Workshop 1: Ecology and Evolution of Cancer

(September 15,2014 - September 19,2014 )

Organizers


David Basanta
Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center
Rick Durrett
Department of Mathematics, Duke University
Jasmine Foo
Department of Mathematics, University of Minnesota
Carlo Maley
Department of Surgery, University of California, San Francisco

Beginning with PC Nowell's work in the 1970s, we know that starting from a single clone, cancers show a striking amount of intratumor heterogeneity. This heterogeneity results from the accumulation of genetic mutations and epigenetic changes as cells divide and means that tumor cells inside the same tumor can be different. Not all genetic mutations have the same impact on the fitness of a tumor cell: We know evolution selects for phenotypes (and the genotypes responsible for those phenotypes) that can better exploit the dynamic environment in which they live. Thus those cells that can better take advantage of their environment in terms of other tumor and non-tumor cells as well as the physical microenvironment (space, oxygen, nutrients...) will be more successful and eventually constitute the majority of the tumor population. Understanding the interactions between the cellular and physical agents in the tumor microenvironment will require an evolutionary and ecological perspective that can only be fulfilled with the help of mathematical models that can integrate the wealth of biological and clinical data being produced. This workshop will bring together cancer researchers and mathematical oncologists as well as ecologists with the aim of understanding how ecological principles can be used to understand cancer, how the mathematical tools used by theoretical ecologists could be used to gain new insights in cancer research and what principles of ecological management could be used to produce new therapies to treat cancer in the clinic.

Accepted Speakers

Athena Aktipis
Psychology, Arizona State University
Philipp Altrock
Program for Evolutionary Dynamics, Harvard University
Sandy Anderson
Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Tibor Antal
School of Mathematics, Edinburgh University
Arturo Araujo
Integrated Mathematical Oncology, Moffitt Cancer Center
David Axelrod
Department of Genetics, Rutgers University
Niko Beerenwinkel
Department of Biosystems Science and Engineering, ETH Zurich
Ivana Božić
Department of Mathematics, Program for Evolutionary Dynamics, Harvard University
Joel Brown
Biological Sciences, University of Illinois at Chicago
Ruchira Datta
Surgery, University of California, San Francisco
Jill Gallaher
Integrated Mathematical Oncology, Moffitt Cancer Center
Robert Gatenby
H. Lee Moffitt Cancer Center & Research Institute
Trevor Graham
Tumour Biology, Barts Cancer Institute, QMUL
Kamran Kaveh
Applied Mathematics, University of Waterloo
Artem Kaznatcheev
Computer Science, McGill University
Natalia Komarova
Department of Mathematics, University of California, Irvine
Kevin Leder
Industrial and Systems Engineering, University of Minnesota
Katherine Liu
Ecology, Evolution, and Behavior, University of Minnesota, Twin Cities
Shannon Mumenthaler
Medicine, University of Southern California
John Nagy
Life Sciences, Scottsdale Community College
Kenneth Pienta
Brady Urological Institute, Johns Hopkins University
John Potter
Public Health Sciences Division, Fred Hutchinson Cancer Research Center
Marc Ryser
Mathematics, Duke University
Joshua Schiffman
Pediatrics and Oncological Sciences, Huntsman Cancer Institute/University of Utah
Darryl Shibata
School of Medicine/Pathology, USC Keck School of Medicine
Arne Traulsen
Evolutionary Theory, Max-Planck Institute for Evolutionary Biology
Richard White
Gastrointestinal Oncology Service, Memorial Sloan-Kettering Cancer Center
Monday, September 15, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:00 AM

Greetings and info from MBI - Marty Golubitsky

09:00 AM
09:45 AM
Robert Gatenby - MBI Colloquium: Bringing evolutionary dynamics to clinic oncology

Abstract not submitted.

10:00 AM
10:45 AM
Darryl Shibata - Reconstructing Early Human Tumorigenesis From Present Day Genomic Alterations

The “start” of human tumorigenesis is difficult to study because most human tumors are undetectable until they reach about 1 cm in size (~1 billion cells). However, it may be possible to reconstruct even the first few divisions after tumor initiation through the analysis of somatic mutations in large present day tumors. Using coalescent theory, “public” mutations in the initiating cell will be present in all present day tumor cells. Assuming a simple exponential clonal expansion, “private” mutations that arise during the first few cell divisions will be present in most but not all present day tumor cells. The earlier a private mutation occurs, the greater its frequency in the final tumor. By sampling multiple regions from the same large human tumor, it is possible to identify public and private mutations, and then infer the early events after human tumor initiation.

10:45 AM
11:15 AM

Break

11:15 AM
12:00 PM
John Potter - Nutrition and Cancer: choosing the right model

In the light of known associations between cancer and specifically: alcohol; dietary fat; obesity; vegetables, fruit, and single nutrients; hormones; and inflammation, I will make the case that the dominant theory of carcinogenesis does not do a very good job of underpinning widespread coherent epidemiologic findings.

The talk will begin with the dominant theory of carcinogenesis. What we know about some nutritional/lifestyle causes of cancer (with occasional asides on anomalies and policy implications) will follow. I will make the case that the empirical findings and the theory are ill-matched but, also, that there are other theories that can help us think more clearly about diet and cancer particularly. From this point, the talk will focus on insights from development and morphogenesis – invoking clear evidence for the capacity of developing organisms to respond to environmentally generated signals and to modify their development accordingly. Noting that an important universal (but often ignored) characteristic of cancer is disrupted tissue microarchitecture, I will suggest that we can consider cancer as something like disordered development and will discuss the role of morphostats in its genesis; analogous to agents that shape developing organisms (morphogens), morphostats are agents that maintain adult tissues. I will then ask the crucial mechanistic question as to whether there is any evidence that cells in developing organisms (and, by implication, perhaps cancer cells) can directly read signals from their environment. Indeed, there is evidence that developing cells can sense their systemic and nutritional environment and that exogenous nutrients and endogenous hormones can directly regulate at least one key morphogenetic/morphostatic signaling system and determine cell fate.

Thinking about more appropriate theories of carcinogenesis may allow us to ask better questions in studies of nutrition and lifestyle.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:45 PM
Richard White - Modeling metastasis using zebrafish

Metastatic disease is the defining feature of advanced malignancy, yet the mechanisms by which it occurs and affects host physiology are poorly understood. Comprehensive genomic studies of human metastatic cancers has revealed striking heterogeneity both within primary tumors, but also between different metastases from the same patient. For these reasons, models which capture this heterogeneity will be necessary to design effective strategies to abrogate the metastatic phenotype. The zebrafish has recently emerged as a genetic model system in which to study cancer because of several key strengths: 1) small size allows for study of vast numbers of animals, 2) optical transparency facilitates in vivo imaging of even single cancer cells, and 3) amenability to unbiased genetic and small molecule screens. My laboratory has developed a zebrafish model of melanoma in which the BRAFV600E allele is expressed in the mitf+ melanocyte lineage. These animals develop stereotyped, 100% penetrant melanomas when crossed to a p53-/- mutant. Using highly sensitive fluorescent detection and automated imaging algorithms, we have defined metastatic capacity of these tumors, and demonstrate a metastasis initiating cell frequency of 1/250,000 cells. These cells show preferential metastases to locations such as skin, bone marrow, and eye. Using this as a platform, we are now defining the genomic characteristics of the metastatic clones, and designing unbiased screens to find genetic or epigenetic pathways that modify metastatic progression. The zebrafish offers a highly scalable in vivo system for interrogating the dynamics of metastasis over both time and space at a resolution unavailable in other model systems.

03:00 PM
03:45 PM
Kenneth Pienta - The Cancer Ecosystem: Niche construction without homeostatic controls

Niche construction is the process whereby organisms modify their own and/or each other’s niches through their metabolism, activities, and/or choices. This can result in changes in one or more natural selection pressures in the external environment of populations. Niche-constructing species may either alter the natural selection pressures of their own population, of other populations, or of both. In ecology, foundation species are species that have a strong role in structuring a community. Cancer cells act as a foundation species and also act as ecosystem engineers to construct new system niches. This may lead to increased genetic instability through evolutionary adaptation. Most constructed ecosystems eventually reach a point of homeostasis (equilibrium) that creates an environment that allows the foundation species to thrive. There is no evidence that cancer reaches this ecological endpoint. It is worth exploring if this can be exploited as a therapeutic target.

04:00 PM
05:00 PM
Joshua Schiffman
05:00 PM
07:00 PM

Reception and Poster Session in MBI Lounge

07:00 PM

Shuttle pick-up from MBI

Tuesday, September 16, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:45 AM
David Basanta
10:00 AM
10:45 AM
Joel Brown - Tumor heterogeneity and therapy as a rock-scissors-paper game

Androgen receptors provide an Achilles heel for treating prostate cancer. Once cancerous, prostate tumor cells still rely on testosterone for successful cell division and proliferation. Anti-androgens and testosterone suppression can halt cell proliferation and provide an attractive therapy. Distance from vasculature may promote tumor heterogeneity and at least two “cytotypes” --- testosterone requiring cells near vessels, testosterone independent ones far from vasculature. Furthermore, therapy may select for a third, testosterone producing cytotype. As a game of Darwinian dynamics (ecological and evolutionary changes), we present a model for the dynamics of each of these cytotpyes in response to: 1) the frequency of the different cytotypes, 2) the scale and degree of angiogenesis, and 3) different therapeutic strategies. With and without therapy 1, 2 and 3 strategy cytotype ESSs emerge. Abundant vasculature and no therapy permit T-requiring cells to outcompete all others. With anti-androgen therapy, R-S-P can ensue as an evolutionary game. The testosterone independent (T-) cytotype can invade the testosterone positive (T+) cytotype, the testosterone producing (TP) cytotype can invade T-, and T+ can invade TP. The nature of the tumor microenvironments strongly influences the pre- and post-therapy outcomes. As importantly, the resulting ESS following anti-androgens may strongly influence the efficacy of second line therapies specifically targeting T+ and TP cytotypes.

10:45 AM
11:15 AM

Break

11:15 AM
12:00 PM
Ruchira Datta
12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:45 PM
Tibor Antal - Multitype branching processes: from bacteria to cancer

We'll review recent developments in the theory of two type birth-death branching processes. These studies were pioneered by Salvador Luria and Max Delbruck in 1943 to model genetic mutations arising in bacterial populations. More recent applications include the development of resistance to chemotherapy of cancer.

03:00 PM
03:45 PM
Jill Gallaher - Shaping Tumor Heterogeneity: Phenotypic selection versus Clonal targeting

By distinguishing an individual tumor's heterogeneous mix of cells, it is often the goal of personalized cancer medicine to design targeted drug combinations that facilitate optimal outcomes and crucially are patient specific. These targeted drugs focus on blocking specific pathways identified by genetic alterations, but often a single biopsy reveals only a portion of the genetic heterogeneity. Even with a complete characterization of the whole tumor, successful treatment relies on targeting all of the major driver mutations, which furthermore may fail due to acquired resistance. With such a heterogeneous disease as cancer, this feels like a point-and-shoot approach with many moving targets.

While the genotypes become more heterogeneous over time, the phenotypes tend to converge as the environment selects for the most fit subtypes of cells. Also genetic mutation happens stochastically, while phenotypic adaptation occurs in response to environmental changes. By focusing on phenotypic traits, we are targeting the highest level of functional cell behavior. But even at this scale there is complexity. For example, how should a phenotype propagate - do all clones share the same phenotype, or is there some plasticity? The right timing and sequence of drugs could shape the population to be more targetable instead of mutationally resistant.

We build an agent based model to explore genotypic and phenotypic progression and selection as a result of different sequences of treatment environments. This approach allows us to investigate interactions of single cells and evolution of the collective heterogeneous population in an environment with spatial competition.

04:00 PM
05:00 PM
Trevor Graham - Quantifying clonal evolution in the human colon

The process of clonal evolution underpins the maintenance of a normal healthy colon, and the “unwanted evolution” of mutant cells leads to the development of colon cancer. However, despite the central importance, a quantification of the parameters that define the clonal evolutionary process in human colon (and indeed all human tissues) has remained lacking. Our current understanding is derived from studies performed in model organisms, and it is uncertain if and how these insights apply to humans. I will describe how we coupled a novel “lineage tracing” strategy in human colon, that allows the fate of different clonal lineages to be visualised, with a reductionist mathematical analysis that allows us to infer the parameters governing clonal evolution in the human gut.

Our analysis has shown that human intestinal stem cells evolve through a process of neutral drift, and that the neutrality of this process is disrupted by mutation to the APC gene that functions as a key tumour-suppressor in the colon. In the colon, cells are organized into millions of “crypts” – small tubular structures each housing a few thousand cells. Through our quantitative analysis of lineage-tracing data, we have been able to infer the number of functional stem cells per human crypt, and also how they behave over time. Further, our mathematical analysis reveals how often colon crypts divide, both in normal colon and in colon tumours. This parameterisation allows the age of colon tumours to be determined.

Finally, we have coupled multi-region sampling of established colorectal cancers with whole-genome sequencing and other genomic analysis to infer how colorectal cancers evolve. Our results imply that clonal evolution is not a process of stepwise clonal sweeps as the “textbook” model implies.

My particular excitement about this work is that it demonstrates how quantitative analysis of a static picture can resolve temporal dynamics. Application of these methods quantifies the dynamic process of clonal evolution that occurs in human tissues.

05:00 PM

Shuttle pick-up from MBI

Wednesday, September 17, 2014
Time Session
02:00 AM
02:25 AM
Shannon Mumenthaler
02:30 AM
03:00 AM
Artem Kaznatcheev - Edge effects in evolutionary dynamics of spatially structured tumors

A typical assumption in analytic evolutionary game theory models of cancer is that the population is inviscid: the probability of a cell with a given phenotypic strategy interacting with another depends exclusively on the respective abundance of those strategies in the population. To overcome this limitation, we show how to use the Ohtsuki-Nowak transform to approximate spatial structure and study the effect of interaction neighborhood size. In particular, we focus on the change in neighborhood size at a static boundary -- such as a blood-vessel, organ capsule, or basement membrane. In the case of the go vs. grow game, this edge effect allows a tumor with no invasive phenotypes expressed internally to have a polyclonal boundary with both invasive and non-invasive cells. We hope that our approach serves as a useful analytic compliment to the more common simulation based methods of modeling the effects of spatial structure on cancer dynamics.

03:15 AM
04:00 AM
Sandy Anderson - An integrated approach to understanding tumor-stromal interactions in cancer progression and treatment

An evolving tumour interacts with and manipulates its surrounding microenvironment in a complex dynamic spatio-temporal manner. Microenvironmental heterogeneity has long been an accepted aspect of tumor progression and recently intratumor heterogeneity has become more widely accepted. The complex dialogue between these heterogeneous populations ultimately drives tumor progression, and highlights the fact that purely experimental approaches are unpractical given the multitude of interactions and time scales involved. Our focus here will be to highlight the potential of using an integrated theoretical and experimental approach to tackle this complexity through two distinct examples. The first will consider the role of reactive stroma in prostate cancer evolution using a hybrid multiscale mathematical model that incorporates a histologically accurate representation of the peripheral zone. The model specifically considers how stormal dependent and stromal independent prostate cancers evolve and how interactions between tumor and stroma facilitate or inhibit tumor evolution. The second will consider melanoma and focuses on the role of senescent fibroblasts. We develop a hybrid multiscale mathematical model of normal skin (vSkin) and use it to understand how the key cellular (keratinocytes, melanocytes and fibroblasts) and microenvironmental variables regulate skin homeostasis and how their transformation can lead to cancer. Based on our experimental and theoretical results we conclude that, senescent fibroblasts create a pro-oncogenic environment that synergizes with mutations to drive melanoma initiation and progression and should therefore be considered as a potential future therapeutic target. We use our vSkin model to test such a therapeutic strategy, aimed at restoring homeostasis via manipulation of the tumor microenvironment. This study also suggests a potential link between aging in the skin microenvironment and the development of melanocytic neoplasms.

04:15 AM
05:00 AM
Natalia Komarova - Cancer: evolution, space, cooperation

Complex traits in biology arise from the interactions among multiple genes. Sometimes, before the complex phenotype is generated, a so-called "fitness valley" must be crossed, where things get worse before they get better. In this case, the generation of a complex phenotype may take a relatively long evolutionary time. Interestingly, the rate of evolution depends in nontrivial ways on various properties of the underlying stochastic process, such as the spatial organization of the population and social interactions among cells. The role of spatial constraints is quite complex. We identify realistic cases where spatial constrains can accelerate or delay evolution, or even influence it in a non-monotonic fashion, where evolution works fastest for intermediate-range constraints. Social interactions among cells are studied in the context of the division of labor games. Under a range of circumstances, cooperation among cells can lead to a relatively fast creation of a complex phenotype as an emerging (distributed) property. If we further assume the presence of cheaters, we observe the emergence of a fully-mutated population of cells possessing the complex phenotype. Applications of these ideas to cancer initiation and progression are discussed.

05:00 AM

Shuttle pick-up from MBI

08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:45 AM
David Axelrod - Stem Cell Dynamics in the Microenvironment of Normal Colon Crypts, and the Initiation, Progression and Therapy of Colon Cancer

An agent-based model of stochastic cell dynamics in human colon crypts was developed in the application NetLogo, and calibrated by measurements of numbers of stem cells, proliferating cells, and differentiated cells in human biopsy specimens. It was assumed that each cell’s probability of proliferation and probability of death is determined by its position in two microenvironment gradients along the crypt axis, a divide gradient and in a die gradient. A cell’s type is not intrinsic, but rather is determined by its position in the divide gradient. Cell types are dynamic, plastic, and inter-convertible. Parameter values were determined for the shape of each of the gradients, and for a cell’s response to the gradients. This was done by parameter sweeps that indicated the values that reproduced the measured number and variation of each cell type, and produced quasi-stationary stochastic dynamics. The behavior of the model was verified by its ability to reproduce the experimentally observed monoclonal conversion by neutral drift, the formation of adenomas resulting from mutations either at the top or bottom of the crypt, and by the robust ability of crypts to recover from perturbation by cytotoxic agents. An example of the use of the virtual crypt will be given, viz., the evaluation of different cancer chemotherapy protocols.

10:00 AM
10:45 AM
Marc Ryser - Tracking the invisible: a probabilistic approach to field cancerization in head and neck carcinoma

Head and neck cancers often emerge within genetically altered fields of premalignant cells that appear histologically normal but have a high chance of progression to malignancy. Clinical consequences of this so-called field cancerization are multifocal lesions and high recurrence risks after excision of the primary tumor. We develop a spatiotemporal stochastic model of head and neck tumorigenesis, combining evolutionary dynamics at the phenotypic level with a general framework for multi-stage progression to cancer. Based on the model, we derive probabilistic distributions for clinically relevant quantities such as size of the invisible premalignant field at time of cancer diagnosis, and risk of local and distant recurrences. Finally, we discuss how our model can be combined with patient-specific measurements to optimize surgical excision margins and post-operative monitoring.

10:45 AM
11:15 AM

Break

11:15 AM
11:40 AM
Kamran Kaveh - Evolutionary Dynamics of Tumour Heterogeneity and Plasticity

Ubiquitous proliferation scheme of stem cells let them not only to replenish their own population but also nourish the population of non-stem tumour cells in a hierarchal form and create strong epigenetic heterogeneity in tumours. Cancer stem cells are believed to have strong plastic phenotypic property tuned by microenvironment which can affect their selection dynamics. We construct a general Moran type model to include differentiation and plasticity for cancer stem cell selection. We present analytical and simulation results for fixation probability and time to fixation in such a model. We apply our model to niche succession and clonal conversion in colorectal cancer both in the presence and absence of primary plasticity between stem cells in the niche and their early progenitors. We also address the effect of microenvironment by introducing a spatial model which incorporates variations in fitness parameters as well as geometry of the the organ. Our finding shows that the fixation probability is a strong function of plasticity rate and differentiation probabilities inside stem cell niche. We compare our findings with observations of Vermeulen et al (Science 2013) on stem cell dynamics of intestinal tumour initiation.

11:40 AM
02:00 AM

Lunch Break

Thursday, September 18, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:45 AM
Arne Traulsen - Stochastic and deterministic evolutionary dynamics in hierarchically organized tissues

Tissues are typically organized hierarchically. The dynamics of cancer progression can be strongly affected by this population structure. Mutations arising in primitive cells can lead to long lived or even persistent clones, but mutations arising in further differentiated cells are short lived and do not affect the organism. A generic model for such tissue structures, which is non-spatial, but considers various steps of differentiation, can be used to model various cancers. In particular, we can use this to address the somatic evolution in Chronic Myeloid Leukemia, Paroxysmal Nocturnal Hemoglobinuria, or Acute Promyelocytic Leukemia.

10:00 AM
10:45 AM
Ivana Božić - Evolutionary dynamics of resistance to cancer therapy

Metastatic dissemination to surgically inaccessible sites is the major cause of death in cancer patients. Targeted therapies, often initially effective against metastatic disease, invariably fail due to resistance. Mathematical modeling can be used to illuminate the evolutionary dynamics of resistance to anti-cancer treatment and provide important information for the design of treatments that aim to control resistance. We discuss recent approaches, which combine mathematical modeling of resistance together with clinical data, and point to the reasons behind treatment failure in patients with metastatic disease.

10:45 AM
11:15 AM

Break

11:15 AM
11:40 AM
Philipp Altrock - Tumor growth and clonal heterogeneity during expansion and treatment

Cancers arise through a process of somatic evolution. This evolutionary process can result in substantial clonal heterogeneity. The mechanisms responsible for the coexistence of distinct clonal lineages and the biological consequences of this coexistence remain poorly understood. Based on in vivo data from a mouse xenograft model, we investigate the influence of clonal heterogeneity on tumor properties, and mathematically model competitive expansion of individual clones. We find that tumor growth can be driven by a minor cell subpopulation. This minor population of cells enhances the proliferation of all cells within a tumor by overcoming environmental constraints. Yet, this driving cell population can be outcompeted by faster proliferating competitors. This can result in tumor collapse. We describe how that non-cell autonomous driving of tumor growth supports clonal interference, stabilizes clonal heterogeneity and enables inter-clonal interactions, which can lead to new phenotypic tumor traits. When treatment is administered, heterogeneity can be reduced, also reducing evolutionary and metastatic potential. We adjust and inform our mathematical framework to model different treatment strategies and optimize treatment processes, in particular in HER2+ breast cancer tumors.

11:45 AM
12:15 PM
Lin Liu
12:15 PM
02:00 PM

Lunch Break

02:00 PM
02:45 PM
John Nagy - The Creative Roles of Selection and Drift in the Angiogenic Switch in Cancer

According to one influential paradigm, malignant phenotypes characterizing the "hallmarks of cancer" arise in part via natural selection acting on genetically diverse clones within a tumor. Among these hallmarks, the angiogenic switch is one of the most difficult to explain using an evolutionary narrative. While neoangiogenesis clearly benefits tumor cells, the signal creating it is a public good and therefore susceptible to free-riders. Previous modeling studies predicted that these free-riders can invade, damage and perhaps destroy developing tumors, growing as a tumor-on-a-tumor, or hypertumor. The open question becomes, why are hypertumors apparently rare? Here we show, using more realistic extensions of the original models, that selection favoring free-riding is expected to be overwhelmed by genetic drift in most cases. Adaptive dynamics analysis of a deterministic model of the energetic costs and benefits of angiogenesis and proliferation predicts the existence of an evolutionary stable (ESS) angiogenesis commitment, but this ESS is always a repeller. The expectation, then, is runaway selection for extreme vascular hypo- or hyperplasia. However, the selection gradient is very shallow compared to that for other traits, specifically proliferation. Therefore, evolutionarily unfavorable angiogenesis phenotypes may still invade if they are coupled to even marginally more favorable proliferation strategies through a mechanism logically identical to linkage disequilibrium. A simulation of this evolutionary theater predicts that this disequilibrium mechanism dominates the evolution of the angiogenic switch. We predict, then, that angiogenesis arises as an evolutionary rider on the back of selection for proliferative potential and other malignant hallmarks.

03:00 PM
03:45 PM
Arturo Araujo - TGFBeta inhibition in Prostate to Bone Metastasis

Prostate cancer frequently metastasizes to bone with approximately 90% of the men displaying evidence of skeletal lesions upon autopsy (1). Despite medical advances, prostate to bone metastases remain incurable with treatments being mainly palliative (2). Advances in our knowledge of the molecular mechanisms underlying the disease should provide therapeutic opportunities to improve overall survival rates but on a more microenvironmental scale, predicting how putative therapies will impact multiple cellular responses remains a challenge. However, integrating key biologic findings with the power of computational modeling offers a unique opportunity to assess the impact of putative therapies on the progression of prostate cancer.

The vicious cycle of bone degradation and formation driven by metastatic prostate cells in bone yields factors that drive cancer growth. Mechanistic insights into this vicious cycle have suggested new therapeutic opportunities, but complex temporal and cellular interactions in the bone microenvironment make drug development challenging. To tackle this, we have integrated biologic and computational approaches to generate a hybrid cellular automata model of normal bone matrix homeostasis and the prostate cancer-bone microenvironment. Understanding the normal basic multicellular unit (BMU) bone remodeling process is critical for the generation of a robust computational model (3). The initiation of the BMU by local or systemic signals results in retraction of osteoblasts from the bone surface and the formation of a canopy. Local mesenchymal stromal cells (MSC) generate RANKL- expressing osteoblasts precursors that subsequently facilitate osteoclast recruitment, maturation, and bone resorption. Degradation of the bone results in the release of sequestered growth factors such as TGF-b that in turn serve to control the extent of bone degradation and osteoblast expansion. After osteoclast apoptosis, osteoblasts rebuild the bone with a portion terminally differentiating into osteocytes and the remainder reconstituting the bone lining, ready for the next remodeling cycle.

The model accurately reproduces the basic multicellular unit bone coupling process, such that introduction of a single prostate cancer cell yields a vicious cycle similar in cellular composition and pathophysiology to models of prostate-to-bone metastasis. Notably, the model revealed distinct phases of osteolytic and osteogenic activity, a critical role for mesenchymal stromal cells in osteogenesis, and temporal changes in cellular composition. To evaluate the robustness of the model, we assessed the effect of established bisphosphonate and anti-RANKL therapies on bone metastases. At approximately 100% efficacy, bisphosphonates inhibited cancer progression while, in contrast with clinical observations in humans, anti- RANKL therapy fully eradicated metastases. Reducing anti-RANKL yielded clinically similar results, suggesting that better targeting or dosing could improve patient survival. Our work establishes a computational model that can be tailored for rapid assessment of experimental therapies and delivery of precision medicine to patients with prostate cancer with bone metastases.

REFERENCES

[1] Keller ET, Brown J. Prostate cancer bone metastases promote both osteolytic and osteoblastic activity. J Cell Biochem 2004;91:718–29.

[2] Brown JE, Coleman RE. Denosumab in patients with cancer-a surgical ?strike against the osteoclast. Nat Rev Clin Oncol 2012;9:110–8.

[3] Bilezikian J, Raisz L, Martin T. Principles of Bone Biology: Academic ?Press; 2008.

04:00 PM

Shuttle pick-up from MBI

05:30 PM
08:30 PM

Banquet in the Fusion Room at Crown Plaza

Friday, September 19, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:45 AM
Ian Tomlinson
10:00 AM
10:45 AM
Kevin Leder - Optimization of radiation schedules for proneural gliomas via mathematical modeling

Gliomas are the most common and malignant primary tumors of the brain and are commonly treated with radiation therapy. Despite modest advances in chemotherapy and radiation, survival has changed very little over the last 50 years. Radiation therapy is one of the pillars of adjuvant therapy for GBM but despite treatment, recurrence inevitably occurs. Here we develop a mathematical model for the tumor response to radiation that takes into account the plasticity of the hierarchical structure of the tumor population. Based on this mathematical model we develop an optimized radiation delivery schedule.

10:45 AM
11:15 AM

Break

11:15 AM
12:00 PM
Niko Beerenwinkel - Modeling cancer evolution from genomic data

Cancer evolution is a stochastic evolutionary process characterized by the accumulation of mutations and responsible for tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to describe the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular profiling data. We present recent approaches to modeling the evolution of cancer, including population genetics models of tumorigenesis, phylogenetic methods of intra-tumor subclonal diversity, and probabilistic graphical models of tumor progression, and we discuss methods for distinguishing driver from passenger mutations.

12:00 PM

Shuttle pick-up from MBI (One to Hotel / One to Airport)

Name Email Affiliation
Aktipis, Athena aktipis@asu.edu Psychology, Arizona State University
Altrock, Philipp paltrock@jimmy.harvard.edu Program for Evolutionary Dynamics, Harvard University
Anderson, Alexander alexander.Anderson@moffitt.org Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Antal, Tibor Tibor.Antal@ed.ac.uk School of Mathematics, Edinburgh University
Araujo, Arturo arturo@CancerEvo.org Integrated Mathematical Oncology, Moffitt Cancer Center
Axelrod, David axelrod@biology.rutgers.edu Department of Genetics, Rutgers University
Badri, Hamidreza badri019@umn.edu ISyE, University of Minnesota
Basanta, David david@cancerevo.org Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center
Beerenwinkel, Niko niko.beerenwinkel@bsse.ethz.ch Department of Biosystems Science and Engineering, ETH Zurich
Bloemendal, Alex alexb@math.harvard.edu Mathematics, Program for Evolutionary Dynamics, Harvard University
Botesteanu, Dana dboteste@math.umd.edu Applied Mathematics & Scientific Computing, University of Maryland
Bozic, Ivana ibozic@fas.harvard.edu Department of Mathematics, Program for Evolutionary Dynamics, Harvard University
Brown, Joel squirrel@uic.edu Biological Sciences, University of Illinois at Chicago
Chifman, Julia jchifman@wakehealth.edu Cancer Biology, Wake Forest School of Medicine
Cross, William Charles Hemming w.c.h.cross@qmul.ac.uk Tumour Biology, Barts Cancer Institute
Datta, Ruchira datta@Math.Berkeley.EDU Surgery, University of California, San Francisco
Durrett, Rick rtd@math.duke.edu Department of Mathematics, Duke University
Ebsch, Christopher cebsch@nd.edu Applied and Computational Mathematics and Statistics, University of Notre Dame
Feldges, Robert feldges.1@osu.edu Mathematics, The Ohio State University
Flores Castillo, Nicolas nicolas@rice.edu Department of Statistics, Rice University
Foo, Jasmine jyfoo@math.umn.edu Department of Mathematics, University of Minnesota
Frieboes, Hermann hbfrie01@louisville.edu Bionegineering, University of Louisville
Gallaher, Jill jill.gallaher@moffitt.org Integrated Mathematical Oncology, Moffitt Cancer Center
Gatenby, Robert robert.gatenby@moffitt.org H. Lee Moffitt Cancer Center & Research Institute
Gazi, Nurul Huda nursha@rediffmail.com Mathematics, Aliah University, Dept of Mathematics
Ghadiali, Samir ghadiali.1@osu.edu Biomedical Engineering, The Ohio State University
Ghim, Cheol-Min cmghim@unist.ac.kr School of Life Sciences, Ulsan National Institute of Science and Technology
Graham, Trevor t.graham@qmul.ac.uk Tumour Biology, Barts Cancer Institute, QMUL
Greene, James jmgreene@math.umd.edu Mathematics, University of Maryland
Heilmann, Silja heilmans@mskcc.org Computational Biology, Memorial Sloan-Kettering Cancer Center
Jacobsen, Karly jacobsen.50@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Jang, Sophia srjjang@gmail.com Mathematics, Texas Tech University
Kaveh, Kamran kkavehma@gmail.com Applied Mathematics, University of Waterloo
Kaznatcheev, Artem artem.kaznatcheev@mail.mcgill.ca Computer Science, McGill University
Komarova, Natalia komarova@uci.edu Department of Mathematics, University of California, Irvine
Koslosky, Josh Koslosky504@gmail.com Mathematics, University of Minnesota
Kroeger, Cornelia ckroeger@gmx.net
Leder, Kevin kevin.leder@isye.umn.edu Industrial and Systems Engineering, University of Minnesota
Liebner, David david.liebner@osumc.edu Internal Medicine, Division of Medical Oncology, Ohio State University
Lindsay, Danika linds427@umn.edu Mathematics, University of Minnesota
Lipinski, Kamil kamil.a.lipinski@gmail.com Institute of Cancer Research, Centre for Evolution and Cancer
Liu, Katherine liuxx971@umn.edu Ecology, Evolution, and Behavior, University of Minnesota, Twin Cities
Liu, Lin lliu.hsph@gmail.com Biostatistics, Harvard University
Lu, Rong lu.550@buckeyemail.osu.edu Biostatistics, The Ohio State University
Mo, Xiaokui mo.7@osu.edu Biomedical Informatics, Ohio State University
Mumenthaler, Shannon smumenth@usc.edu Medicine, University of Southern California
Nagy, John john.nagy@scottsdalecc.edu Life Sciences, Scottsdale Community College
Najera Chesler, Aisha aisha.najera@cgu.edu Mathematics, Claremont Graduate University
Pepper, John pepperjw@mail.nih.gov Biometry Research Group, Division of Cancer Prevention, National Cancer Institute
Perez-Velazquez, Judith judith.perezvelazquez@gmail.com Institute of Biomathematics and Biometry, Helmholtz Zentrum München (German Research Center for Enviromental Health)
Pienta, Kenneth kpienta1@jhmi.edu Brady Urological Institute, Johns Hopkins University
Potter, John jpotter@fhcrc.org Public Health Sciences Division, Fred Hutchinson Cancer Research Center
Rezaei Yousefi, Mohammadmahdi rezaeiyousefi.1@osu.edu Electrical and Computer Engineering, The Ohio State University
Ryser, Marc ryser@math.duke.edu Mathematics, Duke University
Schiffman, Joshua joshua.schiffman@hci.utah.edu Pediatrics and Oncological Sciences, Huntsman Cancer Institute/University of Utah
Shibata, Darryl dshibata@hsc.usc.edu School of Medicine/Pathology, USC Keck School of Medicine
Shirinifard, Abbas abbas.shirinifard@stjude.org Information Sciences,
Sinkala, Zachariah Zachariah.Sinkala@mtsu.edu Mathematical Sciences, Middle Tennessee State University
Storey, Katie store050@umn.edu Mathematics, University of Minnesota
Taylor-King, Jake jake.taylor-king@dtc.ox.ac.uk Mathematical Institute, The University of Oxford
Traulsen, Arne traulsen@evolbio.mpg.de Evolutionary Theory, Max-Planck Institute for Evolutionary Biology
Travisano, Michael travisan@umn.edu Department of Ecology, Evolution and Behavior, University of Minnesota - Twin Cities
Werner, Benjamin werner@evolbio.mpg.de Institute for Evolutionary Theory, Max Planck Institute for Evolutionary Biology
White, Richard whiter@mskcc.org Gastrointestinal Oncology Service, Memorial Sloan-Kettering Cancer Center
Zhu, Junfeng zhuxx793@umn.edu Industrial and System Engineering, University of Minnesota
Cancer as somatic cheating: Resource acquisition and monopolization in cancer evolution

Cancer is a problem of somatic cheating, where cells of the body enhance their fitness at the expense of the organism as a whole. The evolution of multicellularity represents a highly sophisticated form of cooperation and cheater suppression. Each independent evolution of multicellularity required suppressing somatic cheating (i.e., cancer) long enough for the organism to survive and reproduce. Here I provide a review of somatic cheating in cancer like phenomena across the tree of life including the 6 independent branches of complex multicellularity. I focus on forms of cheating that involve resource acquisition and monopolization, including upregulated metabolism and disregulated signaling for limiting resources. I describe model results showing that resource cheating may be central to cancer evolution and progression to malignant disease.

Tumor growth and clonal heterogeneity during expansion and treatment

Cancers arise through a process of somatic evolution. This evolutionary process can result in substantial clonal heterogeneity. The mechanisms responsible for the coexistence of distinct clonal lineages and the biological consequences of this coexistence remain poorly understood. Based on in vivo data from a mouse xenograft model, we investigate the influence of clonal heterogeneity on tumor properties, and mathematically model competitive expansion of individual clones. We find that tumor growth can be driven by a minor cell subpopulation. This minor population of cells enhances the proliferation of all cells within a tumor by overcoming environmental constraints. Yet, this driving cell population can be outcompeted by faster proliferating competitors. This can result in tumor collapse. We describe how that non-cell autonomous driving of tumor growth supports clonal interference, stabilizes clonal heterogeneity and enables inter-clonal interactions, which can lead to new phenotypic tumor traits. When treatment is administered, heterogeneity can be reduced, also reducing evolutionary and metastatic potential. We adjust and inform our mathematical framework to model different treatment strategies and optimize treatment processes, in particular in HER2+ breast cancer tumors.

An integrated approach to understanding tumor-stromal interactions in cancer progression and treatment

An evolving tumour interacts with and manipulates its surrounding microenvironment in a complex dynamic spatio-temporal manner. Microenvironmental heterogeneity has long been an accepted aspect of tumor progression and recently intratumor heterogeneity has become more widely accepted. The complex dialogue between these heterogeneous populations ultimately drives tumor progression, and highlights the fact that purely experimental approaches are unpractical given the multitude of interactions and time scales involved. Our focus here will be to highlight the potential of using an integrated theoretical and experimental approach to tackle this complexity through two distinct examples. The first will consider the role of reactive stroma in prostate cancer evolution using a hybrid multiscale mathematical model that incorporates a histologically accurate representation of the peripheral zone. The model specifically considers how stormal dependent and stromal independent prostate cancers evolve and how interactions between tumor and stroma facilitate or inhibit tumor evolution. The second will consider melanoma and focuses on the role of senescent fibroblasts. We develop a hybrid multiscale mathematical model of normal skin (vSkin) and use it to understand how the key cellular (keratinocytes, melanocytes and fibroblasts) and microenvironmental variables regulate skin homeostasis and how their transformation can lead to cancer. Based on our experimental and theoretical results we conclude that, senescent fibroblasts create a pro-oncogenic environment that synergizes with mutations to drive melanoma initiation and progression and should therefore be considered as a potential future therapeutic target. We use our vSkin model to test such a therapeutic strategy, aimed at restoring homeostasis via manipulation of the tumor microenvironment. This study also suggests a potential link between aging in the skin microenvironment and the development of melanocytic neoplasms.

Multitype branching processes: from bacteria to cancer

We'll review recent developments in the theory of two type birth-death branching processes. These studies were pioneered by Salvador Luria and Max Delbruck in 1943 to model genetic mutations arising in bacterial populations. More recent applications include the development of resistance to chemotherapy of cancer.

TGFBeta inhibition in Prostate to Bone Metastasis

Prostate cancer frequently metastasizes to bone with approximately 90% of the men displaying evidence of skeletal lesions upon autopsy (1). Despite medical advances, prostate to bone metastases remain incurable with treatments being mainly palliative (2). Advances in our knowledge of the molecular mechanisms underlying the disease should provide therapeutic opportunities to improve overall survival rates but on a more microenvironmental scale, predicting how putative therapies will impact multiple cellular responses remains a challenge. However, integrating key biologic findings with the power of computational modeling offers a unique opportunity to assess the impact of putative therapies on the progression of prostate cancer.

The vicious cycle of bone degradation and formation driven by metastatic prostate cells in bone yields factors that drive cancer growth. Mechanistic insights into this vicious cycle have suggested new therapeutic opportunities, but complex temporal and cellular interactions in the bone microenvironment make drug development challenging. To tackle this, we have integrated biologic and computational approaches to generate a hybrid cellular automata model of normal bone matrix homeostasis and the prostate cancer-bone microenvironment. Understanding the normal basic multicellular unit (BMU) bone remodeling process is critical for the generation of a robust computational model (3). The initiation of the BMU by local or systemic signals results in retraction of osteoblasts from the bone surface and the formation of a canopy. Local mesenchymal stromal cells (MSC) generate RANKL- expressing osteoblasts precursors that subsequently facilitate osteoclast recruitment, maturation, and bone resorption. Degradation of the bone results in the release of sequestered growth factors such as TGF-b that in turn serve to control the extent of bone degradation and osteoblast expansion. After osteoclast apoptosis, osteoblasts rebuild the bone with a portion terminally differentiating into osteocytes and the remainder reconstituting the bone lining, ready for the next remodeling cycle.

The model accurately reproduces the basic multicellular unit bone coupling process, such that introduction of a single prostate cancer cell yields a vicious cycle similar in cellular composition and pathophysiology to models of prostate-to-bone metastasis. Notably, the model revealed distinct phases of osteolytic and osteogenic activity, a critical role for mesenchymal stromal cells in osteogenesis, and temporal changes in cellular composition. To evaluate the robustness of the model, we assessed the effect of established bisphosphonate and anti-RANKL therapies on bone metastases. At approximately 100% efficacy, bisphosphonates inhibited cancer progression while, in contrast with clinical observations in humans, anti- RANKL therapy fully eradicated metastases. Reducing anti-RANKL yielded clinically similar results, suggesting that better targeting or dosing could improve patient survival. Our work establishes a computational model that can be tailored for rapid assessment of experimental therapies and delivery of precision medicine to patients with prostate cancer with bone metastases.

REFERENCES

[1] Keller ET, Brown J. Prostate cancer bone metastases promote both osteolytic and osteoblastic activity. J Cell Biochem 2004;91:718–29.

[2] Brown JE, Coleman RE. Denosumab in patients with cancer-a surgical ?strike against the osteoclast. Nat Rev Clin Oncol 2012;9:110–8.

[3] Bilezikian J, Raisz L, Martin T. Principles of Bone Biology: Academic ?Press; 2008.

Stem Cell Dynamics in the Microenvironment of Normal Colon Crypts, and the Initiation, Progression and Therapy of Colon Cancer

An agent-based model of stochastic cell dynamics in human colon crypts was developed in the application NetLogo, and calibrated by measurements of numbers of stem cells, proliferating cells, and differentiated cells in human biopsy specimens. It was assumed that each cell’s probability of proliferation and probability of death is determined by its position in two microenvironment gradients along the crypt axis, a divide gradient and in a die gradient. A cell’s type is not intrinsic, but rather is determined by its position in the divide gradient. Cell types are dynamic, plastic, and inter-convertible. Parameter values were determined for the shape of each of the gradients, and for a cell’s response to the gradients. This was done by parameter sweeps that indicated the values that reproduced the measured number and variation of each cell type, and produced quasi-stationary stochastic dynamics. The behavior of the model was verified by its ability to reproduce the experimentally observed monoclonal conversion by neutral drift, the formation of adenomas resulting from mutations either at the top or bottom of the crypt, and by the robust ability of crypts to recover from perturbation by cytotoxic agents. An example of the use of the virtual crypt will be given, viz., the evaluation of different cancer chemotherapy protocols.

Modeling cancer evolution from genomic data

Cancer evolution is a stochastic evolutionary process characterized by the accumulation of mutations and responsible for tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to describe the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular profiling data. We present recent approaches to modeling the evolution of cancer, including population genetics models of tumorigenesis, phylogenetic methods of intra-tumor subclonal diversity, and probabilistic graphical models of tumor progression, and we discuss methods for distinguishing driver from passenger mutations.

Evolutionary dynamics of resistance to cancer therapy

Metastatic dissemination to surgically inaccessible sites is the major cause of death in cancer patients. Targeted therapies, often initially effective against metastatic disease, invariably fail due to resistance. Mathematical modeling can be used to illuminate the evolutionary dynamics of resistance to anti-cancer treatment and provide important information for the design of treatments that aim to control resistance. We discuss recent approaches, which combine mathematical modeling of resistance together with clinical data, and point to the reasons behind treatment failure in patients with metastatic disease.

Tumor heterogeneity and therapy as a rock-scissors-paper game

Androgen receptors provide an Achilles heel for treating prostate cancer. Once cancerous, prostate tumor cells still rely on testosterone for successful cell division and proliferation. Anti-androgens and testosterone suppression can halt cell proliferation and provide an attractive therapy. Distance from vasculature may promote tumor heterogeneity and at least two “cytotypes” --- testosterone requiring cells near vessels, testosterone independent ones far from vasculature. Furthermore, therapy may select for a third, testosterone producing cytotype. As a game of Darwinian dynamics (ecological and evolutionary changes), we present a model for the dynamics of each of these cytotpyes in response to: 1) the frequency of the different cytotypes, 2) the scale and degree of angiogenesis, and 3) different therapeutic strategies. With and without therapy 1, 2 and 3 strategy cytotype ESSs emerge. Abundant vasculature and no therapy permit T-requiring cells to outcompete all others. With anti-androgen therapy, R-S-P can ensue as an evolutionary game. The testosterone independent (T-) cytotype can invade the testosterone positive (T+) cytotype, the testosterone producing (TP) cytotype can invade T-, and T+ can invade TP. The nature of the tumor microenvironments strongly influences the pre- and post-therapy outcomes. As importantly, the resulting ESS following anti-androgens may strongly influence the efficacy of second line therapies specifically targeting T+ and TP cytotypes.

Shaping Tumor Heterogeneity: Phenotypic selection versus Clonal targeting

By distinguishing an individual tumor's heterogeneous mix of cells, it is often the goal of personalized cancer medicine to design targeted drug combinations that facilitate optimal outcomes and crucially are patient specific. These targeted drugs focus on blocking specific pathways identified by genetic alterations, but often a single biopsy reveals only a portion of the genetic heterogeneity. Even with a complete characterization of the whole tumor, successful treatment relies on targeting all of the major driver mutations, which furthermore may fail due to acquired resistance. With such a heterogeneous disease as cancer, this feels like a point-and-shoot approach with many moving targets.

While the genotypes become more heterogeneous over time, the phenotypes tend to converge as the environment selects for the most fit subtypes of cells. Also genetic mutation happens stochastically, while phenotypic adaptation occurs in response to environmental changes. By focusing on phenotypic traits, we are targeting the highest level of functional cell behavior. But even at this scale there is complexity. For example, how should a phenotype propagate - do all clones share the same phenotype, or is there some plasticity? The right timing and sequence of drugs could shape the population to be more targetable instead of mutationally resistant.

We build an agent based model to explore genotypic and phenotypic progression and selection as a result of different sequences of treatment environments. This approach allows us to investigate interactions of single cells and evolution of the collective heterogeneous population in an environment with spatial competition.

MBI Colloquium: Bringing evolutionary dynamics to clinic oncology

Abstract not submitted.

Quantifying clonal evolution in the human colon

The process of clonal evolution underpins the maintenance of a normal healthy colon, and the “unwanted evolution” of mutant cells leads to the development of colon cancer. However, despite the central importance, a quantification of the parameters that define the clonal evolutionary process in human colon (and indeed all human tissues) has remained lacking. Our current understanding is derived from studies performed in model organisms, and it is uncertain if and how these insights apply to humans. I will describe how we coupled a novel “lineage tracing” strategy in human colon, that allows the fate of different clonal lineages to be visualised, with a reductionist mathematical analysis that allows us to infer the parameters governing clonal evolution in the human gut.

Our analysis has shown that human intestinal stem cells evolve through a process of neutral drift, and that the neutrality of this process is disrupted by mutation to the APC gene that functions as a key tumour-suppressor in the colon. In the colon, cells are organized into millions of “crypts” – small tubular structures each housing a few thousand cells. Through our quantitative analysis of lineage-tracing data, we have been able to infer the number of functional stem cells per human crypt, and also how they behave over time. Further, our mathematical analysis reveals how often colon crypts divide, both in normal colon and in colon tumours. This parameterisation allows the age of colon tumours to be determined.

Finally, we have coupled multi-region sampling of established colorectal cancers with whole-genome sequencing and other genomic analysis to infer how colorectal cancers evolve. Our results imply that clonal evolution is not a process of stepwise clonal sweeps as the “textbook” model implies.

My particular excitement about this work is that it demonstrates how quantitative analysis of a static picture can resolve temporal dynamics. Application of these methods quantifies the dynamic process of clonal evolution that occurs in human tissues.

Evolutionary Dynamics of Tumour Heterogeneity and Plasticity

Ubiquitous proliferation scheme of stem cells let them not only to replenish their own population but also nourish the population of non-stem tumour cells in a hierarchal form and create strong epigenetic heterogeneity in tumours. Cancer stem cells are believed to have strong plastic phenotypic property tuned by microenvironment which can affect their selection dynamics. We construct a general Moran type model to include differentiation and plasticity for cancer stem cell selection. We present analytical and simulation results for fixation probability and time to fixation in such a model. We apply our model to niche succession and clonal conversion in colorectal cancer both in the presence and absence of primary plasticity between stem cells in the niche and their early progenitors. We also address the effect of microenvironment by introducing a spatial model which incorporates variations in fitness parameters as well as geometry of the the organ. Our finding shows that the fixation probability is a strong function of plasticity rate and differentiation probabilities inside stem cell niche. We compare our findings with observations of Vermeulen et al (Science 2013) on stem cell dynamics of intestinal tumour initiation.

Edge effects in evolutionary dynamics of spatially structured tumors

A typical assumption in analytic evolutionary game theory models of cancer is that the population is inviscid: the probability of a cell with a given phenotypic strategy interacting with another depends exclusively on the respective abundance of those strategies in the population. To overcome this limitation, we show how to use the Ohtsuki-Nowak transform to approximate spatial structure and study the effect of interaction neighborhood size. In particular, we focus on the change in neighborhood size at a static boundary -- such as a blood-vessel, organ capsule, or basement membrane. In the case of the go vs. grow game, this edge effect allows a tumor with no invasive phenotypes expressed internally to have a polyclonal boundary with both invasive and non-invasive cells. We hope that our approach serves as a useful analytic compliment to the more common simulation based methods of modeling the effects of spatial structure on cancer dynamics.

Cancer: evolution, space, cooperation

Complex traits in biology arise from the interactions among multiple genes. Sometimes, before the complex phenotype is generated, a so-called "fitness valley" must be crossed, where things get worse before they get better. In this case, the generation of a complex phenotype may take a relatively long evolutionary time. Interestingly, the rate of evolution depends in nontrivial ways on various properties of the underlying stochastic process, such as the spatial organization of the population and social interactions among cells. The role of spatial constraints is quite complex. We identify realistic cases where spatial constrains can accelerate or delay evolution, or even influence it in a non-monotonic fashion, where evolution works fastest for intermediate-range constraints. Social interactions among cells are studied in the context of the division of labor games. Under a range of circumstances, cooperation among cells can lead to a relatively fast creation of a complex phenotype as an emerging (distributed) property. If we further assume the presence of cheaters, we observe the emergence of a fully-mutated population of cells possessing the complex phenotype. Applications of these ideas to cancer initiation and progression are discussed.

Optimization of radiation schedules for proneural gliomas via mathematical modeling

Gliomas are the most common and malignant primary tumors of the brain and are commonly treated with radiation therapy. Despite modest advances in chemotherapy and radiation, survival has changed very little over the last 50 years. Radiation therapy is one of the pillars of adjuvant therapy for GBM but despite treatment, recurrence inevitably occurs. Here we develop a mathematical model for the tumor response to radiation that takes into account the plasticity of the hierarchical structure of the tumor population. Based on this mathematical model we develop an optimized radiation delivery schedule.

The Creative Roles of Selection and Drift in the Angiogenic Switch in Cancer

According to one influential paradigm, malignant phenotypes characterizing the "hallmarks of cancer" arise in part via natural selection acting on genetically diverse clones within a tumor. Among these hallmarks, the angiogenic switch is one of the most difficult to explain using an evolutionary narrative. While neoangiogenesis clearly benefits tumor cells, the signal creating it is a public good and therefore susceptible to free-riders. Previous modeling studies predicted that these free-riders can invade, damage and perhaps destroy developing tumors, growing as a tumor-on-a-tumor, or hypertumor. The open question becomes, why are hypertumors apparently rare? Here we show, using more realistic extensions of the original models, that selection favoring free-riding is expected to be overwhelmed by genetic drift in most cases. Adaptive dynamics analysis of a deterministic model of the energetic costs and benefits of angiogenesis and proliferation predicts the existence of an evolutionary stable (ESS) angiogenesis commitment, but this ESS is always a repeller. The expectation, then, is runaway selection for extreme vascular hypo- or hyperplasia. However, the selection gradient is very shallow compared to that for other traits, specifically proliferation. Therefore, evolutionarily unfavorable angiogenesis phenotypes may still invade if they are coupled to even marginally more favorable proliferation strategies through a mechanism logically identical to linkage disequilibrium. A simulation of this evolutionary theater predicts that this disequilibrium mechanism dominates the evolution of the angiogenic switch. We predict, then, that angiogenesis arises as an evolutionary rider on the back of selection for proliferative potential and other malignant hallmarks.

The Cancer Ecosystem: Niche construction without homeostatic controls

Niche construction is the process whereby organisms modify their own and/or each other’s niches through their metabolism, activities, and/or choices. This can result in changes in one or more natural selection pressures in the external environment of populations. Niche-constructing species may either alter the natural selection pressures of their own population, of other populations, or of both. In ecology, foundation species are species that have a strong role in structuring a community. Cancer cells act as a foundation species and also act as ecosystem engineers to construct new system niches. This may lead to increased genetic instability through evolutionary adaptation. Most constructed ecosystems eventually reach a point of homeostasis (equilibrium) that creates an environment that allows the foundation species to thrive. There is no evidence that cancer reaches this ecological endpoint. It is worth exploring if this can be exploited as a therapeutic target.

Nutrition and Cancer: choosing the right model

In the light of known associations between cancer and specifically: alcohol; dietary fat; obesity; vegetables, fruit, and single nutrients; hormones; and inflammation, I will make the case that the dominant theory of carcinogenesis does not do a very good job of underpinning widespread coherent epidemiologic findings.

The talk will begin with the dominant theory of carcinogenesis. What we know about some nutritional/lifestyle causes of cancer (with occasional asides on anomalies and policy implications) will follow. I will make the case that the empirical findings and the theory are ill-matched but, also, that there are other theories that can help us think more clearly about diet and cancer particularly. From this point, the talk will focus on insights from development and morphogenesis – invoking clear evidence for the capacity of developing organisms to respond to environmentally generated signals and to modify their development accordingly. Noting that an important universal (but often ignored) characteristic of cancer is disrupted tissue microarchitecture, I will suggest that we can consider cancer as something like disordered development and will discuss the role of morphostats in its genesis; analogous to agents that shape developing organisms (morphogens), morphostats are agents that maintain adult tissues. I will then ask the crucial mechanistic question as to whether there is any evidence that cells in developing organisms (and, by implication, perhaps cancer cells) can directly read signals from their environment. Indeed, there is evidence that developing cells can sense their systemic and nutritional environment and that exogenous nutrients and endogenous hormones can directly regulate at least one key morphogenetic/morphostatic signaling system and determine cell fate.

Thinking about more appropriate theories of carcinogenesis may allow us to ask better questions in studies of nutrition and lifestyle.

Tracking the invisible: a probabilistic approach to field cancerization in head and neck carcinoma

Head and neck cancers often emerge within genetically altered fields of premalignant cells that appear histologically normal but have a high chance of progression to malignancy. Clinical consequences of this so-called field cancerization are multifocal lesions and high recurrence risks after excision of the primary tumor. We develop a spatiotemporal stochastic model of head and neck tumorigenesis, combining evolutionary dynamics at the phenotypic level with a general framework for multi-stage progression to cancer. Based on the model, we derive probabilistic distributions for clinically relevant quantities such as size of the invisible premalignant field at time of cancer diagnosis, and risk of local and distant recurrences. Finally, we discuss how our model can be combined with patient-specific measurements to optimize surgical excision margins and post-operative monitoring.

Reconstructing Early Human Tumorigenesis From Present Day Genomic Alterations

The “start” of human tumorigenesis is difficult to study because most human tumors are undetectable until they reach about 1 cm in size (~1 billion cells). However, it may be possible to reconstruct even the first few divisions after tumor initiation through the analysis of somatic mutations in large present day tumors. Using coalescent theory, “public” mutations in the initiating cell will be present in all present day tumor cells. Assuming a simple exponential clonal expansion, “private” mutations that arise during the first few cell divisions will be present in most but not all present day tumor cells. The earlier a private mutation occurs, the greater its frequency in the final tumor. By sampling multiple regions from the same large human tumor, it is possible to identify public and private mutations, and then infer the early events after human tumor initiation.

Stochastic and deterministic evolutionary dynamics in hierarchically organized tissues

Tissues are typically organized hierarchically. The dynamics of cancer progression can be strongly affected by this population structure. Mutations arising in primitive cells can lead to long lived or even persistent clones, but mutations arising in further differentiated cells are short lived and do not affect the organism. A generic model for such tissue structures, which is non-spatial, but considers various steps of differentiation, can be used to model various cancers. In particular, we can use this to address the somatic evolution in Chronic Myeloid Leukemia, Paroxysmal Nocturnal Hemoglobinuria, or Acute Promyelocytic Leukemia.

Modeling metastasis using zebrafish

Metastatic disease is the defining feature of advanced malignancy, yet the mechanisms by which it occurs and affects host physiology are poorly understood. Comprehensive genomic studies of human metastatic cancers has revealed striking heterogeneity both within primary tumors, but also between different metastases from the same patient. For these reasons, models which capture this heterogeneity will be necessary to design effective strategies to abrogate the metastatic phenotype. The zebrafish has recently emerged as a genetic model system in which to study cancer because of several key strengths: 1) small size allows for study of vast numbers of animals, 2) optical transparency facilitates in vivo imaging of even single cancer cells, and 3) amenability to unbiased genetic and small molecule screens. My laboratory has developed a zebrafish model of melanoma in which the BRAFV600E allele is expressed in the mitf+ melanocyte lineage. These animals develop stereotyped, 100% penetrant melanomas when crossed to a p53-/- mutant. Using highly sensitive fluorescent detection and automated imaging algorithms, we have defined metastatic capacity of these tumors, and demonstrate a metastasis initiating cell frequency of 1/250,000 cells. These cells show preferential metastases to locations such as skin, bone marrow, and eye. Using this as a platform, we are now defining the genomic characteristics of the metastatic clones, and designing unbiased screens to find genetic or epigenetic pathways that modify metastatic progression. The zebrafish offers a highly scalable in vivo system for interrogating the dynamics of metastasis over both time and space at a resolution unavailable in other model systems.