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March 29-31, 2012
Workshop on Mathematical Oncology IV: Integrative Cancer Biology


John Dick, Ontario Cancer Institute
Towards unification of genetic and hierarchy models of tumor heterogeneity

The cellular and molecular basis for intra-tumoral heterogeneity is poorly understood. Tumor cells can be genetically diverse due to mutations and clonal evolution resulting in intra-tumoral functional heterogeneity. Often proposed as mutually exclusive, cancer stem cell (CSC) models postulate that tumors are cellular hierarchies sustained by CSC heterogeneity due to epigenetic differences (i.e. long term tumor propagation only derives from CSC). The clinical relevance of CSC has been challenged by recent reports that some tumours may actually not adhere to a CSC model when the xenograft system is enhanced. Two lines of evidence support the CSC model in AML and B-ALL. We have recently developed gene signatures specific to either AML LSC or normal HSC and found they share a set of genes that define a common stemness program. Only these stem cell related gene signatures were found to be highly significant independent predictors of patient survival when large clinical databases were introgated. Thus, determinants of stemness influence clinical outcome of AML establishing that LSC are clinically relevant and not artifacts of xenotransplantation. Second, we have carried out a series of combined genetic and functional studies of Ph+ B-ALL leukemic initiating cells (L-IC) that point to commonalities between clonal evolution and CSC models of cancer. L-IC from diagnostic patient samples were genetically diverse and reconstruction of their genetic ancestry showed that multiple L-IC subclones were related through a complex evolutionary process that involved both linear or branching leukemic progression. The discovery that specific genetic events influence L-IC frequency and that genetically distinct L-IC evolve through a complex evolutionary process indicates that a close connection must exist between genetic and functional heterogeneity. Finally, our study points to the need to develop effective therapies to eradicate all genetic subclones in order to prevent further evolution and recurrence.

Jasmine Foo, University of Minnesota
Modeling tumor heterogeneity and drug resistance

I will discuss a stochastic model of tumorigenesis where mutations confer random fitness changes sampled from a distribution. We investigate the overall growth rate and diversity of the population in the asymptotic limit, and the dependence of these features on parameters of the mutational fitness landscape. Using experimental data, we apply this model to study characteristics of a drug-resistant subpopulation in chronic myeloid leukemia. We also consider the impact of treatment strategies and compliance on the development of resistance in EGFR mutant non-small cell lung cancer using tyrosine kinase inhibitors.

Robert A. Gatenby, Dept of Integrated Mathematical Oncology, Moffitt Cancer Center
Evolutionary dynamics in cancer therapy

A number of successful systemic therapies are available for treatment of disseminated cancers. However, tumor response is often transient and therapy frequently fails due to emergence of resistant populations. The latter reflects the temporal and spatial heterogeneity of the tumor microenvironment as well as the evolutionary capacity of cancer phenotypes to adapt to therapeutic perturbations. Although cancers are highly dynamic systems, cancer therapy is typically administered according to a fixed, linear protocol. An alternative approach, termed adaptive therapy, evolves in response to the temporal and spatial variability of tumor microenvironment and cellular phenotype as well as therapy- induced perturbations. Initial mathematical models find that when resistant phenotypes arise in the untreated tumor, they are typically present in small numbers because they are less fit than the sensitive population. This reflects the "cost" of phenotypic resistance such as additional substrate and energy utilized to upregulate xenobiotic metabolism and, therefore, not available for proliferation, or the growth inhibitory nature of environments (i.e. ischemia or hypoxia) that confer resistance on phenotypically sensitive cells. Thus, in the Darwinian environment of a cancer, the fitter chemo-sensitive cells will ordinarily proliferate at the expense of the less fit chemo-resitant cells. The models demonstrate that, if resistant populations are present prior to administration of therapy, treatments designed to kill maximum numbers of cancer cells removes this inhibitory effect and actually promotes more rapid growth of the resistant populations. We present an alternative approach in which treatment is continuously modulated to achieve a fixed tumor population. The goal of adaptive therapy is to enforce a stable tumor burden by permitting a significant population of chemosensitive cells to survive so that they, in turn, suppress proliferation of the less-fit but chemo-resistant subpopulations. Computer simulations demonstrate this strategy can result in prolonged survival that is substantially in greater than that of high dose density or metronomic therapies. The feasibility of adaptive therapy is supported by in-vivo experiments.

Richard Hill, Ontario Cancer Institute/Princess Margaret Hospital
Cancer Metastases (slides)

Metastatic spread of cancer is very often the ultimate cause of death in patients. Yet the efficiency with which cancer cells form metastases appears to be very low. Multiple possible causes for this inefficiency have been proposed, including surmounting multiple steps in the metastatic process as well as low percentages of stem cells in tumours but the exact mechanisms remain unclear and may be both heterogeneous and different for different cancers. Recent studies have also suggest the induction of metastatic niches in certain organs in the body that may specifically support the development of metastases. The microenvironment of the primary tumour, particularly hypoxia, can also influence metastasis formation and may predispose to the formation of such niches. Understanding and predicting the presence of micrometastases prior to their detectability by imaging could identify patients who need more aggressive initial treatment.

Harsh Vardhan Jain, Mathematical Biosciences Institute, The Ohio State University

Optimizing ovarian cancer treatment with Mathematics: Carboplatin + Anti-Bcl-2/xL combination therapy (slides)

In this talk, I will present a new approach to anti-cancer therapy modeling that reconciles existing observations for the combined action of carboplatin (a Pt-based chemotherapeutic agent) and ABT-737 (a small molecule inhibitor of Bcl-2/xL) against ovarian cancers. To accurately simulate the action of these drugs, an age-structure together with a delay is imposed on proliferating cancer cells, and intracellular signaling pathways relevant to drug action explicitly modeled. The resultant delayed partial differential equation (PDE) model thus accounts for cell cycle arrest and cell death induced by chemotherapy. The model is calibrated versus in vitro experimental results, and is then used to predict optimal doses and administration time scheduling for the treatment of a tumor growing in vivo.

Mohammad Kohandel, University of Waterloo
Quantitative approaches to cancer stem cell hypothesis

The last decade has witnessed significant advances in the application of physical, mathematical and computational models to biological systems, especially to cancer biology. In this presentation, we examine mathematical models describing tumour growth based on the cancer stem cell hypothesis, and present the application of these models to various cancer treatments, as well as to the epithelial-mesenchymal transition. In addition, we discuss how quantitative approaches can be used to investigate the tumour heterogeneities exposed to various microenvironmental conditions of the cancerous tissue. Finally, the role of the mesenchymal transition and neural stem cells, and their mutual interaction, in molecular subtypes of glioblastoma multiforme, are presented based on genetic data.

Natalia Komarova, University of California, Irvin
Cellular cooperation as a pathway to cancer

Cancer comes about by a sequence of mutations that change the cells' fitness and create advantageous phenotypes. These phenotypes displace other cells and spread, thus winning the evolutionary competition. It is possible that in order to create those advantageous mutants, several different mutations have to be accumulated in a cell, such that each individual mutation is disadvantageous, and together they comprise a fitness advantage. In the literature, this is often called "crossing a fitness valley". In this talk I will present a novel mechanism by which such fitness valleys can be crossed. It envolves the notion of cooperation among the cells. I will show how cooperation can speed up the evolutionary process.

Sendurai A. Mani, Department of Molecular Pathology & Metastasis Research Center, University of Texas M. D. Anderson Cancer Center
EMT and Stem Cells in Cancer Progression

Despite considerable advances in our understanding of tumor biology at the primary site, metastasis remains a major cause for the majority of carcinoma-related mortalities. Metastasis is a complex multi-step process, wherein tumor cells detach from the initial site, invade the surrounding stroma, intravasate and survive in the circulation, extravasate at distant organs to form micrometastases. Eventually, a few of these micrometastatic colonies expand to become macrometastatic nodules. Studies have shown that the activation of a latent embryonic program-epithelial-mesenchymal transition (EMT) plays a critical role in cancer metastasis. Independently, Cancer Stem Cells (CSCs) are also shown to play a central role in tumor initiation and tumor progression. Recently, we and others have found that the CSCs could be generated from differentiated cells through the activation of EMT program. These findings uncovered a unique window of opportunity and suggests that the CSCs could be targetted using the EMT pathways. My presentation will summarize our current effort in understanding of the EMT pathways and their relevance to breast cancer progression.

Christopher McFarland, Harvard University/Program in biophysics
The impact of deleterious passenger mutations on cancer progression

Cancer development is an evolutionary process within an organism: cells acquire mutations, compete for resources, and are subject to natural selection. During this transformation, malignant tissues acquire tens of thousands of somatic mutations, yet only a handful, called driver alterations, are believed to be responsible for the cancer phenotype. The vast majority of remaining alterations are called passenger alterations and believed to be evolutionarily neutral in phenotype. Our hypothesis is that many passengers are deleterious to cancer cells, yet still accumulate.

We developed a novel stochastic population genetics model of cancer progression where cells can acquire both advantageous driver and deleterious passenger mutations. We found that mildly deleterious passengers accumulate in populations by both mutational ratcheting and by hitchhiking with drivers, and that their accumulation can slow or revert neoplastic progression. Using comparative genomics, we analyzed known driver and passenger mutations and found that many passengers possess deleterious phenotype--corroborating our model.

Using combined numerical and analytical analysis, we discovered two phases of cancer dynamics: one where driver mutations dominate and populations grow exponentially, and another where deleterious passengers overwhelm populations, resulting in prolonged dormancy or extinction. This phase transition results from a critical population size,
akin to a activation barrier, that populations must first overcome to progress to cancer. Interestingly, there exists an optimal mutation rate for cancer. Low mutation rates lead to slow driver accumulation, while very high rates prevent cancer development because drivers typically arise in cells with an excessively damaging load of passenger mutations that prevents clonal expansion. Our results explain observed clinical patterns of mutations and patient outcomes.

Finally, we compare therapeutic strategies that could exploit the effects of these deleterious passenger alterations.

Michael Milosevic, University of Toronto Department of Radiation Oncology, and Radiation Medicine Program, Princess Margaret Hospital - University Health Network
Imaging Biology and Treatment Response in Cervical Cancer

Cervical cancer, like other human tumors, is characterized by an abnormal vascular network that develops because of unregulated angiogenesis. This, in turn, is an important determinant of microenvironmental abnormalities like hypoxia, acidosis and high interstitial fluid pressure (IFP) that influence treatment response and patient survival. There is an important clinical need to develop new minimally invasive tools for characterizing the tumor microenvironment at diagnosis, and monitoring changes during treatment with radiotherapy, chemotherapy or new biologically targeted drugs. MR and PET-based imaging approaches offer exciting possibilities that have yet to be fully exploited. Dynamic contrast enhanced (DCE) MR allows the functional characteristics of the tumor vasculature to be interrogated serially over time. Studies in cervical cancer have shown substantial differences in DCE MR parameters between tumor and normal muscle in keeping with higher blood flow and vascular permeability, and substantial variation in these parameters from one tumor to the next and within individual tumors. Pre-treatment DCE MR has been shown to correlate with response to radiotherapy or drugs that specifically target the tumor vasculature. MR techniques have also been used to assess tumor interstitial fluid dynamics and IFP, using either conventional low molecular weight contrast agents or new liposomal agents. PET imaging of tumor perfusion and hypoxia using radiolabeled nitroimidazole tracers is being investigated in clinical studies. Despite important advances, none of these approaches has been adopted in routine clinical practice because of a lack of consensus on optimal imaging techniques, analysis methods and reporting metrics. Further refinement and standardization is required founded on interdisciplinary collaboration among clinicians, medical imagers, biologists, physicists and mathematicians to make these techniques robust and clinically applicable.

Colin Phipps, University of Waterloo
Mathematical model for angiogenic behaviour in solid tumours:

A mathematical model is presented for the concentrations of proangiogenic and antiangiogenic growth factors, and interstitial fluid pressure, in solids tumours embedded in host tissue. In addition to production, diffusion, and degradation of these angiogenic growth factors (AGFs), we include interstitial convection to study the locally destabilizing effects of interstitial fluid pressure (IFP) on the angiogenic activity endowed by these factors. The molecular sizes of representative AGFs and the outward flow of interstitial fluid in tumors suggest that convection is a significant mode of transport for these molecules. The resulting balance or imbalance of proangiogenic and antiangiogenic serves as a possible mechanism for determining whether blood vessels are stable, developing or regressing. The results of our modeling approach suggest that changes in the physiological parameters that determine interstitial fluid pressure have as profound an impact on tumor angiogenesis as those parameters controlling production, diffusion, and degradation of AGFs. This model has predictive potential for determining the angiogenic behavior of solid tumors and the effects of cytotoxic and antiangiogenic therapies on tumor angiogenesis.

Vito Quaranta, Vanderbilt University & VICBC
Cancer cell population dynamics of drug response derived from single-cell data.

Typical cell proliferation assays estimate cell counts at fixed time-points, not dynamically. In the presence of perturbations affecting proliferation, they provide little information on underlying individual cellular behaviors (e.g., apoptosis, decreased cell division rate, etc.). We present Fractional Proliferation, an integrated method, based on extended time-resolved automated microscopy that quantifies cell proliferation dynamics in response to perturbations by integrating population- and single-cell level. Direct cell count data, collected every 6 minutes, are initially fit with a novel Quiescence-Growth mathematical model, based on three parameters: division, death and quiescence rates. This model is then substantiated by extracting these rates from experimental observations of hundreds of single cells, fitted with an Exponentially Modified Gaussian model. In the final output graphs, Fractional Proliferation describes the underlying behavioral dynamics that result in proliferative changed by perturbations. Using this method, we discovered that the response of cell lines to erlotinib, an epidermal growth factor receptor tyrosine kinase inhibitor, is a nonlinear process dominated by an increased rate of cell entry into quiescence. Even in highly sensitive "oncogeneaddicted" cells, quiescence prevailed, with only a modest increase in death rate. Similar results were obtained with oncogene-addicted melanoma and breast cancer cell lines treated with the respective targeted oncogene inhibitors. In contrast to our results, drug targeting of addicting oncogenes has thus far been thought to result in massive cell death. Instead, our findings indicate that it may cause response behaviors other than death, underscoring the realistic in vitro representation of cell proliferative response to perturbagens provided by Fractional Proliferation, and providing means to optimize and improve discovery and deployment of targeted therapy.

Sheila Kumari Singh, Stem Cell & Cancer Research Institute, McMaster University
Medulloblastoma stem cells: where development and cancer cross pathways (slides)

Brain tumours represent the leading cause of childhood cancer mortality, with medulloblastoma (MB) representing the most frequent malignant tumor. Due to morphological similarities between MB cells and proliferating external granule cells of the postnatal cerebellum, recent studies have merged cancer genomics and developmental biology approaches to demonstrate the presence of different MB molecular subtypes. The identification of cancer stem cell populations, termed brain tumour initiating cells (BTICs), in MB has provided novel cellular targets for the study of aberrantly activated signaling pathways, namely Sonic hedgehog and Wingless, along with the identification of novel BTIC self-renewal pathways. Here, we discuss recent evidence for the presence of a MB stem cell, which may drive tumorigenesis in the most aggressive subtypes of this malignant childhood tumour. We focus on evidence from cerebellar development, the recent identification of BTICs, the presence of activated developmental signaling pathways in MB, the role of epigenetic stem cell regulatory mechanisms, and how these developmental and epigenetic pathways may be targeted with novel therapeutic options

Sasmit Sarangi, Harvard-MIT Health Sciences & Technology
Large Post-treatment with PI3-Kinase inhibitor enhances the
chemotherapeutic effect of cisplatin nanoparticles in breast cancer

Nanoformulations~of chemotherapeutic drugs are increasingly being studied for their potential to improve efficacy and safety. However, limited studies have been done on sequential dosing of nanochemotherapeutics and signal transduction inhibitors.

In this study, we determined the optimal combination regimen of PI-3 kinase inhibitor PI828 and cisplatin nanoparticles in~murine breast cancer model to achieve maximal cell killing. Western blot analysis showed a time dependent upregulation of phospho- AKT expression after administration of cisplatin nanoparticles. We also observed a time dependent decrease in expression of XIAP which corroborated with an increased expression of Cleaved Caspase-3. PiAkt overexpression induced by cisplatin liposome was was efficiently suppressed by PI828 in the post-treatment schedule resulting in significantly increased apoptosis as measured by Caspase-3 expression. The upregulation of piAKT dependent signalling was mediated by both an EGFR dependent downstream activation of PI3 kinase pathway and an increased nuclear transcription of Akt gene.

A simple mathematical model using the quantitative expression of the above
mentioned cellular proteins( piAKT, Cleaved Casapse-3 and XIAP) was designed to predict the optimal combination regimen of the two drugs . The mathematical model predicted that a combination regimen using PI828 for after 24-36 hurs Cisplatin nanoparticle therapy would achieve maximal cell killing.

In vitro cell proliferation assay validated the modeling results with PI828
post-treatment showing significantly increased cell death as compared to controls and pretreatment.

In a 4T1 syngenic murine cancer model, post-treatment with PI828 following
cisplatin nanoparticles treatment significantly suppressed tumour growth as
compared to the pre-treatment or nanoparticles alone. These results indicate that sequence of administration of signal transduction inhibitors like PI828 can
impact the outcome of treatment with cisplatin nanotherapeutics.

Edwin Wang, National Research Council Canada/McGill University
Personalized cancer healthcare: A systems biology approach (slides)

Large-scale sequencing and gene profiling of cancer genomes have generated huge amount of data. It is increasingly realized that these information could be useful in guiding personalized care and treatment to cancer patients. However, it is very challenging in how to making sense of and making use of these data toward personalized medicine.

I will talk about using network approach to analyze tumor signaling networks to get insights and developing new algorithms to get cell-specific drug targets, and molecular markers for prognosis and drug response.

Kathleen Wilkie, Center of Cancer Systems Biology, Tufts University School of Medicine
A Mathematical Model of Immune Modulation of Tumor Growth

Cancer cells can elicit an immune response in the host, which is generally tumor-suppressive, but for weak responses may actually be tumor-promoting. We propose that this complex dynamic may be understood as a process of immune stimulation by the tumor, followed by cytotoxic targeting by the immune cells, which acts to alter tumor size and growth characteristics and subsequent immune stimulation. Just how these influences interact has complex implications for tumor development and cancer dormancy. To show this, we have developed a two-compartment model consisting of a population of cancer cells and a population of immune cells. The model incorporates the combined effects of the various immune cell types, exploiting general principles of self-limited logistic growth and the physical process of tumor-promoting inflammation. A Markov chain Monte Carlo method is used to determine parameter sets that predict tumor growth equally well, but at the same time also predict fundamentally different underlying dynamics. The results underscore the ultimately polar nature of final tumor fate (escape or elimination), while at the same time showing how persistent regions of near-dormancy may precede either of these two outcomes. Another important finding is that near-{} and long-term responses of a tumor to immune interaction may be opposed; that is to say, a response dynamic that appears to be more promoting of tumor growth than another in the near term may be superior at curtailing tumor growth in the long-term, even to the point of establishing dormancy while the other allows for tumor escape. The striking variability observed even in this simple model demonstrates the significance of intrinsic and unmeasurable factors determining the complex biological processes involved in tumor growth in an immune competent host. Consequences and biological interpretations of this work will be discussed in terms of treatment approaches that exploit immune response to improve tumor suppression, including the potential attainment of an immune-induced dormant state.Kathleen Wilkie and Philip Hahnfeldt

Brad Wouters, OCI/Princess Margaret Hospital, UHN, UofT, OICR
Biological responses to tumor hypoxia and their potential as therapeutic targets (slides)

Spatial and temporal variations in oxygen are observed in the majority of solid tumours and function as a major contributor to phenotypic diversity and a significant barrier to current curative treatment approaches. Tumor hypoxia elicits profound changes in cell behaviour through multiple mechanisms that influence cellular metabolism, genetic stability, angiogenesis, and self-renwal. In this session, I will review recent discoveries of oxygen-sensitive signalling pathways that help to explain these phenotypes including activation of the unfolded protein response (UPR) and regulation of autophagy. These new findings help to explain the adverse effect of hypoxia on tumor behaviour but also reveal potential therapeutic targets for improving treatment efficacy.

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