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Modeling anti-tumoral effects of drug-induced activation of the cell-extrinsic apoptotic pathway

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Modeling anti-tumoral effects of drug-induced activation of the cell-extrinsic apoptotic pathway

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Content MODELING ANTI-TUMORAL EFFECTS OF DRUG-INDUCED
ACTIVATION OF THE CELL-EXTRINSIC APOPTOTIC PATHWAY
by
Brittany Kay
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)
August 2012
Copyright 2012 Brittany Kay
Dedication
Thank you, Mom, Dad, Morgan, and Sean for making it possible for me to focus on
my studies and for supporting me in my work - I could never have done this without
all of you.
Dr. D'Argenio, I am so grateful to have had such a kind and thoughtful advisor
guide me through this process. Thank you for being such a wonderful mentor.
ii
Table of Contents
Dedication ii
List of Tables vi
List of Figures viii
Abbreviations xii
Abstract xv
Chapter 1. Background and Introduction 1
1.1 Cancer in Society 1
1.2 Apoptosis 3
1.2.1 Extrinsic Apoptotic Pathway 3
1.2.2 Intrinsic Apoptotic Pathway 7
1.2.3 Lymphocyte-Mediated Apoptotic Pathway 9
1.2.4 Cross-Talk Among Apoptotic Pathways 11
1.2.5 Cancer and Dysregulation of Apoptosis 12
1.3 Apoptotic Pathways as Targets for Anti-Cancer Drugs 13
1.3.1 Death Receptor Ligands & Antibodies and the
Extrinsic Pathway 13
1.3.2 Cytotoxic Drugs and the Intrinsic Pathway 14
1.3.3 Combination Therapies Exploit Intrinsic and Extrinsic
Pathway Cross-Talk 14
1.3.4 Drugs Targeting the Extrinsic Pathway 15
1.3.5 Drugs Targeting the Intrinsic Pathway 20
1.4 Potential Challenges Faced by Anti-Cancer Therapies 22
1.4.1 Activation of NF-B by Death Receptors 22
1.4.2 Drug Delivery to Tumor Cells 24
1.4.3 Dose-Limiting Toxicities 25
1.5 Mouse Models for Cancer 26
1.5.1 Mouse Genetic Models for Cancer 26
iii
1.5.2 Mouse Xenograft Models 27
1.5.3 Limitations of Subcutaneous Xenograft Models 28
1.5.4 Advantages of Subcutaneous Xenograft Models 29
1.6 Mathematical Tumor Regression Models for Mouse Xenografts 30
1.6.1 Gompertzian Model 30
1.6.2 Cancer Stem-Cell Models 32
1.6.3 Other Unperturbed-Growth Models 35
1.7 Clinical Relevance of Combination Therapies 39
1.8 Specic Aims 40
Chapter 2. Experimental Data 43
2.1 COLO205 Cell Line 43
2.2 Pharmacokinetic Studies 44
2.2.1 rshApo2L/TRAIL 44
2.2.2 Conatumumab 45
2.2.3 Irinotecan (CPT-11) 47
2.3 Monotherapy Tumor Xenograft Studies 48
2.3.1 rshApo2L/TRAIL (AMG951) 48
2.3.2 Conatumumab (AMG655) 54
2.4 Combination Therapy Tumor Xenograft Studies 58
Chapter 3. Models and Population Analysis 62
3.1 Pharmacokinetic Models 62
3.1.1 rshApo2L/TRAIL Pharmacokinetic Model 63
3.1.2 Conatumumab Pharmacokinetic Model 65
3.1.3 Irinotecan Pharmacokinetic Model 68
3.2 Intracellular Apoptotic Signaling and Tumor Regression Modeling (Base
Model) 69
3.3 Empirical Reduced Drug-Eect Models 73
3.3.1 Reduced Drug-Eect at Upstream Signal Model (K
r
Upstream Model) 75
3.3.2 Reduced Drug-Eect at Apoptosis Signal Model (K
r
Apoptosis Model) 76
3.4 Pro-Survival Signal Model 78
3.5 Combination Therapy Model: Cytotoxic Agent co-dosed with a PARA 80
3.6 Population Analysis 85
3.6.1 Population Modeling Description 85
3.6.2 Analysis Approach 86
Chapter 4. Results 87
4.1 Unperturbed TV
SS
Tumor Growth Model 87
4.2 Intracellular Apoptotic Signaling and Tumor Regression Modeling (Base
Model) 88
iv
4.3 Empirical Reduced Drug-Eect Models 94
4.3.1 Reduced Drug-Eect at Upstream Signal Model (K
r
Upstream
Model) 94
4.3.2 Reduced Drug-Eect at Apoptosis Signal Model (K
r
Apoptosis
Model) 98
4.4 Pro-Survival Signal Model 103
4.5 Simulations using Base Model and Pro-Survival Signal Model 107
4.6 Combination Therapy Model 109
4.7 Simulations using Combination Therapy Model 114
Chapter 5. Discussion and Future Work 117
5.1 Comparison of Model Performances 118
5.2 Comparison of Work to Other Models and Measures 119
5.3 Pro-Survival Signal is Only One Possible Explanation 122
5.4 Combination Data and Clinical Relevance 123
5.5 Future Work 124
5.5.1 Needed Data to Test Hypotheses 124
5.5.2 Improve Combination Therapy Model 124
5.5.3 Suggested Combination Therapy Study 126
5.5.4 Analysis of Other Cell Lines 129
References 130
v
List of Tables
Table 2.1. Conatumumab IP PK study dosing regimens and
observation schedules 46
Table 2.2. RshApo2L/TRAIL dosing regimens for tumor xenograft
studies with individual data 50
Table 2.3. RshApo2L/TRAIL dosing regimens for tumor xenograft
studies with average data 51
Table 2.4. Conatumumab dosing regimens for tumor xenograft studies
with individual data 55
Table 2.5. Irinotecan (CPT-11) and rshApo2L/TRAIL dosing regimens
for combination-therapy tumor xenograft studies with average data 59
Table 2.6. Irinotecan (CPT-11) and Conatumumab dosing regimens
for combination-therapy tumor xenograft studies with individual
data 61
Table 3.1. Parameter estimates for rshApo2L/TRAIL pharmacokinetic
model 64
Table 3.2. Parameter estimates for Conatumumab pharmacokinetic
model 65
Table 3.3. Parameter estimates for Irinotecan pharmacokinetic model 69
Table 4.1. Parameter estimates for the intracellular-signaling
tumor-regression base model 89
Table 4.2. Parameter estimates for the empirical reduced drug eect
at the Upstream Signal model 98
vi
Table 4.3. Parameter estimates for the empirical reduced drug eect
at the Apoptosis Signal model 99
Table 4.4. Parameter estimates for the model incorporating the
Pro-Survival Signal 107
Table 4.5. Parameter estimates for the model describing combination
therapies of either rshApo2L/TRAIL and Irinotecan (CPT-11)
or Conatumumab and Irinotecan 110
Table 5.1. NLL and AIC values for the four monotherapy models
evaluated 118
Table 5.2. A proposed combination-therapy study for CPT-11 and
rshApo2L/TRAIL 127
vii
List of Figures
Figure 1.1. Receptors associated with extrinsic pathway, and
outline of extrinsic pathway's activation process 5
Figure 1.2. Details of the apoptotic caspase cascade 6
Figure 1.3. The action of p53 in the intrinsic apoptotic pathway 9
Figure 1.4. Cross-talk among the three main apoptotic pathways 11
Figure 1.5. Apo2L/TRAIL death receptors and decoy receptors 17
Figure 1.6. Binding of antibody to three associated DR5 receptors 19
Figure 1.7. Activation of NF-B by DR4 and DR5 24
Figure 1.8. Gompertzian growth curve 31
Figure 1.9. Kinetics describing cell populations 34
Figure 1.10. Diagram of the Johnston stem cell model of the colonic
crypt 35
Figure 1.11. Simulation of control data using the base Simeoni model 36
Figure 1.12. Simulation of control data using base model 37
Figure 1.13. Simulation of control data using base model 39
Figure 2.1. Mean plasma concentration data for rshApo2L/TRAIL 45
Figure 2.2. Median plasma concentration data for Conatumumab
given IP 47
Figure 2.3. Mean plasma concentration data for Irinotecan given IP 48
viii
Figure 2.4. RshApo2L/TRAIL control-individual tumor size data
as described in Table 2.2 49
Figure 2.5. RshApo2L/TRAIL treated-individual tumor size data
as described in Table 2.2 52
Figure 2.6. RshApo2L/TRAIL mean tumor size data as described
in Table 2.3 53
Figure 2.7. Conatumumab control-individual tumor size data as
described in Table 2.4 56
Figure 2.8. Conatumumab treated-individual tumor size data as
described in Table 2.4 57
Figure 2.9. Irinotecan (CPT-11) and rshApo2L/TRAIL tumor size
data as described in Table 2.5 60
Figure 2.10. Irinotecan (CPT-11) and Conatumumab tumor size
data as described in Table 2.6 61
Figure 3.1. Schematic of pharmacokinetic model for rshApo2L/TRAIL 64
Figure 3.2. Model t to mean plasma concentration data for
rshApo2L/TRAIL 65
Figure 3.3. Schematic of pharmacokinetic model for Conatumumab 66
Figure 3.4. Model t to median plasma concentration data for
Conatumumab 67
Figure 3.5. Schematic of pharmacokinetic model for Irinotecan 68
Figure 3.6. Model t to mean plasma concentration data for
Irinotecan given IP 69
Figure 3.7. Intracellular apoptotic-signaling model 71
Figure 3.8. Complete model diagram for the separate and shared
components of the apoptotic pathway 72
Figure 3.9. Schematic for empirically modeled reduction of drug
eect at the Upstream Signal 75
Figure 3.10. Schematic for empirically modeled reduction of drug
eect at the Apoptosis Signal 77
Figure 3.11. Schematic for semi-mechanistic Pro-Survival Signal Model 79
ix
Figure 3.12. A detailed diagram of the cross-talk between the extrinsic
and intrinsic apoptotic pathways [Genentech, 2010] 82
Figure 3.13. Combination drug-therapy model for the eects of an
extrinsic apoptotic pathway agonist and a cytotoxic drug 83
Figure 4.1. Base Model population analysis t to the
rshApo2L/TRAIL experiments with individual data 91
Figure 4.2. Base Model population analysis t to the
rshApo2L/TRAIL experiments with average data 92
Figure 4.3. Base Model population analysis t to the Conatumumab
experiments with individual data 93
Figure 4.4. K
r
Upstream Model population analysis t to the
rshApo2L/TRAIL experiments with individual data 95
Figure 4.5. K
r
Upstream Model population analysis t to the
rshApo2L/TRAIL experiments with average data 96
Figure 4.6. K
r
Upstream Model population analysis t to the
Conatumumab experiments with individual data 97
Figure 4.7. K
r
Apoptosis Model population analysis t to the
rshApo2L/TRAIL experiments with individual data 100
Figure 4.8. K
r
Apoptosis Model population analysis t to the
rshApo2L/TRAIL experiments with average data 101
Figure 4.9. K
r
Apoptosis Model population analysis t to the
Conatumumab experiments with individual data 102
Figure 4.10. Pro-Survival Signal Model population analysis t to the
rshApo2L/TRAIL experiments with individual data 104
Figure 4.11. Pro-Survival Signal Model population analysis t to the
rshApo2L/TRAIL experiments with average data 105
Figure 4.12. Pro-Survival Signal Model population analysis t to the
Conatumumab experiments with individual data 106
Figure 4.13. Simulations of tumor volume during administration of
30-day-long constant infusions of varying total dose sizes using
the Base Model and Pro-Survival Signal Model 108
x
Figure 4.14. Combination Therapy Model population analysis t
to the Irinotecan (CPT-11) and rshApo2L/TRAIL tumor size
data as described in Table 2.5 112
Figure 4.15. Combination Therapy Model population analysis t
to the Irinotecan (CPT-11) and Conatumumab tumor size data
as described in Table 2.6 113
Figure 4.16. Simulations of tumor volume using the Combination
Therapy Model 115
xi
Abbreviations
AIC: Akaike's information criterion, a measure of how well the model ts the data
(lower for a better t) and overall complexity of the model (higher for more
estimated parameters)
Apaf-1: Apoptotic protease activating factor 1
Apo2L/TRAIL: Apoptosis-inducing ligand 2/tumor necrosis factor-related apoptosis-
inducing ligand
ASU: Apoptosis Signal unit
Bak: Bcl-2 homologous antagonist/killer
Bax: Bcl-2-associated X protein
Bcl-2: B-cell lymphoma 2
Bcl-xL: B-cell lymphoma 2 { extra large
BH3: Bcl-2 homology domain 3
BID: BH3 interacting domain death agonist
c-FLIP: Cellular FLICE inhibitory protein
c-IAP: Cellular inhibitor of apoptosis protein
CV%: Coecient of variation (standard deviation divided by mean), represented as
a percentage
Cyt c: Cytochrome c
xii
DcR: Decoy receptor
DISC: Death-inducing signaling complex
DR: Death receptor
FADD: Fas-associated death domain protein
FLICE: Fas-associated death domain protein-like interleukin-1 beta converting enzyme
(another term for caspase-8)
IAP: Inhibitor of apoptosis protein
IGF-1R: Insulin-like growth factor-1 receptor
IGF: Insulin-like growth factor
IGFBP-3: Insulin-like growth factor binding protein-3
IgG
1
: Immunoglobulin G
1
IIV: Inter-individual variability
IP: Intraperitoneal
IV: Intravenous
MLEM: Maximum likelihood solution using expectation maximization
NF-B: Nuclear factor kappa B
NLL: Negative log likelihood, the sum of the negative logs of the probability of each
observed data point based on the predictions of the model using the given and
estimated parameter values; it is a measure of how well the model ts the data
(lower for a better t)
NLME: Nonlinear mixed eects
NSCLC: non-small-cell lung cancer
OPG: Osteoprotegerin
PARA: Pro-apoptotic receptor agonist
PD: Pharmacodynamics
xiii
pI: Isoelectric point
PK: Pharmacokinetics
PSSU: Pro-Survival Signal unit
Puma: P53 upregulated modulator of apoptosis
r
2
: The square of Pearson's Correlation or the Correlation Coecient (r), which is
itself the covariance between the dependent and independent variables divided
by the product of the two variables' standard deviations; it is a measure of the
quality of a least squares tting of the data (1.0 being the best t)
RIP: Receptor-interacting protein
RSE%: Relative standard error (standard error divided by estimate), represented as
a percentage
rshApo2L/TRAIL: Recombinant soluble human apoptosis-inducing ligand 2/tumor
necrosis factor-related apoptosis-inducing ligand
Smac/DIABLO: Second mitochondria-derived activator of caspases/direct IAP-
binding protein with low pI
tBID: Truncated BH3 interacting domain death agonist
TNF: Tumor necrosis factor
TNFR1: tumor necrosis factor receptor 1
TRADD: Tumor necrosis factor receptor 1-associated death domain protein
TRAF2: Tumor necrosis factor receptor-associated factor 2
TRAIL: Tumor necrosis factor-related apoptosis-inducing ligand
TRAIL-R: TRAIL receptor
USU: Upstream Signal unit
XIAP: X chromosome-linked inhibitor of apoptosis protein
xiv
Abstract
RshApo2L/TRAIL and Conatumumab bind to transmembrane death receptors and
trigger the extrinsic cellular apoptotic pathway through a caspase-signaling cascade
resulting in cell death. Tumor size time series data from rodent tumor xenograft
(COLO205) studies following administration of either of these two pro-apoptotic
receptor agonists (PARAs) were combined to develop an intracellular-signaling tumor-
regression model that includes two levels of signaling: upstream signals unique to each
compound (representing initiator caspases), and a common downstream apoptosis sig-
nal (representing executioner caspases) shared by the two agents. Pharmacokinetic
(PK) models for each drug were developed based on plasma concentration data fol-
lowing intravenous (IV) and/or intraperitoneal (IP) administration of the compounds
and were used in the subsequent intracellular-signaling tumor-regression modeling. A
model relating the PK of the two PARAs to their respective and common downstream
signals, and to the resulting tumor burden was developed using mouse xenograft
tumor size measurements from 448 experiments that included a wide range of dose
sizes and dosing schedules.
Deciencies in the original model's ability to describe data from some of the experi-
mental groups led to exploration of several hypotheses for a reduction of drug eect.
xv
Both empirical and semi-mechanistic reduction-of-drug-eect models were investi-
gated. All three modied models showed marked improvement of t, especially for
data from the long-term dosing experiments; the greatest improvement (by model-
comparison metrics) came from incorporation of a pro-survival signal { consistent
with the hypothesis that PARAs may also cause the upregulation of pro-survival
factors that can lead to a reduction in their eectiveness with treatment.
Combination therapy data, for which a PARA was co-dosed with a cytotoxic agent,
was analyzed using an interaction model. The model was generally able to describe the
data; however, the type of data available could only minimally inform the interaction
model because of the substantial eects of the chosen monotherapy regimens.
xvi
Chapter 1.
Background and Introduction
1.1 Cancer in Society
Cancer is a collection of diseases that involve the abnormal and excessive proliferation
of cells in the body, generally the result of genetic mutations. These mutations cause
a loss of balance between the signals that promote cell synthesis and those that
trigger apoptosis (controlled cell death), resulting in unchecked growth, invasion of
surrounding tissues, and sometimes metastasis (the spread of cancer cells to distant
sites in the body). Cancers are also characterized by deviant cell structure.
Although rates of cancer deaths and rates of new cancer diagnoses have shown a mod-
erate decline in the U.S. in recent years [Edwards et al., 2010], cancer is still the second
leading cause of death in \high-income" countries, according to a 2008 World Health
Organization report [World Health Organization, 2008a]. The American Cancer Soci-
ety (ACS) estimated that there were 569,490 cancer-related deaths and 1,529,560 new
cancer cases in the U.S. in 2010 [American Cancer Society, 2010]. The National Insti-
tutes of Health estimated the cost of treating cancer in the U.S. in 2010 amounted
1
to approximately $102.8 billion for direct medical costs, with an additional burden of
$161 billion in lost productivity due to illness or premature death [American Cancer
Society, 2010]. On a global scale, the most recent World Cancer Report estimated
that there were 12.4 million new cases of cancer and 7.6 million cancer-related deaths
in the world in 2008 [World Health Organization, 2008b].
The ACS predicted that, of new cancer cases diagnosed in the U.S. in 2010, the ve
most common types of cancer for men would turn out to be cancers of the prostate
(28%), cancers of the lung and bronchus (15%), cancers of the colon and rectum (9%),
cancers of the urinary bladder (7%), and melanoma of the skin (5%); and the ve most
common cancers for women would be cancers of the breast (28%), lung and bronchus
(14%), colon and rectum (10%), uterine corpus (6%), and thyroid (5%). Additionally,
the ACS predicted that in 2010 the top ve contributors to cancer-related deaths in
the U.S. would be, for men, cancers of the lung and bronchus (29%), prostate (11%),
colon and rectum (9%), pancreas (6%), and liver and intrahepatic bile duct (4%);
for cancer-related deaths in women, the predicted top ve cancers were those of the
lung and bronchus (26%), breast (15%), colon and rectum (9%), pancreas (7%), and
ovary (5%) [American Cancer Society, 2010]. (The ACS cancer-incidence estimates
did not include basal and squamous cell skin cancers and in situ carcinomas except
those of the urinary bladder.) In the World Health Organization's 2008 list of \The
Top Ten Causes Of Death," four of the top ten causes of death for \high-income"
countries are cancers (cancers of the trachea, bronchus and lung rank third; colon and
rectum cancers rank seventh; breast cancer ranks ninth; and stomach cancer ranks
tenth) [World Health Organization, 2008a].
Given that cancer imposes a high cost on individuals and society, it is not surpris-
ing that organizations such as the National Cancer Institute (NCI) spend billions of
2
dollars annually on research and treatment development for cancers. The NCI's
total 2008 budget was approximately $4.8 billion, with the top ve best funded
cancers being breast cancer ($572.6 million), prostate cancer ($285.4 million), col-
orectal cancer ($273.7 million), lung cancer ($247.6 million), and leukemia ($216.4
million) [National Cancer Institute, 2008].
1.2 Apoptosis
Apoptosis is the process of controlled cell death and is an integral part of normal
tissue development and function, allowing for the orderly removal of cells that are
no longer needed without damaging surrounding cells. In healthy human adults,
more than 10 billion cells go through apoptosis each day. Additionally, apoptosis is
used to eliminate cells that the body recognizes as abnormal. Apoptosis comprises
the organized activation of a series of enzymes that cause a cell's loss of adhesion
to surrounding cells, cleavage of its cytoskeleton and DNA, and packaging of its
intracellular components into apoptotic bodies that can be ingested by phagocytes.
There are three main pathways for apoptosis: the intrinsic pathway, the extrinsic
pathway, and the lymphocyte-mediated (or granzyme B) pathway [Weinberg, 2007,
Rockefeller University, 2010].
1.2.1 Extrinsic Apoptotic Pathway
When the extrinsic apoptotic pathway is engaged, an intracellular signal cascade is
induced (see Figure 1.1). Initially, the adapter protein FADD (Fas-associated death
domain protein) is recruited and activated by the death domains of the intracellular
3
components of the death receptors. Activated FADD, in turn, recruits procaspases-
8 and -10 to form the death-inducing signaling complex (DISC). Within the DISC,
procaspases-8 and -10 go through self-cleavage to produce the activated forms of
caspases-8 and -10 (both are initiator caspases). Activated caspases-8 and -10 then
trigger the conversion of procaspases-3, -6, and -7 to the executioner caspases-3, -6,
and -7 [Almasan and Ashkenazi, 2003, Bouralexis et al., 2005, Kelley and Ashkenazi,
2004, LeBlanc and Ashkenazi, 2003]. The activated executioner caspases cause the
release from inhibition of a set of enzymes that cleave a number of molecules that
include components of the nuclear membrane, chromosomal DNA, cytoskeleton pro-
teins, and components of the electron transport chain (see Figure 1.1 and the \death
substrates" of Figure 1.2) [Weinberg, 2007].
4
Figure 1.1. Receptors associated with extrinsic pathway, and outline of extrinsic
pathway's activation process [Weinberg, 2007]
5
Figure 1.2. Details of the apoptotic caspase cascade [Weinberg, 2007]
6
1.2.2 Intrinsic Apoptotic Pathway
The intrinsic, or mitochondria-mediated, pathway is triggered by cell stress or abnor-
malities in the intracellular signaling networks, and is initiated by activation of the
monitoring protein p53. There are a number of stimuli that cause the activation of
p53, including anoxia, exposure to extreme heat, DNA damage, disruption of the
cytoskeleton, and imbalances in the signals that control growth [Weinberg, 2007].
When the intrinsic apoptotic pathway is initiated, p53 stimulates the transcription
of several key sets of proteins that cause the cell to undergo apoptosis (see Fig-
ure 1.3). One protein whose transcription is upregulated is the Fas transmembrane
receptor, which sensitizes the cell to any Fas ligand (FasL) in the extracellular space;
binding of the Fas receptor by FasL triggers the extrinsic apoptotic pathway (see Sec-
tion 1.2.1). Insulin-like growth factor binding protein-3 (IGFBP-3) is another protein
whose expression is increased by the activation of p53. IGFBP-3 is translocated to the
extracellular space where it binds and sequesters insulin-like growth factor-1 and -2
(IGF-1/2). Over-expression of IGFBP-3 and the resulting sequestration of IGF-1/2
reduces the amount of IGF-1/2 available to bind to insulin-like growth factor-1 recep-
tor (IGF-1R), thereby diminishing the associated pro-survival/anti-apoptotic signal
initiated by that binding (one set of pro-survival signals comes from the activation
of NF-B [nuclear factor kappa B]; see Section 1.4.1 for more details on this path-
way). A third important group of proteins upregulated by p53 includes Bax (B-cell
lymphoma 2 [Bcl-2]-associated X protein), Noxa (latin for `damage'), and Puma (p53
upregulated modulator of apoptosis). Noxa and Puma inhibit dierent members of
the pro-survival Bcl-2 family of proteins, thereby releasing Bax and Bak (Bcl-2 homol-
ogous antagonist/killer) from their inhibited states. Activated Bax and Bak cause
7
pores to open in the mitochondrial membranes, allowing cytochrome c (Cyt c) and
Smac/DIABLO (second mitochondria-derived activator of caspases/direct inhibitor
of apoptosis protein-binding protein with low pI) to move into the cytosol. Cyt c
joins with cytosolic Apaf-1 (apoptotic protease activating factor 1) and procaspase-
9 to form apoptosomes that contain activated caspase-9. Apoptosomes activate
procaspases-3, -6, and -7 to their active forms, executioner caspases-3, -6, and -7.
The released Smac/DIABLO acts to block inhibitor of apoptosis proteins (IAPs),
present in the cytosol to prevent the activity of executioner caspases, thus freeing
executioner caspases-3, -6, and -7 to enact the nal stages of apoptosis (see Fig-
ures 1.2 and 1.3). As described above, the executioner caspases activate a number of
proteases and DNAses that result in the actual event of apoptosis [Weinberg, 2007].
8
Figure 1.3. The action of p53 in the intrinsic apoptotic pathway [Weinberg, 2007]
1.2.3 Lymphocyte-Mediated Apoptotic Pathway
A third pathway for inducing apoptosis is one that involves cytotoxic T-cells and
natural killer cells. Both types of lymphocytes can induce apoptosis in target cells
either through activation of extracellular death receptors (see Section 1.2.1 for details)
or through the exocytosis of cytotoxic granules from the lymphocytes that contain
membrane-perturbing proteins and a family of proteases [Weinberg, 2007, Lieberman,
2003, Trapani and Smyth, 2002, Caligiuri, 2008]. When the cytotoxic granules go
through exocytosis, perforin and granulysin (both membrane-disturbing proteins) and
a variety of granzymes (a set of proteases) are released into the secretory synapse (the
9
space formed where the lymphocyte and target cell make contact) [Raja et al., 2003].
The exact mechanism of how perforin, granulysin, and the proteases enter the target
cell is still under investigation. One of the earlier proposed means of entry was that
perforin molecules polymerize to form pores in the plasma membrane of the target cell
that allow other molecules (including granzyme B) into the cytoplasm of the cell to be
destroyed [Lieberman, 2003]. However, more recent theories involve the endocytosis
of granulysin, perforin, and granzyme proteases, and their subsequent endosomal
release into the cytosol [Trapani and Smyth, 2002, Raja et al., 2003, Metkar et al.,
2002]; or possibly direct endocytosis of granzyme B after it binds to some extracellular
receptor [Weinberg, 2007, Trapani and Smyth, 2002].
Once granzyme B has gained entrance to the target cell, it activates procaspases-3,
-8, and -9, and also directly truncates BID (BH3 interacting domain death agonist) to
produce its active form, tBID [Weinberg, 2007, Lieberman, 2003, Trapani and Smyth,
2002]. These activated molecules proceed to engage the mitochondrial pathway and
additional executioner caspases that ultimately lead to apoptosis, as described above
(a summary depiction of the granzyme B pathway is included in Figure 1.4) [Weinberg,
2007].
Several of the granzymes in the cytotoxic granules (including granzymes A and B) are
also involved in a caspase-independent apoptotic pathway, as well. In general, these
granzymes activate the downstream targets of initiator and executioner caspases, and
even cleave DNA themselves [Lieberman, 2003, Trapani and Smyth, 2002, Metkar
et al., 2002].
10
Figure 1.4. Cross-talk among the three main apoptotic pathways [Weinberg, 2007]
1.2.4 Cross-Talk Among Apoptotic Pathways
The intrinsic apoptotic pathway can augment the eects of the extrinsic apoptotic
pathway by upregulating the expression of death receptors, as well as by downregu-
lating pro-survival factors that decrease the activation and ecacy of initiator and
executioner caspases (see Figure 1.3 and Section 1.2.2) [Weinberg, 2007, Vanhoefer
et al., 2001]. One important pathway in this downregulation of pro-survival factors
is the upregulation of IGFB-3, which reduces the activation of IGF-1R by sequester-
ing IGF-1/2; this, in turn, reduces the activation of NF-B, which is a pro-survival
transcription factor (see Section 1.4.1).
11
The extrinsic apoptotic pathway interacts with the intrinsic apoptotic pathway
through the truncation of BID: activated caspase-8 augments the intrinsic pathway
by cleaving BID directly, and caspases-8 and -10 activate executioner caspase-3 that
then cleaves BID [Weinberg, 2007, Kaplan-Lefko et al., 2010, Daniel et al., 2007].
The active tBID molecules then inhibit pro-survival members of the Bcl-2 family
of proteins (e.g., Bcl-2, Bcl-xL [B-cell lymphoma 2 { extra large]), which conse-
quently releases Bax and Bak { one of the sets of proteins that are also activated by
the upstream action of p53 { from inhibition. Activated Bax and Bak then induce
the formation of pores in mitochondrial membranes, thereby releasing Cyt c and
Smac/DIABLO into the cytosol. The downstream elements of the intrinsic apop-
totic pathway (including activated caspase-9) also enhance the conversion of inactive
executioner procaspases to their active forms. The lymphocyte-mediated apoptosis
pathway converges on the other two pathways through the activation of initiator and
executioner caspases and the truncation of BID (see Figure 1.4) [Weinberg, 2007,
Almasan and Ashkenazi, 2003].
1.2.5 Cancer and Dysregulation of Apoptosis
Cancer can be viewed as a consequence of the dysregulation of apoptosis. Abnormally
growing cells that would usually be eliminated through apoptosis instead escape apop-
tosis through a wide variety of mutations. A frequent group of mutations in cancer
cells, occurring in 30 to 50 percent of common human cancers, involve the gene
encoding p53 [Weinberg, 2007]. These mutations cause p53 to lose some, or all, of
its ecacy as the primary monitor of the cell's well-being and the initiator of the
12
intrinsic pathway. However, the extrinsic pathway is often still intact in these cells,
making the extrinsic pathway an intriguing target for anti-cancer treatments.
1.3 Apoptotic Pathways as Targets for Anti-
Cancer Drugs
Anti-cancer therapies exploit a number of cancer cell features. Many cancer cells
express distinctive proteins on their surfaces or have metabolic needs that set them
apart from most normal cells.
1.3.1 Death Receptor Ligands & Antibodies and the
Extrinsic Pathway
A promising target for anti-cancer drugs is activation of the extrinsic pathway. Often,
a number of pro-apoptotic signaling pathways are primed in cancer cells, making
them more susceptible to activation of their extrinsic apoptotic pathways than nor-
mal cells [Ashkenazi, 2008]. Additionally, expression of several types of decoy recep-
tors is believed to potentially confer protection to normal cells against wayward pro-
apoptotic signals [Almasan and Ashkenazi, 2003, Bouralexis et al., 2005, Kelley and
Ashkenazi, 2004, Chen et al., 2003]. Thus, activation of the extrinsic pathway can
provide an appealingly high kill ratio of cancer cells to normal cells.
The human body produces a number of endogenous ligands that activate various
death receptors expressed on the surface of cells (see Figure 1.1 for examples). Some
13
of these ligands have been cloned, in whole or in part, to be used as anti-cancer drugs;
antibodies that bind and activate a number of these death receptors are also being
developed [Ashkenazi, 2008].
1.3.2 Cytotoxic Drugs and the Intrinsic Pathway
A common feature of cancer cells is that they proliferate rapidly. A frequent target
of anti-cancer drugs is the replicating DNA in these rapidly proliferating cells. These
cytotoxic drugs generally bind to the replication machinery or the DNA itself, stalling
the replication machinery or creating irreparable DNA strand breaks and thereby
triggering the intrinsic apoptotic pathway [Weinberg, 2007, Vanhoefer et al., 2001].
Since these cytotoxic drugs target cells that are in the DNA replication stage of
the cell cycle, most cells in the body are not substantially aected by this kind of
anti-cancer therapy. However, normal hair cells, the cells lining the intestine, and a
number of blood-precursor cells in the bone marrow turn over rapidly as well and are
also killed by cytotoxics, causing a number of adverse side eects including hair loss,
gastrointestinal sensitivity or bleeding, and anemia or immunodeciency.
1.3.3 Combination Therapies Exploit Intrinsic and Extrinsic
Pathway Cross-Talk
In some cell lines, activation of only the extrinsic pathway or the intrinsic pathway
is sucient to induce apoptosis. However, for cell lines that are resistant to the
activation of a single pro-apoptotic pathway, triggering both pathways can sometimes
14
overcome this resistance [Almasan and Ashkenazi, 2003]. One of the advantages of
co-dosing agonists of both the intrinsic and extrinsic pathways is that it is often
possible to give smaller doses of the cytotoxic (intrinsic agonist) agent being used,
thereby reducing the likelihood of adverse side eects [Sugamura et al., 2008, Ray
et al., 2007].
In general, because activation of the intrinsic pathway (1) induces the expression
of death ligands on the cell surface, (2) upregulates a number of intracellular pro-
apoptotic molecules, and (3) downregulates a number of intracellular anti-apoptotic
molecules, combination treatments have been found to be most successful when the
drug targeting the intrinsic pathway is given one to several days in advance of the
drug targeting the extrinsic pathway, a process called chemosensitization [Almasan
and Ashkenazi, 2003, Vanhoefer et al., 2001, Sugamura et al., 2008, Merino et al.,
2007, Debatin and Krammer, 2004, Wang and El-Deiry, 2003].
1.3.4 Drugs Targeting the Extrinsic Pathway
A number of drugs have been developed to target the extrinsic pathway in cancer
cells. Pro-apoptotic receptor agonists (PARAs) constitute the main sub-group of these
drugs, and primarily target DR4 (death receptor 4) and/or DR5 (death receptor 5).
DR4 is targeted by Mapatumumab (HGS-ETR1), a fully human immunoglobulin G1
(IgG1) monoclonal antibody. DR5 is targeted by fully human IgG1 monoclonal anti-
bodies Lexatumumab (HGS-ETR2), Apomab, Conatumumab (AMG655), and HGS-
TR2J (KMTR2); humanized IgG1 monoclonal antibody Tigatuzumab (CS-1008);
and chimeric (mouse/human) IgG1 monoclonal antibody LBY135. The recombinant
human protein rshApo2L/TRAIL (AMG951, PRO1762, Dulanermin) targets both
15
DR4 and DR5 [Ashkenazi, 2008, Fox et al., 2010, Storey, 2008, Ashkenazi and Herbst,
2008]. Below, two of these compounds (rshApo2L/TRAIL and Conatumumab) are
described in more detail.
Recombinant Soluble Human (rsh)Apo2L/TRAIL (AMG951, PRO1762,
Dulanermin)
Native Apo2L/TRAIL (apoptosis-inducing ligand 2/tumor necrosis factor-related
apoptosis-inducing ligand) is a member of the tumor necrosis factor (TNF) gene
superfamily, and was originally cloned because of its genetic similarity to the Fas lig-
and [Chen et al., 2003]. Apo2L/TRAIL naturally occurs as a type II transmembrane
protein, whose extracellular region can be cleaved to produce a soluble polypep-
tide [Kelley and Ashkenazi, 2004]. The soluble portion of Apo2L/TRAIL forms a
homotrimer that is stabilized by the binding of a zinc atom; without stoichiometric
amounts of zinc atoms available, Apo2L/TRAIL molecules tend to aggregate and lose
solubility, which may contribute to drug-related hepatotoxicity [Almasan and Ashke-
nazi, 2003, LeBlanc and Ashkenazi, 2003]. However, with the appropriate formulation,
Apo2L/TRAIL has little toxicity against normal cells [Almasan and Ashkenazi, 2003,
Kelley and Ashkenazi, 2004, LeBlanc and Ashkenazi, 2003, Hellmann et al., 2004].
When zinc atoms are available, Apo2L/TRAIL forms a stable 60 kDa homotrimer
that simultaneously binds three death receptors (there are two death receptor types
that bind Apo2L/TRAIL: DR4 and DR5) on the surface of the target cell, where
each death receptor binds to the homotrimer at the junction between two adjacent
Apo2L/TRAIL molecules [Almasan and Ashkenazi, 2003, Hellmann et al., 2004].
DR4 and DR5 are also called TRAIL receptors 1 and 2 (TRAIL-R1 and TRAIL-R2).
16
Some cells only express either DR4 or DR5, but in cells that express both, heterocom-
plexes can form in which both receptor types are bound by the same Apo2L/TRAIL
homotrimer. However, it is unknown if these heterocomplexes have a signaling func-
tion distinct from those involving only one receptor type [LeBlanc and Ashkenazi,
2003]. Once the Apo2L/TRAIL homotrimer binds three death receptors, the extrinsic
apoptotic pathway is initiated (see Section 1.2.1). Of the two types of death receptors
bound by Apo2L/TRAIL, DR5 appears to contribute a greater pro-apoptotic eect
than does DR4 when activated in cells that express both receptors [Kelley et al.,
2005].
Figure 1.5. Apo2L/TRAIL death receptors and decoy receptors [Almasan and
Ashkenazi, 2003]
Amgen and Genentech co-developed rshApo2L/TRAIL (Amgen compound name
AMG951) by synthesizing the soluble extracellular portion (amino acids 114 through
281) of the native transmembrane Apo2L/TRAIL protein using Escherichia coli [Fox
et al., 2010, Hellmann et al., 2004]. In a proof-of-concept study on mice bearing
COLO205 xenografts, administration of AMG951 increased serum levels of caspases-
3 and -7 in a dose-dependent manner [Amgen, 2007]. (COLO205 is a human colon
cancer cell line descended from a sample taken from a Caucasian male; it is one of
17
many cell lines commonly used to screen the ecacy of new anti-cancer drugs; see Sec-
tion 2.1 for more details.) RshApo2L/TRAIL has been shown to successfully induce
apoptosis in in vitro and in vivo cultures of cancer cell lines that include those derived
from the colon, kidney, lung, prostate, pancreas, and breast [Kelley and Ashkenazi,
2004, LeBlanc and Ashkenazi, 2003]. Moreover, co-dosing of rshApo2L/TRAIL with
cytotoxic agents has been shown to be more eective in inducing apoptosis than either
agent alone [Sugamura et al., 2008, Ray et al., 2007, Ray and Almasan, 2003].
In addition to the two death receptors, DR4 and DR5, there are two other receptors
expressed on the surface of cells that interact with Apo2L/TRAIL: decoy receptor 1
(DcR1) and decoy receptor 2 (DcR2). Both DcR1 and DcR2 closely resemble DR4 and
DR5 in their extracellular domains; however, DcR1 completely lacks a cytosolic region
and DcR2 possesses a truncated intracellular region, thereby rendering both decoy
receptors incapable of initiating the extrinsic apoptotic pathway (see Figure 1.5) [Kel-
ley and Ashkenazi, 2004]. There is an additional, soluble, decoy receptor called osteo-
protegerin (OPG) that interacts with Apo2L/TRAIL; its anity for Apo2L/TRAIL
is relatively low, but high levels of OPG have been associated with a diminished
capacity of Apo2L/TRAIL to induce apoptosis in OPG-producing prostate cancer
cells [Almasan and Ashkenazi, 2003, Bouralexis et al., 2005]. Although by no means
fully elucidated, the function of these decoy receptors appears to be to confer protec-
tion to normal cells against wayward pro-apoptotic signals [Bouralexis et al., 2005,
Kelley and Ashkenazi, 2004, Chen et al., 2003].
18
Conatumumab (AMG655)
Conatumumab (Amgen compound name AMG655) is a 145 kDa fully human mon-
oclonal IgG1 antibody that binds and activates DR5/TRAIL-R2, resulting in the
activation of the extrinsic pathway (see Section 1.2.1) [Kaplan-Lefko et al., 2010,
Zoog et al., 2010, American Medical Association, 2008].
Conatumumab has been shown to induce apoptosis in in vitro and in vivo cul-
tures of cancer cell lines derived from the colon, lung, and pancreas; and like
rshApo2L/TRAIL, Conatumumab has shown increased ecacy when co-dosed with
cytotoxic agents [Fox et al., 2010, Zoog et al., 2010]. However, activity of Conatu-
mumab has been found to be dependent on cross-linking of the antibodies bound to
clustered receptors to augment the pro-apoptotic signal to sucient levels to provide
anti-tumoral eect (see Figure 1.6) [Kaplan-Lefko et al., 2010, Zoog et al., 2010].
Figure 1.6. a) Binding of antibody to three associated DR5 receptors; b) Clustering
of pre-associated receptors by simultaneous binding of antibodies; c) Cross-linking
of the Fc regions of antibodies bound to clustered receptors [Ashkenazi, 2008]
19
1.3.5 Drugs Targeting the Intrinsic Pathway
As mentioned in Section 1.3.2, cytotoxic agents are cell-cycle specic and take advan-
tage of the rapidly dividing nature of most cancer cells, frequently targeting the
replicating DNA of these cells, as it is in a particularly vulnerable state during syn-
thesis. Other cytotoxic drugs disrupt the cell-cycle by targeting RNA or cell-division
machinery in dividing cells. These approaches ultimately result in halting of the
cell-cycle and the activation of the intrinsic apoptotic pathway. There are a number
of cytotoxic agents, including Paclitaxel (Taxol), Vinorelbine, Irinotecan (CPT-11),
Doxorubicin, and Fluorouracil (5-FU). Vinorelbine and Paclitaxel disrupt cell divi-
sion by interacting with microtubules and inhibiting proper formation of the mitotic
spindle [Long and Fairchild, 1994, Livingston et al., 1997]; Irinotecan and Doxoru-
bicin both stabilize DNA Topoisomerases (types I and II, respectively) while they
are covalently bonded to the DNA, resulting in replication machinery problems and
DNA strand breaks [Armand et al., 1995, Burden and Oshero, 1998]; metabolites
of Fluorouracil interfere with DNA and RNA synthesis, and act as pyrimidine com-
petitors for inclusion in newly-synthesized DNA and RNA [Parker and Cheng, 1990,
Eaglstein et al., 1970]. Below, Irinotecan is described in more detail.
Irinotecan (CPT-11)
Irinotecan hydrochloride trihydrate (also referred to as CPT-11) is a semi-synthetic
derivative of the plant-derived compound camptothecin, designed to be a water-
soluble molecule to aid in eectiveness of the drug and to reduce its toxicity [Stewart
et al., 1997, Mathijssen et al., 2001, Armand et al., 1995]. It is active against a
20
number of cancer cell types, but has particularly notable antitumorigenic eects on
cancers of the colon and rectum.
Although CPT-11 has some anti-cancer activity, its primary function is as a prodrug:
CPT-11 is converted to its more active metabolite, SN-38, through the cleavage of the
ester bond at C10 by carboxyl esterase [Mathijssen et al., 2001, Drengler et al., 1999].
Both CPT-11 and SN-38 act as inhibitors of the enzyme DNA topoisomerase I; how-
ever, SN-38 is approximately 100 to 1000-fold more potent than is CPT-11 [Stewart
et al., 1997, Mathijssen et al., 2001, Kawato et al., 1991].
During the DNA synthesis phase of cell division, DNA Topoisomerase-I and
Topoisomerase-II allow the progression of the replication fork by facilitating the
unwinding of the super-coiled DNA ahead of the replication machinery through the
creation of single-stranded (type I) and double-stranded (type II) breaks in the DNA.
Both topoisomerase types produce breaks in the DNA through a process that creates
a covalent bond between the enzyme and the DNA, which is referred to as a cleavable
complex. SN-38 interacts with this cleavable complex to stabilize the covalent bond.
As a result, the moving replication fork collides with the xed cleavable complex,
causing DNA replication to halt, irreversible DNA strand breaks, and, nally, cell
death [Armand et al., 1995, Drengler et al., 1999].
Because SN-38 requires the presence of the cleavable complexes associated with DNA
synthesis to have its cytotoxic eect, CPT-11's agency is temporally limited to the
S-phase of a cell's replication cycle. As a result, it has been found that protracted
dosing schedules are the most eective way of administering CPT-11, since that allows
a much larger portion of the replicating tumor cells to be exposed to the drug during
their S-phase [Mathijssen et al., 2001, Drengler et al., 1999].
21
Because SN-38 is potentially cytotoxic to any cell that is going through the process
of DNA replication, many normal cells that divide rapidly as part of their natural
function in the body are also susceptible to its eects. As a result, the most common
side eects of CPT-11 chemotherapy are neutropenia and diarrhea (particularly for
oral dosing), but adverse side eects include nausea/anorexia, hair loss, and physical
weakness [Armand et al., 1995, Drengler et al., 1999].
1.4 Potential Challenges Faced by Anti-Cancer
Therapies
1.4.1 Activation of NF-B by Death Receptors
The activation of TNFR1 (tumor necrosis factor receptor 1) by binding of TNF
has been shown to produce both pro-apoptotic and pro-survival intracellular sig-
nals through divergent signaling cascades. Initiation of the pro-apoptotic signal is
discussed in Section 1.2.1. The pro-survival signal is brought about by the acti-
vation of TRAF2 (tumor necrosis factor receptor-associated factor 2) by TRADD
(tumor necrosis factor receptor 1-associated death domain protein, an adapter pro-
tein for TNFR1) or RIP (receptor-interacting protein), and the subsequent activation
of NF-B by TRAF2 (see Figure 1.7) [Chaudhary et al., 1997, Hsu et al., 1996, Liu
et al., 1996]. Activation of NF-B results in its translocation to the nucleus, where
it promotes the transcription of a number of genes associated with immunity and
in
ammation, as well as angiogenesis and cell invasion. NF-B activation also pro-
duces intracellular pro-survival/anti-apoptotic signals by upregulating a number of
22
pro-survival factors that directly and indirectly aect the activity of caspases in the
cell [Ahn et al., 2007, Karin and Lin, 2002, Aggarwal, 2004, Micheau et al., 2001].
Some of the pro-survival products include c-FLIP (cellular FLICE [Fas-associated
death domain protein-like interleukin-1 beta converting enzyme] inhibitory protein),
which inhibits the activation of caspase-8 (also known as FLICE); c-IAP1 and 2
(cellular inhibitor of apoptosis protein 1 and 2), which inhibit the activity of execu-
tioner caspases-3 and -7 and inhibit the activation of procaspases-6 and -9; and XIAP
(X chromosome-linked inhibitor of apoptosis protein), which inhibits the activation
and/or activity of caspases-3, -6, -7, -8, -9, and -10 [Karin and Lin, 2002, Aggar-
wal, 2004, Micheau et al., 2001, Salvesen and Duckett, 2002]. Other studies have
found that at least part of the IAPs' ability to inhibit executioner caspase function is
through the mechanism of polyubiquitination (a process wherein a protein, such as a
caspase, is tagged at multiple sites with a small protein called ubiquitin) whereby the
caspase is directed to a proteasome for degradation, speeding the removal of active
caspases from the cytosol [Zhang et al., 2004, Choi et al., 2009].
Some studies have shown that DR4 and DR5 can activate NF-B through the
TRADD/TRAF2 pathway, thereby producing a simultaneous pro-survival signal
alongside the expected pro-apoptotic signal [Chaudhary et al., 1997, Hsu et al., 1996,
Liu et al., 1996, Van Antwerp et al., 1996, Ashkenazi, 2000, Schneider et al., 1997].
The pro-survival factors upregulated as a result of NF-B activation inhibit the activa-
tion of executioner caspases, inhibit the function of executioner caspases, and increase
the removal of executioner caspases.
23
Figure 1.7. Activation of NF-B by DR4 and DR5 [Chaudhary et al., 1997]
1.4.2 Drug Delivery to Tumor Cells
Diculties with drug delivery to the site of action have become an increasingly
explored source of drug resistance: an anti-cancer drug must be able to kill can-
cer cells when it comes in contact with them, but the drug must also be able to reach
the cancer cells in order for it to be a viable treatment [Dreher et al., 2006, Curnis
et al., 2002, Sugahara et al., 2010]. Delivery of an anti-cancer drug to its target
(cancer) cells involves three basic processes: distribution through the vascular space,
transportation across the capillary walls into the interstitium, and diusion through
the interstitial space to the cells [Zheng et al., 2001, Jain, 1998, 1994].
24
When tumor cells proliferate, their growth is often more rapid than the requisite
growth of blood vessels to adequately perfuse the new tissue volume. In addition,
the blood vessels that are produced are often less functional than those in normal
tissues, which can result in regions of the tumor that are so poorly perfused that
the cells actually necrose as the tumor continues to grow [Dreher et al., 2006, Jain,
1994, Minchinton and Tannock, 2006]. Moreover, because the lymphatic system is
often underdeveloped in tumor tissue, the interstitial pressure is much higher than in
normal tissue, which impedes the pressure-gradient-dependent convection of the drug
across blood vessel walls and through the interstitial space [Jain, 1994]. It is likely
that in xenografts drug penetration is even worse because cells are more tightly packed
than in naturally occurring tumors, and the denser the cell matrix, the more dicult
it is for drugs to move through the tissue [Zheng et al., 2001, Grantab et al., 2006].
Increasing tumor size appears to exacerbate drug delivery diculties associated with
poor perfusion and unfavorable interstitial pressures. Moreover, tumor regression due
to treatment may selectively leave more poorly perfused regions of the tumor.
1.4.3 Dose-Limiting Toxicities
A primary issue with cytotoxic agents is that they do not discern between normal
cells and cancer cells. As a result, a number of normal cells that happen to be in the
process of cell-divsion are also killed during anti-cancer therapies that utilize cyto-
toxics, often leading to dangerous side eects [Weinberg, 2007]. These toxicities can
be so problematic that therapy has to be reduced or stopped altogether, limiting
25
the therapeutic ecacy of these drugs. Such dose-limiting toxicities include neu-
tropenia/myelosuppression, neuromuscular toxicity, mucositis, and diarrhea [Rowin-
sky et al., 1993, Mahood et al., 1991, Livingston et al., 1997, Abigerges et al., 1995].
It was recognized long ago that reduction of these dangerous side eects is necessary
to allow for more eective dosing strategies using cytotoxics, and work in this eld
continues [Livingston et al., 1997, Mahood et al., 1991, Pettengell et al., 1992, Putz
et al., 2009, Stathopoulos et al., 2010, Chang et al., 2010].
1.5 Mouse Models for Cancer
Usually a potential anti-cancer drug is rst tested via in vitro screening against a
wide range of cancer cell lines. If the anti-cancer drug shows ecacy in vitro against
certain cell lines or against general categories of cancer, mice are usually used for
early in vivo studies to determine the ecacy of the drug against these cell lines or
cancer types in the more complex environment of a living system.
1.5.1 Mouse Genetic Models for Cancer
One form of in vivo testing involves mice that have been genetically modied through
transfection with mutant, activated oncogenes (cancer-promoting genes) in order to
make them predisposed to certain types of cancer; these mice are bred over generations
to develop well-characterized genetic proles for a particular cancer. Another method
is to expose mice to mutagenic chemicals to induce cancer in the desired tissue or
tissues. Both of these methods produce what are referred to as mouse models for
cancer. In these mouse models, the cancers develop in analogous (though somewhat
26
extreme) situations to human cancers, providing a model that mimics the matrix of
support cells that human tumors have [Weinberg, 2007].
These genetic models were developed to overcome some of the shortcomings of the
mouse xenograft model (see Section 1.5.3) [Garber, 2006]. However, because these
tumors are derived from and composed of solely murine cells, sometimes the cell-
surface molecules or intracellular signaling complexes are substantially dierent from
those of human cancer cells [Mattern et al., 1988]. As a result, there is still a need to
explore a drug's eect on actual human cancer cells within the complexity of a living
system, but before putting actual humans at risk for possibly dangerous side eects.
1.5.2 Mouse Xenograft Models
When studying the molecular mechanisms of the interaction of an anti-cancer drug
with a human cancer, one of the models that can be useful is the mouse xenograft.
In the mouse xenograft model, a mouse that has been bred to be immunologically
compromised (common strains include Nude, NOD/SCID, and Rag1/2 mutant mice)
is implanted with human cancer cells [Weinberg, 2007]. There are two basic kinds
of xenografts: (1) orthotopic xenografts involve implantation of cancer cells into the
same tissue-type they originated from (e.g., human breast cancer cells implanted into
mouse breast pads) to create a more realistic growth environment; (2) subcutaneous
or intraperitoneal xenografts involve the injection of cancer cells under the skin (often
on the
ank) or into the intraperitoneal cavity of the mouse.
In most pre-clinical studies the injected tumor cells are allowed to grow unperturbed
for several days or weeks before any drug is given. Once the average tumor volume of
27
all the test animals has reached a certain size (e.g., 300 mm
3
), the animals are usually
randomized into one or several treatment groups, and one untreated control group
(which often receives the drug vehicle). The animals are then followed throughout
the duration of the treatment schedule, and sometimes for a period of time afterward,
with tumor measurements usually taken every few days.
Since it is dicult to actually measure the volume of a tumor, even one implanted
subcutaneously on a
ank, there are many methods for approximating tumor volume.
The most common calculations involve taking the greatest and smallest longitudinal
measurements of the tumor (referred to as L and W, respectively) and multiplying
them together in some third-order combination of the two (e.g.,LW
2
=2 or=6L
W
2
[Rocchetti et al., 2007, Bueno et al., 2008, Norton et al., 1976]).
1.5.3 Limitations of Subcutaneous Xenograft Models
Several disadvantages to the use of subcutaneous xenograft models have been pointed
out. The biggest limitation is that the growth environment for the tumor cells is not
human: it is smaller, with a dierent time scale and dierent enzymes present, thereby
providing dierent pharmacokinetics for the tumor and a dierent (non-human) set
of cells for the tumor to communicate with and adhere to. Moreover, the tumor is
implanted in a non-physiologically relevant location: it can be dicult for tumors
to get the blood supply they need in their subcutaneous site, which hinders both
nutrient-dependent growth and the ability of the drug to reach the tumor. The
implantation of cancer cells without their support matrix may also substantially alter
their growth behavior [Garber, 2006]. Additionally, the human cell lines used to
initiate tumor growth in these xenograft models have generally been maintained in
28
culture dishes for many generations, thereby selecting for cells that may not be good
representations of the original tumor [Becher and Holland, 2006].
1.5.4 Advantages of Subcutaneous Xenograft Models
Despite the limitations associated with subcutaneous xenograft models, they are still
a useful part of the anti-cancer drug-evaluation process. Because of the unknown
ecacy and risks, it is not ethical to begin the drug evaluation in people; however,
there is a need for more realistic conditions than an in vitro study can provide. Thus,
there is a demand for some kind of physiological environment for tumor growth and
drug delivery. Mice are an ideal species for such testing because many strains of
mice have been bred to possess highly conserved genes (mice are genetically the best
categorized of all mammals), thereby reducing variability from individual to indi-
vidual and providing researchers with experimental settings they can tailor to their
needs [Weinberg, 2007]. Moreover, because it is possible to implant human cancer
cells in immunocompromised strains, it is possible to test new drugs or combinations
of drugs directly on human tumors, providing the opportunity to determine the direct
killing mechanism of the drug [Lowenstein and Castro, 2009].
While orthotopic models are useful, it is not always practical or cost-eective to
implant tumors in their physiologically analogous location. Subcutaneous implanta-
tion is quick and inexpensive, allows for fairly easy monitoring of tumor volume, and
usually promotes rapid initial tumor growth, making research using subcutaneous
implantation economical and ecient [Weinberg, 2007, Garber, 2006]. Ultimately, it
29
is a good starting place for in vivo drug evaluation. Understanding the drug's molec-
ular mechanism of action in a mouse xenograft can provide important insights into
the drug's action in humans, allowing for a better transition to treatments in humans.
1.6 Mathematical Tumor Regression Models for
Mouse Xenografts
A number of mathematical models have been proposed to describe the general unper-
turbed growth behavior and treated regression behavior of xenograft tumors. Some
models attempt to include a mechanistic component in the mathematical equations,
while others are fairly utilitarian in their approach to describe the overall tumor
growth/regression behavior.
1.6.1 Gompertzian Model
One of the earliest equations to be applied to tumor growth was the Gompertz equa-
tion, which was derived from the law of mortality published by Benjamin Gompertz
in 1825 [Norton et al., 1976]. The model produces a sigmoidal growth curve that has
three basic phases: near-exponential growth when the tumor is small, approximately
linear growth in the middle, and an exponential decay in growth rate as the tumor
reaches its maximum size (see Figure 1.8).
The equation for Gompertzian growth comes from the simultaneous solution of
two dierential equations, which describe exponential growth with an exponentially
decreasing growth rate:
30
Figure 1.8. Gompertzian growth curve; N
0
is the initial tumor size, N
i
is the tumor
size at the in
ection point, and N
1
is the maximum tumor size [Kozusko and
Bajzer, 2003]
(1.1)
d
dt
N(t) =N(t)G(t)
(1.2)
d
dt
G(t) =KG(t)
where N(t) represents the total tumor size, G(t) represents the tumor growth rate,
and K is a constant that is greater than zero. The combined dierential equation
and nal solution for Gompertzian growth are:
(1.3)
d
dt
N(t) =KN(t) ln

N(1)
N(t)

=KN(t) ln

N(t)
N(1)

(1.4) N(t) =e
ln(N(1))(1e
Kt
)
31
where ln(x) is the natural log of x, N(1) is the asymptote for the maximum tumor
size, and e
x
is Eulers number raised to the power of x [Norton et al., 1976, Kendal,
1985, Kozusko and Bourdeau, 2007].
1.6.2 Cancer Stem-Cell Models
Over the last decade, the theory of cancer stem cells or cancer-initiating cells has been
proposed as an explanation for a number of cancer characteristics. Cancers have long
been recognized as having a heterogeneous cell make-up, both in terms of phenotype
and in their ability to proliferate, even when they are originally derived from a single
cell [Ward and Dirks, 2007, Pardal et al., 2003]. Additionally, growth of a new tumor
from the gross transplantation of cancer cells from one animal to another or from one
culture plate to another is only successful a fraction of the time [Ward and Dirks,
2007, Pardal et al., 2003, Reya et al., 2001]. The discovery that particular cell-surface
markers can be highly indicative of a cell's ability to generate a viable cancer when
transplanted into NOD/SCID mice helped the theory of cancer-initiating cells gain
credibility [Ward and Dirks, 2007, Reya et al., 2001]. Since then, suspected cancer-
initiating cells have been identied for a number of cancers, including cancers of the
breast, skin, and brain [Ward and Dirks, 2007].
The main feature of the cancer-initiating-cell model is that there is a small sub-
population of cells that are capable of both self-renewal, to maintain their numbers,
and dierentiation, to produce the variety of phenotypically dierent cells present in a
tumor. Dierentiated cells generally have reduced proliferative potential as compared
to the cancer-initiating cells, and make up the bulk of the tumor [Ward and Dirks,
2007, Pardal et al., 2003, Reya et al., 2001].
32
In most cancer-initiating-cell models, the cells are divided into three groups: stem
cells, which proliferate relatively slowly and have the ability for ongoing cell renewal;
semi-dierentiated cells or intermediate cells, which proliferate rapidly and have the
ability for limited cell renewal; and fully-dierentiated or non-proliferative cells, which
have no proliferative capacity [Boman et al., 2007, Johnston et al., 2007a, Tomlinson
and Bodmer, 1995]. In the model presented by Boman et al. [2007], stem cells (SCs)
self-renew, produce intermediate cells (ICs), or produce non-proliferative cells (NCs),
and are removed from the SC population by symmetric division to become two ICs
or by becoming an NC. ICs self-renew or produce NCs, and are removed from the IC
population by becoming an NC. NCs do not perform any kind of cell replication; the
only kinetic process they go through is their removal from the tumor cell population.
See Figure 1.9 for a schematic of the dierent events that govern the kinetics of the
three cell populations.
In the models presented by Tomlinson and Bodmer [1995] and Johnston et al. [2007a],
stem cells (N
0
) self-renew, become semi-dierentiated cells, or die; semi-dierentiated
cells (N
1
) self-renew, become fully-dierentiated cells, or die; and fully dierentiated
cells (N
2
) die (see Figure 1.10). The dierential equations for this growth are:
(1.5)
d
dt
N
0
(t) = (
3

2

1
)N
0
(t)
(1.6)
d
dt
N
1
(t) = (
3

2

1
)N
1
(t) +
2
N
0
(t)
(1.7)
d
dt
N
2
(t) =
2
N
1
(t)
N
2
(t)
where
3
,
2
, and
1
are the per-capita rates of N
0
proliferation, dierentiation,
and death, respectively;
3
,
2
, and
1
are the per-capita rates of N
1
proliferation,
33
Figure 1.9. Kinetics describing the relationships between stem cell (SC),
intermediate cell (IC), non-proliferative cell (NC), and eradicated cell (EC)
populations [Boman et al., 2007]
dierentiation, and death, respectively; and
is the per-capita rate of removal ofN
2
.
Johnston et al. [2007a,b], also suggested possible alterations to these equations to
cause a plateau in the tumor size; these involved adding a linear or saturable term
that increased the dierentiation rate ofN
0
andN
1
based on the value ofN
0
andN
1
,
respectively.
34
Figure 1.10. Diagram of the Johnston stem cell model of the colonic crypt [Johnston
et al., 2007a]
1.6.3 Other Unperturbed-Growth Models
After exploring several stem cell models, we considered the simpler models for unper-
turbed growth described below. Unlike the more complex stem cell models, these
more compact models can be applied to tumor size data from xenograft experiments
without additional information such as the fraction of cells actively proliferating or
the cell-cycle time of various tumor cell sub-populations.
Model 1: Simeoni Model
The rst unperturbed-growth model was taken from Simeoni et al. [2004], which
describes net unperturbed tumor proliferation as having two phases: an exponential
phase followed by a linear phase (see Figure 1.11). No plateau is modeled because,
throughout the duration of their studies, there was no indication of a plateau in tumor
growth. The dierential equation that describes unperturbed growth in the Simeoni
model is:
35
d
dt
TV (t) =

0
TV (t)

1 +

0

1
TV (t)

1=
(1.8)
where
0
is the exponential growth rate,
1
is the linear growth rate, is a term that
facilitates the switch between exponential and linear growth (Simeoni et al. [2004]
found that a value of 20 provides a suciently sharp transition), and TV (t) is the
total tumor volume.
Figure 1.11. Simulation of control data using the base Simeoni model;
0
= 0.2/day,

1
= 80 mm
3
/day, TV (0) = 30 mm
3
Model 2: TV
SS
Model
The second model we used describes net unperturbed growth as a sigmoidal curve
using two parameters: K
G
, the rst-order net growth rate constant; and TV
SS
, the
36
steady-state (maximum) tumor volume [Kozusko and Bourdeau, 2007, Yang et al.,
2010]. This equation, also referred to as a logistic function, is very similar to the
Gompertz equation; the main dierence between the two is that the logistic curve
approaches its upper asymptote more sharply than does the Gompertzian curve. Fig-
ure 1.12 shows a typical growth curve for the TV
SS
Model. The dierential equation
describing this growth is:
d
dt
TV (t) =K
G

1
TV (t)
TV
SS

TV (t) (1.9)
Figure 1.12. Simulation of control data using the base TV
SS
model; K
G
= 0.2/day,
TV
SS
= 2000 mm
3
, TV (0) = 30 mm
3
37
Model 3: TG
50
Model
The third model we used came from Yamazaki et al. [2008]; Figure 1.13 shows a
typical growth curve for the TG
50
Model. It diers from the rst two models in that
it does not lump unperturbed growth and cell turnover together into a `net-growth'
function, but rather, it has separate terms for both cell proliferation and natural cell
removal. It also incorporates a term that decreases the proliferation rate as the tumor
size increases:
d
dt
TV (t) =K
inTV

1
TV (t)
TG
50
+TV (t)

TV (t)K
outTV
TV (t) (1.10)
where K
inTV
represents the rst-order intrinsic tumor growth rate constant, TG
50
represents the tumor size that inhibits tumor growth by 50 percent, and K
outTV
represents the rst-order intrinsic removal rate constant of the tumor [Yamazaki et al.,
2008].
38
Figure 1.13. Simulation of control data using the base TG
50
model; K
inTV
=
0.8/day, K
outTV
= 0.6/day, TG
50
= 6000 mm
3
, TV (0) = 30 mm
3
1.7 Clinical Relevance of Combination Therapies
In a clinical setting, by far the most common approach to anticancer treatment is
some kind of combination therapy utilizing multiple drugs, usually of complementary
types (e.g., cytotoxics that target dierent elements of dividing cells or a cytotoxic
and a PARA) [Stathopoulos et al., 2010, Rowinsky et al., 1993, Pettengell et al.,
1992, Moulder, 2010, Lane, 2006]. Additionally, many novel cancer treatments are
evaluated as an addition to an already established anticancer regimen. However,
few eorts have been made to quantify the synergistic eects of these combination
therapies (when they exist), and even fewer eorts have been made to model such
drug-eect interactions. One notable exception is the work of Harrold et al. [2012];
39
their focus is on modeling the eects of the CD20 agonist Rituximab, but their work
also incorporates mechanisms of interaction with the PARA rshApo2L/TRAIL.
Moreover, a number of early clinical trials have shown little or no additional eect
when a targeted therapy is added to an established cytotoxic regimen. There are a
few possible explanations for this, including mechanistic antagonism (e.g., one drug
negatively aects the PK of another drug or one drug aects the cancer cells in
such a way that they are no longer aected by another drug, especially when drugs
are given simultaneously), and overlapping targets within the tumor cells to multiple
components of the combination therapy such that no net clinical gain is observed when
the compounds are given together [Chen and Dancey, 2008, Zwitter, 2010, Woodcock
et al., 2011]. Whether a combination therapy shows synergism, antagonism, or no
interaction at all has been shown to be schedule-dependent in in vitro studies [Zwitter,
2010]. Thus, understanding and modeling these interactions pre-clinically may allow
for a better clinical approach to both de-facto and tailored combination therapies.
1.8 Specic Aims
The overall goal of this research is to develop systems models for the cell-extrinsic
apoptotic pathway based on the mechanism of action of the two pro-apoptotic agonists
rshApo2L/TRAIL (a ligand that binds to DR4/TRAIL-R1 and DR5/TRAIL-R2) and
Conatumumab (an anti-DR5/TRAIL-R2 monoclonal antibody). While the pathways
involved in the mechanism of action of these two drugs (i.e., activation of the extrin-
sic pathway) have been studied (see Section 1.2.1), and while the kinetics of both
caspase-activating molecular reactions and apoptosis of individual cells have been
40
evaluated [Albeck et al., 2008a, Stennicke et al., 1998, Wolf and Green, 1999], a quan-
titative understanding (exposure-response models) of the action of these PARAs is
limited (Harrold et al. [2012] do provide a quantitative model for rshApo2L/TRAIL).
In this work, plasma drug concentration data as well as time series measurments of
tumor burden from mouse COLO205 tumor xenograft experiments following adminis-
tration of rshApo2L/TRAIL, or Conatumumab, or each of the PARAs in combination
with the cytotoxic Irinotecan are used to address the following specic aims:
1. Develop descriptive models for plasma pharmacokinetics of rshApo2L/TRAIL
following intravenous (IV) and intraperitoneal (IP) administration, and develop
a descriptive model of plasma pharmacokinetics of Conatumumab following IP
administration for use in modeling xenograft tumor burden data.
2. Investigate existing models for tumor progression suitable for use with the tumor
burden data from the current PARA COLO205 xenograft experiments.
3. Develop systems models for the cell-extrinsic apoptotic pathway linking
drug plasma kinetics to tumor burden time series data using pooled
rshApo2L/TRAIL and Conatumumab tumor size data.
(a) Using alternate models, investigate hypotheses regarding reduced ecacy
of the PARAs on tumor progression during extended dosing.
(b) Using the developed models, relate kinetics of specic model signals to
measured kinetics of the extrinsic apoptotic pathway.
41
4. Extend the extrinsic apoptotic pathway model to allow investigation of the
action of the cytotoxic Irinotecan when given in combination with each of the
two PARAs.
(a) Develop descriptive model for plasma pharmacokinetics of Irinotecan fol-
lowing IP administration.
(b) Model regression in COLO205 xenograft models following co-
administration of rshApo2L/TRAIL and Irinotecan.
(c) Model regression in COLO205 xenograft models following co-
administration of Conatumumab and Irinotecan.
(d) Simultaneously model regression in COLO205 xenograft models follow-
ing either co-administration of rshApo2L/TRAIL and Irinotecan or co-
administration of Conatumumab and Irinotecan.
(e) Using the developed combination model, investigate the level of interac-
tion eect between Irinotecan and rshApo2L/TRAIL, and Irinotecan and
Conatumumab.
42
Chapter 2.
Experimental Data
Mouse pharmacokinetic and tumor xenograft data following rshApo2L/TRAIL
(AMG951) and Conatumumab (AMG655) administration in COLO205 xenograft
bearing Nude mice were made available by Amgen (Dr. Thomas Sun and Dr.
Matthew Hsu) and were collected as part of pre-clinical trials of these two compounds.
The experimental procedures are summarized brie
y below for each compound and
pharmacokinetic and tumor xenograft size data are presented for each study used in
the modeling analysis.
2.1 COLO205 Cell Line
COLO205 is a human colon adenocarcinoma cell line derived from a Caucasian male.
It was chosen as one of the cell lines used for pre-clinical xenograft studies involv-
ing agonists of DR4 and DR5 because it is sensitive to Apo2L/TRAIL and would
therefore give insight into the anti-tumor eects of other DR4 and/or DR5 agonists.
This sensitivity also allowed for exploration of the ecacy of dierent dose sizes and
43
dosing regimens of these DR4 and/or DR5 agonists in COLO205 xenograft models
(as opposed to a number of other cell lines that are Apo2L/TRAIL resistant, such as
COLO320 and ARH-77, which would provide no information regarding dosing size or
regimen).
2.2 Pharmacokinetic Studies
2.2.1 rshApo2L/TRAIL
Mean plasma concentration data were obtained for two rshApo2L/TRAIL PK studies:
one IV study and one IP study. For the IV PK study, 10 milligrams per kilogram
(mg/kg) of rshApo2L/TRAIL was administered IV to COLO205 xenograft bearing
Nude mice; a total of seven plasma concentration observations were made 5, 15, 30,
45, 60, 120, and 180 minutes after the drug was administered. For the IP PK study,
60 mg/kg of rshApo2L/TRAIL was administered IP to COLO205 xenograft bearing
Nude mice; a total of eight plasma concentration observations were made 2, 5, 30,
60, 120, 240, 360, and 480 minutes after the drug was administered. (PK analyses
were done with time converted from minutes to days.) Figure 2.1 presents the mean
plasma concentration data for these two studies (only mean data was available).
44
Figure 2.1. Mean plasma concentration data for rshApo2L/TRAIL given IV and IP
2.2.2 Conatumumab
Plasma concentration data were available for 13 Conatumumab IP PK studies (no
data from IV-dosing studies were available). The IP dosing regimens, number of
observations, and observation times are given in Table 2.1, and median plasma con-
centration data for three of the 13 studies are shown in Figure 2.2. PK studies were
performed on Nude COLO205 xenograft bearing mice.
45
Dosing Regimen
Number of
Observations
Observation Times
(days after rst dose)
0.3 g/dose 2 times per week
for 5 doses
8 7, 10, 14, 14.042, 14.25, 15,
16, 17
1 g/dose 2 times per week for
5 doses
8 7, 10, 14, 14.042, 14.25, 15,
16, 17
3 g/dose 2 times per week for
5 doses
8 7, 10, 14, 14.042, 14.25, 15,
16, 17
10g/dose 2 times per week for
5 doses
8 7, 10, 14, 14.042, 14.25, 15,
16, 17
12.3 g/dose 2 times per week
for 4 weeks
17 0.25, 3, 3.25, 7, 7.25, 10,
10.25, 14, 14.25, 17, 17.25,
21, 21.25, 24, 24.25, 28,
32.29
30g/dose 2 times per week for
5 doses
8 7, 10, 14, 14.042, 14.25, 15,
16, 17
36.9 g/dose 2 times per week
for 4 weeks
17 0.25, 3, 3.25, 7, 7.25, 10,
10.25, 14, 14.25, 17, 17.25,
21, 21.25, 24, 24.25, 28,
32.29
36.9 g/dose 2 times per week
for 4 weeks
19 0.25, 3, 3.25, 7, 7.25, 10,
10.25, 14, 14.25, 17, 17.25,
21, 21.25, 24, 24.25, 28,
31.29, 35, 38.25
Single 80 g dose 8 0.25, 1, 3, 7, 14, 21, 28,
32.29
87.5 g/dose 1 time per week
for 4 weeks
14 0.25, 3, 7, 7.25, 10, 14,
14.25, 17, 21, 21.25, 24, 28,
35, 28.25
100 g/dose 2 times per week
for 5 doses
8 7, 10, 14, 14.042, 14.25, 15,
16, 17
Single 240 g dose 8 0.25, 1, 3, 7, 14, 21, 28,
32.29
Single 1600 g dose 9 0.25, 1, 3, 7, 14, 21, 28, 35,
38.25
Table 2.1. Conatumumab IP PK study dosing regimens and observation schedules
46
Figure 2.2. Median plasma concentration data for Conatumumab given IP (3 of 13
shown)
2.2.3 Irinotecan (CPT-11)
Mean plasma concentration data following an IP administration of 66 mg/kg of
Irinotecan were taken from Guichard et al. [1998] (see Figure 2.3). A total of eight
plasma concentration observations were made 5, 15, and 30 minutes and 1, 2, 4, 8,
and 24 hours after the drug was administered. (PK analyses were done with time
converted from minutes or hours to days.) The data consist of the average plasma
concentrations of Irinotecan taken from six animals sacriced at each of the eight
time points. It is important to note that the animals used in the study were female
BALB/c mice bearing P388 murine leukemia cells implanted IP [Guichard et al.,
47
1998]; therefore, it is possible that the PK behavior does not accurately re
ect the
PK of Irinotecan in the COLO205 subcutaneous xenograft Nude mouse model under
investigation.
Figure 2.3. Mean plasma concentration data for Irinotecan given IP
2.3 Monotherapy Tumor Xenograft Studies
2.3.1 rshApo2L/TRAIL (AMG951)
For rshApo2L/TRAIL, xenograft-time data from 221 individual animals were avail-
able, along with mean xenograft-time data for 13 additional experiments. The indi-
vidual data include 41 control animals that did not receive rshApo2L/TRAIL, and
the mean data include three control groups that did not receive rshApo2L/TRAIL.
General study protocols consisted of implanting COLO205 tumor cells in one
ank
of approximately 20 to 25 gram Nude mice, then allowing those tumor cells to grow
unperturbed for some time before drug administration (usually about two weeks,
at which time most tumors measured approximately 200-300 mm
3
; however, in one
48
study, dosing started with tumors as small as 30 mm
3
). (Where specied, the mice
used in these studies were female.)
Tables 2.2 and 2.3 list the details of the dierent doses and regimens examined. The
data for each individual animal are shown in Figures 2.4 and 2.5, while Figure 2.6
displays the mean tumor xenograft data. The solid thick grey line along the abscissa
of each sub-plot represents the duration of drug administration for that treatment
group.

Figure 2.4. RshApo2L/TRAIL control-individual tumor size data as described in
Table 2.2. Each panel represents a subgroup of Apo1.
1
a, b, c, etc. denote treatment groups of the same dosing regimen that may dier in minor
specics of the study design, such as measurement times or the rst day of dosing, and therefore
cannot be graphed together.
49
Treatment
Group ID
Dose
(mg/kg/dose)
Dose Regimen
Number of
Animals
Apo1 (a, b, c,
d, e, f)
1
Control No Drug 41
Apo2 20
1-hour IV infusion for 5 consecutive days (days 0, 1,
2, 3, 4)
6
Apo3 30 IV bolus for 5 consecutive days (days 0, 1, 2, 3, 4) 10
Apo4 30
1-hour IV infusion for 5 consecutive days (days 0, 1,
2, 3, 4)
5
Apo5 30
3-hour IV infusion for 5 consecutive days (days 0, 1,
2, 3, 4)
3
Apo6 30
IP bolus for 5 consecutive days per week for 2 weeks
(days 0, 1, 2, 3, 4, 7, 8, 9, 10, 11)
6
Apo7 30
IP bolus for 2 cycles of 5 consecutive days, with 21
days of rest between cycles (days 0, 1, 2, 3, 4, 26, 27,
28, 29, 30)
10
Apo8 60 IV bolus for 5 consecutive days (days 0, 1, 2, 3, 4) 10
Apo9 (a, b) 60
3-hour IV infusion for 5 consecutive days (days 0, 1,
2, 3, 4)
13
Apo10 60 IP bolus for 5 consecutive days (days 0, 1, 2, 3, 4) 10
Apo11 60
IP bolus for 5 consecutive days per week for 2 weeks
(days 0, 1, 2, 3, 4, 7, 8, 9, 10, 11)
6
Apo12 60
IP bolus for 2 cycles of 5 consecutive days, with 21
days of rest between cycles (days 0, 1, 2, 3, 4, 26, 27,
28, 29, 30)
20
Apo13 80
IP bolus for 5 consecutive days per week for 2 weeks
(days 0, 1, 2, 3, 4, 7, 8, 9, 10, 11)
6
Apo14 90 IV bolus for 5 consecutive days (days 0, 1, 2, 3, 4) 10
Apo15 90
1-hour IV infusion for 5 consecutive days (days 0, 1,
2, 3, 4)
5
Apo16 (a, b) 90
3-hour IV infusion for 5 consecutive days (days 0, 1,
2, 3, 4)
13
Apo17 90
IP bolus for 2 cycles of 5 consecutive days, with 21
days of rest between cycles (days 0, 1, 2, 3, 4, 26, 27,
28, 29, 30)
10
Apo18 100
3-hour IV infusion for 5 consecutive days (days 0, 1,
2, 3, 4)
7
Apo19 120 IV bolus for 5 consecutive days (days 0, 1, 2, 3, 4) 10
Apo20 120
IP bolus for 2 cycles of 5 consecutive days, with 21
days of rest between cycles (days 0, 1, 2, 3, 4, 26, 27,
28, 29, 30)
10
Apo21 200
1-hour IV infusion for 5 consecutive days (days 0, 1,
2, 3, 4)
5
Apo22 800
96-hour continuous IV infusion (days 0 through 3, ends
at beginning of day 4)
5
Table 2.2. RshApo2L/TRAIL dosing regimens for tumor xenograft studies with
individual data
50
Treatment
Group ID
Dose
(mg/kg/dose)
Dose Regimen Number of
Sets of
Average
Data
Apo23 (a,
b, c)
Control No Drug 3
Apo24 25
IP bolus for 2 cycles of 5 consecutive
days, with 16 days of rest between
cycles (days 0, 1, 2, 3, 4, 21, 22, 23,
24, 25)
1
Apo25 25
IP bolus 3 times per week for 5
weeks
1
Apo26 25
IP bolus for 2 cycles of 14 con-
secutive days, with 7 days of rest
between cycles
1
Apo27 30
IV bolus for 2 cycles of a dose given
every 24 hours for 5 consecutive
doses, with 3 days of rest between
cycles
1
Apo28 30
IV bolus for 2 cycles of a dose given
every 12 hours for 5 consecutive
doses, with 5
1
2
days of rest between
cycles
1
Apo29 30
IV bolus for 2 cycles of a dose
given every 2 hours for 5 consecutive
doses, with 7
2
3
days of rest between
cycles
1
Apo30 60 IV bolus on day 0 1
Apo31 60 IV bolus on days 0 and 3 1
Apo32 60
IV bolus for 5 consecutive days
(days 0, 1, 2, 3, 4)
1
Apo33 90 IV bolus on day 0 1
Table 2.3. RshApo2L/TRAIL dosing regimens for tumor xenograft studies with
average data
51

Figure 2.5. RshApo2L/TRAIL treated-individual tumor size data as described in
Table 2.2
52

Figure 2.6. RshApo2L/TRAIL mean tumor size data as described in Table 2.3
53
2.3.2 Conatumumab (AMG655)
For Conatumumab, xenograft-time data from 214 individual animals were available,
including 70 control animals that received one of several dosing regimens of a human
isotype control IgG
1
instead of Conatumumab. There was no visually discernible dif-
ference among these control groups, despite their receiving dierent dosing regimens
of the human isotype control IgG
1
. (An isotype control antibody is an antibody of
the same class/isotype { e.g., IgG or IgA { as the antibody being studied, but that
has no specicity for the epitope targeted by the antibody under investigation.) This
visual inspection was conrmed using a one-way analysis of variance test on the nal
tumor size measurements for all six control groups (nal measurements were taken 27
days after implantation for two of the studies and 28 days after implantation for the
third study). Accordingly, all control groups were included as non-treated animals in
the modeling analysis.
General study protocols consisted of implanting COLO205 tumor cells in one
ank
of approximately 20 to 25 gram female Nude mice, then allowing those tumor cells
to grow unperturbed for one to two weeks before drug administration, at which time
most tumors measured approximately 200-300 mm
3
. Table 2.4 lists the specics of
the dierent doses and regimens examined. The data for each individual animal are
shown in Figures 2.7 and 2.8, with the data arranged in ascending dose size.
54
Treatment
Group ID
Dose
(g/dose)
Dose Regimen
Number of
Animals
Cmab1 (a,
b, c, d, e, f)
Control No Drug 70
Cmab2 0.3
IP bolus 2 times per week for 5 doses
(days 1, 4, 8, 11, 15)
10
Cmab3 1
IP bolus 2 times per week for 5 doses
(days 1, 4, 8, 11, 15)
10
Cmab4 3
IP bolus 2 times per week for 5 doses
(days 1, 4, 8, 11, 15)
10
Cmab5 10
IP bolus 2 times per week for 5 doses
(days 1, 4, 8, 11, 15)
10
Cmab6 12.3
IP bolus 2 times per week for 4
weeks (days 1, 4, 8, 11, 15, 18, 22,
25)
12
Cmab7 30
IP bolus 2 times per week for 5 doses
(days 1, 4, 8, 11, 15)
10
Cmab8 (a,
b)
36.9
IP bolus 2 times per week for 4
weeks (days 1-25 or 2-26)
24
Cmab9 80 Single IP bolus on day 1 12
Cmab10 87.5
IP bolus 1 time per week for 4 weeks
(days 2, 9, 16, 23)
12
Cmab11 100
IP bolus 2 times per week for 5 doses
(days 1, 4, 8, 11, 15)
10
Cmab12 240 Single IP bolus on day 1 12
Cmab13 1600 Single IP bolus on day 2 12
Table 2.4. Conatumumab dosing regimens for tumor xenograft studies with
individual data
55

Figure 2.7. Conatumumab control-individual tumor size data as described in
Table 2.4. Each panel represents a subgroup of Cmab1.
56

Figure 2.8. Conatumumab treated-individual tumor size data as described in
Table 2.4
57
2.4 Combination Therapy Tumor Xenograft Stud-
ies
Two sets of combination therapy data were available: mean xenograft-time data from
7 experiments in a study combining Irinotecan and rshApo2L/TRAIL and xenograft-
time data from 60 individual animals from a study combining Irinotecan and Conatu-
mumab. The details of the Irinotecan-rshApo2L/TRAIL treatment groups are given
in Table 2.5 and the data are shown in Figure 2.9. The details of the Irinotecan-
Conatumumab treatment groups are given in Table 2.6 and the data are shown in
Figure 2.10.
58
Treatment
Group ID
RshApo2L/TRAIL
Dosing
(mg/kg/dose)
CPT-11 Dosing
(mg/kg/dose)
Number of
Sets of
Average
Data
CPT11&Apo1 None None 1
CPT11&Apo2 None
80; IP bolus on days 0,
4, 8
1
CPT11&Apo3
60; IV bolus for 5 con-
secutive days per week
for 2 weeks (days 0, 1,
2, 3, 4, 7, 8, 9, 10, 11)
None 1
CPT11&Apo4
60; IV bolus on days 0
and 7
80; IP bolus on days 0,
4, 8
1
CPT11&Apo5
60; IV bolus on days 0,
2, 7, 10
80; IP bolus on days 0,
4, 8
1
CPT11&Apo6
60; IV bolus on days 0,
2, 5, 7, 9, 11
80; IP bolus on days 0,
4, 8
1
CPT11&Apo7
60; IV bolus for 5 con-
secutive days per week
for 2 weeks (days 0, 1,
2, 3, 4, 7, 8, 9, 10, 11)
80; IP bolus on days 0,
4, 8
1
Table 2.5. Irinotecan (CPT-11) and rshApo2L/TRAIL dosing regimens for
combination-therapy tumor xenograft studies with average data
59

Figure 2.9. Irinotecan (CPT-11) and rshApo2L/TRAIL tumor size data as
described in Table 2.5. The orange-red triangles represent CPT-11 dosing events,
and the yellow squares represent rshApo2L/TRAIL dosing events.
60
Treatment
Group ID
Conatumumab
Dosing (g/dose)
CPT-11 Dosing
(mg/kg/dose)
Number of
Animals
CPT11&Cmab1
(a, b)
2.5; IP bolus on days 0,
2, 4
None 20
CPT11&Cmab2 None
20; IP bolus on days 0,
2, 4
10
CPT11&Cmab3 None
80; IP bolus on days 0,
2, 4
10
CPT11&Cmab4
2.5; IP bolus on days 0,
2, 4
20; IP bolus on days 0,
2, 4
10
CPT11&Cmab5
2.5; IP bolus on days 0,
2, 4
80; IP bolus on days 0,
2, 4
10
Table 2.6. Irinotecan (CPT-11) and Conatumumab dosing regimens for
combination-therapy tumor xenograft studies with individual data

Figure 2.10. Irinotecan (CPT-11) and Conatumumab tumor size data as described
in Table 2.6. The orange-red triangles represent CPT-11 dosing events, and the
yellow squares represent Conatumumab dosing events.
61
Chapter 3.
Models and Population Analysis
3.1 Pharmacokinetic Models
The pharmacokinetic (PK) model for rshApo2L/TRAIL was developed using mean
plasma concentration data from a single IV dosing event and mean plasma concen-
tration data from a single IP dosing event. The rshApo2L/TRAIL PK data were
collected from an independent set of COLO205 xenograft-bearing animals (i.e., ani-
mals not included in the tumor regression studies presented in Section 2.3.1).
The PK model for Conatumumab was developed using plasma concentration data
following IP dosing (see Section 2.2.2 for details of the 13 dosing and observation
schedules) in some of the mice also used in the tumor regression studies presented
in Section 2.3.2. The median plasma concentration data from these studies were used
to assess potential PK models.
62
3.1.1 rshApo2L/TRAIL Pharmacokinetic Model
The rshApo2L/TRAIL PK model was developed in two stages. Initially, the IV data
were analyzed, and a two-compartment model was found to t the data well. The
parameters found for this two-compartment model were comparable to those reported
by others [Kelley et al., 2001]. Then, with the IV PK parameters xed, the IP data
were analyzed. The slow, late peak in plasma drug concentration prompted the
formulation of separate slow and rapid absorption components of the model (see Fig-
ure 3.1). It is important to note that since all rshApo2L/TRAIL IP doses used in
the analyzed studies were very close to the amount dosed for the IP PK study, this
PK model was formulated with the purpose of closely reproducing the observed PK
data, and is not intended to be used to extrapolate to dierent doses.
The parameter estimates for the rshApo2L/TRAIL PK model are presented
in Table 3.1. Instead of estimating the fraction taken-up into the slow-absorption
component of the model (F
1
) and the fraction that was taken-up into the rapid-
absorption component of the model (F
2
), the total fraction absorbed (F
Total
) and F
1
were estimated. F
2
can be found by subtracting F
1
from F
Total
, giving F
2
an esti-
mated value of 0.0966. The model t to the mean plasma concentration data for
rshApo2L/TRAIL given IV and IP can be found in Figure 3.2.
63
Figure 3.1. Schematic of pharmacokinetic model for rshApo2L/TRAIL; all rate
constants are rst order
Parameter (Units) Estimate (% RSE)
1
V
1
(mL/kg) 48.6 (18.0)
K
10
(1/day) 232 (5.51)
K
12
(1/day) 3.76 (15.3)
K
21
(1/day) 10.8 (28.4)
F
1
0.242 (4710)
F
Total
0.339 (15.0)
K
a
(1/day) 18.9 (11800)
K
aa
(1/day) 19.6 (164)
1
Relative standard error of estimate (standard error
divided by estimate), presented as a percentage
Table 3.1. Parameter estimates for rshApo2L/TRAIL pharmacokinetic model
represented in Figure 3.1
64
Figure 3.2. Model t to mean plasma concentration data for rshApo2L/TRAIL
given IP and IV
3.1.2 Conatumumab Pharmacokinetic Model
Median data from the 13 IP dosing regimens were used simultaneously to develop a
model to describe the collected plasma concentration data following IP administra-
tion of Conatumumab. Several models were evaluated, including a two-compartment
model with a single, one-way transfer rate constant from the peritoneal compartment
to the plasma compartment, which was chosen as the nal PK model for Conatu-
mumab (see Figure 3.3).
The parameter estimates for the Conatumumab PK model are presented in Table 3.2.
Figure 3.4 displays the measured data and model ts for three of the 13 sets of median
plasma concentration data.
Parameter (Units) Estimate (% RSE)
V
1
/F (mL) 2.99 (6.42)
K
10
(1/day) 0.0913 (5.29)
K
12
(1/day) 0.251 (41.9)
K
21
(1/day) 0.403 (28.6)
K
a
(1/day) 8.17 (16.8)
Table 3.2. Parameter estimates for Conatumumab pharmacokinetic model
represented in Figure 3.3
65
Figure 3.3. Schematic of pharmacokinetic model for Conatumumab; all rate
constants are rst order
66
Figure 3.4. Model t to median plasma concentration data for Conatumumab given
IP (3 of 13 shown)
67
3.1.3 Irinotecan Pharmacokinetic Model
The mean plasma concentration data taken from Guichard et al. [1998] were used
to develop a PK model for Irinotecan dosed IP. The nal model chosen was a two-
compartment model with a single, one-way transfer rate constant from the peritoneal
compartment to the plasma compartment (see Figure 3.5).
Figure 3.5. Schematic of pharmacokinetic model for Irinotecan; all rate constants
are rst order
The parameter estimates for the Irinotecan PK model are presented in Table 3.3. Fig-
ure 3.6 displays the measured data and model ts for the mean plasma concentration
data following an IP dose of 66 mg/kg.
68
Parameter (Units) Estimate (% RSE)
V
1
/F (mL/kg) 212E+02 (320.E+02)
K
10
(1/day) 7.10 (320.E+02)
K
12
(1/day) 20.0 (610.E+02)
K
21
(1/day) 21.4 (168)
K
a
(1/day) 45.3 (321E+02)
Table 3.3. Parameter estimates for Irinotecan pharmacokinetic model represented
in Figure 3.5
Figure 3.6. Model t to mean plasma concentration data for Irinotecan given IP
3.2 Intracellular Apoptotic Signaling and Tumor
Regression Modeling (Base Model)
Three models for unperturbed tumor growth (presented in Section 1.6.3) were con-
sidered, each coupled with a signal-transduction drug-action term used to model the
drug-related removal of tumor cells from the tumor cell population. All three models
described the data fairly well, but the steady-state tumor volume dierential equation
(described in Equation 1.9) was chosen for the nal model because it described the
data well (especially those data sets that showed some plateau in tumor growth), was
69
tractable when analyzed by the dierential equation solver, and had relatively few
parameters to estimate.
The simplied pathway and corresponding model diagrams in Figure 3.7 represent the
action of a PARA on the extrinsic apoptotic system, and include two signaling levels: a
drug-specic Upstream Signal, and a drug-independent downstream Apoptosis Signal
whose dynamics are not specic to any particular PARA. In the model, the Upstream
Signal is linked to the PARA's plasma concentration and represents the delivery of
the PARA to the cells, its binding to the death receptors and the dissociation of
the PARA from its target receptor(s), each of which is likely to be dierent for the
two PARAs. The Apoptosis Signal represents the executioner caspases, and as such
the model for the Apoptosis Signal should account for the action of any PARA. It
is the Apoptosis Signal that increases the turnover rate of the tumor cells as shown
in Figure 3.7. This decomposition of an overall model of drug action for tumor growth
inhibition into drug-specic and drug-independent components is discussed in Bruno
et al. [2011].
To exploit the information obtained from the separate xenograft studies with
rshApo2L/TRAIL and Conatumumab, a shared-pathway modeling framework was
adopted, whereby the data from both sets of studies are pooled to allow each to
inform the model for the Apoptosis Signal state that is common to both PARA path-
ways (see Figure 3.8). It is important to emphasize, however, that each study animal
received only one of the two drugs (or, for controls, no drug), thus engaging either
the rshApo2L/TRAIL Upstream Signal or the Conatumumab Upstream Signal (or
neither Signal in the case of the non-treated animals).
70
Figure 3.7. Intracellular apoptotic-signaling model: the left panel shows a schematic
of the extrinsic apoptotic pathway, while the right panel indicates the model
elements and their pathway correspondence for a single PARA (extrinsic pathway
diagram courtesy of Genentech/Dr. Matthew Hsu)
The following equations describe the complete intracellular-signaling tumor-regression
model:
(3.1)
d
dt
UpSig
Apo
(t) =K
inUp;Apo
C
Apo
(t)K
outUp;Apo
UpSig
Apo
(t)
(3.2)
d
dt
UpSig
Cmab
(t) =K
inUp;Cmab
C
Cmab
(t)K
outUp;Cmab
UpSig
Cmab
(t)
(3.3)
d
dt
ApopSig(t) =K
inApop;UpSig
UpSig(t)K
outApop
ApopSig(t)
(3.4)
d
dt
TV (t) =K
G

1
TV (t)
TV
SS

TV (t)K
Death
ApopSig(t)TV (t)
71
Figure 3.8. Complete model diagram for the separate and shared components of the
apoptotic pathway, used for joint analysis of both rshApo2L/TRAIL and
Conatumumab monotherapies
where C
Apo
(t) is the plasma concentration of rshApo2L/TRAIL; UpSig
Apo
(t) is the
Upstream Signal produced by rshApo2L/TRAIL; K
inUp;Apo
is the production con-
stant of the rshApo2L/TRAIL Upstream Signal; K
outUp;Apo
is the turnover rate con-
stant of the rshApo2L/TRAIL Upstream Signal; C
Cmab
(t) is the plasma concentra-
tion of Conatumumab; UpSig
Cmab
(t) is the Upstream Signal produced by Conatu-
mumab; K
inUp;Cmab
is the production constant of the Conatumumab Upstream Sig-
nal;K
outUp;Cmab
is the turnover rate constant of the Conatumumab Upstream Signal;
ApopSig(t) is the Apoptosis Signal that is produced by the administration of either
of the two drugs;K
inApop;UpSig
is the production constant of the Apoptosis Signal due
72
to the Upstream Signal (it is the same for UpSig
Apo
(t) and UpSig
Cmab
(t) since the
Upstream Signal represents activated upstream/initiator caspases which, regardless
of how they are engaged, have the same eect on downstream/executioner caspases
once they are activated); UpSig(t) is eitherUpSig
Apo
(t) orUpSig
Cmab
(t);K
outApop
is
the turnover rate constant of the Apoptosis Signal; and K
Death
is the rate constant
for cell loss due to the Apoptosis Signal. See Section 3.6.2 for variable and parameter
units.
Other models evaluated included sigmoidal (i.e., E
max
) terms relating the PARA
plasma concentrations to the Upstream Signals, a sigmoidal function relating the
Upstream Signals to the Apoptosis Signal, or a sigmoidal function relating the Apop-
tosis Signal to tumor turnover (models not shown). Upon inspection of the results
from these sigmoidal models it was clear that the dose range of the data set was
unable to inform the saturation component(s) of the models; accordingly, the coe-
cients for the eect of each Signal on its target were kept as linear terms (results not
shown).
3.3 Empirical Reduced Drug-Eect Models
The Base Model resulted in good ts to a preliminary set of rshApo2L/TRAIL and
Conatumumab xenograft tumor size data in which the treatment groups had initial
tumor volumes in the 200-300 mm
3
range and dosing ended no later than day 11
of the study. The Base Model was then applied to a small number of treatment
groups in which the starting volumes were smaller (approximately 30 mm
3
) and for
which the dosing periods were longer than the other treated groups (lasting as long
73
as day 34 of the study; see the dosing regimens for Apo24-26 in Table 2.3). For these
long-term-dosing treatment groups, the model t the data less well, and showed a
systematic overestimation of tumor regression. Moreover, regardless of initial tumor
volume, the model ts were poorer as the dosing period and total amount of drug
administered increased (see Apo24-26 and Cmab8a, 8b, and 10). The smaller initial
tumor volumes do not immediately explain the inability of the model to describe
these data, since a control group with a similarly small volume (Apo23a) is described
well by the model. Also the total amount of drug administered does not explain
this observation, because data from other treated groups that received more total
drug (such as Apo21 and Apo22, which received 800 mg/kg total) were described
better than groups Apo24-26, which received less total drug (Apo26 received 700
mg/kg, which was the most total drug of groups Apo24-26). Other models tested
that included the sigmoidal terms noted at the end of Section 3.2 did not result in
improved ts to the long-term-dosing data, each showing overestimation of tumor
regression similar to that estimated by the Base Model (results not shown).
The failure of both the Base Model and the various sigmoidal models to describe the
long-term-dosing data suggested that the drug's apoptotic eectiveness is reduced
through the action of some characteristic of the tumor that changes with time, which
led to the exploration of a diminished drug eect hypothesis. While there are sev-
eral possible mechanisms that could account for this loss of eect { e.g., increased
intracellular pro-survival signaling (see Section 1.4.1) or a drug's decreased ability to
penetrate a larger tumor (see Section 1.4.2) { two empirical models were implemented
that re
ect the diminished eect of the drug over time as decaying exponentials. These
two models are detailed in the following two subsections.
74
3.3.1 Reduced Drug-Eect at Upstream Signal Model (K
r
Upstream Model)
In the reduction of drug eect at the Upstream Signal model, the assumption is
made that the reduction of eect occurs in the ability of the PARA to cause the
activation of initiator caspases intracellularly. This is modeled by a drug-specic
time-decaying exponential multiplying the production term of the Upstream Signal
for each of the two PARAs. See Figure 3.9 for a schematic of the K
r
Upstream Model,
and Equations 3.5 and 3.6 for details of the changed model formulation.
Tumor Volume
Apoptosis Signal
rshApo2L/TRAIL
Upstream
Signal
Conatumumab
Upstream
Signal
rshApo2L/TRAIL
Plasma PK
Conatumumab
Plasma PK
(+)
(+)
(+) (+)
(+)
OR
Figure 3.9. Schematic for empirically modeled reduction of drug eect at the
Upstream Signal
75
The following equations describe the complete empirically-modeled reduced drug
eect at the Upstream Signal model (Equations 3.7 and 3.8 are the same as for
the Base Model):
d
dt
UpSig
Apo
(t) =K
inUp;Apo
C
Apo
(t)e
K
r;ApoUpSig
t
K
outUp;Apo
UpSig
Apo
(t)
(3.5)
(3.6) d
dt
UpSig
Cmab
(t) =K
inUp;Cmab
C
Cmab
(t)e
K
r;CmabUpSig
t
K
outUp;Cmab
UpSig
Cmab
(t)
(3.7)
d
dt
ApopSig(t) =K
inApop;UpSig
UpSig(t)K
outApop
ApopSig(t)
(3.8)
d
dt
TV (t) =K
G

1
TV (t)
TV
SS

TV (t)K
Death
ApopSig(t)TV (t)
whereK
r;ApoUpSig
is the loss of eect time-constant for the production of the Upstream
Signal by rshApo2L/TRAIL, and K
r;CmabUpSig
is the loss of eect term for the pro-
duction of the Upstream Signal by Conatumumab.
3.3.2 Reduced Drug-Eect at Apoptosis Signal Model (K
r
Apoptosis Model)
In the reduction of drug eect at the Apoptosis Signal model, the assumption is
made that the reduction of eect occurs in the ability of the initiator caspases to
cause the activation of the executioner caspases. This is modeled by a single time-
decaying exponential multiplying the production term of the Apoptosis Signal driven
76
by the Upstream Signal. There is only a single decaying exponential because the
Upstream Signal (roughly) represents the initiator caspases and the Apoptosis Signal
(roughly) represents the executioner caspases, and the kinetics of the activation of the
executioner caspases by the initiator caspases should be the same regardless of which
drug drove the production of the initiator caspases. See Figure 3.10 for a schematic
of the K
r
Apoptosis Model, and Equation 3.11 for the specics of the changed model
formulation.
Tumor Volume
Apoptosis Signal
rshApo2L/TRAIL
Upstream
Signal
Conatumumab
Upstream
Signal
rshApo2L/TRAIL
Plasma PK Conatumumab
Plasma PK
(+)
(+)
(+) (+)
(+)
OR
Figure 3.10. Schematic for empirically modeled reduction of drug eect at the
Apoptosis Signal
The following equations describe the complete empirically modeled reduced drug
eect at the Apoptosis Signal model(Equations 3.9, 3.10 and 3.12 are the same as for
the Base Model):
77
(3.9)
d
dt
UpSig
Apo
(t) =K
inUp;Apo
C
Apo
(t)K
outUp;Apo
UpSig
Apo
(t)
(3.10)
d
dt
UpSig
Cmab
(t) =K
inUp;Cmab
C
Cmab
(t)K
outUp;Cmab
UpSig
Cmab
(t)
(3.11) d
dt
ApopSig(t) =K
inApop;UpSig
UpSig(t)e
K
r;ApopSig
K
outApop
ApopSig(t)
(3.12)
d
dt
TV (t) =K
G

1
TV (t)
TV
SS

TV (t)K
Death
ApopSig(t)TV (t)
whereK
r;ApopSig
is the loss of eect time-constant for the production of the Apoptosis
Signal by the Upstream Signal (it is the same regardless of which drug drove the
production of the Upstream Signal).
3.4 Pro-Survival Signal Model
In an eort to incorporate the action of pro-survival factors (in addition to pro-
apoptotic factors) in a more mechanistic manner, the model was extended to include
a Pro-Survival Signal (represented as a transduction delayed version of the Upstream
Signal), which in turns modulates the production of the Apoptosis Signal. This Pro-
Survival Signal represents the upregulated pro-survival factors that are produced by
TRAF2-activated NF-B translocating to the nucleus and promoting the expression
of select genes (see Section 1.4.1). The Upstream Signal is used to drive the Pro-
Survival Signal as it represents the activation of multiple factors at the intracellular
regions of death receptors, including TRADD. See Figure 3.11 for a schematic of the
Pro-Survival Signal Model.
78
Tumor Volume
Apoptosis Signal
Upstream
Signal
Pro-Survival
Signal
PARA
Plasma PK
(+)
(+) (-)
(+)
(+)
Figure 3.11. Schematic for semi-mechanistic Pro-Survival Signal Model
The complete model incorporating the hypothesis of the activation of concurrent
pro-survival signals is now dened by the equations given below. Equations 3.15
and 3.16 describe the kinetics of the Pro-Survival Signal and the Pro-Survival Signal's
eect on the kinetics of the Apoptosis Signal. An I
max;ProSrvlSig
term was originally
used in Equation 3.16 to modulate the Pro-Survival Signal's eect in reducing the
production of the Apoptosis Signal. However, after running a number of analyses,
thisI
max;ProSrvlSig
term was found to be so close to the value of 1 every time that the
decision was made to x I
max;ProSrvlSig
to 1.
(3.13)
d
dt
UpSig
Apo
(t) =K
inUp;Apo
C
Apo
(t)K
outUp;Apo
UpSig
Apo
(t)
79
(3.14)
d
dt
UpSig
Cmab
(t) =K
inUp;Cmab
C
Cmab
(t)K
outUp;Cmab
UpSig
Cmab
(t)
(3.15)
d
dt
ProSrvlSig(t) =K
Trnsd
UpSig(t)K
Trnsd
ProSrvlSig(t)
(3.16) d
dt
ApopSig(t) =K
inApop;UpSig
UpSig(t)

1
ProSrvlSig(t)
IC
50;ProSrvlSig
+ProSrvlSig(t)

K
outApop
ApopSig(t)
(3.17)
d
dt
TV (t) =K
G

1
TV (t)
TV
SS

TV (t)K
Death
ApopSig(t)TV (t)
where ProSrvlSig(t) is the Pro-Survival Signal that is produced by the adminis-
tration of either of the two drugs; K
Trnsd
is the transduction rate constant for the
Pro-Survival Signal; and IC
50;ProSrvlSig
is the amount of Pro-Survival Signal that
would result in half of the maximum inhibition of the production of the Apoptosis
Signal caused by the Pro-Survival Signal.
3.5 Combination Therapy Model: Cytotoxic
Agent co-dosed with a PARA
As discussed in Sections 1.3.3 and 1.3.4, administering agonists of the intrinsic and
extrinsic apoptotic pathways in combination can produce greater ecacy with fewer
adverse side eects than either agent alone. In order to take full advantage of the coop-
erative nature of these two classes of drugs, it is important to understand and quan-
tify how they interact. Thus, modeling the interrelated eects of these drugs becomes
important, as well. With this in mind, the Pro-Survival Signal Model was extended
80
to incorporate the action of the cytotoxic drug Irinotecan (CPT-11). Because the
combination-therapy data available are sparse, the model was developed to allow for
data sets that had rshApo2L/TRAIL co-dosed with Irinotecan and data sets that had
Conatumumab co-dosed with Irinotecan in order to utilize as much information from
the data as possible.
Figure 3.12 is a fairly well integrated diagram of the interactions between the intrinsic
and extrinsic apoptotic pathways, and Figure 3.13 shows the schematic for a combi-
nation drug-therapy model. Only one extrinsic apoptotic pathway agonist and one
cytotoxic drug are included in the model for visual clarity.
The model depicted in Figure 3.13 shows the cytotoxic drug inducing a Midstream
Signal that loosely represents the activation of the mitochondrial pathway in the
cytosol (dynamics of this signal would include the drug's reaching the cell, entering
the cell, causing DNA damage, and activating p53 and other related factors). The
Midstream Signal increases the production of the Apoptosis Signal on its own to
account for the activation of caspase-9 units within apoptosomes, which then activate
executioner caspases. The Midstream Signal also increases the rate of production of
the Apoptosis Signal by the PARA's Upstream Signal to account for the intrinsic
apoptotic pathway's role in upregulating death receptors and downregulating factors
such as c-FLIP that inhibit the activity of upstream caspases [Weinberg, 2007, Budd
et al., 2006, Panka et al., 2001] and the eect of Smac/DIABLO inhibiting the activity
of IAPs, which interfere with the activity of executioner caspases (see Section 1.4.1 for
details of IAP eects). The value of theE
max
parameter in Equation 3.17 determines
whether the interaction is synergistic (E
max
would be greater than 0), antagonistic
(E
max
would be less than 0), or if there were no interaction and the eects of the two
81
Figure 3.12. A detailed diagram of the cross-talk between the extrinsic and intrinsic
apoptotic pathways [Genentech, 2010]
82
Tumor Volume
Apoptosis Signal
PARA
Upstream
Signal
Cytotoxic
Midstream
Signal
PARA
Plasma PK Cytotoxic
Plasma PK
(+)
(+)
(+) (+)
(+)
(+)
Figure 3.13. Combination drug-therapy model for the eects of an extrinsic
apoptotic pathway agonist and a cytotoxic drug
drugs were simply additive (E
max
would be equal to 0). The Combination Therapy
Model incorporating the Midstream Signal is given in Equations 3.18 to 3.23.
(3.18)
d
dt
UpSig
Apo
(t) =K
inUp;Apo
C
Apo
(t)K
outUp;Apo
UpSig
Apo
(t)
(3.19)
d
dt
UpSig
Cmab
(t) =K
inUp;Cmab
C
Cmab
(t)K
outUp;Cmab
UpSig
Cmab
(t)
(3.20)
d
dt
ProSrvlSig(t) =K
Trnsd
UpSig(t)K
Trnsd
ProSrvlSig(t)
(3.21)
d
dt
MidSig(t) =K
inMid
C
CPT 11
(t)K
outMid
MidSig(t)
83
(3.22)
d
dt
ApopSig(t) =K
inApop;UpSig
UpSig(t)

1
ProSrvlSig(t)
IC
50;ProSrvlSig
+ProSrvlSig(t)

1 +
E
max;MidSig
MidSig(t)
EC
50;MidSig
+MidSig(t)

+K
inApop;MidSig
MidSig(t)K
outApop
ApopSig(t)
(3.23)
d
dt
TV (t) =K
G

1
TV (t)
TV
SS

TV (t)K
Death
ApopSig(t)TV (t)
where MidSig(t) is the Midstream Signal produced by the cytotoxic drug; K
inMid
is
the production rate constant of the Midstream Signal due to the cytotoxic drug (CPT-
11, in this case); C
CPT 11
(t) is the plasma concentration of CPT-11 drug; K
outMid
is
the loss rate constant of the Midstream Signal;E
max;MidSig
is the maximum amount of
Midstream-Signal-caused excitation of the production of the Apoptosis Signal by the
Upstream Signal; EC
50;MidSig
is the amount of Midstream Signal that would result
in half of the maximum Midstream-Signal-caused excitation of the production of the
Apoptosis Signal by the Upstream Signal; and K
inApop;MidSig
is the production rate
constant of the Apoptosis Signal due to the Midstream Signal.
If more varied data were available (i.e., more varied dosing regimens in both dose
size and relative timing of the two types of drugs) the model might be reformulated
to have the Midstream Signal increase the production of the Upstream Signal of the
extrinsic apoptotic pathway agonist to more accurately re
ect the fact that activa-
tion of the intrinsic pathway results in the upregulation of death receptors and the
downregulation of factors such as c-FLIP that inhibit the activation of upstream
caspases [Weinberg, 2007, Budd et al., 2006, Panka et al., 2001]. Moreover, to bet-
ter account for the eect of Smac/DIABLO's inhibiting the activity of IAPs, the
Midstream Signal might also be modeled to decrease the loss/turnover rate of the
Apoptosis Signal.
84
3.6 Population Analysis
3.6.1 Population Modeling Description
Population modeling involves the simultaneous analysis of multiple data sets collected
from the population of interest, with the goal of quantifying multiple sources of vari-
ability; this type of modeling is also called nonlinear mixed eects (NLME) modeling.
The two most common sources of variability sought to be quantied are within-
individual variability and between-individual variability, which are both assumed to
be randomly distributed eects [D'Argenio et al., 2009].
Within-individual variability is accounted for in the following parametric-system out-
put equation:
Y
i
=h
i
(
i
) +e
i
(3.24)
where i indicates values associated with the i
th
subject, and i = 1, 2, 3,. . . , N (the
total number of subjects);
i
represents the vector of system parameters for the
i
th
subject; h
i
(
i
) represents the vector of model outputs for the i
th
subject; e
i
represents the vector of output errors for thei
th
subject; andY
i
represents the vector
of all measurements for the i
th
subject. The output error vector e
i
is assumed to be
an independent, random variable with the following distribution:
e
i
N (0;G
i
(h
i
(
i
);)) (3.25)
where represents the vector of parameters that are unique to the error variance
model, assumed to be the same for all subjects, and G
i
(h
i
(
i
);) is a positive
85
denite covariance matrix [D'Argenio et al., 2009]. As indicated in Equation 3.25,
the average output error is assumed to be zero.
To account for between-individual variability, the system parameters
i
are assumed
to be independent, identically distributed random vectors of the form:

i
N(; ) or LN(; ) (3.26)
where represents the vector of mean system parameter values for the population
and represents the population covariance matrix of the model parameters.
3.6.2 Analysis Approach
To solve the population modeling problem we implemented the maximum likeli-
hood solution using the expectation maximization (MLEM) algorithm of ADAPT
5 [D'Argenio et al., 2009]. We analyzed our data using the options in MLEM that
assume that the parameters are distributed normally with zero covariance. We chose
the diagonal covariance matrix (i.e., no covariance among parameters) option because
the program was having diculty inverting the full covariance matrix for some of the
calculations. Since the equation used to estimate measured tumor volumes was a
product of two caliper measurements, the error variance model for tumor volume
was chosen to be proportional; a nominal additive component was included to aid in
calculations because error variance values of zero cause the program to stop.
86
Chapter 4.
Results
The rst results shown are from a population analysis t to all of the control data
in Tables 2.2 to 2.4 using the unperturbed TV
SS
tumor-growth model. This was
done to provide a reference for the tumor-growth parameters estimated in the four
monotherapy tumor-regression models.
Next, the results from each of the four monotherapy tumor-regression models will be
presented in turn. The results include tables of the population estimates (mean and
inter-individual variability) and model t plots for each treatment group.
Finally, the results of the combination-therapy model are presented. Population
parameter estimates and model t plots are shown.
4.1 Unperturbed TV
SS
Tumor Growth Model
To assess the suitability of the tumor growth model to describe the dynamics of tumor
volume change in the untreated animals, and to provide an internal validation for the
87
estimated parameters of the tumor growth model obtained below using the treatment
groups, data from all the control animals (114 experiments in total, Treatment Group
IDs Apo1a-1f, Apo23a-23c, Cmab1a-1f in Tables 2.2 to 2.4) were used in a population
analysis with the tumor growth model given by Equation 1.9 and recapitulated below:
d
dt
TV (t) =K
G

1
TV (t)
TV
SS

TV (t) (4.1)
The results of this population analysis yielded a population mean for the rst-order
net growth rate constant, K
G
, of 0.166/day (4.64% RSE) with an inter-animal vari-
ability of 0.0480/day (16.8% RSE). The population mean for TV
SS
, the steady-state
(maximum) tumor volume, was estimated as 2630 mm
3
(9.20% RSE) with an inter-
animal variability of 1120 mm
3
(12.6% RSE); and the estimated population mean for
the initial tumor volume is 296 mm
3
(5.43% RSE) with an inter-animal variability
of 109 mm
3
(6.67% RSE). The r
2
value for the measured data versus the individual
model predictions is 0.890.
4.2 Intracellular Apoptotic Signaling and Tumor
Regression Modeling (Base Model)
Table 4.1 presents the parameter estimates for the intracellular-signaling tumor-
regression Base Model. The population mean and inter-individual variability standard
deviation are given for each parameter. Relative standard errors are also shown.
88
Parameter (Units) Population
Mean (% RSE)
IIV
1
Standard
Deviation as
CV%
2
(% RSE)
K
inUp;Apo
(USU/(ng/ml)/day)
3
0.0944 (8.96) 36.2 (18.6)
K
outUp;Apo
(1/day) 8.45 (6.73) 30.7 (19.8)
K
inUp;Cmab
(USU/(ng/ml)/day)
3
0.00543 (4.86) 45.8 (9.82)
K
outUp;Cmab
(1/day) 11.9 (9.38) 34.8 (20.9)
K
inApop;UpSig
(ASU/USU/day)
3,4
0.0253 (11.1) 34.1 (28.4)
K
outApop
(1/day) 1.62 (8.63) 38.9 (17.5)
K
Death
(1/ASU/day)
4
0.514 (11.3) 32.9 (32.2)
K
G
(1/day) 0.124 (3.14) 47.2 (5.80)
TV
SS
(mm
3
) 4890 (10.9) 28.0 (28.4)
TV(0) (mm
3
) 275 (2.59) 36.0 (3.74)
Proportional Error Variance 0.326
NLL
5
23492
AIC
6
47115
1
Inter-individual variability
2
Coecient of variation, presented as a percentage
3
Upstream Signal unit
4
Apoptosis Signal unit
5
Negative log likelihood
6
Akaikes information criterion
Table 4.1. Parameter estimates for the intracellular-signaling tumor-regression base
model
The Upstream Signal production constant for Conatumumab is considerably smaller
than that for rshApo2L/TRAIL, which in part (potentially) re
ects the slower
delivery of the larger Conatumumab molecule to the active site in comparison to
rshApo2L/TRAIL and the fact that rshApo2L/TRAIL targets both DR4 and DR5,
whereas Conatumumab targets only DR5. No parameter has an estimated inter-
individual variability exceeding 50% CV and all relative standard errors are modest.
The conditional standardized residuals show good scattering and no obvious trends
(not shown). The estimated mean steady state untreated tumor volume of 4890 mm
3
89
is somewhat large, but still a physiologically plausible value; however, it is substan-
tially larger than the value estimated for the control data alone (2630 mm
3
). More-
over, the estimated mean rst-order tumor net growth rate constant of 0.124/day is a
bit smaller than the value estimated for the control-only data, which was 0.166/day.
In the following model-t plots, each panel represents the dierent treatment groups
as dened in Tables 2.2 to 2.4 and show the average data and ts for all of the animals
in that treatment group. In Figures 4.1 and 4.3, the solid circles represent the mean
of the measured data at each time point for that dose regimen, while the error bars
represent the standard error of the mean at each time point; the dotted lines represent
the average of the model predictions for each animal in the dosing group obtained
using the conditional mean estimated for that animal from the MLEM population
analysis. In Figure 4.2, the solid circles represent the mean of the measured data at
each time point, while the dotted lines represent the model predictions for each dosing
group obtained using the conditional mean estimated for that experiment from the
MLEM population analysis.
It is important to note the model's inability to describe the prolonged dosing regimens
of rshApo2L/TRAIL (see Apo17, 20, 25, and 26 and Cmab5, 7, 8a, 8b, and 10),
particularly as the length of dosing and total dosing amount increased (all other
models t these data quite well, see subsequent Results sub-sections).
90

Figure 4.1. Base Model population analysis t to the rshApo2L/TRAIL
experiments with individual data. For the six control group experiments, only the
results from the Apo1b study are shown.
91

Figure 4.2. Base Model population analysis t to the rshApo2L/TRAIL
experiments with average data. For the three control group experiments, only the
results from the Apo23a study are shown.
92

Figure 4.3. Base Model population analysis t to the Conatumumab experiments
with individual data. For the six control group experiments, only the results from
the groups Cmab1d-1f are shown.
93
4.3 Empirical Reduced Drug-Eect Models
The results for the two empirically-formulated reduced-eect models are presented
below. Both models show similar improvements of t over the Base Model.
4.3.1 Reduced Drug-Eect at Upstream Signal Model (K
r
Upstream Model)
Table 4.2 presents the parameter estimates for the intracellular-signaling tumor-
regression K
r
Upstream Model. The Upstream Signal production constant for Cona-
tumumab is again considerably smaller than that for rshApo2L/TRAIL. The expo-
nential decay time constant for Conatumumab is nearly an order of magnitude larger
than that estimated for rshApo2L/TRAIL. Only one parameter has an estimated
inter-individual variability that slightly exceeds 50% CV and all relative standard
errors are modest. The conditional standardized residuals show good scattering and
no obvious trends (not shown). The estimated mean steady state untreated tumor
volume of 2120 mm
3
is fairly similar to the value estimated for the control data
alone (2630 mm
3
). The estimated mean rst-order tumor net growth rate constant
of 0.157/day is fairly similar to the value estimated for the control-only data, which
was 0.166/day.
The following are model-t plots for the K
r
Upstream Model. The description of the
symbols used in Figures 4.1 to 4.3 in Section 4.2 apply to Figures 4.4 to 4.6, as well.
Apo17, 25, and 26 show noticeable improvements, and Cmab5, 7, 8a, 8b, and 10 show
modest improvements in their model ts over the results from the Base Model. There
is little or no improvement of t to treatment groups Apo4 and Apo20.
94

Figure 4.4. K
r
Upstream Model population analysis t to the rshApo2L/TRAIL
experiments with individual data. For the six control group experiments, only the
results from the Apo1b study are shown.
95

Figure 4.5. K
r
Upstream Model population analysis t to the rshApo2L/TRAIL
experiments with average data. For the three control group experiments, only the
results from the Apo23a study are shown.
96

Figure 4.6. K
r
Upstream Model population analysis t to the Conatumumab
experiments with individual data. For the six control group experiments, only the
results from the groups Cmab1d-1f are shown.
97
Parameter (Units) Population
Mean (% RSE)
IIV Standard
Deviation as
CV% (% RSE)
K
inUp;Apo
(USU/(ng/ml)/day) 0.0656 (10.3) 24.1 (33.5)
K
outUp;Apo
(1/day) 5.81 (5.24) 25.1 (18.2)
K
r;ApoUpSig
(1/day) 0.173 (9.90) 27.3 (34.4)
K
inUp;Cmab
(USU/(ng/ml)/day) 0.00649 (10.8) 42.4 (23.3)
K
outUp;Cmab
(1/day) 0.159 (7.16) 34.8 (21.0)
K
r;CmabUpSig
(1/day) 1.28 (7.33) 30.2 (18.9)
K
inApop;UpSig
(ASU/USU/day) 0.130 (9.17) 32.7 (22.5)
K
outApop
(1/day) 0.796 (7.13) 35.2 (16.9)
K
Death
(1/ASU/day) 0.0924 (9.37) 32.0 (23.1)
K
G
(1/day) 0.157 (2.99) 40.7 (6.52)
TV
SS
(mm
3
) 2120 (4.44) 52.3 (6.05)
TV(0) (mm
3
) 288 (2.81) 36.2 (3.33)
Proportional Error Variance 0.264
NLL 22920.
AIC 46022
Table 4.2. Parameter estimates for the empirical reduced drug eect at the
Upstream Signal model
4.3.2 Reduced Drug-Eect at Apoptosis Signal Model (K
r
Apoptosis Model)
Table 4.3 presents the parameter estimates for the intracellular-signaling tumor-
regression K
r
Apoptosis Model. The Upstream Signal production constant for Cona-
tumumab is once more considerably smaller than that for rshApo2L/TRAIL. Only
one parameter has an estimated inter-individual variability that slightly exceeds 50%
CV and all relative standard errors are modest. The conditional standardized resid-
uals show good scattering and no obvious trends (not shown). The estimated mean
steady state untreated tumor volume of 2010 mm
3
is fairly similar to the value esti-
mated for the control data alone (2630 mm
3
). The estimated mean rst-order tumor
98
net growth rate constant of 0.163/day is quite similar to the value estimated for the
control-only data, which was 0.166/day.
Parameter (Units) Population
Mean (% RSE)
IIV Standard
Deviation as
CV% (% RSE)
K
inUp;Apo
(USU/(ng/ml)/day) 0.0293 (6.03) 30.1 (18.7)
K
outUp;Apo
(1/day) 9.33 (5.46) 32.8 (13.1)
K
inUp;Cmab
(USU/(ng/ml)/day) 0.00593 (7.12) 43.4 (14.2)
K
outUp;Cmab
(1/day) 8.97 (7.89) 27.3 (22.1)
K
inApop;UpSig
(ASU/USU/day) 0.237 (6.48) 41.1 (14.1)
K
outApop
(1/day) 0.576 (4.75) 31.8 (13.3)
K
r;ApopSig
(1/day) 0.175 (7.60) 26.0 (31.3)
K
Death
(1/ASU/day) 0.139 (5.88) 42.9 (12.5)
K
G
(1/day) 0.163 (2.94) 38.4 (6.79)
TV
SS
(mm
3
) 2010 (4.50) 55.8 (5.71)
TV(0) (mm
3
) 288 (2.82) 36.0 (3.33)
Proportional Error Variance 0.264
NLL 22912
AIC 45981
Table 4.3. Parameter estimates for the empirical reduced drug eect at the
Apoptosis Signal model
The following are model-t plots for the K
r
Apoptosis Model. The description of
the symbols used in Figures 4.1 to 4.3 in Section 4.2 apply to Figures 4.7 to 4.9, as
well. Apo17, 25, and 26 show noticeable improvements, and Cmab5, 7, 8a, 8b, and 10
show modest improvements in their model ts over the results from the Base Model.
Overall, the model ts are quite similar to those from the K
r
Upstream Model. There
is little or no improvement of t to treatment groups Apo4 and Apo20.
99

Figure 4.7. K
r
Apoptosis Model population analysis t to the rshApo2L/TRAIL
experiments with individual data. For the six control group experiments, only the
results from the Apo1b study are shown.
100

Figure 4.8. K
r
Apoptosis Model population analysis t to the rshApo2L/TRAIL
experiments with average data. For the three control group experiments, only the
results from the Apo23a study are shown.
101

Figure 4.9. K
r
Apoptosis Model population analysis t to the Conatumumab
experiments with individual data. For the six control group experiments, only the
results from the groups Cmab1d-1f are shown.
102
4.4 Pro-Survival Signal Model
Table 4.4 presents the parameter estimates for the intracellular-signaling tumor-
regression Pro-Survival Signal Model. The Upstream Signal production constant for
Conatumumab is still considerably smaller than that for rshApo2L/TRAIL; however,
now the Upstream Signal loss rate constant for Conatumumab is nearly two orders of
magnitude larger than that for rshApo2L/TRAIL. All parameters have an estimated
inter-individual variability less than 50% CV and most relative standard errors are
modest, although some are as large as 50-75%. The conditional standardized residuals
show good scattering and no obvious trends (not shown). The estimated mean steady
state untreated tumor volume of 2530 mm
3
is quite similar to the value estimated
for the control data alone (2630 mm
3
). The estimated mean rst-order tumor net
growth rate constant of 0.186/day is somewhat larger than the value estimated for
the control-only data, which was 0.166/day.
The following are model-t plots for the Pro-Survival Signal Model. The description
of the symbols used in Figures 4.1 to 4.3 in Section 4.2 apply to Figures 4.10 to 4.12,
as well. Apo17, 25, and 26 show noticeable improvements, and Cmab5, 7, 8a, 8b,
and 10 show modest improvements in their model ts over the results from the Base
Model. Overall, the model ts are generally similar to those produced from the two
empirical reduced-eect models. There is little or no improvement of t to treatment
groups Apo4 and Apo20.
103

Figure 4.10. Pro-Survival Signal Model population analysis t to the
rshApo2L/TRAIL experiments with individual data. For the six control group
experiments, only the results from the Apo1b study are shown.
104

Figure 4.11. Pro-Survival Signal Model population analysis t to the
rshApo2L/TRAIL experiments with average data. For the three control group
experiments, only the results from the Apo23a study are shown.
105

Figure 4.12. Pro-Survival Signal Model population analysis t to the Conatumumab
experiments with individual data. For the six control group experiments, only the
results from the groups Cmab1d-1f are shown.
106
Parameter (Units) Population
Mean (% RSE)
IIV Standard
Deviation as
CV% (% RSE)
K
inUp;Apo
(USU/(ng/ml)/day) 20.9 (18.2) 28.2 (57.6)
K
outUp;Apo
(1/day) 1.43 (7.56) 38.2 (17.1)
K
inUp;Cmab
(USU/(ng/ml)/day) 3.38 (18.8) 31.1 (49.5)
K
outUp;Cmab
(1/day) 85.0 (20.4) 23.5 (73.8)
K
Trnsd
(1/day) 0.283 (6.53) 40.3 (15.2)
IC
50;ProSrvlSig
(PSSU)
1
9.79 (6.76) 39.0 (15.9)
K
inApop;UpSig
(ASU/USU/day) 0.0927 (5.13) 29.4 (15.3)
K
outApop
(1/day) 0.319 (5.35) 29.5 (16.4)
K
Death
(1/ASU/day) 0.0314 (4.49) 32.5 (10.5)
K
G
(1/day) 0.186 (3.33) 32.5 (9.62)
TV
SS
(mm
3
) 2530 (5.12) 41.4 (7.77)
TV(0) (mm
3
) 296 (3.03) 34.7 (4.13)
Proportional Error Variance 0.274
NLL 22686
AIC 45555
1
Pro-Survival Signal unit
Table 4.4. Parameter estimates for the model incorporating the Pro-Survival Signal
4.5 Simulations using Base Model and Pro-
Survival Signal Model
In an eort to visualize the consequences of the addition to the model of a reduction
in drug eect, simulations of continuous infusions of several sizes were performed.
The simulations consist of a total dose amount (210-1200 mg/kg, see Figure 4.13)
given through a constant infusion lasting 30 days. The resulting plots, shown in
Figure 4.13 below, indicate the key dierence between the Base Model and any of
the three reduced-drug-eect models: while there exists some tumor-static continuous
dose such that no net growth will occur for the Base Model, no such dose exists for the
reduced-drug-eect models and re-growth of the tumor occurs prior to the removal
107
of the drug. The Pro-Survival Signal Model was used in this exercise, but the results
would be similar for either of the empirical reduced-eect models.
Figure 4.13. Simulations of tumor volume during administration of 30-day-long
constant infusions of varying total dose sizes using the Base Model and Pro-Survival
Signal Model
While these simulations show the fundamental dierence between the two types
of models, it is risky to attempt to extrapolate too far with even the more
108
mechanistically-based model; for example, when the Pro-Survival Signal is removed
(i.e., K
Trnsd
is set to zero) in a simulation, the results show an unrealistically large
tumor-suppression eect. The various factors contributing to drug eect have still
not been deconvolved, and as such, the models must be treated with caution.
4.6 Combination Therapy Model
Data from the monotherapy studies were used to help inform the combination ther-
apy analysis. The groups used were: Apo1c, 3, 8, 10, 14, 19, 23b, 23c, 27, 28, 29,
30, 31, 32, 33; and Cmab1b, and 1c. Table 4.5 presents the parameter estimates
for the intracellular-signaling tumor-regression Combination Therapy Model. For
the Combination Therapy Model analysis, the monotherapy PARA parameters were
xed to the population mean values derived from the Pro-Survival Signal analysis
(see Table 4.4), and only parameters potentially informed by the administration of
Irinotecan were estimated. All parameters have an estimated inter-individual vari-
ability less than 50% CV; however, the relative standard errors are fairly large for
some of the parameters that are only informed by data that were limited (i.e., from
studies with Irinotecan dosed alone or in combination with Apo2L/TRAIL or Cona-
tumumab). Parameters informed by all of the data (including PARA monotherapies)
{ such as K
outApop
, K
Death
, and the tumor growth parameters { have fairly modest
standard errors.
The conditional standardized residuals show good general scattering with a few clus-
terings that indicate that the model somewhat overestimates tumor volume at the
very small tumor sizes and somewhat underestimates tumor volume at the very large
109
tumor sizes (not shown). The estimated mean steady state untreated tumor volume
of 2360 mm
3
is fairly close to the value estimated for the control data alone (2630
mm
3
). The estimated mean rst-order tumor net growth rate constant of 0.174/day
is only slightly larger than the value estimated for the control-only data, which was
0.166/day.
Parameter (Units) Population
Mean (% RSE)
IIV Standard
Deviation as
CV% (% RSE)
K
inMid
(MSU
1
/(ng/ml)/day) 0.172 (32.5) 38.6 (69.7)
K
outMid
(1/day) 0.211 (35.9) 41.9 (68.8)
E
max;MidSig
3.75 (44.6) 37.1 (79.5)
EC
50;MidSig
(MSU) 3.33 (51.2) 28.0 (140.)
K
inApop;MidSig
(ASU/MSU/day) 0.0383 (33.4) 43.5 (54.2)
K
outApop
(1/day) 0.379 (11.1) 34.5 (25.0)
K
Death
(1/ASU/day) 0.0384 (12.0) 46.4 (30.4)
K
G
(1/day) 0.174 (8.99) 44.4 (21.0)
TV
SS
(mm
3
) 2360 (18.1) 27.0 (55.0)
TV(0) (mm
3
) 236 (6.11) 32.4 (15.3)
Proportional Error Variance 0.246
NLL 6519
AIC 13170
1
Midstream Signal unit
Table 4.5. Parameter estimates for the model describing combination therapies of
either rshApo2L/TRAIL and Irinotecan (CPT-11) or Conatumumab and Irinotecan
Figures 4.14 and 4.15 are model-t plots for the Combination Therapy Model. Gen-
erally, the ts are good; CPT11&Cmab2, one of the Irinotecan monotherapy groups,
is the only group for which the average t does not match the average measured data
well. The model appears to underestimate the eect of the drug. It is important
to note that this group lost two of its 10 animals before the last few measurements
were taken. Since, generally, animals are euthanized for necrotic and/or excessively
large tumors, the loss of these animals may skew the average of the measured data
110
smaller than it would otherwise have been had these measurements been possible. A
supporting piece of evidence for this explanation is that the CPT11&Cmab3 group
had the same dosing regimen as CPT11&Cmab2, but with 80 mg/kg per dose as
opposed to 20 mg/kg per dose. However, despite receiving four times as much drug,
the CPT11&Cmab3 group had a slightly larger average ending tumor volume than
CPT11&Cmab2 (approximately 400 versus approximately 350, respectively). It is
unclear if some of the issues with tting this Irinotecan monotherapy group were due
to the irregularity of the data from the Conatumumab and Irinotecan study overall:
the control data from this study were completely excluded from the analysis because
many of the animals showed large drops in tumor volume (e.g., from approximately
755 mm
3
to approximately 15 mm
3
) during the study, despite not having received
any treatment.
111

Figure 4.14. Combination Therapy Model population analysis t to the Irinotecan
(CPT-11) and rshApo2L/TRAIL tumor size data as described in Table 2.5. The
orange-red triangles represent CPT-11 dosing events, and the yellow squares
represent rshApo2L/TRAIL dosing events.
112

Figure 4.15. Combination Therapy Model population analysis t to the Irinotecan
(CPT-11) and Conatumumab tumor size data as described in Table 2.6. The
orange-red triangles represent CPT-11 dosing events, and the yellow squares
represent Conatumumab dosing events.
113
4.7 Simulations using Combination Therapy
Model
In an eort to examine the model-estimated interaction between the PARA (either
rshApo2L/TRAIL or Conatumumab) and Irinotecan, the Combination Therapy
Model was used to perform several simulations for four of the combination ther-
apy groups: CPT11&Apo4, CPT11&Apo7, CPT11&Cmab4, and CPT11&Cmab5.
The simulations performed were of tumor volume over time following administra-
tion of only the PARA (rshApo2L/TRAIL or Conatumumab), administration of only
Irinotecan, or administration of both drugs but with the assumption of only additive,
not synergistic, eects (i.e., E
max
set equal to zero; see Section 3.5 for details). See
Figure 4.16 for an overlay of these simulations for each of the four selected groups.
For the two combination groups wherein the PARA used was rshApo2L/TRAIL, the
data available were average group data. Thus, the parameters used for the simulations
were the conditional means estimated for that average data set, taken directly from
the MLEM population analysis results. The data plotted in Figure 4.16 are the actual
data used in the MLEM population analysis for these two groups.
For the two combination groups wherein Conatumumab was used as the PARA,
individual data were available. In order to perform simulations for each group, the
parameter conditional means estimated for each animal from the MLEM population
analysis were averaged and simulations were performed using these group-average
parameters. The data plotted in Figure 4.16 are the average tumor size data for each
of these two groups.
114
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)" $& $!)" " " "

')& & $)% *&
" ) ! ( $# $ $( & )' + ( # ( & ( $ # " ) ! ( $# $ $( & )' + ( $)( # ( & ( $ # ")!( $#$ $#!, " ) ! ( $# $ $#! , " ,'
)" $& $!)" " " Figure 4.16. Simulations of tumor volume using the Combination Therapy Model.
Shown are simulations of tumor volume following administration of only the PARA,
only Irinotecan (CPT-11), both drugs with only additive eects (\without
interaction"), and both drugs with synergistic eect (\with interaction"). The
orange-red triangles represent CPT-11 dosing events, and the yellow squares
represent PARA (either rshApo2L/TRAIL or Conatumumab) dosing events.
The simulations shown in Figure 4.16 suggest that the combined eects of Irinotecan
and each of the two PARAs is synergistic; however, the large eect of the monothera-
pies on tumor regression diminishes the ability to reliably quantify the interaction. For
example, the eect of Irinotecan in groups CPT11&Apo4 and CPT11&Apo7 is nearly
the entire observed drug eect. (Note: the Irinotecan eect in these plots is very simi-
lar to that seen in the actual experimental data of the Irinotecan monotherapy group,
115
CPT11&Apo2, and the rshApo2L/TRAIL eect in the CPT11&Apo7 plot is very
similar to the actual experimental data of the rshApo2L/TRAIL monotherapy group
with the same dosing regimen, CPT11&Apo3. Therefore, it does not appear that the
model had to alter the monotherapy of the drugs to produce these results.) Addi-
tionally, CPT11&Cmab4, which received three 20 mg/kg doses of Irinotecan, shows a
much larger dependence on synergy to describe the data than does CPT11&Cmab5,
which received three 80 mg/kg doses of Irinotecan.
116
Chapter 5.
Discussion and Future Work
Four models for the action of two PARAs, rshApo2L/TRAIL and Conatumumab,
on tumor regression in a mouse xenograft preparation were presented that include
each drug's specic action on upstream signaling pathways (initiator caspases) and
on a shared downstream signaling component (executioner caspases). By pooling
experimental data from separate xenograft experiments with each PARA, the com-
mon signaling components of the model are informed simultaneously by the PK and
tumor burden data from both of the PARAs. The resulting models describe serial
tumor regression measurements from a large number of xenograft experiments, rep-
resenting a wide range of drug doses and exposure patterns for each compound. A
semi-mechanistic extension of the Base Model consistent with the hypothesis that
PARAs may also result in the upregulation of pro-survival factors that can lead to a
reduction in eectiveness of PARAs with treatment was found to better describe those
experiments (particularly those with rshApo2L/TRAIL) involving both longer-term
drug exposure and experiments of longer duration.
117
The modeling results presented in this work provide support for a semi-mechanistic
implementation of one hypothesis for the resistance to the action of pro-apoptotic
receptor agonists that may develop during treatment. In addition, the pathway mod-
eling approach adopted is an illustration of a more general framework for building cell
signaling models, whereby data from studies involving dierent compounds but with
shared signaling pathway elements can be co-analyzed to yield more nearly complete
systems-pharmacology-pathway models.
5.1 Comparison of Model Performances
Table 5.1 lists the negative log likelihood and AIC values for each of the four
monotherapy models considered. The Pro-Survival Signal Model had the lowest AIC
value of all the models. The model with no reduction of drug eect (the Base Model)
performed far worse than the other three models, especially in its ability to describe
data from Apo17, 20, 25, and 26 and Cmab5, 7, 8a, 8b, and 10 with longer drug expo-
sure and longer study duration; moreover, the proportional error variance was much
larger for the Base Model than for the other three models. And, while there was a bit
of variation in the tumor growth parameters estimated for the dierent monotherapy
models, the estimates from the Base Model diered the most from those estimated
from the control-only data.
Model NLL AIC
Base Model 23492 47115
K
r
Upstream Model 22920 46022
K
r
Apoptosis Model 22912 45981
Pro-Survival Signal Model 22686 45555
Table 5.1. NLL and AIC values for the four monotherapy models evaluated
118
Overall, all four monotherapy models were able to describe fairly well a wide variety
of dosing regimens for the two drugs. However, there is not enough information, based
on the performance measures of the three reduced-drug-eect models, to point toward
the site of drug eect reduction as being at either the production of the Upstream
Signal or the Apoptosis Signal.
5.2 Comparison of Work to Other Models and
Measures
Harrold et al. [2012] have developed a mechanistic cell-signaling-ecacy model for the
CD20 agonist rituximab that also includes a death receptor occupancy model for the
PARA rshApo2L/TRAIL. Their model incorporates the fractions of death receptors
DR4 and DR5 bound by rshApo2L/TRAIL, which in turn are related directly to the
apoptotic action of the drug. The model simulation shown in Figure 2A of Harrold
et al. [2012] indicates that the fraction of occupied receptors is reduced ten-fold at
approximately 2-4 hours following an IV dose of 10 mg/kg (sooner for DR4, later for
DR5). Simulation of the time course of the rshApo2L/TRAIL Upstream Signal in the
Base Model presented herein following a 10 mg/kg IV dose shows that the Upstream
Signal is reduced ten-fold at approximately 7 hours after drug administration, which
includes time not only for dissociation of the drug from its target receptors, but
also for removal of the drug from the site of action, as well as multiple intracellular
events, including the degradation of activated initiator caspases. It is also important
to note that the Upstream Signal represents production from a collection of tumor
cells, which causes the kinetics to be less sharp for any given intracellular event.
119
The kinetics of initiator and executioner caspase activation have been explored in
single-cell models by several groups [Spencer and Sorger, 2011, Spencer et al., 2009,
Albeck et al., 2008a,b, Fussenegger et al., 2000]. In Spencer and Sorger [2011], Spencer
et al. [2009], Albeck et al. [2008a,b], HeLa cells were bathed in a solution with a
constant concentration of rshApo2L ranging from 2 to 1000 ng/mL; the HeLa cells
were co-dosed with cycloheximide to prevent new protein synthesis, which changes
the behavior of the cells and may limit direct comparisons with the modeling work
presented here. Because the kinetics of the Base Model Signals are all linear, a
simulation was performed assuming a constant plasma concentration of 10 ng/mL
with the understanding that the time-prole of the Signals will be the same no matter
the dose size (that is, the only dierence will be the scale of the Signals, not the shape
or time-prole). Simulation of the time course of the rshApo2L/TRAIL Upstream
Signal in the Base Model with the plasma concentration xed at 10 ng/mL shows that
the Upstream Signal reaches half of its maximal value at approximately 2 hours. In
the Spencer and Albeck papers noted above, T
d
represents the time to half-maximal
activation of the initiator caspases and depends on dose size, but generally ranges
between 2 and 16 hours.
In Fussenegger et al. [2000], the caspase cascade response to an extracellular pro-
apoptotic stimulus of unknown size from FAS ligands binding to Fas receptors is
simulated in a generic cell type. The simulations in the Fussenegger paper of the
initiator and executioner caspases show half-maximal activation is achieved at around
10 and 20 minutes, respectively. This is much faster than the simulated Base Model
results for time-to-half-maximum of the Upstream and Apoptosis Signals, which are
about 2 hours (as mentioned above) and about 13 hours, respectively. It is unclear if
the dierences are due to the dierent ligand/receptor under investigation, or if this
120
is more a consequence of models in this paper describing entire populations of cells.
However, the times shown in the Fussenegger paper are also much faster than those
shown in the Spencer and Albeck papers.
In an Amgen presentation titled \AMG 951 Preclinical Data Review" made Novem-
ber 9, 2007, data for treatment-induced activation of executioner caspases-3 and -7
were presented for rshApo2L/TRAIL. The data show high plasma concentrations of
activated caspases-3 and -7 at 24, 72, and 96 hours after the beginning of a regimen
where COLO205-xenograft-bearing mice were administered a bolus of 10, 30, 60, or
90 mg/kg once a day for three consecutive days. The method of administration is
not noted in the slide; simulations were performed assuming either an IV or an IP
administration route, with a dose size of 10 mg/kg/dose (again, dose size does not
matter because both the PK and the kinetics of the Upstream and Apoptosis Signals
are linear in the Base Model). Both simulations resulted in three Apoptosis Signal
peaks (for each of the three doses administered) at very similar times: approximately
5, 28, and 52 hours after the start of dosing for the IV simulation; and as expected,
the IP regimen produced slightly later peaks than did the IV regimen, at approxi-
mately 7, 30, and 55 hours after the start of dosing. The Apoptosis Signal had gone
back to nearly zero by 96 hours after the rst dose. Because the Apoptosis Signal
roughly represents the intracellular executioner caspases, and the measurements were
taken in the plasma, the timing of the Apoptosis Signal peaks is reasonable, since it
will still take some time for the activated executioner caspases to cause apoptosis, be
released from the tumor cells, and make their way into the circulatory system. As a
result, the peaks and troughs of the Apoptosis Signal would likely be smoothed out
and the observed plasma eect would likely be protracted.
121
The comparability of the timing of both the activation and inactivation of the
Upstream Signal to in vitro measures of initiator caspase activation and receptor
occupancy support the idea that the Upstream Signal roughly represents the intra-
cellular activation of the initiator caspases, although the model does represent a much
larger pool of cells. Similarly, the comparability of the Apoptosis Signal with the in
vivo activated executioner caspase data lends support for the idea that the Apoptosis
Signal roughly represents the executioner caspases.
5.3 Pro-Survival Signal is Only One Possible
Explanation
While development of the Pro-Survival Signal Model presented herein was motivated
by consideration of pro-survival factor activation, the production of a concurrent
pro-survival signal is not the only possible explanation for the observed diminished
drug eect and there is currently not enough information to identify reduction of
drug eect as occurring at the production of the Upstream Signal or the Apoptosis
Signal. Another explanation involves reduced drug delivery to the site of action
(Upstream Signal in our model), an increasingly studied source of drug resistance
(see Section 1.4.2) [Dreher et al., 2006, Curnis et al., 2002, Sugahara et al., 2010].
When tumor cells proliferate, they often outgrow their blood supply, the vessels are
frequently defective, and the interstitial pressure tends to be abnormally high due to
an underdeveloped lymphatic system in the region, all of which reduce the ability of
drugs to reach and penetrate the tumor [Dreher et al., 2006, Jain, 1994, Minchinton
and Tannock, 2006, Jain, 1994]. Finally, in humans with heterogeneous tumors,
122
developed resistance in a subset of cells would contribute to reduced ecacy following
treatment with PARAs. However, this hypothesis has not been explored in the context
of the current xenograft-modeling work.
5.4 Combination Data and Clinical Relevance
There were substantial diculties in modeling the combination therapy data, which
curtailed meaningful exploration of the model. The model was generally able to t
the monotherapy and combination data; however, there was not a signicant amount
of information about the interaction of the drugs due to the fairly large eects of the
chosen monotherapy regimens (see Section 4.7).
The experience of attempting to obtain and model combination therapy data points
toward a need for better pre-clinical combination studies. Because new anticancer
agents generally enter the clinical setting as part of a multi-drug `cocktail', it is
valuable to be able to suggest an optimal dosing schedule for a given drug knowing
its particular drug environment. As evidenced in the Conatumumab and Irinotecan
study, the fact that scheduling is very important in determining antagonistic, additive,
or synergistic eects [Zwitter, 2010] does not appear to be a priority in designing these
studies. Furthermore, the goal of these studies should not necessarily be to show
the maximal eect possible, but rather to allow for quantication of the dierences
between regimens, which will likely occur with far less dramatic eects than complete
tumor regression in every treatment group.
Much more work would have to be done to produce a model that accurately quanties
the interaction of these dierent classes of drugs before any extrapolation can be
123
done. Something like the Midstream Signal in the Combination Therapy Model might
provide insight into the timing necessary to see the greatest benets of the new drug.
5.5 Future Work
5.5.1 Needed Data to Test Hypotheses
The aforementioned processes associated with drug delivery, as well as the produc-
tion of a pro-survival signal, could produce the diminished drug eect observed. Thus
any model developed from the data available in the current studies would be unable
to distinguish between these possible mechanisms. While the current model of the
PARA-stimulated extrinsic apoptotic pathway can provide a framework for investigat-
ing these mechanisms, additional experiments would be required; for example, includ-
ing time series measurements of activated initiator caspases (caspases-8 and -10) and
activated executioner caspases (caspases-3, -6, and -7) in tumor xenografts exposed
to PARAs (e.g., intra-tumor measurements of these activated caspases). Moreover,
to fully elucidate any contribution of the pro-survival signal process, information on
the time course of pro-survival factors related to NF-B (such as cFLIP and one or
several IAPs) would be needed.
5.5.2 Improve Combination Therapy Model
The linear relationships between the Irinotecan plasma concentration and the produc-
tion of the Midstream Signal, and the eect of the Midstream Signal on the production
of the Apoptosis Signal (in the absence of an Upstream Signal), were informed by
124
previous work that had been done by Simeoni et al. [2004] and work done with ear-
lier, simpler versions of the models presented herein. These linear models were able to
describe fairly well the tumor regression of xenografts in animals treated with Irinote-
can. However, given the dierent structure of the Combination Therapy Model, it
may be necessary to explore more complex relationships for the production (and loss)
of the dierent Signals related to the cytotoxic agent.
Similarly, the linear production terms of the two PARA Upstream Signals and the
Apoptosis Signal were used because the monotherapies of the PARAs could not inform
an E
max
model for Upstream or Apoptosis Signals, even though there is certainly a
physiological limit to the amount of initiator and executioner caspase activation that
can occur. It is possible that, while the PARA monotherapies could not inform any
E
max
models, the combination therapies might provide sucient stimulation of the
system to identify saturable processes. Thus, it might be useful to explore alternatives
to the PARA monotherapy models, as well.
It may also be benecial to expand the combination model to include a more realis-
tic relationship between the extrinsic and intrinsic apoptotic pathways. To do this,
the eect of the PARA would need to increase the production of the Midstream
Signal (likely through the Upstream Signal) to capture the eect of caspase-8's acti-
vating the mitochondrial pathway (see Section 1.2.4). This would also more closely
recapitulate the intracellular signaling of cells that display type II receptor-mediated
apoptosis, which requires the activation of both the initiator-and-executioner caspase
cascade and the mitochondrial pathway [Aldridge et al., 2011]. It would also allow for
modeling of the priming of the intrinsic pathway by the extrinsic pathway through
caspase-8.
125
5.5.3 Suggested Combination Therapy Study
As has been discussed, the scheduling of the two compounds is very important: syn-
ergism or antagonism have been shown to be schedule-dependent in in vitro stud-
ies [Zwitter, 2010]. In addition, improved ecacy has been shown in in vitro studies
where the cytotoxic agent precedes the PARA by at least 24 hours [Xiang et al., 2002].
One of the shortcomings of the available combination data is that monotherapy doses
are so large that they produce substantial tumor-regression independently, such that
it is dicult to assess the combination data for additive or synergistic responses;
that is, the tumor volume can only shrink from its maximal size to zero, and if
each monotherapy decreases the tumor volume by, for example, more than half of its
starting value, the contributions of each drug in the combination therapy are dicult
to tease out. A second major issue is that the dosing regimens often do not take
advantage (or explore) the element of relative timing when giving the cytotoxic agent
and PARA, even though it has been shown to be an important element in determining
overall ecacy. An example of this is the Conatumumab combination study presented
in Table 2.6, wherein the cytotoxic drug and PARA were both dosed on the same
days as each other (days 0, 2, and 4).
Therefore, a potentially useful combination therapy study could have monotherapy
doses that only produce moderate tumor regression on their own, and combination
scheduling that explores the relative timing of the cytotoxic and the PARA. Table 5.2
shows an example of such a study. Irinotecan (CPT-11) is used as the cytotoxic agent
in this example because that is the cytotoxic drug used in the previously explored
studies, providing familiarity with the dosing of this agent. RshApo2L/TRAIL is
the suggested PARA because its monotherapy tumor growth is better described as
126
compared to that of Conatumumab, and therefore would provide a more tractable
starting point for assessing the combination therapies.
Treatment
Group ID
RshApo2L/TRAIL
Dosing
(mg/kg/dose)
CPT-11 Dosing
(mg/kg/dose)
Number of
Animals
CPT11&Apo1
20; IV bolus on days 1,
8, 15
None 10
CPT11&Apo2 None
20; IP bolus on days 0,
7, 14
10
CPT11&Apo3
20; IV bolus on days 0,
7, 14
20; IP bolus on days 0,
7, 14
10
CPT11&Apo4
20; IV bolus on days 1,
8, 15
20; IP bolus on days 0,
7, 14
10
CPT11&Apo5
20; IV bolus on days 3,
10, 17
20; IP bolus on days 0,
7, 14
10
CPT11&Apo6
20; IV bolus on days 0,
7, 14
20; IP bolus on days 1,
8, 15
10
Table 5.2. A proposed combination-therapy study for CPT-11 and
rshApo2L/TRAIL
Twenty mg/kg was chosen for the rshApo2L/TRAIL dose because it is a small but
still pre-clincially eective dose; the fairly sparse, spread-out dosing regimen was
chosen in order to avoid a substantial monotherapy-induced tumor regression and to
make room in the schedule for dierent relative timings of the PARA and cytotoxic
agent. Similarly, 20 mg/kg of CPT-11 per dose was chosen to produce a modest
monotherapy response and the doses are again spread out to allow for variation in
the relative timings of the administration of the two drugs.
Four cytotoxic-PARA timings are proposed: one on the same day as each other, one
with the PARA dosed one day after the cytotoxic, one with the PARA dosed three
127
days after the cytotoxic agent, and one with the PARA dosed one day before the
cytotoxic agent. The goal with these four regimens is to explore { with the goal of
quantifying { the eect of timing on the synergistic properties of this combination
therapy. The emphasis on schedules with the cytotoxic agent preceding the PARA is
motivated by earlier work that showed improved ecacy in vitro when the cytotoxic
preceded the PARA by at least 24 hours [Xiang et al., 2002]. The kinetics of the
Midstream Signal similarly inform the suggested cytotoxic-PARA timings: peaks in
the Midstream Signal occur approximately 20-30 hours after the cytotoxic dose is
administered, and the Midstream Signal remains relatively high several days after
the cytotoxic dose. One treatment group is designed to have the PARA precede the
cytotoxic agent by one day, because the extrinsic pathway can augment the intrinsic
pathway through the truncation of BID to tBID (see Section 1.2.4). Ten animals
is generally a sucient number of subjects to see the basic behavior of a treatment
group.
While this study lay-out focuses on exploring the impact of the relative timings of the
cytotoxic agent and PARA, a more ambitious study would also vary dose sizes to allow
for assessment of dose and regimen eects. One possibility would be to evaluate two
dose sizes for each drug, perhaps 20 mg/kg and 40 mg/kg to keep the monotherapy
eects modest, which would produce four dose-size combinations for each cytotoxic-
PARA timing regimen: 20 mg/kg of both the PARA and the cytotoxic; 20 mg/kg of
the PARA and 40 mg/kg of the cytotoxic; 40 mg/kg of the PARA and 20 mg/kg of
the cytotoxic; and 40 mg/kg of both the PARA and the cytotoxic.
128
5.5.4 Analysis of Other Cell Lines
All work presented here was performed on COLO205 xengoraft data. However, data
from several other cell lines are available: human non-small-cell lung cancer (NSCLC)
cell lines H2122 and H460; and human pancreatic cancer cell line MiaPaCa/T2. An
extension of this work might involve analyzing this new data with the models already
developed, to then allow for comparison of the results (e.g., parameter estimates,
emerging model-t trends).
The data are fairly spread out among these three cell lines, but one possible area to
look at would be the results for the dierent NSCLC cell lines versus those of the
pancreatic cancer cell line or the COLO205 results already obtained.
129
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Abstract (if available)

Abstract RshApo2L/TRAIL and Conatumumab bind to transmembrane death receptors and trigger the extrinsic cellular apoptotic pathway through a caspase-signaling cascade resulting in cell death. Tumor size time series data from rodent tumor xenograft (COLO205) studies following administration of either of these two pro-apoptotic receptor agonists (PARAs) were combined to develop an intracellular-signaling tumor-regression model that includes two levels of signaling: upstream signals unique to each compound (representing initiator caspases), and a common downstream apoptosis signal (representing executioner caspases) shared by the two agents. Pharmacokinetic (PK) models for each drug were developed based on plasma concentration data following intravenous (IV) and/or intraperitoneal (IP) administration of the compounds and were used in the subsequent intracellular-signaling tumor-regression modeling. A model relating the PK of the two PARAs to their respective and common downstream signals, and to the resulting tumor burden was developed using mouse xenograft tumor size measurements from 448 experiments that included a wide range of dose sizes and dosing schedules. ❧ Deficiencies in the original model's ability to describe data from some of the experimental groups led to exploration of several hypotheses for a reduction of drug effect. Both empirical and semi-mechanistic reduction-of-drug-effect models were investigated. All three modified models showed marked improvement of fit, especially for data from the long-term dosing experiments

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Asset Metadata

Creator Kay, Brittany P. (author)

Core Title Modeling anti-tumoral effects of drug-induced activation of the cell-extrinsic apoptotic pathway

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 07/15/2012

Defense Date 06/06/2012

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

Tag apoptosis,cancer,caspase,extrinsic apoptotic pathway,Modeling,OAI-PMH Harvest,Pará,PKPD

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor D'Argenio, David Z. (committee chair), Khoo, Michael C.K. (committee member), Mackay, John Andrew (committee member)

Creator Email bkay@usc.edu,brittany.p.kay@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-57385

Unique identifier UC11290405

Identifier usctheses-c3-57385 (legacy record id)

Legacy Identifier etd-KayBrittan-954.pdf

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Document Type Dissertation

Rights Kay, Brittany P.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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