth dynamics at bulk population level
To determine if results from the microwell measurements agreed with growth at the
population level, we ran a bulk growth assay starting at the cell densities used in the
microwell measurements. Both species were grown to OD 600 0.2 and concentrated via
centrifugation and resuspended in fresh 10% LB medium at OD 600 0.7. This initial cell
density was similar to the microwell experiments of approximately 2.4 x 10
8
cells mL
-1
.
Bulk cultures were shaken at 180 rpm and incubated at 37°C. Changes in the cell density
of E. coli and E. cloacae were measured by selective plating of each species over time.

22

Figure 3.2 Simulation from single-cell doubling time to bulk growth shows high
consistency with measurement.
(A) Doubling times of E. coli and E. cloacae measured in microwells were used to
simulate growth curves in the bulk and compared to experimental measurements of
large volume cultures. The simulated curves are the average of 50 repetitions, with the
shaded region showing the maximum and minimum curves. (B) The doubling time of
the simulated bulk growth curve was calculated from the first 2 hours of simulated
growth. The measured and simulated doubling times of the bulk population are
compared. Error bars indicate the standard error of 3 replicates for bulk measurements
and standard error of 50 repetitions of the simulation.
For a comparison of growth at the single-cell and bulk-population levels, we ran a
simulation using the distributions of doubling times of E. coli and E. cloacae measured in
the microwell array (Fig. 3.1E, 3.1F). In the simulation, we assumed a linear correlation
between the doubling time of the mother cell and the variance of doubling time of
daughter cells (see Materials and Methods for details)(111). The simulated growth curves
of single-species cultures of both E. coli and E. cloacae were consistent with the bulk
measurements as shown in Fig. 3.2A. The simulated growth curves did not saturate
because the calculated doubling times were from exponential growth and food and space
limitations were not considered in the simulation.

23

The measured and simulated doubling times of the bulk population are compared as
shown in Fig. 3.2B, validating that the single-cell experiments are consistent with the
growth dynamics of large cultures. Interestingly, both measured and simulated doubling
times are smaller than the mean doubling time of single cells (111), suggesting the overall
growth rate in bulk cultures is driven by the fast growing cells. As bacterial growth is often
probed as the average property of a population, our study highlights the importance of
single-cell heterogeneity for a better understanding of bulk population growth.
3.3 Interaction of two species at single-cell level
A similar growth experiment was run with mixed cultures of E. coli and E. cloacae to
investigate single-cell aspects of cell-cell interactions. Again, E. coli or E. cloacae were
grown separately in overnight cultures inoculated from frozen stock, diluted in 10% LB
medium and regrown for 4 hours. The two cell suspensions were then rinsed and adjusted
to the same cell density as in the previous experiments. The two cultures were mixed in
a 1:1 ratio and immediately loaded into the microwell device as shown in Fig. 3.3.1A
resulting in microwells containing one or two species with initial average loading of 5 cells
per well.

24

Figure 3.3.1 Mixed culture of E. coli and E. cloacae growing in the same microwell.
(A) Cultures of RFP-labeled E. coli and YFP-labeled E. cloacae cells were mixed together
and loaded into the microwell device. (B) Fluorescent images show E. coli and E. cloacae
cells growing within the same microwell. (C,D) Growth curves for both E. coli and E.
cloacae were obtained from each well and used to calculate the doubling time for each
species. Doubling times for wells containing both species increased as compared to the
doubling times for wells containing only single species. Comparison data is shown from
Fig. 3.1E and 3.1F.
The microscope was programmed to take both RFP and YFP images every 15 minutes to
monitor the growth of both species. Fig. 3.3.1B shows a sequence of overlayed
fluorescence images from a microwell containing both species. 114 microwells with only
E. coli, 61 microwells with only E. cloacae, and 104 microwells with both species were
analyzed as described above to calculate the distribution of doubling times of each

25

species. As shown in Fig. 3.3.1C and D (growth curves shown in Fig. A.2.5), the mean
doubling time changed from 76.5 minutes to 169.8 minutes for E. coli, and 153.9 minutes
to 205.1 minutes for E. cloacae. For both species, the distribution of doubling times
shifted towards longer doubling times, indicating an overall competitive interaction
between the two species.

Figure 3.3.2 Correlation between doubling times of the two species in mixed microwells.
(A) The scatter plot of doubling times of E. coli and E. cloacae from 104 microwells
containing both species. (B) Predicted distribution assuming no growth interaction
between E. coli and E. cloacae. 104 doubling times reported in Fig. 3.1E and 3.1F,
measured in wells containing only one species, were randomly paired. (C) Doubling
times for E. coli and E. cloacae reported in (A) were randomly repaired to determine if
growth correlations for cells in the same microwell were the result of noise. One
example set of randomized data is plotted, and the average Spearman’s rho was
calculated for 10,000 randomized data sets. Plots have been divided into four regions,
indicating whether or not the doubling time of each strain was above or below the
median doubling time of the two species when grown alone. Dashed lines show the
median doubling time of each species.
For a better understanding of cell-cell interaction within the two-species
microcommunity, we depicted the doubling times of both species as a scatter plot, as
shown in Fig. 3.3.2A. Each point represents a set of doubling times for E. coli and E.
cloacae extracted from a single microwell. The two dash lines shown in Fig. 3.3.2A
represent medians of doubling time of the two species when grown alone (shown in Fig.
3.1E and 3.1F). The interspecific interaction between E. coli and E. cloacae was then
divided into four regions depending on whether the doubling time of each species was

26

above or below the median doubling time, for example in the competition region the
doubling times of both species were longer than the median doubling time. In total 66.3%
of microwells showed competition, 6.7% mutualism, 10.6% predation by E. coli, and 16.4%
predation by E. cloacae. If the doubling times were predicted based on single-species
growth measurements, i.e. assuming no growth interactions between species, the scatter
plot would resemble Fig. 3.3.2B with approximately equal numbers of points in all four
regions.
The fact that predation_B involves more microcommunities than predation_A suggests
E. cloacae has an advantage over E. coli in competition. Only 6.7% of the
microcommunities fall into mutualism. As a comparison, Fig. 3.3.2B show a similar scatter
plot that doubling times of E. coli and E. cloacae grown alone are randomly paired.
Microcommunities uniformly scatter in the four regions described above.
A positive correlation was observed between the growth rates of species found in the
same microwell. The Spearman’s rho is 0.264 for 104 pairs of data points, which is above
the critical value 0.197 of 100 samples at 5% significance level (112). As a test of the
potential background correlation, Fig. 3.3.2C shows the scatter plot when the doubling
times reported in Fig. 3.3.2A were randomly repaired. 10,000 repetitions of this random
procedure give the mean Spearman’s rho as -0.0021 with a standard error of 0.00098.
The positive correlation does not seem to be volume-related, as shown in Fig. A.2.3B, or
related to location of the microwell on the chip, as shown in Fig. A.2.6.
3.4 Discussion
We have demonstrated a high-throughput method for measuring single-cell
heterogeneity that is inaccessible to traditional ensemble measurements of growth (113-
116). Applying microfabrication on glass cover slip coated with a hydrophobic layer, we
generate hundreds of microwells containing individual bacterial cells. Our device provides
high-resolution images at 100X magnification, enabling accurate measurements of single-
cell physiology. In addition, our microwell device allows long-term monitoring of
hundreds of isolated monoculture or coculture populations, which makes it possible to

27

probe cell-cell interactions at single-cell level. Patchy distributions of cells are common in
the nature, with groups of cells often existing in largely isolated microcolonies for long
periods of time (117, 118). Understanding local interactions within these small groups is
essential for the study of overall activity at larger scales. Our device enables measurement
of activity in single cells within small volume droplets, which has the potential to activate
high-density behaviors, such as quorum sensing (119-122), often associated with
interspecies competition (123, 124).
We utilized our microwell device to measure growth interactions at the single-cell level
between the bacterial species E. coli and E. cloacae. The distribution of doubling time
shows great variability of single cells behavior, and the distributions were shifted when
the two species were allowed to interact. Overall the interactions between species were
competitive, resulting in increased doubling times.
Using doubling times extracted from single-cell experimental measurements, our
simulation of population-level growth agrees closely with bulk measurements. Moreover,
the population-level doubling time is smaller than the mean doubling time of single cells,
suggesting fast growing cells dominate the growth dynamics of large populations. This
emphasizes the importance of single-cell analysis as bulk measurements assume identical
properties of individual population members and skew our understanding of the function
of individual cells (25, 125, 126). Simulations using parameters calculated from single-cell
experimental measurements agree closely with the growth of the bulk population,
suggesting growth within microwells accurately reflected growth dynamics observed in
well-mixed bulk cultures.
Our single-cell view of competition between these species indicates a contest type of
interaction (56, 127, 128), with both species enacting antagonistic interactions between
competitors. Within individual microwells, we observe pairs of doubling times that are
above or below the median doubling times of each species. As shown in Fig. 3.3.2, each
doubling time falls into the category of competition, mutualism, or predation.
Comparison of Fig. 3.3.2A and Fig. 3.3.2C suggests that randomly repairing the growth

28

measurements of each species result in a similar distribution of points into these four
interaction regions, suggesting that the interactions between cells in the same microwell
were largely deterministic. However, the measured Spearman’s rho indicates a
monotonic relationship between the doubling times of E. coli and E. cloacae that was not
observed for the randomly repaired growth measurements. The weak correlation in
doubling times suggests that some cells adjust interactions depending on the activity of
neighbors. Interspecies interaction might be tunable and incorporate feedback from the
local community. The device reported here will enable future studies to examine
mechanisms by which the variability of single-cell activity is modulated by local cell-cell
interactions.
3.5 Materials and Methods
3.5.1 Microwell device fabrication
The microwell device used here is based on a device reported previously for studying the
activity of single cells or single enzymes (48). Previous studies have shown similar
microwell devices made from SU-8, PDMS, and CYTOP (120, 129, 130). The device was
fabricated by dry etching a hydrophobic polymer (CYTOP; Asahi Glass, Japan) coated on a
glass cover slip (131) (Fig. 3.3.2A). 30 µl of 9% CYTOP solution (CTL-809M) was deposited
on a 25 x 25 mm micro cover glass (VWR) and spun at 1200 rpm for 30 s. After 5 min at
room temperature, the device was baked on a hot plate at 80
o
C for 30 min followed by
180
o
C for 1 h. To improve adhesion of the photoresist to the CYTOP layer, the surface
was treated with O2 plasma under 100 mTorr and 100 W for 3 s (132). 100 µl of
photoresist (AZ P4620) was deposited on the CYTOP layer, and spun at 1200 rpm for 50 s.
The device was then baked at 110
o
C for 20 min. The photoresist was patterned in a mask
aligner by exposure to UV light with light intensity 800 mJ cm
-2
. After developing for 6
min, the device was baked again at 110
o
C for 20 min to reinforce the photoresist layer.
The microwell pattern was etched into the Cytop layer with oxygen plasma at 100 mTorr
and 100 W for 5 min. The remaining photoresist was removed using acetone, and the
device was baked at 180
o
C for 5 min.

29

3.5.2 Loading microwells with cells
To capture bacteria cells in the microwells, the device was attached to a 3D printed frame
made from polylactic acid, as shown in Fig. 3.4B. 600 µl of cell suspension was pipetted
onto the surface of the device to fully cover the microwell array. It was found that E. coli
culture with an OD 600 of 0.2 and E. cloacae culture with an OD 600 of 0.02 resulted in
sufficient loading of the device, suggesting that E. cloacae might more easily be captured
by microwells during the loading process. Starting from a corner, we slowly pipetted a
fluorinated oil (Fluorinert™ FC-40, Sigma-Aldrich, US) onto the surface. As the oil layer
sweeps over the microarray surface, cells are loaded into the microdroplets (Fig. 3.4C).
The fluorinated oil covers each droplet, inhibiting the exchange of biomolecules between
microwells due to very poorly solubility in the fluorinated oil. Thus each droplet is
chemically isolated, enabling the simultaneous examination of cellular activity in many
independent, replicate droplets. The setup is enclosed with a top coverslip to prevent
evaporation. Typically 1 hour was needed to transfer the device to the microscope and
set up time-lapse microscopy. Cell division occurred in 98.8% and 98.3% microwells within
2 hours for E. coli and E. cloacae respectively as shown in Fig. A.2.1. Fig. 3.4D shows a
microscopic image of the array of microwells with bacterial cells enclosed. Fig. 3.4E shows
an example of a single E. coli cell in the microwell filled with 100% LB medium divided
multiple times to more than 30 cells. Bacteria have been monitored for up to 16 hours in
this device.

30

Figure 3.5 Fabrication, seeding procedures, and microscopic images of the microwell
device.
(A) Process flow of making the microwell device. (B) Microwell device with holder. (C)
Bacterial loading procedures. (D) Phase contrast image of E. coli cells captured in
microwells. (E) Phase images show division of E. coli cells in LB medium. In D and E cells
are marked in light blue.
3.5.3 Cell culture and growth measurements
The growth of two bacterial species, Escherichia coli and Enterobacter cloacae, was
examined in the both bulk and microscale experiments. These species have similar
growth requirements and are capable of expressing fluorescent marker proteins to
distinguish the two cell types in experiments. Plasmids encoding fluorescent proteins
were incorporated into the strains, a plasmid to express RFP in E. coli and a plasmid to
express YFP in E. cloacae. E. coli is strain MG1655 (133) and E. cloacae is a wild strain as
reported in (134). Plasmid details can be found in Fig. A.2.2.

31

Cells were inoculated from a frozen stock and grown in 5 mL scale cultures of LB media
with antibiotics at 37
o
C while shaking at 200 rpm. The next day cells were diluted in 10%
LB medium without antibiotic and regrown to OD 600 of 0.2. The cell suspension was rinsed
and adjusted to the appropriate cell density in fresh 10% LB. 100% LB was used in Fig. 3.4,
but for the remainder of the paper cells are grown in 10% LB, as this was the media
originally used to isolate Enterobacter cloacae. Cell density of the bulk culture sets the
average number of cells per well. Cell density was adjusted such that the averaging
loading of each microwell was 5 cells.
Cell growth was monitored using fluorescent and phase contrast microscopy. The device
was placed in a 37°C temperature controlled chamber on the microscope (OKO labs,
H201-T-UNIT) and imaged every 15 minutes with a 40x objective using Nikon C-FL Y-2E/C
and C-FL FITC HYQ fluorescence filters for E. coli and E. cloacae respectively. The
illuminator voltage was 3.5 v for phase contrast images. The exposure time for fluorescent
images is 70 ms to 500 ms depending on the brightness of the cells.
3.5.4 Bulk growth measurements
Both E. coli and E. cloacae were grown to OD600 0.2 and concentrated to 0.7 in fresh 10%
LB medium, giving an initial cell density similar to the microwell experiments of
approximately 2.4 x 10
8
cells mL
-1
. Bulk cultures were shaken at 180 rpm and incubated
at 37°C. Changes in the cell density of E. coli and E. cloacae were measured by selective
plating of each species over time.
3.5.5 Image analysis
Cells were counted manually in each frame of the fluorescence, time-lapse microscopy
data. As observed in Fig. 3.1, both cell types are easily discriminated from the background
in fluorescent images. Comparison of phase contrast and fluorescence images verified
that all cells were detectable by fluorescence throughout the growth experiment.
3.5.6 Calculation of the doubling time from growth in microwells
The doubling time for each growth curve was calculated using a linear fit of the log of the
cell number versus time. To determine the most linear part of the curve, the coefficient

32

of determination was calculated starting from t=0 up to a minimum of 5 data points. The
time window with the largest coefficient of determination was used to calculate the
doubling time.
3.5.7 Simulation of the bulk growth curves
The bulk simulation started from 100 representative cells with random doubling times
sampled from the microwell measurements. Initially each cell was placed at a random
point in time between cells divisions, such that some cells would divide near t=0, and
others would wait until nearly one doubling time to divide. The growth of individual cell
was calculated as
𝑁(𝑡+∆𝑡) =𝑁(𝑡)∙2
∆7
O
P
, (Equation 3)
where 𝑁 is the status of cell division (ranging from 1 to 2), ∆𝑡 is 1 minute, and 𝑇
R
is the
doubling time. Growth was simulated up to 2000 cells, approximately 4 doubling times.
In Fig. 3.2A, simulated cell numbers were multiplied by 10
6
to approximate growth of large
populations.
After division, new doubling times were assigned to the two daughter cells. The new
doubling times were randomly chosen from a normal distribution with 𝑇
R
as the mean
and 𝑇
R
− 𝑇
R_UVW
as the variance, where 𝑇
R_UVW
is the minimum doubling time measured.
The linear relationship between the mean and the variance of 𝑇
R
constrained the possible
doubling time to be no less than the minimum doubling time observed. The linear
relationship between the mean and variance of the doubling times is as reported in (111).

33

Chapter 4: Single-cell properties and collective behavior of
Enterobacter wild isolates
This work is currently under review at Plos One. This work was done in collaboration with
Sean Lim.
4.1 Enterobacter Wild Isolates Form Swarm Bands of Varying Propagation Speeds
Traveling waves of high cell density, swarm bands, have been observed in other members
of the Enterobactericiae family such as Salmonella typhimurium and E. coli (75-77). To
compare formation of swarm bands in closely related strains, we isolated a variety of
bacteria strains from freshwater sources. To select strains of the Enterobactericiae family,
we utilized HardyChrom
TM
ECC selection plates to collect multiple strains of the
Enterobacter cloacae complex from the wild. Each isolate was screened for band
formation and the 16S rRNA region was sequenced.
Following previous studies, we inoculate 10µL of bacteria culture grown overnight onto
migration media, an M9 Minimal Salts-based semisolid agar (0.26%) (75-77). We observe
bacterial migration over 2 days at 25°C using a custom setup (Fig. A.3.1A). Before
migration commences, the cells grow into a dense colony at the point of inoculation (Fig.
4.1A). About 12-18 hours after inoculation, the swarm band coalesces at the center of the
colony and begins to radiate outward as a ring (77). The ring is visible by eye and can be
tracked easily without magnification through time-lapse imaging (Fig. A.3.1B). Starting
out slowly, the ring then attains a near-constant propagation speed held over the next 1-
2 days (Fig. 4.1B). The band maintains its shape until it has completely propagated to the
other side of the well. Our custom setup allowed for rapid simultaneous quantification of
the migration patterns of several bacterial strains.
We turned our attention to assess the variation of band speeds in wild Enterobacter. To
compute average velocity for a specific strain, band positions were collected every 30
minutes using manual tracking starting 1.5 cm away from the inoculation point. A linear
fit gave the band velocities, and in replicate experiments, the band speed was

34

reproducible within about 1 mm/hr (Fig. A.3.1C). For the several isolates compared, the
average of the band speeds ranged on average from 2 mm/hr to 5 mm/hr, which is on the
order of 1 cell length per second (Fig. 4.1C). Such variation between strains was the
motivation for us to subsequently investigate the motility and growth of each strain and
their relationship to band speed.

Figure 4.1 Propagation of the Bacterial Swarm Band formed by Strains of the
Enterobacter cloacae complex in Semisolid (0.26% agar) Migration Media.
(A) The bacterial swarm band begins at the inoculation point (as denoted by the star)
and travels along the channel. See also Video S1. (B) A representative position vs. time
plot of the band from 3 different Enterobacter strains. The band speeds are nearly
constant and differ from strain to strain. (C) Band speeds of each strain represented as
mean ± SEM (n≥5 independent experiments). See also Fig. A.3.1C.

35

4.2 Band Speed is not Correlated Any Individual Strain Properties
To explore the correlations between the observed variation in macroscopic band speed
and several strain properties, we analyzed both single-cell motility and the growth rate of
each strain. For motility, we used time-lapse microscopy on cells in a microfluidic chamber
(C-Chip DHC-S02-2, INCYTO) where we recorded the run-and-tumble behavior of each
strain. Microfluidic devices with thin chambers have previously been used to capture the
motility of cells by constraining cell motion to a plane and to prevent net movement of
fluid, allowing for longer observation times (89, 135). The cells, after a 100-fold dilution
from overnight culture, were grown at 25°C to early exponential phase in M9 medium.
Cells were diluted to a density which gives approximately 300 cells/mm
2
in the chip and
then injected into the chip’s microchamber with a depth of 20 µm. 5-minute movies of
the cells were recorded in phase contrast illumination with a 40X microscope objective.
We characterized the run-and-tumble behaviors to each strain (Fig. 4.2A) (82-84, 89).
Single-cell trajectories were compiled using the TrackMate plugin of the image processing
program ImageJ (136). We collected trajectories from 3 separate areas of the
microchamber for each strain. Trajectories less than 5 seconds long were discarded, giving
more than 140 trajectories per location. Following analysis of trajectories presented in
(135), we measured the angular velocity of each cell over time. We detected tumbling
events of cells using an algorithm comparing local maxima to neighboring minima of
angular velocity (see Trajectory Feature Detection in Materials and Methods). A run event
was defined as any trajectory segment between two tumbling events that was at least 0.5
seconds long.
To quantify strain properties, we calculated the run speed as the average speed of all run
events captured in a video. The tumbling frequency is the inverse of the average run time
between two tumbling events (135) (Fig. A.3.2 and A.3.3B). We utilized Spearman’s rho
rank correlation coefficient to assess how monotonic the quantitative connections are
between a strain property and the band speed (137). Fig. 4.2B shows no strong correlation
between the run speed and the band speed. However, the band speed shows weak

36

positive correlation with tumbling frequency (Fig. 4.2C). Therefore, an examination of one
motility property by itself was not adequate to explain increasing band speeds.
We found similar weak trends between band speeds and other properties of the strains
that may also contribute to the band speed. Previous studies have shown differences in
the fraction of motile cells between strains of the same species (138, 139). Theories on
collective behavior also propose the key role of the mixture of non-swimming and
swimming cells in governing collective motility (140-142). We found a subpopulation of
non-swimming cells for each strain. The proportion of swimming cells was calculated as
the average amount of cells observed with an average speed less than 0.32 µm/s, which
is a tenth of their body length per second. Strains assessed here had low proportions of
swimmers, ranging from less than 10% to a little over 40% (Fig. 4.2D). However, the band
speed was not correlated with fraction of swimmers.

Figure 4.2 Strain Properties and their Correlations with Band Speed.
(A) Example trajectory showing tumbling events. The bottom trajectory is from a non-
swimming cell. See also Fig A.3.2. Correlations are shown between the band speed and
(B) the run speed, (C), the tumbling frequency, (D) the proportion of swimming cells,
and (E) the growth rate. Plotted is the mean band speed ± SEM, with n≥5 independent
experiments. Each strain property is the mean ± SEM, with n=3 independent
measurements. See also Fig. A.3.3A.

37

Cells growth rate has been shown to contribute to the band speed (142). We measured
the exponential growth rates of all Enterobacter strains in the same migration media and
temperature as the band speed experiments. Although varying between strains, these
mesoscopic properties also lack a monotonic relationship with increasing band speeds.
We also correlated every strain property we measured to each other and also found no
striking monotonic relationships (Fig. A.3.4A, blue scatter). In summary, these results
suggest that no single single-cell property is dominant in setting the band speed.
4.3 Band Speed and Strain Properties are Perturbed by Exclusion of Methionine
from Media
As a variety of strain properties underlie band propagation speeds, we then aimed to
perturb these properties in each strain. Previous studies have characterized cells grown
without methionine and found cells have a reduced frequency of tumbling in chemotactic
response (143-145). Apart from cell motility, methionine, as a required amino acid for
growth, can also influence the growth rate. Synthesizing methionine has been shown to
be an energy-consuming process that delays growth (146). Given methionine is a
modulator of both motility behavior and growth, we removed methionine from the media
to determine how this perturbation would impact both single-cell properties and the
band speed of each strain.

38

Figure 4.3 Removal of Methionine from Migration Media Altered Both Strain Properties
and Band Speed.
(A) The band speeds of all Enterobacter strains shown in Fig. 4.1 are compared to the
band speeds when cells are grown on migration media without methionine. Band
speeds of each strain represented as mean ± SEM (n≥3 independent experiments). (B)
Single-cell motility properties and exponential growth rates also changed upon removal
of methionine from the media. Strain properties represented as mean ± SEM (n=3
independent measurements).
We conducted migration experiments as shown in Fig. 4.1A but without methionine
added to the migration media. The band speeds of Enterobacter strains in an initially
methionine-free environment are compared to the band speeds with methionine as
shown in Fig. 4.3A. The response to the removal of methionine was heterogeneous among
the seven wild isolates; some band speeds decreased to a variable extent while others
remained unchanged (Fig. 4.3A). We then assessed single-cell swimming behavior and
growth rates in the absence of methionine to better understand which of these properties
may be associated with the alteration of band speed (Fig. 4.3B). There is no universal

39

pattern of the effect of methionine on the run speed and proportion of swimming cells of
each strain. However, 6 out of 7 Enterobacter strains tumble less frequently in
environment without methionine, and growth is slower for all isolates in the absence of
methionine (Fig. 4.3B). Therefore, comparing Fig. 4.3A and 3B, the growth rate and
tumbling frequency might seem to be a positive contributor to the band speed as their
shifts are most similar.
Although band speed is negatively correlated with growth rate as shown in Fig. 4.2E, in
the absence of methionine, all growth rates decrease whereas band speeds also
decreased by variable amounts. Nevertheless, the shifts of other strain properties are not
monotonically associated with the shift of band speed.
4.4 Run Speed and Tumbling Frequency in Combination are Most Connected to
Band Speed
We then considered the band speeds of strains in environments with and without
methionine as response variables and the four strain properties as predictor variables. To
examine whether combinations of predictor variables were correlated with the response
variable, we applied multiple linear regression (MLR) to infer the regression coefficient of
each property. Since different properties have different units and magnitudes, we defined
the rescaled sensitivity as the regression coefficient of a property multiplied by the
average value of that property of all strains analyzed in conditions, both including and
excluding methionine.

40

Figure 4.4.1 Multiple Linear Regression Reveals Band Speed is Connected with Run
Speed and Tumbling Frequency.
(A) The rescaled sensitivity found from multiple linear regression is the regression
coefficient of the single-cell characteristic multiplied by the average value of that
characteristic of all strains. The results indicate run speed and tumbling frequency are
the dominant factors that influence the band speed. Error bars indicate rescaled
standard error. (B) The p-values for F statistic of all characteristics. The values are 0.019,
0.016, 0.762, and 0.929 for run speed, tumbling frequency, proportion of swimming
cells, and growth rate respectively.
Fig. 4.4.1A shows the rescaled sensitivities of run speed, tumbling frequency, proportion
of swimming cells, and growth rate. Only two parameters were significantly non-zero, run
speed and tumbling frequency (Fig. 4.4.1B). The p-value for each property was calculated
using a null hypothesis that the corresponding coefficient is equal to zero. Both run speed
and tumbling frequency were positively correlated with band speed and were nearly
equally predictive of the band speed.
Given the rescaled sensitivities and p-values of all properties, the run speed and tumbling
frequency both significantly contribute to the band speed to a similar extent. This
conjecture is supported by a linear combination of both properties with the coefficients
found in MLR to the band speed (Fig. A.3.4B). The proportion of swimming cells and the
growth rate, even in combination with other strain properties, were not predictive of the
band speed (Fig. A.3.4B). This analysis shows that the band speed is equally influenced by
two single-cell properties, run speed and tumbling frequency, and that the strain-to-strain

41

variability in both parameters modulates the collective motility of populations. Amongst
the 7 strains studied, similar band speeds were detected in strains with different
combinations of run speed and tumbling frequency, as shown in Fig. 4.4.2. Fig. 4.4.2 also
shows that band speed was similar for closely related strains, as measured by 16S rRNA
comparison.

Figure 4.4.2 Related Enterobacter Strains Have Distinct Combinations in Strain
Properties and Band Speeds.
A spectrum of strain properties underlies the band speed in nutrient-supplemented
semisolid media (Row 1: with methionine, Row 2: without methionine). Each strain’s
property has an associated Z-score from the mean value of that property across the 7
strains analyzed in this study. The red circle represents a Z-score of 0 (no deviation from
the mean), and each gray concentric circle is an increment of a Z-score of 1. The band
speed is the color of the plot. Below, the phylogenetic tree from 16S sequences are
plotted. E. coli K-12 MG1655 is provided as a reference outgroup. The scale bar
represents 0.01 changes per base pair.
4.5 Discussion
In addition, we examine the band speed within a set of closely related natural isolates of
the Enterobacter cloacae complex (Ecc). The band that propagates in semisolid media has
been previously examined experimentally and modeled in several species, notably E. coli
and Salmonella typhimurium (69, 77, 78, 147). Here for the first time we have described

42

the band speed in the Ecc. Unlike the collective behavior of some E. coli or Salmonella
typhimurium, this band does not break up into smaller “droplets” or “spots,” which are
regions of bacteria aggregation (76) (Fig. 4.1A). The band resembles the radiating
structure observed by Adler, for which he associated with propagating glucose or oxygen
gradients (77). These bands move at speeds of 2 mm/hr to 5 mm/hr, which is comparable
to strains in other migratory studies in semisolid agar (78) (Fig. 4.1B). This means the
population of cells perform a collective unidirectional motion at about 1 cell length per
second. We demonstrate that a strain with both high run speed and tumbling rate may
increase how fast strains move as a group, which may help to understand migration in
environments such as host tissue or soil (148-150).
Another novel report is our comparison of varying band speeds formed by closely-related
wild strains (Fig. 4.1C). As the traveling band is composed of a large number swimming
bacterial cells, the study of single-cell motility from a microscopic perspective is essential
for a better understanding of the band speed. Despite having high genetic similarity, the
differences in band speed across strains varied by more than a factor of 2 (Fig. 4.4.2).
These phenotype differences have previously been elucidated by genetic knockout
studies in a single strain (69, 88, 89), revealing that collective motility is a complex
phenotype influenced by many genes and microscopic properties of the strain. By
comparing variability of both band formation and single-cell level properties across
several closely-related wild strains, we sought to better understand how the band speed
is set by the behavior of individual cells.
Intrigued by the natural variability of band speed, we took an in-depth look at the
properties of the different Ecc strains. The strain properties we measured were the
average run speed, tumbling frequency, proportion of swimming cells, and exponential
growth rate. Runs, tumbles, and number of swimming cells are quantities that pertain to
single-cell motility, and we obtain these quantities from measuring individual cells in a
population. Upon comparison, no obvious correlation was found between the band speed
and any one strain property, suggesting that the band speed is a complex property and
dependent on multiple factors (Fig. 4.2B-E and A.3.4A). Multiple linear regression

43

revealed that a combination of both run speed and tumbling frequency is the most
significant predictor of the band speed (Fig. 4.4.1B). Here we focused on properties
previously shown to resolve single-cell motility differences between closely-related
strains (19, 36, 49). Other strain properties not measured here may strongly contribute
to collective behavior, such as the average tumbling angle, chemotactic adaptation rate,
and intracellular redox activity (62-67). Further studies are needed to connect the band
speed to additional single-cell properties to determine if additional strain properties are
needed to predict the band speed in other systems.
Previously, it was found that collective migration was proportional to tumbling rate,
which is partially consistent with our findings (69, 84). Our results emphasize that, for
complex behaviors such as band formation, analysis within a variable set of related cell
types may be necessary to resolve relationships between single-cell and collective
behaviors. High run speed and high tumbling rate may facilitate cells to successfully
“reverse-out” of and escape such dead-ends in gel matrices, allowing swimming cells to
collectively move at a higher rate (78, 84, 151). Tumbling frequency is also an essential
component of chemotaxis as shown by studies with E. coli (152, 153). In certain ranges,
higher basal tumbling frequency or run speed may allow cells to more efficiently rise
chemical gradients (86, 154, 155). It should be noted that, in previous proposed physical
models, growth rate is often positively associated with faster colony expansion (156-158).
Indeed, the exclusion of methionine attenuated growth rate for all strains while also
reducing the band speed of some strains (Fig. 4.3). Here, however, we show growth rate
is not a predictive indicator of band speed across the Ecc strains that we studied,
suggesting that relationships between single-cell motility characteristics and different
collective behaviors, such as swarm ring formation and colony expansion, are not
universal.
Connecting single-cell properties with collective behavior is a necessary stepping stone
for synthetic biology (159, 160). Wild strains that demonstrate complex behaviors, such
as the formation of a swarm band, are influenced by a combination of single-cell
properties. Some properties are more dominant in setting collective behaviors (83, 93).

44

In the Ecc strains characterized here, the combination of run speed and tumbling
frequency was sufficient to explain the overall band speed (Fig. 4.4.1). Although, as shown
in Fig. 4.4.2, some strains have evolved different combinations of tumbling frequency and
run speed to achieve the same band speed. In engineering collective behaviors of cellular
networks, it may be possible to take advantage of different combinations of properties to
achieve the same behavior, or it may be more efficient to build off of an existing
combination of properties found in the wild. Each property likely has consequences on
other cell behaviors, enabling simultaneous optimization of multiple phenotypes.
Although, in this context, the proportion of swimming cells did not impact the overall
band speed, introducing multiple phenotypic states into bacterial populations may be a
useful approach to engineer other collective properties (138, 159, 161, 162). Our results
highlight the importance of comparing the characteristics of similar strains to untangle
the connections between single-cell and collective behaviors. Environmental isolates are
a good natural source of such variability and should serve to deepen our understanding
of complex cellular phenotypes.
4.6 Materials and Methods
4.6.1 Migration Screening
Enterobacter strains used in this study are listed in Table. 1. Ecc1 was a member of a
collection of wild isolates in a previous study (163). To search for additional isolates that
can form similar migration patterns, freshwater samples were collected from lakes and
ponds in Los Angeles County. For isolation, samples were grown on HardyCHROM
TM
ECC
selection plates. Six of these colonies were selected and identified to form a swarm band.
After re-streaking the colonies on a fresh LB plate, the strains of interest were grown in
LB media overnight and stored as frozen glycerol stocks at -80°C. 16S rRNA sequencing
revealed the strain to be most closely related to members of the Enterobacter cloacae
complex (Table. 1).
For assessing each strain’s migration pattern, strains were inoculated from frozen glycerol
stocks and grown to saturation overnight in M9 minimal salts (BD) supplemented with

45

2mM MgSO 4, 0.1mM CaCl 2, and 0.25% glycerol as the carbon source, as in (164).
Incubation condition was 200 rpm orbital shaking at 37°C Celsius. The following day,
stationary phase cultures were diluted to an OD 600 of 0.2. 10µL of this culture (about 10
Z

cells) was inoculated on the migration medium at this density for each experiment.
4.6.2 Band Visualization
Strains migrated on 4-well Rectangular plates (Nunc; ThermoScientific) at 25°C. Each
well’s inner dimensions measured 80mm by 30mm, containing 6mL of migration media
in semisolid agar, whose thickness is about 2.5 mm after settling. The migration media
consisted of 0.26% agar, and M9 minimal salts (BD), 2mM MgSO 4, 0.1mM CaCl 2, 22mM
(0.4%) glucose, 3mM sodium succinate, and 20µg/mL (0.002%) each of the amino acids
histidine (0.13mM), methionine (0.13mM), threonine (0.17mM), and leucine (0.15mM)
as previously utilized in similar experiments (69). Components were excluded as noted.
The liquefied gel, after being poured, was allowed to set on the benchtop for 1 hour. Then,
at the lateral side of the major axis of the well, 10µL of bacteria culture at 0.2 OD 600 was
inoculated, following previous procedures (75-77). Plates were lidded and sealed on all
sides with parafilm to slow evaporation. To track the progress of the migration, each plate
was mounted right-side up inside an enclosed imaging apparatus which held 4 plates at a
time. The sole source of illumination were two white LED light fixture placed bilaterally
on the same level as the plates. To avoid image aberrations from the lid, the camera (HD
Pro C920; Logitech) imaged plates from the bottom. Time-lapse images over several days
were recorded (VideoVelocity3; CandyLabs).
Changes in the bacterial cell density were shown as whiter pixels due to the contrast
against a black background (Fig. 4.1A). The position of the band could be easily tracked
manually on ImageJ without further image processing. Coordinates of the band were
measured at the center of band. Speeds of the bands were obtained by applying linear
regression on the positions of the bands at 30 minute intervals and extracting the slope.
Slopes were calculated for positions between 1.5 cm to 6 cm from the inoculation point
to reduce boundary effects at the edge of the well.

46

4.6.3 Tracking Single-Cell Trajectories
In order to associate strain swimming properties at exponential phase to the band velocity
observations, videos of cells in liquid media in a microfluidic device were obtained and
analyzed for their trajectory features. Trajectories were not monitored during band
propagation due to difficulty in obtaining long, single-cell trajectories within the band.
Cells were grown overnight at 25°C in migration media described above without agar with
orbital shaking at 200 rpm and diluted the next day 100-fold in fresh migration media.
Cells were gently pipetted and not subject to vortexing in order to reduce flagella shearing.
Cells were harvested at early exponential phase (3-4 hrs) and diluted again with fresh
migration media to obtain tens of cells were field of view. The number of cells on screen
(about a 0.15 mm
2
area) was kept at about 50 cells to discourage cells from overlapping
each other. This culture was injected into a 20µm high microfluidic chamber in a C-Chip
(DHC-S02-2; INCYTO) and subsequently sealed with wax. The thin, sealed chamber was
used to prevent directional fluid drift and to restrict the trajectories in a quasi-2D plane
(89). Before imaging, cells were incubated in the channel for at least 5 minutes to adapt
to the fresh media. To avoid catching interaction of the swimming cells with the walls of
the device, cells in the device were imaged as far away as possible (10µm) from the upper
and lower walls of the chamber. Videos at 10 fps with a 40X Objective were taken for 5
minutes with an inverted phase-contrast microscope (Ti Eclipse; Nikon). At least 3 videos
were taken at different areas of the chamber. A rolling paraboloid was used to accentuate
the position of each cell by lowering the intensity of the background. Cell trajectories
were obtained using the ImageJ plugin TrackMate, which detects positions of cells using
a Gaussian profile fitter and subsequently forms links between spots that are proximal in
position (136).
4.6.4 Trajectory Feature Detection
Feature detection of runs and tumbles were performed following a previous study (135).
All trajectories shorter than 5 s were discarded. The percent of trajectories that were used
for analysis after filtering for each strain was 20% to 33%, and the length of trajectories

47

on average were 20 to 80 seconds long (Table. 3). The time interval 𝛥𝑡 of recorded
positions is 0.1 s.
A tumble was defined as previously described based on sudden changes in direction (135).
We calculated the angular change 𝛥𝜑 at time 𝑡 as the angle between two vectors around
𝑡 (𝑡−𝛥𝑡 to 𝑡 and 𝑡 to 𝑡+𝛥𝑡). We defined the time of local maximum angular change as
𝑡
U$(
and the times of two neighboring minima as 𝑡
-
and 𝑡
]
. If any angular change 𝛥𝜑
during 𝑡
]
−𝑡
-
satisfied

|𝛥𝜑|>𝛾a𝐷
c
(𝑡
]
−𝑡
-
), (Equation 4.1)

in which 𝛾 =5 and 𝐷
c
=0.1 𝑟𝑎𝑑
]
𝑠
h-
, the cell was identified as in turning state. Within
the time interval, a tumbling event at time 𝑡 was defined as when

𝜑(𝑡
U$(
)−𝜑(𝑡) ≤ 0.5𝛥𝜑 , (Equation 4.2)
where
𝛥𝜑 =𝑚𝑎𝑥[𝜑(𝑡
U$(
)−𝜑(𝑡
-
),𝜑(𝑡
U$(
)−𝜑(𝑡
]
)]. (Equation 4.3)

By this definition, a trajectory segment with a smoothly curving path would not have
tumbles associated with it.
Other studies report tumbling as either run time (152) or tumbling frequency (165). After
extracting these features from the trajectories in each video, distributions of each feature
type were compiled for each strain. The tumbling frequency was then defined as the
inverse of the average time length between two tumbling events. The run speed was
calculated as the average speed of trajectory segments longer than 0.5 s between two
successive tumbling events. The run time was calculated for all trajectory segments longer

48

than 0.5 s. In calculating the average and standard deviation of the run time, data was fit
to an exponential function to account for run times for run times than 0.5 s.
Swimming cells for each frame were counted by the number of cells in the frame with an
average trajectory speed of at least 0.32 µm/s. The proportion of swimming cells in a
frame was then calculated as the swimming cell number divided by the total number of
trajectories in that frame. The proportion of swimming cells as a strain property was the
average proportion of swimming cells per frame of the video.
4.6.5 Growth Curves
Cultures were grown in M9 media overnight, and the following day the cells in stationary
phase were diluted to an OD 600 of 0.01 in fresh M9 migration media. 200µL of each diluted
culture was distributed in triplicates for each nutrient condition into 96 well plate (Costar).
Edge wells were not used but rather were filled with water to prevent evaporation from
the center wells. OD 600 was read every 10 minutes at 25°C with 7 minutes of orbital
shaking (Tecan M200; Tecan Group Ltd.). Exponential growth rates for each strain were
obtained by considering an OD 600 between 0.25 and 0.7 (between x and y cells for each
strain), the range where the semilogarithmic plot of the growth curve was most linear.
That means at least 10 absorbance measurements were used to calculate the growth rate.
The experiment was repeated with the same settings for a total of 3 independent
replicates. Plate counts were performed to calibrate absorbance measurements using the
drop plate method (166).
4.6.6 Multiple linear regression
Multiple linear regression has been widely used as a general approach for a variety of
research problems (167-171). The model for multiple linear regression, given the band
speed as response variable and bacterial properties as predictor variables, is
𝐵𝑆 =𝛽
q
+𝛽
-
𝑅𝑆+𝛽
]
𝑇𝐹+𝛽
s
𝑃𝑆+𝛽
u
𝐺𝑅, (Equation 4.4)
where BS, RS, TF, PS, GR are band speed, run speed, tumbling frequency, proportion of
swimming cells, and growth rate respectively. 𝛽
-
, 𝛽
]
, 𝛽
s
, 𝛽
u
are regression coefficients of
predictor variables, and 𝛽
q
is the intercept.

49

The band speeds of all Enterobacter strains with and without methionine were analyzed,
and corresponding bacterial properties into the design matrix. The equation can be
written as
⎣
⎢
⎢
⎢
⎡
𝐵𝑆
-z
𝐵𝑆
-h
⋮
𝐵𝑆
|z
𝐵𝑆
|h
⎦
⎥
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎡
1
1
𝑅𝑆
-z
𝑇𝐹
-z
𝑃𝑆
-z
𝐺𝑅
-z
𝑅𝑆
-h
𝑇𝐹
-h
𝑃𝑆
-h
𝐺𝑅
-h
⋮
1
1
⋮ ⋮ ⋮ ⋮
𝑅𝑆
|z
𝑇𝐹
|z
𝑃𝑆
|z
𝐺𝑅
|z
𝑅𝑆
|h
𝑇𝐹
|h
𝑃𝑆
|h
𝐺𝑅
|h
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
𝛽
q
𝛽
-
𝛽
]
𝛽
s
𝛽
u
⎦
⎥
⎥
⎥
⎤
(Equation 4.5)
with 1 to 7 stand for Ecc1 to Ecc7, + stands for with methionine, and - stands for without
methionine. The regression coefficients and p-values were inferred using fitlm in
MATLAB (MathWorks, Natick, MA).
The rescaled sensitivity was defined as the regression coefficient multiplied by the
corresponding average measurement of all strains to make different properties
comparable. For example, the rescaled sensitivity of run speed is
𝛽
-
⋅𝑚𝑒𝑎𝑛(𝑅𝑆
-z
,𝑅𝑆
-h
,...,𝑅𝑆
|z
,𝑅𝑆
|h
) (Equation 4.6)
4.6.7 16S Tree Construction
For Ecc1 to Ecc6, genomic DNA was extracted using a DNeasy UltraClean Microbial Kit
(Qiagen) and sequenced via Illumina HiSeq 2500 (UPC Genome Core; USC). The short
reads were assembled by SPADES with a coverage depth of at least 100, and from the
resulting contigs the 16S sequence was recovered (172). For Ecc7, the 16S rRNA gene was
amplified using colony PCR with the 8F and 1492R primers (173) and was sent for
purification and Sanger sequencing (Laragen; Culver City). The 16S tree was constructed
using base pairs 93 through 1436 of the 16S rRNA reference sequence of E. coli K-12
MG1655 on the online platform phylogeny.fr (174) and re-visualized using MATLAB’s
Bioinformatics Toolbox. These strains were assigned to the Enterobacter cloacae complex
by their similarity to Enterobacter strains using the EZBioCloud online platform (175)
(Table. 2). Ecc1 and Ecc4 seem to have identical 16S rRNA sequences over the analyzed
region, although comparison of other genomic regions revealed these strains are not
genetically identical.

50

4.6.8 Statistical Methods
To detect a monotonic relationship between two strain properties, a Spearman’s rho
rank coefficient was computed (137).

51

Chapter 5: Critical transition in collective behavior for a two-
species microbial community
This work is currently under review at Biophysical Journal. This work was done in
collaboration with Sean Lim.
5.1 Co-migration of Enterobacter strains in semisolid medium

Figure 5.1.1 Enterobacter strains form traveling band with different speeds in
semisolid medium.
(A) Bacterial band formed by Enterobacter emerged from the initial inoculation point,
and traveled along rectangular petri dish filled with soft agar. (B) Two Enterobacter
strains (EcSlow and EcFast) traveled at different but consistent speeds. (C) The bacterial
band of a 1:1 mixture of the two stains experienced a switching from low speed to high
speed around 6 hour after the band formed. Red lines are best-fit lines through the
origin. Arrow and circle indicate the speed switch. Error bar indicates standard error of
three replicates on different days.

52

We isolated two Enterobacter strains from freshwater sources that both formed bacterial
band on soft agar plate (see Materials and Methods). 10 µl of cell culture was inoculated
on one side of a rectangular petri dish (30 mm by 80 mm). Starting from a stationary
colony, bacterial cells concentrate into a traveling band radiating from the colony after
12-18 hours of inoculation. The shape changes from a ring to a near-linear band in the
rectangular petri dish. The swarm band, composed of high-density cells, is visible to naked
eye. Using a webcam (Logitech, C920), we were able to track the band every 30 minutes
until it reached the other side of the well. Fig. 5.1.1A shows a time lapse of bacterial band
formed by one of the Enterobacter strain at room temperature in the rectangular petri
dish filled with 0.26% semisolid agar.
The center position of the band, representing the band position, was manually
determined whenever the band was distinctly visible. A linear fit through the origin of the
band position gave the band speed. We examined the two Enterobacter strains, EcSlow
and EcFast, formed bands with distinctly different speeds as shown in Fig. 5.1.1B. EcSlow
and EcFast were fluorescently labeled with YFP and RFP. Replicate experiments on
different days implied reproducible and constant propagation rate. The average band
speeds we observed were 2.4 ± 0.6 mm/h and 5.2 ± 1.4 mm/h for EcSlow and EcFast
respectively.
As the slowest and fastest strains we isolated, we were interested in the co-migration of
EcSlow and EcFast. Similar to the monoculture experiment, a 1:1 mixture of EcSlow and
EcFast was inoculated onto the rectangular petri dish filled with soft agar. Band position
over time of the mixed culture is shown in Fig. 5.1.1C. Interestingly, the bacterial band
initially propagated at a constant speed, which is similar to the band speed of EcSlow, up
to 6 hours. Afterwards, the band suddenly accelerated, and remained at a constant speed
as of EcFast until it reached the other side of the well. The “kink”, indicated by circle and
arrow in Fig. 5.1.1C, is defined as when the instantaneous band speed is 20% larger than
the band speed of EcSlow. The speed switch we observed suggests that the co-migration
of two Enterobacter strains in semisolid medium is not naively the average of both strains,
nor dominated by either one.

53

Figure 5.1.2 Influence of composition of the original mixture on the speed switch.
(A) Two experiments starting with different ratios of EcSlow and EcFast were conducted.
The speed switch was observed sequentially, depending on the ratio of the original
mixture. Arrows and circles indicate when the speed switches happened. (B) The
bacterial band traveled at a constant speed as of EcSlow in the beginning, and started
speeding up until it reached the speed of EcFast. Error bar indicates standard error of
three replicates.
To verify the consistency of speed switch, we ran the experiments with two more
different mixtures of EcSlow and EcFast. 3:1 and 1:3 mixtures of EcSlow and EcFast were
inoculated onto the rectangular plate. Fig. 5.1.2A shows the displacement of the band of
3:1, 1:3, and 1:1 mixtures (same as in Fig. 5.1.1C) over time. Initially, the band speed was
quite consistent and similar to the band speed of EcSlow regardless of the composition as
shown in Fig. 5.1.2B. After 4 to 8 hours, the bacterial bands started gradually speeding up
until they reached the speed of EcFast. The acceleration process took about 4 hours.
Moreover, the results shown in Fig. 5.1.2 indicate the speed switch occurred after 4.5, 6,
and 9.5 hours for 1:3, 1:1, and 3:1 mixtures respectively. The switch was postponed as
more EcSlow cells were added to the initial mixture, suggesting that transition might
dependent on the composition of the migrating microbial community. As the bacterial

54

band propagates, more and more EcFast cells comprise the band, eventually triggering
the speed switch. In order to examine if the composition of the band changes over time,
we repeated the experiment in a 3D-printed device that can be used for microscopy.
5.2 Tracking bacterial band under the microscope

Figure 5.2 Tracking bacterial band in 3D-printed device under the microscope.
(A) The design of the 3D-printed device for microscopy. (B) Fluorescence microscopy
reveals the bacterial band as a brighter region compared to the background. (C) The
bright region also shows higher cell density. (D) The bacterial bands in the 3D-printed
device travel at similar speeds as in the rectangular petri dish. Red lines are best-fit lines
through the origin. Error bar indicates standard error of three replicates.
To probe the composition of traveling band under the microscope, we designed a 3D-
printed holder with a cover slip attached to the bottom as shown in Fig. 5.2A. Since the

55

device is smaller than the rectangular plate, we reduced the amount of agar added to the
device to ensure equal thickness as in the big plate (see Materials and Methods). 1 µl of
cell culture was inoculated onto the agar on one side of the channel. It took about 24
hours for the bacterial band to emerge at room temperature. After the formation of the
band, the device was moved to the microscope to take fluorescent images using a 100x
objective every 30 minutes. We used the microscope to scan a 3.58 mm by 0.15 mm area
across the center of the band. Due to higher cell density, the bacterial band appeared to
be a bright region as shown in Fig. 5.2B. EcSlow had a narrower and sharp band, while
EcFast had a wider and shallow band.
Using particle counting in ImageJ, we obtained the cell distribution along the scanned
area. The frequency of cells shown in Fig. 5.2C, extracted from the same fluorescent
images in Fig. 5.2B, displays a similar pattern as the fluorescence intensity. The position
of the band was determined by locating the bright region, calculating the cumulative
frequency of 3 successive bins, and finding the maxima (see Materials and Methods).
Interestingly, EcFast cells tend to congregate in front of the band, while EcSlow cells
prefer the space behind the band. This might be due to the distinct optimal concentration
of chemoattractant for the two strains. Fig. 5.2D shows the displacement over time of
traveling band in the device for EcSlow and EcFast. The band speeds for EcSlow and EcFast
were 2.3 ± 0.4 mm/h and 4.9 ± 0.1 mm/h respectively, indicating very similar propagation
dynamics as in the larger rectangular plate.
5.3 Fluorescence microscopy reveals the composition of the migrating band

56

Figure 5.3.1 Composition of the dual-strain migrating band formed by an original 1:1
mixture of EcSlow and EcFast.
(A) Fluorescence microscopy shows temporal composition of the traveling bacterial
band. (B) shows the band position over time of an original 1:1 mixture of EcSlow and
EcFast. Arrow and circle indicate the speed switch. (C) Composition of the mixture
changes (D) shows a nonlinear relationship between the band speed and the fraction of
EcFast cells composing the band. Error bar indicates standard error of three replicates.
1:1 mixture of EcSlow and EcFast was inoculated into the device to inspect the temporal
composition of the dual-strain migrating band. Using ImageJ, we counted the cell number

57

of the two strains separately. The traveling band was located in a similar way as described
above, based on the sum of EcSlow and EcFast cells. Fig. 5.3.1A shows sample fluorescent
images within the band at three time points, revealing increasing and decreasing number
of cells of EcFast and EcSlow as the band propagated (see Fig. A.4.4 for details of cell
distribution under the microscope). After 4 hours, the speed switch was observed in the
device for the 1:1 mixture as shown in Fig. 5.3.1B.
A close investigation of the cell number within the band is shown in Fig. 5.3.1C. Although
the original mixture contained equal amounts of EcSlow and EcFast, more than 80% cells
within the initial band were EcSlow. The composition slowly changed in the first a few
hours as EcFast cells became more and more. After about 3 hours, number of EcFast cells
rapidly increased and started dominating the band. The composition eventually ended up
with almost no EcSlow cells after 6 hours. The relationship between the band speed and
fraction of EcFast cells is shown in Fig. 5.3.1D. The band speed went all the way from the
speed of EcSlow to EcFast. Unexpectedly, the relationship seemed to be nonlinear. As the
fraction of EcFast cells changed from 15% to 64%, the band speed only increased by 1.1
mm/h. Then the band speed increased from 2.9 mm/h to 4.3 mm/h when the fraction
changed from 64% to 92%.

58

Figure 5.3.2 Relationship between the band speed and composition reveals a critical
fraction for the timing of speed switch.
(A) The band position over time for mixtures of different ratios of EcSlow and EcFast.
Arrow and circle indicate the speed switch. (B) The speed switch starts to happen only
after the fraction of EcFast cells composing the migrating band is above 65%.
Similarly, we ran the experiments with 3:1 and 1:3 mixtures of EcSlow and EcFast. The
speed switch was observed 2.5, 4, and 5.5 hours after the band formed for 1:3, 1:1, and
3:1 mixtures respectively as shown in Fig. 5.3.2A. The timing of speed switch was deferred
as fraction of EcFast cells increased in the original mixture.
The relationship between the band speed and fraction of EcFast cells combining three
ratios is shown in Fig. 5.3.2B. The initial fraction of EcFast cells within the band varied
from 5.8% to 34.7% depending on the ratio of the mixture. All 3 ratios showed consistent
pattern that the dual-strain band speed was initially quite constant and close to the band
speed of EcFast even though the band was composed of more than 50% EcFast cells. After

59

EcFast composed about 60% of the traveling band, the band speed started increasing and
approaching the band speed of EcFast. The speed switch occurred at 67.7%, 65.2%, and
65.2% for 3:1, 1:1, and 1:3 mixtures respectively. 65.7% of EcFast cells, as the average,
was the critical fraction for the dual-strain band to start transforming into the “high-speed”
mode. The critical point implies a transition between two states of the dual-strain
migrating community. EcSlow has advantage over EcFast in the early stage in terms of the
composition and migration speed. As the band propagates, EcFast has to be the majority
of the community to accelerate the migration.
5.4 Simulations reproduce the speed switch

Figure 5.4 Simulation results of the dual-strain migration in soft agar.
(A) The simulated distribution of cells 20h, 24h, and 28h after inoculation. Initial
inoculation contains 25% EcFast cells. (B) Simulated band position over time starting
with low, medium, and high fraction of EcFast cells, corresponding to experimental
bands with ratios of 25%, 50%, and 75% EcFast within the initial inoculation respectively.

60

Circles indicate the speed switch. (C) shows the relationship between the band speed
and fraction of EcFast cells, corresponding to the same simulations in (B). (D) The band
speed has a negative relationship with the concentration of glucose at the band location.
(E) The concentration of glucose at the band location is nonlinearly related to the
fraction of EcFast cells within the band. The arrow indicates the kink.
Mathematical modeling has been widely used for simulating traveling band of bacteria in
many studies (69, 78, 82, 156-158, 165, 176). Considering the complexity of the cell-cell
and cell-environment interactions, it is a challenge to explain the observed two-state
transition from biological intuition. Hence, we performed a simulation with minimum
assumptions based on a Keller-Segel kind model (see Materials and Methods) to
reproduce the migration of the dual-strain band.
After inoculation at one end of the channel, the cells gradually accumulated and starting
occupying the farther area. The traveling band usually formed 18 h after the inoculation,
consistent with the experiment results. The simulation was first performed when EcSlow
and EcFast propagated by themselves, resulting in band speeds of 2.5 mm/h and 4.2
mm/h for EcSlow and EcFast respectively (see Fig. A.4.5). Afterwards, we performed the
simulations with 25% EcFast cells, which is the same as ratio 3:1 in the experiment, in the
original mixed culture. Fig. 5.4A shows the simulated propagation and composition of the
bacterial band. After 20 h of inoculation, the early band appeared with EcSlow constituted
the majority of the band. A few hours later, the band comprised of EcFast cells, migrating
towards the same direction. Eventually, EcSlow cells were replaced with EcFast cells
within the band, just as the microscopic data revealed (Fig. 5.3.1A and C).
In addition, we ran the simulations starting with 50% and 75% EcFast cells in the initial
inoculation, as in the experiments. The displacement of the band over time of these 3
initial conditions (low, medium, and high, referring to 25%, 50%, and 75%) is shown in Fig.
5.4B. The simulations reproduced the speed two-state transition from low speed to high
speed, where speed switch marked by circles with the same 120% criteria described
above. The timing of speed switch was related to the initial composition of the cell culture
as the experiment results implied (Fig. 5.1.2A and Fig. 5.3.2A). The non-linear relationship
between the band speed and fraction of EcFast shown in Fig. 5.4B is highly consistent with

61

our experiments (Fig. 5.3.2B). The critical point was 67.1% EcFast, on the average of all 3
simulations, to trigger the speed switch. Despite bacterial chemotaxis and co-migration
are complex systems and even harder to interpret when combined, our numerical
simulation has good agreement with the experimental data.
The simulations also provide us a hint of the explanation of the critical transition. The
essential reason of the traveling bacterial band is the shift of chemotactic gradient.
Bacterial cells sense the gradient of glucose, and concentrate in the “comfort zone”. The
cell aggregation rapidly consume the glucose at the band location, reconstruct the
chemotactic gradient, and further follow the shifted comfort zone. Our simulation results
imply the band speed is highly dependent on the concentration of glucose at the band
location as shown in Fig. 5.4D (also see Fig. A.4.5A). When bacterial cells gather in low-
chemoattractant area, the band tends to move faster, and vice versa. Unlike the band
formed by monoculture (Fig. A.4.5), the concentration at the band location significantly
changes over time for the mixed bacterial community. The simulation shows a nonlinear
relationship between the concentration of glucose and fraction of EcFast cells at the band
location (Fig. 4.11E). An accelerating change of comfort zone is observed when EcFast
reaches about 75% of the composition. In summary, this unexpected relationship might
be an explanation of the speed switch. The hybrid collective behavior of chemotactic
strains has more complicated dynamics than we expected.
5.5 Discussion
Collective behavior, as a widespread phenomenon in the nature, also exists in microbial
world. Many studies have reported certain chemotactic bacterial species can concentrate
into traveling band that spreads outwards from the inoculation point (75-77), which is an
example of a collective behavior arising from intercellular interaction. Isolating closely
related bacterial strains and fluorescently labeling each strain enabled us to examine the
hybrid collective behavior of a mixed population. As individual strains, EcSlow migrates at
half of the speed of EcFast in rectangular plate filled with soft agar. However, the mixed
culture of EcSlow and EcFast shows an interesting transition from low speed to high speed
during the migration. The two-state transition we observed emphasizes the complexity in

62

group behavior of microbial environments with diverse composition. The hybrid collective
behavior of microorganisms may not be dominated by a regnant species, nor represented
by the average behavior of community members.
Co-migration of multiple strains or species of bacteria has been observed in other systems.
For example Paenibacillus vortex can swarm into a toxic environment by carrying
antibiotic-degrading bacteria (177). Other bacterial species are able to ride on other
bacteria to spread in environments that are inaccessible in absence of this cooperation
(178, 179). Pseudomonas and Pedobacter co-migrate on hard agar only when mixed
together (180). Facilitated dispersal not only happens between bacterial species but also
between bacteria and fungus. The nonmotile fungus Aspergillus fumigatus utilizes the
swarming bacterium Paenibacillus vortex to disperse (181). The interaction within co-
migration can also be detrimental. Mixing Pseudomonas aeruginosa and its quorum-
sensing mutants may result in loss of swarming motility (182). Here we have
demonstrated yet another cooperative migration that occurs in the microbial world. By
examine how co-migration scales with community composition we revealed a critical
transition as a function of cell ratio.
The concept of emergent properties of bacterial networks is relevant in many contexts:
such as community composition in metabolic networks (183), bacterial communication
networks (184), biofilm development (185), and human health (186, 187). Predicting
these collective behaviors and their consequences will require the both identification of
control parameters and the determination of how these behaviors scale with such
parameters. Non-linear scaling, as observed here, can lead to critical behavior (188, 189).
Some systems might take advantage of critical behavior to stabilize the functional state
of such networks in uncertain and dynamic conditions (190-192). Identifying the scaling
of coordinated behaviors by parameters such as community composition will be an
essential step in predicting, controlling, and designing the emergent behaviors of diverse
microbial networks.

63

5.6 Materials and Methods
5.6.1 Strains and sample preparation
EcSlow and EcFast were originally isolated from Caltech Turtle Pond and Huntington
Gardens in Pasadena, CA respectively. To label the two strains with fluorescence, plasmid
pZE25O1+11-YFP (193) and pZE25+11-mCherry (see Fig. A.4.1) were then transformed
into EcSlow and EcFast respectively using electroporation. The strains were inoculated
from glycerol frozen stocks and grown overnight at 37°C (200 rpm) in 1x M9 minimal salts
medium (BD), supplemented with 2 mM MgSO 4, 0.1 mM CaCl 2, and 0.25% glycerol (164).
The overnight cultures were diluted to OD600 of 0.2 on the following day. For mixed
cultures, the diluted EcSlow and EcFast were mixed at appropriate ratios. The semisolid
medium for cell migration was made of 1x M9 minimal salts (BD) and 0.26% agar. After
autoclaved and cooled down to about 55°C, 0.1 mM CaCl 2, 2 mM MgSO 4, 3 mM sodium
succinate, 22 mM glucose, and 20 µg/mL each of the amino acids histidine (0.13 mM),
methionine (0.13 mM), threonine (0.17 mM), and leucine (0.15 mM) were added to the
soft agar (69). 1 µL/mL of 50 µg/mL kanamycin was also added to maintain plasmids.
5.6.2 Band formation and imaging in rectangular plate
A 4-well rectangular plate (Nunc Cell-Culture Treated Multidishes, Thermo Scientific) was
used for strain migration at room temperature. 6 mL soft agar was added to each well
with 24 cm
2
culture area (inner dimensions measured 30 mm by 80 mm), giving an
approximate 2.5 mm thickness. The plate containing liquefied soft agar was left at room
temperature for 1h to allow for solidifying. Afterwards, 10 µL of either monoculture or
mixture of EcSlow and EcFast at 0.2 OD600 was inoculated on one end of each well (75-
77), located at the center and about 1 cm away from the wall. The plate with lid was
sealed with parafilm to reduce evaporation. To track the migration, the plate was
mounted in a self-made enclosed imaging apparatus with two white LED light fixture
placed bilaterally on the same level as the plates, providing adequate illumination. A
webcam (Logitech, C920) was set up on the bottom of the apparatus to take time-lapse
images every 10 minutes, controlled by software (VideoVelocity3, CandyLabs). The
position of the band was determined as the center of the band, and manually tracked

64

using ImageJ. The band speed was calculated as the slope of 3 positions over 1 hour at
30-minute intervals.
5.6.3 Microscopy in 3D-printed device and data processing
A 3D-printed holder made of ABS was used to make the device for probing the
composition of the bacterial band. The inner dimensions of the holder were 15 mm by 45
mm. A 22 mm by 60 mm micro cover glass (VWR) was glued onto the bottom of the holder
using optical adhesive (Optical Adhesive 81, Norland) to allow for microscopy at high
magnification. 1.47 ml of soft agar was added into the device, giving a thickness about 2.2
mm. After 40 minutes for solidifying, 1 µL of either monoculture or mixture of EcSlow and
EcFast at 0.2 OD600 was inoculated on the end of the well, about 0.5 cm away from the
wall. Another cover glass was placed on top of the holder and sealed with vacuum grease
(High Vacuum Grease, Dow Corning) to reduce evaporation. The device was placed at
room temperature until the band formed.
A visible bacterial band usually formed after 24 h of inoculation. The device was then
moved onto the microscope stage at room temperature. Images were acquired by using
Nikon Eclipse Ti-E microscope with a sCMOS Camera (Zyla 5.5 sCMOS, Andor). The
bacterial band was first roughly located by eye, allowing the objective (CFI Plan Apo
Lambda 100x Oil, Nikon) to move close to the center of the band and focus on the bottom
of the agar. A large image, stitching of 20 individual fluorescent images (Nikon C-FL FITC
HYQ and C-FL Y-2E filters for EcSlow and EcFast respectively), was then taken across the
center of the band using the microscope software (NIS-Elements Advanced Research,
Nikon). The exposure time for fluorescent images was 30ms. The band was usually the
brightest region in the large image due to higher cell density and faster speed of cells.
The fluorescent image was first post processed using Adjust Brightness/Contrast and
Subtract Background in ImageJ. Applying Analyze Particles in ImageJ, we obtained the
distribution of cells along the axis of propagation (Fig. 5.2C). Each bin in Fig. 5.2C
corresponds to an individual image that comprises the large image. The cell frequency of
each image was calculated as the mean cell number (normalized by the total number of

65

cells in the region of interest) of 3 neighboring images centered about the current one.
The position of the band was determined by finding the bright region in the large image
and the coordinate of individual image with the highest mean value. For mixed cultures,
the distribution of cells was calculated based on the sum of EcSlow and EcFast cells. The
fraction of the strains of any individual image was also averaged from 3 neighboring
images, centering about the current image, to reduce the errors.
5.6.4 Mathematical model
We ran the simulation based on an extended Keller-Segel model (94, 194, 195) that
considers the diffusions of bacterial cells and glucose, which is both energy source and
attractant for the bacteria. Studies have shown that non-motile cells play a key role in
governing collective behavior (140, 142). In our simulation, the bacterial cells are either
swimmers (motile cells) or sitters (non-motile cells). The two cell types can convert into
each other with the ratio maintains equilibrium. The cell density 𝑁
+VU
and 𝑁
V"
, and
concentration of glucose are all functions of position and time. The model contains the
following nonlinear partial differential equations:

5
6
"
=𝐷
+VU
∇
]
𝑁
+VU
+𝑝
+VU
𝑟
c#+"
𝑁
+VU
−∇𝜒

+∇𝜒
W
(Equation 4.7)
5
7
"
=(1−𝑝
+VU
)𝑟
c#+"
𝑁
V"
(Equation 4.8)

"
=𝐷
%#
∇
]
𝐺−𝑟
#WU
𝑁. (Equation 4.9)
Here 𝐷
+VU
and 𝐷
%#
are the diffusion coefficients of bacterial cells and glucose,
𝑟
c#+"
and 𝑟
#WU
are the effective growth rates of cells and consumption rate of
glucose, 𝜒

and 𝜒
W
are the bacteria flux determined by chemotaxis and cell density, and
𝑝
+VU
is the proportion of swimmers.
The consumption rate of glucose 𝑟
#WU
in Eq. 4.9 is written as
𝑟
#WU
=𝑘

z
, (Equation 4.10)

66

where 𝑘

and 𝑘

=0.145 M are consumption rate constant and consumption saturation
constant respectively, and 𝑁 is the total number of cells
𝑁 =𝑁
+VU
+𝑁
V"
. (Equation 4.11)
Eq. 4.10 is based on the assumptions that the intensity of the glucose consumption (the
first term in Eq. 4.9) is proportional to 𝐺 when 𝐺 is small, while proportional to 𝑁 when
𝐺 is large, as described in (196).
We adopted the functional form of growth rate described in (197), assuming that the
growth rate is not sensitive to the concentration of glucose 𝐺 and cell density 𝑁 except
when 𝐺 is extremely low (198) or 𝑁 is extremely high (199). Hence, the growth rate is
written in the form as
𝑟
c#+"
=𝑘
5
(1−
5

), (Equation 4.12)
where 𝑘
5
is the intrinsic growth rate, and 𝐶

=4 x 10
12
M
-1
is the carrying capacity of the
glucose.
Bacterial cells sense spatial chemical gradient to bias their migration towards area with
higher concentration of attractant. Due to the limited number of receptors on the
membrane, the chemotactic strength saturates when the concentration or gradient
exceeds the sensing range of bacterial cells (200-202). Considering the above assumptions
and following (203), we write 𝜒

as
𝜒

=

5
6
(-z

)

∇𝐺, (Equation 4.13)
where 𝛽

= 1 x 10
4
M
-1
is the chemotactic saturation parameter, and 𝐴

= 1 x 10
4
mm
2
min
-
1
M
-1
is the proportionality constant. Eq. 4.13 gives a non-linear relationship between the
chemotactic strength and concentration of glucose.
Besides the attraction of higher concentration of glucose, bacterial cells also repel areas
with extremely high cell density due to the lack of oxygen (aerotaxis), collision between
cells, and potential toxic metabolic products. Therefore, we added the last term in Eq. 4.7

67

to simulate the high-density repellent of cells. The density flux term 𝜒
W
is in the same
form as of 𝜒

except that 𝐺 in Eq. 4.13 is replaced with 𝑁:
𝜒
W
=

5
6
(-z

5)

∇𝑁, (Equation 4.14)
where 𝛽
W
= 1 x 10
-5
is the density saturation parameter, 𝐴
W
= 1.6 x 10
-6
mm min
-1
and 8 x
10
-6
mm min
-1
for EcSlow and EcFast respectively is the proportionality constant.
We ran the numerical simulation in one-dimensional system with no-flux boundary
conditions using MATLAB. The space step and time step are 50 µm and 0.01 min
respectively. The initial conditions are 0.022 M glucose, 1 mm starting inoculation point,
and 8 x 10
3
cells mL
-1
within the inoculation point. For influence of model parameters on
the band speed, see Fig. A.4.2. Other model parameters used in the simulation are shown
in Table. 1.
Parameter Value Source
𝐷
+VU
4 x 10
-3
mm
2
min
-1
(204)
𝐷
%#
4 x 10
-2
mm
2
min
-1
(205)
𝑘

6.9 x 10
-14
M min
-1
(206)
𝑝
+VU
(EcSlow) 0.15 (207)
𝑝
+VU
(EcFast) 0.21 (207)
𝑘
5
(EcSlow) 1/52.4 min
-1
SI Fig. A.4.3
𝑘
5
(EcFast) 1/58.2 min
-1
SI Fig. A.4.3
Table 1 Parameter values used in simulations.

68

Chapter 6: Conclusion
In conclusion, my research focuses on understanding microbial cellular networks, and
addressing fundamental questions in predicting activity of microbial systems. Are
pairwise interactions sufficient to predict activity of microbial communities? How do cell-
cell interactions scale down to microscale level? How do single-cell properties set the
collective behavior of a group? What will be the hybrid collective behavior of mixed
systems? During my PhD studies, the important questions I answered include:
6.1 The contribution of high-order interactions to a microbial community
We examine the ability of a modified general Lotka-Volterra model with cell-cell
interaction coefficients to predict the overall metabolic rate of a well-mixed microbial
community comprised of four heterotrophic natural isolates, experimentally quantifying
the strengths of two, three, and four-species interactions. Within this community,
interactions between any pair of microbial species were positive, while higher-order
interactions, between 3 or more microbial species, slightly modulated community
metabolism. For this simple community, the metabolic rate can be well predicted only
with taking into account pairwise interactions, which is supported by subsequent studies
from other groups (58, 208). Simulations using the experimentally determined interaction
parameters revealed that spatial heterogeneity in the distribution of cells increased the
importance of multispecies interactions in dictating function at both the local and global
scales. Our simulation indicates some microcolonies might be key drivers that promote
overall activity of microbial communities that contain high-order interactions. The results
point for new experimental methods to identify such species combinations in real systems.
6.2 How single-cell interactions relate to population-level interactions
Using a microwell device, we analyzed cell growth within hundreds of replicate microbial
communities consisting of two species and small population sizes. The wells of the devices
were inoculated with a coculture of Escherichia coli and Enterobacter cloacae. Each
species expressed a unique fluorescent protein enabling simultaneously tracking of cell
number for each species over time. Growth dynamics within the device were consistent

69

with bulk measurements. The device enabled monitoring of replicate, isolated coculture
populations at high magnification, revealing both the growth interaction between the two
species and the variability of such cell-cell interactions within small groups of cells. The
device enables new experimental measurements of the heterogeneity of interactions
within small, multispecies populations of bacteria. The weak correlation in doubling times
suggests a potential mechanism that cells adjust interactions depending on the activity of
neighbors. Our device also inspires future studies to examine mechanisms by which the
variability of single-cell activity is modulated by local cell interactions.
6.3 How single-cell properties set the collective behavior of bacteria
We isolated 7 wild strains of the Enterobacter cloacae complex capable of forming this
band and found its propagation speed can vary 2.5 fold across strains. To connect such
variability in collective motility to strain properties, each strain’s single-cell motility and
exponential growth rates were measured. The band speed did not correlate with any
individual strain property; however, a multilinear analysis revealed that the band speed
was set by a combination of the run speed and tumbling frequency. Comparison of
variability in closely related wild isolates has the potential to reveal how changes in single-
cell properties influence the collective behavior of populations. Connecting single-cell
properties and collective behaviors is the key for synthetic biology. Our findings suggest
that comparison of variability in closely related wild isolates has the potential to reveal
how changes in single-cell properties influence the collective behavior of populations.
6.4 The mode of emergent behavior of mixed systems
To probe the hybrid collective behavior of a mixed system, we study the collective
behavior of two wild type Enterobacter strains, EcSlow and EcFast, in semisolid medium.
As individual strains, bacterial band of EcFast travels twice as fast as EcSlow on soft agar
plate. The mixture of the EcFast and EcSlow, however, experiences an abrupt transition
from low speed to high speed during the migration. Using fluorescence microscopy, we
track and obtain the temporal composition of the traveling band composed of EcSlow and
EcFast. The results revel that the fraction of EcFast increases as the bacterial band

70

propagates. Interestingly, the band speed barely changes even EcFast cells comprise 60%
of the migrating community. A critical point at 65% of EcFast is observed to trigger the
occurrence of the speed switch. Moreover, our numerical simulation reproduces the two-
state transition, and shows high consistency with experimental data. The two-state
transition in our dual-strain system suggests a possible mode of hybrid collective behavior
of mixed populations. Some systems might take advantage of non-linear scaling and
critical behavior to stabilize the functional state of such networks in uncertain and
dynamic conditions. Identifying the scaling of coordinated behaviors by parameters such
as community composition will be an essential step in predicting, controlling, and
designing the emergent behaviors of diverse microbial networks.
6.5 Future directions
Although we show that pairwise interactions are sufficient to predict the overall
metabolic rate of multispecies community as other studies show (58, 208), high-order
interactions are still intriguing in the respect of controlling and designing synthetic
communities. Utilizing identified regulatory pathways that potentially affect interaction
between two others might be the next step to find high-order interactions in multispecies
community.
Besides the variety of single-cell interaction, the monotonic relationship between the
doubling times of E. coli and E. cloacae at single-cell level we observe suggests that
interspecies interaction might be tunable and incorporate feedback from the local
community. The mechanism of this regulation may open up new areas in cell-cell
interaction. Perhaps new experimental tool and theory are required.
Moreover, the hybrid collective behavior we study only involve two species, which is
much simpler than what happens in the real world. Even though our work sheds lights on
collective behavior of mixed systems, the collective behavior in non-trivial systems are
less predictable, and might display interesting critical behaviors. Studying collective
behavior in systems that are more complex will greatly deepen our understanding of
cellular networks.

71

Appendix
A.1.1 Cell Isolation and Growth
The four strains we used in our experiment were from isolated from freshwater
environments. Strains Av and Ah were isolated from the top 5 cm of the lake in MacArthur
Park in Los Angeles, CA (34.059°N, 118.278°W). Ec was isolated from a freshwater pond
on the campus of the California Institute of Technology in Pasadena, CA (34.138° N
118.125° W), and was indistinguishable from the common lab strain Escherichia coli K-12
by 16S rRNA sequencing. 16s rRNA sequencing results were obtained by Sanger
sequencing of PCR products made using primers 8F (AGAGTTTGATCCTGGCTCAG) and
1492R (CGGTTACCTTGTTACGACTT). Species identifications were made using the RDP
database found at http://rdp.cme.msu.edu/. So is strain Shewanella oneidensis MR-1
obtained from the lab of Ken Nealson, originally isolated from Oneida Lake in New York
State. Strains were preserved in 50% glycerol stock solutions at -80
o
C.

Figure A.1.1 Optical densities (OD 600) of cell cultures growing in 10% LB.

72

Dash line shows linear fit to growth curve during exponential growth. Ec, Av, and Ah
were grown at 37 °C in 10% LB media. So was grown at 30 °C in 10% LB media.
A.1.2 Measuring Interactions
For two-species combinations, we measured different ratios from 1:7 to 7:1. For three-
species combinations, we measured 6:1:1, 1:6:1, 1:1:6, 4:2:2, 2:4:2, 2:2:4, 2:3:3, 3:2:3,
3:3:2. For four-species combinations, we measured 1:2:2:3, 1:2:3:2, 1:3:2:2, 2:1:2:3,
2:1:3:2, 3:1:2:2, 2:2:1:3, 2:3:1:2, 3:2:1:2, 2:2:3:1, 2:3:2:1, 3:2:2:1, 2:2:2:2, 1:1:1:5, 1:1:5:1,
1:5:1:1, 5:1:1:1. Species by themselves have also been measured to obtain the original
metabolic rates. Every combination had been repeated at least three times.
The absorbance and fluorescence were tracked for one hour in the plate reader. The
slope of the first 10 minutes of fluorescence versus time is used to calculate the metabolic
rate at t=0. The measurements were adjusted to the single-species control, thus taking
into account the change in cell number relative to the single-species measurement.
Figure A.1.2 shows that for the range of cell densities used in the experiments, the
metabolic rate, as measured using the AlamarBlue assay, is linearly proportional to the
number of cells for each of the four species in the community. All cultures were grown
to an optical density at 600 nm of approximately 0.2 for all experiments.

Figure A.1.2 Different volumes of cell cultures from 10 to 80 μL were diluted to 180 μL
with 10% LB media.
After incubating at 37°C for 30 minutes, 20 μL of AlamarBlue was added and the
metabolic rates were measured by using a well-plate reader. This graph shows the
metabolic rate is proportional to the cell density. Best-fit lines are constrained to pass
through the origin.

73

A.1.3 Calculating interaction coefficients
Equations 2.1 and 2.3 were used to solve for interaction coefficients. Fig. A.1.3.1 shows
that for most pairwise combinations, our model is in good agreement with experimental
measurements. Fig. A.1.3.2 compares predictions of the 4-species community with 0
th

order (assuming no interactions among species), 1
st
order, 2
nd
order, and 3
rd
order models
for 17 different ratios. The 0
th
order model gives us a metabolic rate that is under
predicted, and adding second order coefficients greatly improves the predictions.

Figure A.1.3.1 Metabolic rates for species ratios from 1:7 to 7:1 for all 6 2-species
combinations.
Interaction coefficients were extracted from the data and used to plot the predictions
lines, which are red. Data in A is also shown in Figure 2.2 of the main text. Each data
point was measured on at least three different days and error bars show standard errors.

74

Figure A.1.3.2 Comparison of predictions to experimental measurements of total
activity of the 4-species community over a wide range of species ratios.
Predictions made assuming no interactions (0
th
order model), 2-species interactions (1
st

order model), and 2 and 3-species interactions (2
nd
order model), and 2, 3, and 4-species
interactions (3
rd
order model). Error bars indicates standard deviations. Red lines
indicate average values.

Figure A.1.3.3 The contribution of each interaction term in Equation in the 4-species
community for different species ratios.
Error bars indicates standard deviations. Red lines indicate average values. Strengths
of interaction were calculated as in Fig. 2.3B.
Interaction parameters were also fit using only the data from 4-species experiments. The
results of these fits are shown in Figures A.1.3.4 and A.1.3.5. Although interaction
parameters were found to be in agreement with the 4-species measurements, the
pairwise interaction parameters were different than those calculated in the main text and
were poorly fit to pairwise measurements of activity.

75

Figure A.1.3.4 Parameters extracted from 4-species experiment data only.
(A) Pairwise, 3-species, and 4-species interactions parameters were fit using only the
data from 4-species experiments. The normalized strengths of pairwise interactions are
shown for each pair of species. Red numbers show confidence intervals at confidence
level 95%. (B) Using the full set of interaction parameters, predictions were in
agreement with measurements of the metabolic activity of the 4-species community.
(C) Predictions made using the pairwise interaction coefficients shown in A are not in
agreement with 2-species measurements of activity.

76

Figure A.1.3.5 Pairwise parameters extracted from 4-species experiment data only
assuming no high-order interaction.
(A) Pairwise parameters were fit using only the data from 4-species experiments,
assuming no higher-order interactions. The normalized strengths of pairwise
interactions are shown for each pair of species. Red numbers show confidence intervals
at confidence level 95%. (B) Using the full set of interaction parameters, predictions
were in agreement with measurements of the metabolic activity of the 4-species
community. (C) Predictions made using the pairwise interaction coefficients shown in A
are not in agreement with 2-species measurements of activity.

77

Figure A.1.3.6 Plate reader data.
(A-D) Measurements of absorbance at 600 nm during the AlamarBlue assay indicate cell
growth. (E) During the assay the no cell negative control measurement remained
constant.

78

Figure A.1.3.7 Simulations for spatially fragmented multispecies microbial community.
(A) A theoretical 4-species microbial community with a positive 3-species interaction
and a negative 4-species interaction. (B) The community is spatially fragmented into
microcolonies of variable size. (C) Simulation result shown how the total metabolic
activity of the system depends on the number of cells per microcolony and the
community composition. The total metabolic rate has been normalized to 1. (D)
Distributions of the metabolic rate of individual cells for microcolony sizes of 2, 4, 16,
and 40. Metabolic activity was calculated using Eq. 2.3, with basal metabolic rates of
0.2 for all species, i BCD = 20, and i ABCD = -110. All other interaction terms were 0. The
fraction of A is 0.5.
A.1.4 16s rRNA Sequences
Ec (Escherichia coli)
GGGTGAGTAATGTCTGGGAAACTGCCTGATGGAGGGGGATAACTACTGGAAACGGTAGCTAA
TACCGCATAACGTCGCAAGACCAAAGAGGGGGACCTTCGGGCCTCTTGCCATCGGATGTGCCC
AGATGGGATTAGCTAGTAGGTGGGGTAACGGCTCACCTAGGCGACGATCCCTAGCTGGTCTGA

79

GAGGATGACCAGCCACACTGGAACTGAGACACGGTCCAGACTCCTACGGGAGGCAGCAGTGG
GGAATATTGCACAATGGGCGCAAGCCTGATGCAGCCATGCCGCGTGTATGAAGAAGGCCTTCG
GGTTGTAAAGTACTTTCAGCGGGGAGGAAGGGAGTAAAGTTAATACCTTTGCTCATTGACGTTA
CCCGCAGAAGAAGCACCGGCTAACTCCGTGCCAGCAGCCGCGGTAATACGGAGGGTGCAAGC
GTTAATCGGAATTACTGGGCGTAAAGCGCACGCAGGCGGTTTGTTAAGTCAGATGTGAAATCC
CCGGGCTCAACCTGGGAACTGCATCTGATACTGGCAAGCTTGAGTCTCGTAGAGGGGGGTAGA
ATTCCAGGTGTAGCGGTGAAATGCGTAGAGATCTGGAGGAATACCGGTGGCGAAGGCGGGCC
CCCTGGACGAAGACTGACGCTCAGGTGCGAAAGCGTGGGGAGCAAACAGGATTAGATACCCT
GGTAGTCCACGCCGTAAACGATGTCGACTTGGAGGTTGTGCCCTTGAGGCGTGGCTTCCGGAG
CTAACGCGTTAAGTCGACCGCCTGGGGAGTACGGCCGCAAGGTTAAAACTCAAATGAATTGAC
GGGGGCCCGCACAAGCGGTGGAGCATGTGGTTTAATTCGATGCAACGCGAAGAACCTTACCTG
GTCTTGACATCCACGGAAGTTTTCAGAGATGAGAATGTGCCTTCGGGAACCGTGAGACAGGTG
CTGCATGGCTGTCGTCAGCTCGTGTTGTGAAATGTTGGGTTAAGTCCCGCAACGAGCGCAACCC
TTATCCTTTGTTGCCAGCGGTCCGGCCGGGAACTCAAAGGAGACTGCCAGTGATAAACTGGAG
GAAGGTGGGGATGACGTCAAGTCATCATGGCCCTTACGACCAGGGCTACACACGTGCTACAAT
GGCGCATACAAAGAGAAGCGACCTCGCGAGAGCAAGCGGACCTCATAAAGTGCGTCGTAGTCC
GGATTGGAGTCTGCAACTCGACTCCATGAAGTCGGAATCGCTAGTAATCGTGGATCAGAATGCC
ACGGTGAATACGTTCCCGGGCCTTGTACACACCGCCCGTCACACCATGGGAGTGGGTTGCAAA
AGAAGTAGGTAGCTTAACCTTCGGGAGG
Av (Aeromonas veronii)
GTAGCTTGCTACTTTTGCCGGCGAGCGGCGGACGGGTGAGTAATGCCTGGGGATCTGCCCAGT
CGAGGGGGATAACTACTGGAAACGGTAGCTAATACCGCATACGCCCTACGGGGGAAAGCAGG
GGACCTTCGGGCCTTGCGCGATTGGATGAACCCAGGTGGGATTAGCTAGTTGGTGAGGTAATG
GCTCACCAAGGCGACGATCCCTAGCTGGTCTGAGAGGATGATCAGCCACACTGGAACTGAGAC
ACGGTCCAGACTCCTACGGGAGGCAGCAGTGGGGAATATTGCACAATGGGGGAAACCCTGAT
GCAGCCATGCCGCGTGTGTGAAGAAGGCCTTCGGGTTGTAAAGCACTTTCAGCGAGGAGGAAA
GGTTGGTAGCTAATAACTGCCAGCTGTGACGTTACTCGCAGAAGAAGCACCGGCTAACTCCGTG
CCAGCAGCCGCGGTAATACGGAGGGTGCAAGCGTTAATCGGAATTACTGGGCGTAAAGCGCAC
GCAGGCGGTTGGATAAGTTAGATGTGAAAGCCCCGGGCTCAACCTGGGAATTGCATTTAAAAC

80

TGTCCAGCTAGAGTCTTGTAGAGGGGGGTAGAATTCCAGGTGTAGCGGTGAAATGCGTAGAGA
TCTGGAGGAATACCGGTGGCGAAGGCGGCCCCCTGGACAAAGACTGACGCTCAGGTGCGAAA
GCGTGGGGAGCAAACAGGATTAGATACCCTGGTAGTCCACGCCGTAAACGATGTCGACTTGGA
GGTTGTGCCCTTGAGGCGTGGCTTCCGGAGCTAACGCGTTAAGTCGACCGCCTGGGGAGTACG
GCCGCAAGGTTAAAACTCAAATGAATTGACGGGGGCCCGCACAAGCGGTGGAGCATGTGGTTT
AATTCGATGCAACGCGAAGAACCTTACCTGGTCTTGACATCCACGGAAGTTTTCAGAGATGAGA
ATGTGCCTTCGGGAACCGTGAGACAGGTGCTGCATGGCTGTCGTCAGCTCGTGTTGTGAAATGT
TGGGTTAAGTCCCGCAACGAGCGCAACCCTTATCCTTTGTTGCCAGCGGTCCGGCCGGGAACTC
AAAGGAGACTGCCAGTGATAAACTGGAGGAAGGTGGGGATGACGTCAAGTCATCATGGCCCTT
ACGACCAGGGCTACACACGTGCTACAATGGCGCATACAAAGAGAAGCGACCTCGCGAGAGCAA
GCGGACCTCATAAAGTGCGTCGTAGTCCGGATTGGAGTCTGCAACTCGACTCCATGAAGTCGG
AATCGCTAGTAATCGTGGATCAGAATGCCACGGTGAATACGTTCCCGGGCCTTGTACACACCGC
CCGTCACACCATGGGAGTGGGTTGCAAAAGAAGTAGGTAGCTTAACCTTCGGGAGGGCG
As (Aeromonas hydrophila)
TAGCTTGCTACTTTTGCCGGCGAGCGGCGGACGGGTGAGTAATGCCTGGGAAATTGCCCAGTC
GAGGGGGATAACAGTTGGAAACGACTGCTAATACCGCATACGCCCTACGGGGGAAAGCAGGG
GACCTTCGGGCCTTGCGCGATTGGATATGCCCAGGTGGGATTAGCTAGTTGGTGAGGTAATGG
CTCACCAAGGCGACGATCCCTAGCTGGTCTGAGAGGATGATCAGCCACACTGGAACTGAGACA
CGGTCCAGACTCCTACGGGAGGCAGCAGTGGGGAATATTGCACAATGGGGGAAACCCTGATG
CAGCCATGCCGCGTGTGTGAAGAAGGCCTTCGGGTTGTAAAGCACTTTCAGCGAGGAGGAAAG
GTCAGTAGCTAATACCTGCTGGCTGTGACGTTACTCGCAGAAGAAGCACCGGCTAACTCCGTGC
CAGCAGCCGCGGTAATACGGAGGGTGCAAGCGTTAATCGGAATTACTGGGCGTAAAGCGCAC
GCAGGCGGTTGGATAAGTTAGATGTGAAAGCCCCGGGCTCAACCTGGGAATTGCATTTAAAAC
TGTCCAGCTAGAGTCTTGTAGAGGGGGGTAGAATTCCAGGTGTAGCGGTGAAATGCGTAGAGA
TCTGGAGGAATACCGGTGGCGAAGGCGGCCCCCTGGACAAAGACTGACGCTCAGGTGCGAAA
GCGTGGGGAGCAAACAGGATTAGATACCCTGGTAGTCCACGCCGTAAACGATGTCGATTTGGA
GGCTGTGTCCTTGAGACGTGGCTTCCGGAGCTAACGCGTTAAATCGACCGCCTGGGGAGTACG
GCCGCAAGGTTAAAACTCAAATGAATTGACGGGGGCCCGCACAAGCGGTGGAGCATGTGGTTT
AATTCGATGCAACGCGAAGAACCTTACCTGGCCTTGACATGTCTGGAATCCTGCAGAGATGCGG

81

GAGTGCCTTCGGGAATCAGAACACAGGTGCTGCATGGCTGTCGTCAGCTCGTGTCGTGAGATG
TTGGGTTAAGTCCCGCAACGAGCGCAACCCCTGTCCTTTGTTGCCAGCACGTAATGGTGGGAAC
TCAAGGGAGACTGCCGGTGATAAACCGGAGGAAGGTGGGGATGACGTCAAGTCATCATGGCC
CTTACGGCCAGGGCTACACACGTGCTACAATGGCGCGTACAGAGGGCTGCAAGCTAGCGATAG
TGAGCGAATCCCAAAAAGCGCGTCGTAGTCCGGATTGGAGTCTGCAACTCGACTCCATGAAGTC
GGAATCGCTAGTAATCGCAAATCAGAATGTTGCGGTGAATACGTTCCCGGGCCTTGTACACACC
GCCCGTCACACCATGGGAGTGGGTTGCACCAGAAGTAGATAGCTTAACC
A.2.1 Time of first division in the microwell

Figure A.2.1 Distribution of time when the first division occurs in the microwell for the
growth curves shown in Fig. 3.1.
(A) Distribution of first-division time for E. coli, indicating the first division occurred
within 60 minutes in 77.5% of the microwells, and within 120 minutes in 98.8% of the
microwells. (B) Distribution of first-division time for E. cloacae, indicating the first
division occurred within 60 minutes in 81.7% of the microwells, and within 120 minutes
in 98.3% of the microwells.
A.2.2 Plasmids of E. coli and E. cloacae

82

Figure A.2.2 Plasmids used for expression of fluorescent proteins.
Plasmid pZS25-YFP was placed into E. cloacae and plasmid ECE174-mCherry was placed
in E. coli. ECE174 was made in (209), and pZS25 was described in (210).
A.2.3 Distribution of droplet volume

Figure A.2.3 Droplet volume and the influence on doubling time.
(A) The distribution of droplet volume. The distribution is generated from 77 microwells
containing both species by measuring the diameter of the droplet and assuming a
uniform height of 5 μm, based on microscopic measurements of cell distributions within
the droplets. (B) The correlation between droplet volumes shown in (A) and
corresponding doubling times of E. coli and E. cloacae in those microwells. The
Spearman’s rho’s are 0.0806 and 0.0933 for E. coli and E. cloacae respectively. The
Spearman’s rho’s are less than the critical value 0.22 at significance level of 5% for 80
pairs of data (112), indicating no effect of volume on the doubling time.

83

A.2.4 Chip-to-chip variability

Figure A.2.4 The mean doubling times from two independent coculture experiments are
compared.
The combined data is shown in Fig. 3.3. (A) The mean doubling times of E. coli and E.
cloacae from wells containing only one species. 52 and 63 microwells were analyzed for
E. coli. 48 and 13 microwells were analyzed for E. cloacae. (B) The mean doubling times
of E. coli and E. cloacae from wells containing both species. 27 and 77 microwells were
analyzed. Error bars indicate standard error.

84

A.2.5 Growth curves in microwells for coculture of E. coli and E. cloacae

Figure A.2.5 Growth curves and distribution of doubling times of E. coli and E. cloacae
growing in the same microwell.
(A) Growth curves for the coculture experiments shown in Fig. 3.2. The top two plots
show the growth curves when E. coli and E. cloacae are in the same microwell. The
Bottom two plots show the growth curves when E. coli and E. cloacae are by themselves.
(B) The distribution of doubling times when E. coli and E. cloacae are by themselves in
the coculture experiments.
For the coculture experiments of E. coli and E. cloacae, the growth curves of the two
species when they grow in the same microwell or separately are shown in Fig. A.2.5A. The
distributions of doubling times when they grow separately are shown in Fig. A.2.5B. The
mean doubling times are 130.6 minutes and 104.1 minutes for E. coli and E. cloacae
respectively. Although the mixture was loaded into the device immediately after they
were mixed, medium conditioning prior to microwell loading might still lead to slower cell
growth than in the monoculture experiment.

85

A.2.6. Spatial correlations of doubling times

Figure A.2.6 Doubling times of E. coli in microwells near the middle and edge (within 10
rows of microwells from the edge) of the device.
The average doubling times in the middle and edge are calculated from 26 and 35
microwells containing E. coli cells respectively. Error bars show standard error. Doubling
times in middle and edge are not significantly different at the 5% significance level.
A.3.1. Swarm Band Detection and Speed Quantification.

Figure A.3.1 Swarm Band Detection and Speed Quantification. Related to Fig. 4.1.

86

(A) Schematics of the imaging device used to take time-lapse images of the swarm band
every 10 minutes. The webcam is fixed 22 cm below the imaging plane, where the plate
sits. Light comes from the sides, illuminating the swarm band, which extends
throughout the whole semisolid medium. Wells are separated such that multiple
experiments could be run simultaneously. (B) A pixel intensity profile along the long
axis of the rectangular well of two frames of a time-lapse of Enterobacter migration.
The position of the band is taken at its peak and at the midline of the rectangular Petri
dish. The band’s peak can be clearly distinguished. (C) Band speeds measurements are
shown as individual points, with error bars indicating the mean and SEM.
A.3.2 Trajectory Feature Detection. Related to Fig. 4.2.

Figure A.3.2 Trajectory Feature Detection. Related to Fig. 4.2.
Tumbles are detected by comparing different local maxima between two local minima
of angular change along a trajectory. A run is detected between two tumbles. The
amount of time between tumbles is the run time. The tumbling frequency is then
calculated as the inverse of the average of the run time.

87

A.3.3 Run Speed and Run Time Distributions for Each Strain.

Figure A.3.3 Run Speed and Run Time Distributions for Each Strain.
Related to Fig. 4.2 and 4.3. (A) Run speed box plots of each strain for trajectories pooled
from all 3 videos. Diamond = mean. Dots = outliers. Horizontal line = median. (B) Run
time distributions of each strain. The inverse of the average run time is the tumbling
frequency.

88

A.3.4. Pairwise Comparisons of Strain Properties with Band Speed.

Figure A.3.4 Pairwise Comparisons of Strain Properties with Band Speed. Related to Fig.
4.4.
(A) All pairwise comparisons of averages of strain single-cell motility and growth
properties. Data is grouped by the presence or absence of methionine. Numbers

89

displayed are Spearman’s rank coefficient. The critical value for significance (p value <
0.05) is 0.679 for 7 samples. No single one of these metrics reach the critical value. (B)
Simultaneous correlations of two strain properties with coefficients found by Multiple
Linear Regression with band speed.
Strain
Number
Closely Related
Taxon
Strain
Name
16S Sequence
Similarity to Taxon
Origin Geocoordinates
Ecc1
Enterobacter
ludwigii EcUSC1
1340/1344 Razo-Mejia et al.
2014 n/a
Ecc2
Enterobacter
homaechei subsp.
steigerwaltii EcUSC2
1343/1344
Caltech Turtle Pond,
Pasadena, CA
34.13695180867859,-
118.12518197782356
Ecc3
Enterobacter
ludwigii EcUSC3
1344/1344 Exposition Park Rose
Garden, Los Angeles,
CA
34.01715461439311,-
118.28612565994263
Ecc4
Enterobacter
ludwigii EcUSC4
1340/1344 Huntington
Gardens, Pasadena,
CA
34.12535874635576,-
118.11155643191762
Ecc5 Enterobacter tabaci EcUSC5
1342/1344 Huntington
Gardens, Pasadena,
CA
34.12535874635576,-
118.11155643191762
Ecc6 Enterobacter tabaci EcUSC6
1342/1344 Huntington
Gardens, Pasadena,
CA
34.12522283194115,-
118.11121542831802
Ecc7
Enterobacter
ludwigii EcUSC7
1339/1344 Caltech Turtle Pond,
Pasadena, CA
34.13698791452894,-
118.12505054958183
Table 2 Bacterial strains used in this study, related to Experimental Procedures.

90

Strain
Number
Methionine
Condition
Percent
Included
Trajectories
Total
Included
Trajectories
Average
Time of
Included
Trajectory
(seconds)
Median
Time of
Included
Trajectory
(seconds)
Average
Tumbles Per
Trajectory
Median
Tumbles Per
Trajectory
Percent
Included
Trajectories
With Tumbles
Ecc1
+
a
23% 917 50.6 12.8 17 5 36%
-
b
24% 1009 49.8 15.3 15 4 28%
Ecc2
+ 31% 711 49.1 12.6 16 8 46%
- 33% 843 42.3 13.4 16 5 53%
Ecc3
+ 32% 743 72.9 29.5 29 5 22%
- 25% 512 80.1 33.2 22 6 27%
Ecc4
+ 24% 1630 25.6 8.6 10 2 47%
- 25% 1055 23.5 8.9 13 2 39%
Ecc5
+ 22% 623 53.2 11.1 10 6 53%
- 20% 655 66.0 19.5 13 6 40%
Ecc6
+ 21% 1319 42.9 10.4 19 8 54%
- 20% 1235 45.2 11.3 13 6 50%
Ecc7
+ 24% 707 56.5 15.5 47 27 37%
- 25% 1068 49.6 14.2 30 23 39%
Table 3 Trajectory statistics, related to Experimental Procedures.
a
0.13mM methionine
b
0mM methionine

91

A.4.1 Plasmids of EcSlow and EcFast

Figure A.4.1 Plasmids used for expression of fluorescent proteins.
Plasmid pZE25O1+11-YFP was placed into EcSlow and plasmid pZE25+11-mCherry was
placed into EcFast.
A.4.2 Influence of model parameters on the band speed

Figure A.4.2 Simulations with 50% and 200% of original parameter values are repeated
to show the influence of model parameters on the band speed.

92

𝑨
𝒏
and 𝜷
𝒏
have the biggest influence on the band speed.
A.4.3 Growth curves

Figure A.4.3 Growth curves of EcSlow and EcFast. Error bar indicates standard error.
The medium for growth curve was made of 1x M9 minimal salts medium (BD),
supplemented with 0.1 mM CaCl 2, 2 mM MgSO 4, 3 mM sodium succinate, 22 mM
glucose, and 20 µg/mL each of the amino acids histidine (0.13 mM), methionine (0.13
mM), threonine (0.17 mM), and leucine (0.15 mM). The strains were inoculated from
glycerol frozen stocks and grown overnight at 37°C (200 rpm) in the medium described
above with antibiotic. The overnight cultures were diluted at 100 folds in fresh media
with antibiotic and regrown for 4 hours. Then we measured the OD600 of the diluted
cultures every 10 minutes using plate reader up to 20 hours as shown in Fig. A.4.3. The
doubling times are 52.4 min and 58.2 min respectively, calculated from 0 to 3 h.

93

A.4.4 Cell distribution of mixture of EcSlow and EcFast

Figure A.4.4 Intensity and cell distribution of the traveling bacterial band along the
direction of propagation.
(A) Fluorescence microscopy of the bacterial band formed by 1:1 mixture of EcSlow and
EcFast. (B) Normalized distribution of EcSlow and EcFast cells separately and together
along the propagation direction.

94

A.4.5 Simulations of band propagation of EcSlow and EcFast by themselves

Figure A.4.5 Simulation results for monocultures of EcSlow and EcFast.
(A) Simulated distribution of cells after 24 hours of inoculation. Dash lines indicate the
concentration of glucose at the band location. EcFast has a significantly lower
concentration of glucose at the band location. (B) Simulated band position over time
for EcSlow and EcFast. The simulated band speeds are 2.5 mm/h and 4.2 mm/h for
EcSlow and EcFast respectively.

95

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Abstract (if available)

Abstract The activity of a biological community is the outcome of complex processes involving interactions between community members. It is often unclear how to accurately incorporate these interactions into predictive models. Previous work has shown a range of positive and negative interactions between species resulting from the exchange of metabolites, molecular signals, and even cell-cell contact. Even though cell-cell interaction networks have been examined in many high diversity microbial communities using macroscale approaches, microscale studies of multispecies communities are lacking and it remains unclear how macroscale trends scale down to small groups of cells. Current models to predict macroscale trends do not account for the heterogeneity of activity in individual cells, and the potential for variability in cell-cell interactions has not been explored. Interactions between cells not only influence the behavior of individuals, but may also result in spontaneous group behavior. Collective behavior, as a complex outcome of interactions between individual members of a population, is observed in many biological systems coordinating cellular activity over multiple time and length scales. The main goal of this work was to connect single-cell behaviors to activities at bulk population level. ❧ To explore our ability to predict the behavior of complex networks of microbes we analyzed the cell-cell interaction and collective behavior of multiple bacterial systems. In a 4 species microbial community, we examined pairwise interactions as well as high-order interactions between community members, and found that pairwise interactions were sufficient to predict the overall metabolic rate of the community. In another project we focused on the single-cell variability of such interactions finding diverse relationships between individual cells that traditional bulk measurement would not reveal. To connect individual and group behavior, we quantitatively studied the correlation between single-cell characteristics and collective behavior at population level. Finally, we found a critical transition in collective behavior within a two-species community, emphasizing the complexity of hybrid collective behavior of mixed populations. As a whole, these project have revealed connections between single-cell activity and population-level behaviors that should deepen understanding of complex cellular networks and help to identify strategies for the control and accurate prediction of microbial community function. ❧ Here we quantify the contribution of interactions between more than two species to the overall metabolic rate of a mixture of four freshwater bacteria. In isolated small microcolonies, high-order interactions could play a dominant role in setting ecosystem outputs. Besides, our single-cell view of interactions implies the importance of cellular heterogeneity in regulating cell-cell interaction networks. The device we report here enables future studies of variability of single-cell activity. We also reveal that single-cell properties are strongly correlated with collective behavior. In synthetic biological systems, it may be possible to achieve desired collective behavior by combining properties found in the wild. Furthermore, the non-linear scaling and critical behavior we observe in the hybrid collective behavior of mixed strains can play a vital role in stabilizing networks in disturbed conditions.

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Asset Metadata

Creator Guo, Xiaokan (author)

Core Title Microbial interaction networks: from single cells to collective behavior

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Physics

Publication Date 11/09/2018

Defense Date 10/22/2018

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

Tag bacterial motility,cell growth,cell-cell interaction,cellular networks,chemotaxis,collective behavior,competition,critical transition,Escherichia coli,high-order interaction,Lotka-Volterra,metabolism,microbial community,microfluidics,multi-species community,OAI-PMH Harvest,pattern pattern formation,single-cell variability

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Language English

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Advisor Boedicker, James (committee chair), Bogdan, Paul (committee member), Ehrenreich, Ian (committee member), El-Naggar, Moh (committee member), Haas, Stephan (committee member)

Creator Email guoxiaokan@gmail.com,xiaokang@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-105025

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