Workshop 7: Stem Cells, Development, and Cancer

(April 13,2015 - April 17,2015 )

Organizers


Heiko Enderling
Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Thomas Hillen
Mathematical and Statistical Sciences, University of Alberta
John Lowengrub
Mathematics, University of California, Irvine

Most tissues are hierarchically organized into lineages. A lineage is a set of progenitor-progeny relationships within which progressive changes in cell character occur. Typically, lineages are traced back to a self-perpetuating stem cell (SC), and end with a postmitotic terminal cell. One of the most exciting recent developments in the field of cancer biology is the recognition that lineage progression continues to occur in tumors. In particular there is an increasing body of evidence that like normal tissues, tumor cells that have the potential for unlimited self-renewal give rise in large numbers to cells that lack this potential - the so-called cancer stem cell hypothesis. By focusing for so many years on the majority cell populations in tumors, and not on the rarer cancer stem cells (cancer initiating cells), scientists and clinicians may have missed out on opportunities to understand, diagnose and treat the processes in cancer that matter most. Further, there is increasing evidence that cell stemness may be a function of the local environment rather than being a predetermined property of a cell. What are the consequences of this plasticity in cell behavior? Other important open questions in the field include: What cell types within the normal tissues are capable of being the cells of origin for tumors? What is the relationship between normal tissue stem cells and tumor-initiating cells (e.g., cancer stem cells)? Which signaling and other regulatory networks are altered in tumors relative to the normal tissues, and how do they function within the tumor? Finally, there is growing evidence that therapies aimed at the major cell types in tumors may sometimes make things worse, by leading to an expansion in the fraction of cancer stem cells. How can this be avoided? This workshop will address these and other questions through discussions among mathematical and computational modelers and experimentalists. In particular, the strong connections between normal development, tumor growth and the use of novel treatment strategies will be discussed.

Accepted Speakers

Zvia Agur
Institute for Medical Biomathematics
David Axelrod
Department of Genetics and Cancer Institute of New Jersey, Rutgers University
Arianna Bianchi
Department of Mathematics, Maxwell Institute for Mathematical Sciences
Helen Byrne
Centre for Mathematical Medicine and Biology, University of Nottingham
Dirk Drasdo
Bioinformatics, Physical and Mathematical Biology, Institut National de Recherche en Informatique Automatique (INRIA)
Avner Friedman
Department of Mathematics, The Ohio State University
Leonid Hanin
Department of Mathematics, Idaho State University
Anita Hjelmeland
Cell, Developmental and Integrative Biology, University of Alabama at Birmingham
Sasha Jilkine
ACMS, University of Notre Dame
Yangjin Kim
Department of Mathematics, Konkuk University
Marek Kimmel
Department of Statistics, Rice University
Natalia Komarova
Department of Mathematics, University of California, Irvine
Michael Lewis
Molecular and Cellular Biology and Radiology,
Paul Macklin
Center for Applied Molecular Medicine, University of Southern California
Anna Marciniak-Czochra
Institute of Applied Mathematics, Ruprecht-Karls-Universit""at Heidelberg
Alexander Pearson
Hematology and Medical Oncology, University of Michigan
Jan Poleszczuk
Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute
Lynne-Marie Postovit
Oncology, University of Alberta
Jeremy Rich
Stem Cell Biology and Regenerative Medicine, Cleveland Clinic
Ignacio Rodriguez-Brenes
Mathematics, University of California, Irvine
Brock Sishc
Radiation Oncology, UT Southwestern Medical Center
Christina Surulescu
Mathematics, Felix-Klein-Zentrum für Mathematik, TU Kaiserslautern
Kristin Swanson
Neurological Surgery, Northwestern University
Jose Ignacio Tello
Department of Applied Mathematics, Universidad Complutense de Madrid
Vitaly Volpert
Mathematics and applications, CNRS
Suzanne L. Weekes
Mathematical Sciences Department, Worcester Polytechnic Institute
Benjamin Werner
Genomics and Modeling Group, The Institute of Cancer Research
Monday, April 13, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Lynne-Marie Postovit
10:00 AM
10:30 AM

Break

10:30 AM
11:10 AM
Zvia Agur
11:15 AM
11:55 AM
Natalia Komarova - Calculus of stem cells

Identifying the exact regulatory circuits that can stably maintain tissue homeostasis is critical for our basic understanding of multicellular organisms, and equally critical for figuring out how tumors circumvent this regulation, thus providing targets fortreatment. Despite great strides in the understanding of the molecular components of stem-cell regulation, the overall mechanisms orchestrating tissue homeostasis are still far from being understood. Typically, tissue contains the stem cells, transit amplifying cells, and terminally differentiated cells. Each of these cell types can potentially secrete regulatory factors and/or respond to factors secreted by other types. The feedback can be positive or negative in nature. This gives rise to a bewildering array of possible mechanisms that drive tissue regulation. In this talk I describe a novel stochastic method of studying stem cell lineage regulation, which allows to identify possible numbers, types, and directions of control loops that are compatible with stability, keep the variance low, and possess a certain degree of robustness.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:40 PM
Leonid Hanin - Cancer Stem Cells Discovered ... Mathematically

Cancer stem cells have a variety of biological characteristics, and categorizing cancer cells as stem cells depends on selection of defining properties. In this work we focus on metastatic potential of cancer cells and answer the following question: Can one characterize the size of the subpopulation of metastasis-producing cells in a solid tumor?

To answer this question, we used a very general mathematical model of cancer progression accounting for primary tumor origination and growth, shedding of metastases off the primary tumor, selection of viable metastases, dormancy of metastases and their inception in a secondary site, and growth of metastases in the site of interest. The model assumes that metastasis shedding off the primary tumor is governed by a Poisson process whose rate at time t is proportional to the number of metastasis-producing cells, N(t), which in turn is assumed proportional to some power of the size of the primary tumor: N(t) = kS^θ (t). The case θ = 0 (or close to 0) suggests the presence within a primary tumor of a relatively stable, and hence self-renewing, subpopulation of metastasis-producing cells.

The model produces an explicit formula for the distribution of the site-specific sizes of metastases at any given time. Fitting the model to clinical data allows one to estimate model parameters including θ. This parameter was estimated for three patients with renal cancer, non-small cell lung cancer and pancreatic cancer. In all these cases, the value of θ was found to be quite small, which serves as an indirect evidence for the existence of cancer stem cells with high metastatic potential.

02:45 PM
03:25 PM
David Axelrod - Stem Cell Dynamics in Normal Human Colon Crypts and the Initiation 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 in stem cells, proliferating cells, or differentiated cells, and by the robust ability of crypts to recover from perturbation by cytotoxic agents due to resistant quiescent stem cells. An example of the use of the virtual crypt will be given, viz., the evaluation of different cancer chemotherapy protocols.

03:25 PM
03:40 PM

Break

03:40 PM
04:20 PM
Avner Friedman - Major Genes in Colorectal Cancer

Major genes are defined as those that are necessary and sufficient for disease causation, with important mutations of the gene as causal mechanism. It is commonly accepted that in colorectal cancer the principal major genes are APC, K-RAS, TGF-B, SMAD and p53. However, it may be important to know which gene is the first to undergo mutation. Patients with ulcerative colitis or Crohn’s disease are at risk of developing colorectal cancer. In the first part of this talk I will show, with a mathematical model that in colitis-associated colon cancer p53 is the first gene that is mutated. In the second part of the talk, I will show, again by a mathematical model (and rigorous mathematical analysis) that on mutation in major genes is not sufficient to cause colorectal cancer.

04:30 PM
06:30 PM

Reception and Poster Session

06:45 PM

Shuttle pick-up from MBI

Tuesday, April 14, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Dirk Drasdo
10:00 AM
10:30 AM

Break

10:30 AM
11:10 AM
Jeremy Rich - Target Identification in Glioma Initiating Cells

Gliomas display cellular hierarchies with tumor initiating cells (TICs) at the apex that are functionally defined by the ability to self renew and propagate tumors similar to the parental tumors from which they are derived. TICs remain controversial, but their clinical relevance has been supported by resistance to cytotoxic therapies (Bao et al. Nature 2006) and promotion of tumor angiogenesis (Bao et al. Cancer Research 2006). TICs reside in specific functional niches in perivascular and hypoxic niches (Li et al. Cancer Cell 2009) that may offer the ability to disrupt tumor maintenance and therapeutic resistance through targeting the niche. Investigating TICs has already yielded novel molecular targets and pathways that are amenable to therapeutic targeting (Kim et al. Genes Development 2012; Eyler et al. Cell 2011; Guryanova et al. Cancer Cell 2011). Using patient-derived tumor models, we have interrogated the regulation of the TIC phenotype by both cell intrinsic and microenvironmental influences present in tumors. TICs are enriched under low nutrient conditions due to the cooption of the high affinity GLUT3 transporter normally expressed by neurons (Flavahan et al. Nature Neuroscience 2013). We have now extended these findings to demonstrate that cellular metabolism is differentially regulated within the tumor hierarchy at several levels to provide resources for sustained self-renewal and proliferation (Xie et al. Nature Neuroscience 2015). We also recently found that TICs have basal genotoxic stress activating PARP permitting radiosensitization (Venere et al. Cell Death Differentiation 2014). To discover novel TIC targets, we are using several technologies, including aptamers (Kim et al. Cancer Research 2013), flow cytometry (Lathia et al. Cell Reports 2014), and phage display (Liu et al. Cell Death Diff. 2014), showing that TICs manifest nodes of fragility mediating cell survival and invasion (e.g. JAM-A, VAV3, and CD97). Combining TIC models from patients with non-neoplastic progenitors from epilepsy resections, we are interrogating additional molecular regulators of the cellular hierarchy that can be distinguished from normal stem cells to minimize toxicity. The conventional pyramidal unidirectional differentiation cascade with TICs at the apex has been called into question by studies demonstrating plasticity of the TIC phenotype (Cheng et al. Cell 2013), thus suggesting that targeting only TICs will likely fail to cure patients and require simultaneous targeting of TICs and the bulk tumor. Although the field of TIC biology is relatively young, continued elucidation of the tumor hierarchy holds promise for development of novel patient therapies.

11:15 AM
11:55 AM
Paul Macklin
12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:40 PM
Ignacio Rodriguez-Brenes - Replicative Senescence as a Tumor Suppressor Pathway

Abstract not submitted.

02:45 PM
03:25 PM
Anita Hjelmeland - Modeling Effects of the Tumor Microenvironment on Brain Tumor Stem Cell Phenotypes

Abstract not submitted.

03:25 PM
03:40 PM

Break

03:40 PM
04:20 PM
Yangjin Kim - Mathematical models of oncolytic virus therapy and characterization of the invasive and non-invasive glioma

In this talk, a mathematical model of Chase-ABC mediated oncolytic virus therapy targeting cancer stem cells and CSPG-driven glioma infiltration will be presented. Glioblastoma is the most aggressive type of brain cancer with the median survival time of one year. Oncolytic viruses are genetically engineered viruses that are designed to kill cancer cells while doing minimal damage to normal healthy tissue. After being injected into a tumor, they infect cancer cells, multiply inside them, and when a cancer cell is killed they move on to spread and infect other cancer cells. Chondroitinase ABC (Chase-ABC) is a bacterial enzyme that can remove a major glioma ECM component, chondroitin sulfate glycosoamino glycans (CSGG) from proteoglycans without any deleterious effects in vivo. It has been shown that Chase-ABC treatment is able to promote the spread of the viruses, increasing the efficacy of the viral treatment. We develop a mathematical model to investigate the effect of the Chase-ABC on the treatment of glioma by oncolytic viruses (OV). We show that the model’s predictions agree with experimental results for a spherical glioma. We then use the model to test various treatment options for both primary tumor and infiltrating tumor cells in the heterogeneous microenvironment of the brain. A new strategy of targeting cancer stem cells in a niche using transported oncolytic viruses will be also presented. The primary treatment option is surgery but invasive cells in brain tissue eventually regrow back even with chemo- and radio-therapy, generating poor clinical outcomes. Therefore, it is important to distinguish invasive glioma phenotypes from non-invasive cells. Experiments by Silver et al illustrated that concentrations of CSPG, one of major extracellular matrix component within a tumor, determine invasive and non-invasive phenotypes. We developed a mathematical model of CSPG-driven dynamics of a growing glioma, using a free boundary framework. We take into account the rich dynamics of astrocytes and microglia in brain tissue as illustrated in Silver et al. The simulation results are in good agreement with experimental data in Silver et al. We also show how oncolytic virus therapy can be used to eradicate tumor cells. There is a critical threshold value of CSPG levels for optimal killing of both invasive and non-invasive tumorcells.

04:30 PM

Shuttle pick-up from MBI

Wednesday, April 15, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Kristin Swanson
10:00 AM
10:30 AM

Break

10:30 AM
11:10 AM
Arianna Bianchi - Neoneurogenesis and tumor metastasis: myth or reality?

Primary tumors infrequently lead to the demise of cancer patients; rather, mortality and a significant degree of morbidity result from the growth of secondary tumors in distant organs (metastasis). Malignant tumors release both lymph- and angio- genic factors, through two specific processes termed lymphangiogenesis and angiogenesis, respectively. In addition, recent experimental evidence shows that tumors initiate their own innervation by the release of neurotrophic factors (neoneurogenesis). The relationship between tumor progression and the nervous system is a complex and poorly understood part of cancer pathogenesis. It is likely that this process is regulated by a multitude of factors in the tumor/nerve microenvironment; these pathways are even further complicated by treatment and disease history as well as other genetic and socioeconomic factors. It is therefore important to study the interactions between the nervous system and tumor cells through mathematical/computational modelling: in this way we will take into account the most significant elements of the plethora of interacting pathways regulating this process. The present work is a first attempt to model the neurobiological aspect of cancer development through a system of differential equations.

NOTE: This is a joint work with Dr Georgios Lolas, TU Dresden (Germany).

11:15 AM
11:55 AM
Sasha Jilkine
12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:40 PM
Christina Surulescu - Mathematical models for anisotropic glioma invasion: a multiscale approach

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main brain cells that can develop into neoplasms. Since they are highly invasive they are hard to remove by surgery, as the tumor margin it most often not precisely enough identifiable. The understanding of glioma spread patterns is hence essential for both radiological therapy as well as surgical treatment. We propose a multiscale framework for glioma growth includinginteractions of the cells with the underlying tissue network, along with proliferative effects. Relying on experimental findings, we assume that cancer cells use neuronal fibre tracts as invasive pathways. Hence, the individual structure of brain tissue seems to be decisive for the tumor spread. Diffusion tensor imaging (DTI) is able to provide such information, thus opening the way for patient specific modeling of glioma invasion. Starting from a multiscale model involving subcellular (microscopic) and individual (mesoscale) cell dynamics, we deduce on the macroscale effective equations characterizing the evolution of the tumor cell population and perform numerical simulations based on DTI data. Particular attention is payed on the modeling of proliferation terms on the mesoscale level, in order to deduce the corresponding source terms on the macroscale.

02:45 PM
03:25 PM
Brock Sishc - Radiation-induced reprogramming of senescent mammary epithelial cells enriches CD44+/CD24low/- putative stem cell populations

The enrichment of CD44+/CD24low/- breast adenocarcinoma putative stem cell populations following exposure to ionizing radiation has been attributed their inherent radio resistance and an elevated frequency of asymmetric division during repopulation. However, recent studies demonstrating radiation induced reprogramming (the transition of non CD44+/CD24low/- cells into the CD44+/CD24low/- phenotype) as a potential mechanism of enrichment have raised the question of whether survival of existing CD44+/CD24low/- cells or their induced reprogramming is the primary mode of enrichment. To answer this question, we have combined a cellular automata model with in vitro experimental data using both non-tumorigenic (MCF-10a) and cancerous (MCF-7) mammary epithelial cell lines, with the aim of evaluating the enrichment of CD44+/CD24-/low cell populations in the context of radiation induced senescence. Modeling determined that the imperfect phenotypic reprogramming of radiation induced senescent cells (conveying the CD44+/CD24low/- phenotype, but with a more limited proliferation capability) could be a major driving force underlying CD44+/CD24low/- enrichment. Further the enrichment response of MCF-7 cells appears to be less regulated (occurring both at lower doses, earlier time points, and lasting longer) than that observed in MCF-10a cells, suggesting a potential role for such enrichment in radiation induced carcinogenesis. Together, these results suggest that reprogramming of senescent cells plays a significant role in the repopulation of cancer and non-cancer breast epithelial cells following exposure to ionizing radiation, a finding with important implications in radiation therapy.

03:25 PM
03:40 PM

Break

03:40 PM
04:20 PM
Benjamin Werner
04:30 PM

Shuttle pick-up from MBI

Thursday, April 16, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Marek Kimmel - Analysis of mutations leading to the myelodysplastic syndrome (MDS) using modified Moran models

Abstract not submitted.

10:00 AM
10:30 AM

Break

10:30 AM
11:10 AM
Alexander Pearson - Modeling Head and Neck Cancer Cellular Plasticity

Head and neck cancer is the sixth most common cancer worldwide, with more than 125,000 persons dying annually from this disease. While improvements in head and neck cancer treatment have been made, they have been less significant than for other cancers of similar prevalence. Overall 5-year survival of 50-60% is attributed to a high recurrence rate. A subpopulation of cancer stem cells (CSC) define augmented tumorigenicity with in vivo models in head and neck cancer. Recent observations lead us to believe that cancer stem cells play a role in helping tumors adapt to their environment. Furthermore, traditional cytotoxic chemotherapy treatment of head and neck cancer may shift the cellular equilibrium, promoting an increased proportion of CSC. I will be discussing our studies combining modeling and laboratory data in order to elucidate the interplay between cancer treatment and CSC promotion.

11:15 AM
11:55 AM
Vitaly Volpert - Mathematical modelling of multiple myeloma

Multiple myeloma is a malignant disease characterized by an abnormal proliferation of plasma cells in the bone marrow. Tumor growth prevents normal functioning of erythropoiesis and leads to anemia. In this lecture we will present the results of mathematical modelling of normal erythropoesis and of multiple myeloma development and treatment. Darwinian evolution of cancer cells will be discussed in a more general context.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:40 PM
Michael Lewis - Data-Driven Mathematical Modeling of Mammary Ductal Elongation

The Terminal End Bud (TEB) at the growing tip of mammary ducts is one of the fastest growing structures in mammals. TEBs drive ductal elongation during puberty and regress once development of the ductal tree is complete. Because of similarities between TEB growth and breast cancer growth, successful modeling of this structure may yield insight into breast development as well as cancer progression. Previous mathematical models have focused on branching morphogenesis, but there are currently no models that address ductal elongation itself. Our model exploits the constrained geometry of the TEB in vivo which provided the framework for an initial mathematical model. Parameters in this model were then informed with measureable data (morphological characteristics, proliferation rate, cell cycle duration, and apoptosis). These data were then used to calculate a value representing the movement of cells from the TEB into the mature duct (termed the flux) and this calculated flux was then used to predict a linear elongation rate. The prediction was compared to an experimentally measured displacement within the mammary fat pad. Our initial measurements of proliferation, apoptosis, and cell sizes, predicted a linear elongation rate of 1.39 mm per day, which was significantly different from our experimentally measured displacement rate of 0.54mm per day. We then refined our model by incorporating changes in the direction of growth due to bifurcation, a cost function for bifurcation (which describes duplication of the TEB), as well as an additional flux term to account for a migration of cap cells into the body cell. Iteration of the revised mathematical model yielded an estimate significantly closer to the measured displacement rate, thus indicating that the most relevant biological parameters have been accounted for. In addition, our data overturned a long held belief that cap cells contribute to the body cell lineage. We are now poised for in silico experiments that may yield predictions consistent with cancer phenotypes, as well as predictions that recapitulate known mutation phenotypes.

02:45 PM
03:25 PM
Anna Marciniak-Czochra
03:25 PM
03:40 PM

Break

03:40 PM
04:20 PM
Jan Poleszczuk - Evolution and phenotypic selection of cancer stem cells

Cells of different organs at different ages have an intrinsic set of kinetics that dictates their behavior. Transformation into cancer cells will inherit these kinetics that determine initial cell and tumor population progression dynamics. Subject to genetic mutation and epigenetic alterations, cancer cell kinetics can change and favorable alterations that increase cellular fitness will manifest themselves and accelerate tumor progression. We set out to investigate the emerging intratumoral heterogeneity and to determine the evolutionary trajectories of the combination of cell-intrinsic kinetics that yield aggressive tumor growth. We develop a cellular automaton model that tracks the temporal evolution of the malignant subpopulation of so-called cancer stem cell, as these cells are exclusively able to initiate and sustain tumors. We explore orthogonal cell traits including cell migration to facilitate invasion, spontaneous cell death due to genetic drift after accumulation of irreversible deleterious mutations, symmetric cancer stem cell division that increases the cancer stem cell pool, and telomere length and erosion as a mitotic counter for inherited non-stem cancer cell proliferation potential. Our study suggests that cell proliferation potential is the strongest modulator of tumor growth. Early increase in proliferation potential yields larger populations of CC that compete with CSC and thus inhibit CSC division while a reduction in proliferation potential loosens such inhibition and facilitates frequent CSC division. The subpopulation of cancer stem cells in itself becomes highly heterogeneous dictating population level dynamics that vary from long-term dormancy to aggressive progression. Our study suggests that the clonal diversity that is captured in single tumor biopsy samples represents only a small proportion of the total number of phenotypes.

04:25 PM
05:05 PM
Suzanne L. Weekes
05:15 PM

Shuttle pick-up from MBI

05:30 PM
06:00 PM

Cash Bar - Crowne Plaza

06:00 PM
07:30 PM

Banquet at Crowne Plaza

Friday, April 17, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Helen Byrne
10:00 AM
10:30 AM

Break

10:30 AM
11:10 AM
Jose Ignacio Tello - On a mathematical model of cancer stem cells with non-local terms

Abstract not submitted.

11:15 AM
11:55 AM
Mohammad Kohandel
12:00 PM

Shuttle pick-up from MBI (One to airport and one back to hotel)

Name Email Affiliation
Agur, Zvia agur@imbm.org Institute for Medical Biomathematics
Alvarado, Cesar calvarad@unm.edu Mathematics and Statistics, University of New Mexico
Axelrod, David axelrod@biology.rutgers.edu Department of Genetics and Cancer Institute of New Jersey, Rutgers University
Bawa, Usman bawa.usman@yahoo.com Biology Education, Federal college of education Technical potiskum
Bianchi, Arianna ab584@hw.ac.uk Department of Mathematics, Maxwell Institute for Mathematical Sciences
Buttenschoen, Andreas andreas.buttenschoen@ualberta.ca Department of Mathematical and Statistical Sciences, University of Alberta
Butuci, Melina butuci@usc.edu Molecular and Computational Biology, USC
Byrne, Helen byrneh@maths.ox.ac.uk Centre for Mathematical Medicine and Biology, University of Nottingham
Curtin, Lee pmxlc1@exmail.nottingham.ac.uk School of Mathematical Sciences, University of Nottingham
de Vries, Gerda gerda.devries@ualberta.ca Department of Mathematical & Statistical Sciences, University of Alberta
Drasdo, Dirk dirk.dras@gmail.com Bioinformatics, Physical and Mathematical Biology, Institut National de Recherche en Informatique Automatique (INRIA)
Durrett, Rick rtd@math.duke.edu Department of Mathematics, Duke University
Eljazi, Radhia radia.omar@yahoo.com Mathematical and Computer Science, Heriot Watt University
Enderling, Heiko heiko.enderling@moffitt.org Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Fessel, Kimberly fessel.6@mbi.osu.edu Mathematical Biosceinces Institute, The Ohio State University
Friedman, Avner afriedman@math.ohio-state.edu Department of Mathematics, The Ohio State University
Friedman, Samuel samuelf@usc.edu
Govinder, Kesh govinder@ukzn.ac.za Mathematics, Statistics and Computer Science, University of KwaZulu-Natal
Hanin, Leonid hanin@isu.edu Department of Mathematics, Idaho State University
Hillen, Thomas thillen@ualberta.ca Mathematical and Statistical Sciences, University of Alberta
Hjelmeland, Anita hjelmea@uab.edu Cell, Developmental and Integrative Biology, University of Alabama at Birmingham
Jaroudi, Rym jaroudirym@gmail.com ENIT/LAMSIN, University of Tunis el Manar
Jilkine, Alexandra ajilkine@nd.edu ACMS, University of Notre Dame
Kang, Hye-Won hkang@math.umn.edu Department of Mathematics, University of Maryland Baltimore County
Kim, Yangjin ahyouhappy@konkuk.ac.kr Department of Mathematics, Konkuk University
Kimmel, Marek kimmel@rice.edu Department of Statistics, Rice University
Knutsdottir, Hildur hildur@math.ubc.ca Mathematics, University of British Columbia
Kohandel, Mohammad kohandel@uwaterloo.ca Applied Mathematics, University of Waterloo
Komarova, Natalia komarova@uci.edu Department of Mathematics, University of California, Irvine
Konstorum, Anna akonstor@uci.edu Mathematics, University of California, Irvine
Kroos, Julia julia_kroos@web.de Mathematical Modeling in Biosciences, Basque Center for Applied Mathematics
Kumar, Sanjeev skumar@dbrau.ac.in Mathematics, Dr. B.R. Ambedkar University, Agra
Lewis, Michael mtlewis@bcm.edu Molecular and Cellular Biology and Radiology,
Macklin, Paul Paul.Macklin@usc.edu Center for Applied Molecular Medicine, University of Southern California
Manem, Venkata vsmanem@math.uwaterloo.ca Radiation Oncology, Massachusetts General Hospital and Harvard Medical School
Marciniak-Czochra, Anna Anna.Marciniak@iwr.uni-heidelberg.de Institute of Applied Mathematics, Ruprecht-Karls-Universit""at Heidelberg
Mohr, Marcel marcel.mohr@bioquant.uni-heidelberg.de Institute of Applied Mathematics, University of Heidelberg
Ogundipe, Olanrewaju loludipe@yahoo.com Drug design, Biochemistry and Cancer Research, University of Salford, UK
Ogundipe, Olanrewaju olobatuy@ualberta.ca School of Environmental and Life Sciences, University of Salford, UK
Paine, Ingrid runquist@bcm.edu Molecular and Cellular Biology, Baylor College of Medicine
Pearson, Alexander pearsona@med.umich.edu Hematology and Medical Oncology, University of Michigan
Picco, Noemi Noemi.Picco@moffitt.org Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Poleszczuk, Jan j.poleszczuk@mimuw.edu.pl Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute
Postovit, Lynne-Marie postovit@ualberta.ca Oncology, University of Alberta
Rich, Jeremy richj@ccf.org Stem Cell Biology and Regenerative Medicine, Cleveland Clinic
Rodriguez-Brenes, Ignacio iarodrig@uci.edu Mathematics, University of California, Irvine
Sishc, Brock Brock.sishc@utsouthwestern.edu Radiation Oncology, UT Southwestern Medical Center
Sontag, Eduardo eduardo.sontag@gmail.com Department of Mathematics and BioMaPS Institute for Quantitative Biology, Rutgers University at New Brunswick
Stocks, Theresa theresa.stocks@gmx.de Department of Mathematics, Stockholm University
Surulescu, Christina surulescu@mathematik.uni-kl.de Mathematics, Felix-Klein-Zentrum für Mathematik, TU Kaiserslautern
Swan, Amanda acswan@ualberta.ca Mathematical and Statistical Sciences, University of Alberta
Swanson, Kristin kristin.swanson@northwestern.edu Neurological Surgery, Northwestern University
Taylor-King, Jake jake.taylor-king@dtc.ox.ac.uk Mathematical Institute, The University of Oxford
Tello, Jose Ignacio jtello@eui.upm.es Department of Applied Mathematics, Universidad Complutense de Madrid
Volpert, Vitaly volpert@math.univ-lyon1.fr Mathematics and applications, CNRS
Weekes, Suzanne sweekes@wpi.edu Mathematical Sciences Department, Worcester Polytechnic Institute
Werner, Benjamin benjamin.werner@icr.ac.uk Genomics and Modeling Group, The Institute of Cancer Research
Ziebell, Frederik f.ziebell@dkfz-heidelberg.de Applied Mathematics, University of Heidelberg
Stem Cell Dynamics in Normal Human Colon Crypts and the Initiation 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 in stem cells, proliferating cells, or differentiated cells, and by the robust ability of crypts to recover from perturbation by cytotoxic agents due to resistant quiescent stem cells. An example of the use of the virtual crypt will be given, viz., the evaluation of different cancer chemotherapy protocols.

Neoneurogenesis and tumor metastasis: myth or reality?

Primary tumors infrequently lead to the demise of cancer patients; rather, mortality and a significant degree of morbidity result from the growth of secondary tumors in distant organs (metastasis). Malignant tumors release both lymph- and angio- genic factors, through two specific processes termed lymphangiogenesis and angiogenesis, respectively. In addition, recent experimental evidence shows that tumors initiate their own innervation by the release of neurotrophic factors (neoneurogenesis). The relationship between tumor progression and the nervous system is a complex and poorly understood part of cancer pathogenesis. It is likely that this process is regulated by a multitude of factors in the tumor/nerve microenvironment; these pathways are even further complicated by treatment and disease history as well as other genetic and socioeconomic factors. It is therefore important to study the interactions between the nervous system and tumor cells through mathematical/computational modelling: in this way we will take into account the most significant elements of the plethora of interacting pathways regulating this process. The present work is a first attempt to model the neurobiological aspect of cancer development through a system of differential equations.

NOTE: This is a joint work with Dr Georgios Lolas, TU Dresden (Germany).

Major Genes in Colorectal Cancer

Major genes are defined as those that are necessary and sufficient for disease causation, with important mutations of the gene as causal mechanism. It is commonly accepted that in colorectal cancer the principal major genes are APC, K-RAS, TGF-B, SMAD and p53. However, it may be important to know which gene is the first to undergo mutation. Patients with ulcerative colitis or Crohn’s disease are at risk of developing colorectal cancer. In the first part of this talk I will show, with a mathematical model that in colitis-associated colon cancer p53 is the first gene that is mutated. In the second part of the talk, I will show, again by a mathematical model (and rigorous mathematical analysis) that on mutation in major genes is not sufficient to cause colorectal cancer.

Cancer Stem Cells Discovered ... Mathematically

Cancer stem cells have a variety of biological characteristics, and categorizing cancer cells as stem cells depends on selection of defining properties. In this work we focus on metastatic potential of cancer cells and answer the following question: Can one characterize the size of the subpopulation of metastasis-producing cells in a solid tumor?

To answer this question, we used a very general mathematical model of cancer progression accounting for primary tumor origination and growth, shedding of metastases off the primary tumor, selection of viable metastases, dormancy of metastases and their inception in a secondary site, and growth of metastases in the site of interest. The model assumes that metastasis shedding off the primary tumor is governed by a Poisson process whose rate at time t is proportional to the number of metastasis-producing cells, N(t), which in turn is assumed proportional to some power of the size of the primary tumor: N(t) = kS^θ (t). The case θ = 0 (or close to 0) suggests the presence within a primary tumor of a relatively stable, and hence self-renewing, subpopulation of metastasis-producing cells.

The model produces an explicit formula for the distribution of the site-specific sizes of metastases at any given time. Fitting the model to clinical data allows one to estimate model parameters including θ. This parameter was estimated for three patients with renal cancer, non-small cell lung cancer and pancreatic cancer. In all these cases, the value of θ was found to be quite small, which serves as an indirect evidence for the existence of cancer stem cells with high metastatic potential.

Modeling Effects of the Tumor Microenvironment on Brain Tumor Stem Cell Phenotypes

Abstract not submitted.

Mathematical models of oncolytic virus therapy and characterization of the invasive and non-invasive glioma

In this talk, a mathematical model of Chase-ABC mediated oncolytic virus therapy targeting cancer stem cells and CSPG-driven glioma infiltration will be presented. Glioblastoma is the most aggressive type of brain cancer with the median survival time of one year. Oncolytic viruses are genetically engineered viruses that are designed to kill cancer cells while doing minimal damage to normal healthy tissue. After being injected into a tumor, they infect cancer cells, multiply inside them, and when a cancer cell is killed they move on to spread and infect other cancer cells. Chondroitinase ABC (Chase-ABC) is a bacterial enzyme that can remove a major glioma ECM component, chondroitin sulfate glycosoamino glycans (CSGG) from proteoglycans without any deleterious effects in vivo. It has been shown that Chase-ABC treatment is able to promote the spread of the viruses, increasing the efficacy of the viral treatment. We develop a mathematical model to investigate the effect of the Chase-ABC on the treatment of glioma by oncolytic viruses (OV). We show that the model’s predictions agree with experimental results for a spherical glioma. We then use the model to test various treatment options for both primary tumor and infiltrating tumor cells in the heterogeneous microenvironment of the brain. A new strategy of targeting cancer stem cells in a niche using transported oncolytic viruses will be also presented. The primary treatment option is surgery but invasive cells in brain tissue eventually regrow back even with chemo- and radio-therapy, generating poor clinical outcomes. Therefore, it is important to distinguish invasive glioma phenotypes from non-invasive cells. Experiments by Silver et al illustrated that concentrations of CSPG, one of major extracellular matrix component within a tumor, determine invasive and non-invasive phenotypes. We developed a mathematical model of CSPG-driven dynamics of a growing glioma, using a free boundary framework. We take into account the rich dynamics of astrocytes and microglia in brain tissue as illustrated in Silver et al. The simulation results are in good agreement with experimental data in Silver et al. We also show how oncolytic virus therapy can be used to eradicate tumor cells. There is a critical threshold value of CSPG levels for optimal killing of both invasive and non-invasive tumorcells.

Analysis of mutations leading to the myelodysplastic syndrome (MDS) using modified Moran models

Abstract not submitted.

Calculus of stem cells

Identifying the exact regulatory circuits that can stably maintain tissue homeostasis is critical for our basic understanding of multicellular organisms, and equally critical for figuring out how tumors circumvent this regulation, thus providing targets fortreatment. Despite great strides in the understanding of the molecular components of stem-cell regulation, the overall mechanisms orchestrating tissue homeostasis are still far from being understood. Typically, tissue contains the stem cells, transit amplifying cells, and terminally differentiated cells. Each of these cell types can potentially secrete regulatory factors and/or respond to factors secreted by other types. The feedback can be positive or negative in nature. This gives rise to a bewildering array of possible mechanisms that drive tissue regulation. In this talk I describe a novel stochastic method of studying stem cell lineage regulation, which allows to identify possible numbers, types, and directions of control loops that are compatible with stability, keep the variance low, and possess a certain degree of robustness.

Data-Driven Mathematical Modeling of Mammary Ductal Elongation

The Terminal End Bud (TEB) at the growing tip of mammary ducts is one of the fastest growing structures in mammals. TEBs drive ductal elongation during puberty and regress once development of the ductal tree is complete. Because of similarities between TEB growth and breast cancer growth, successful modeling of this structure may yield insight into breast development as well as cancer progression. Previous mathematical models have focused on branching morphogenesis, but there are currently no models that address ductal elongation itself. Our model exploits the constrained geometry of the TEB in vivo which provided the framework for an initial mathematical model. Parameters in this model were then informed with measureable data (morphological characteristics, proliferation rate, cell cycle duration, and apoptosis). These data were then used to calculate a value representing the movement of cells from the TEB into the mature duct (termed the flux) and this calculated flux was then used to predict a linear elongation rate. The prediction was compared to an experimentally measured displacement within the mammary fat pad. Our initial measurements of proliferation, apoptosis, and cell sizes, predicted a linear elongation rate of 1.39 mm per day, which was significantly different from our experimentally measured displacement rate of 0.54mm per day. We then refined our model by incorporating changes in the direction of growth due to bifurcation, a cost function for bifurcation (which describes duplication of the TEB), as well as an additional flux term to account for a migration of cap cells into the body cell. Iteration of the revised mathematical model yielded an estimate significantly closer to the measured displacement rate, thus indicating that the most relevant biological parameters have been accounted for. In addition, our data overturned a long held belief that cap cells contribute to the body cell lineage. We are now poised for in silico experiments that may yield predictions consistent with cancer phenotypes, as well as predictions that recapitulate known mutation phenotypes.

TBD

Abstract not submitted.

Modeling Head and Neck Cancer Cellular Plasticity

Head and neck cancer is the sixth most common cancer worldwide, with more than 125,000 persons dying annually from this disease. While improvements in head and neck cancer treatment have been made, they have been less significant than for other cancers of similar prevalence. Overall 5-year survival of 50-60% is attributed to a high recurrence rate. A subpopulation of cancer stem cells (CSC) define augmented tumorigenicity with in vivo models in head and neck cancer. Recent observations lead us to believe that cancer stem cells play a role in helping tumors adapt to their environment. Furthermore, traditional cytotoxic chemotherapy treatment of head and neck cancer may shift the cellular equilibrium, promoting an increased proportion of CSC. I will be discussing our studies combining modeling and laboratory data in order to elucidate the interplay between cancer treatment and CSC promotion.

Evolution and phenotypic selection of cancer stem cells

Cells of different organs at different ages have an intrinsic set of kinetics that dictates their behavior. Transformation into cancer cells will inherit these kinetics that determine initial cell and tumor population progression dynamics. Subject to genetic mutation and epigenetic alterations, cancer cell kinetics can change and favorable alterations that increase cellular fitness will manifest themselves and accelerate tumor progression. We set out to investigate the emerging intratumoral heterogeneity and to determine the evolutionary trajectories of the combination of cell-intrinsic kinetics that yield aggressive tumor growth. We develop a cellular automaton model that tracks the temporal evolution of the malignant subpopulation of so-called cancer stem cell, as these cells are exclusively able to initiate and sustain tumors. We explore orthogonal cell traits including cell migration to facilitate invasion, spontaneous cell death due to genetic drift after accumulation of irreversible deleterious mutations, symmetric cancer stem cell division that increases the cancer stem cell pool, and telomere length and erosion as a mitotic counter for inherited non-stem cancer cell proliferation potential. Our study suggests that cell proliferation potential is the strongest modulator of tumor growth. Early increase in proliferation potential yields larger populations of CC that compete with CSC and thus inhibit CSC division while a reduction in proliferation potential loosens such inhibition and facilitates frequent CSC division. The subpopulation of cancer stem cells in itself becomes highly heterogeneous dictating population level dynamics that vary from long-term dormancy to aggressive progression. Our study suggests that the clonal diversity that is captured in single tumor biopsy samples represents only a small proportion of the total number of phenotypes.

Target Identification in Glioma Initiating Cells

Gliomas display cellular hierarchies with tumor initiating cells (TICs) at the apex that are functionally defined by the ability to self renew and propagate tumors similar to the parental tumors from which they are derived. TICs remain controversial, but their clinical relevance has been supported by resistance to cytotoxic therapies (Bao et al. Nature 2006) and promotion of tumor angiogenesis (Bao et al. Cancer Research 2006). TICs reside in specific functional niches in perivascular and hypoxic niches (Li et al. Cancer Cell 2009) that may offer the ability to disrupt tumor maintenance and therapeutic resistance through targeting the niche. Investigating TICs has already yielded novel molecular targets and pathways that are amenable to therapeutic targeting (Kim et al. Genes Development 2012; Eyler et al. Cell 2011; Guryanova et al. Cancer Cell 2011). Using patient-derived tumor models, we have interrogated the regulation of the TIC phenotype by both cell intrinsic and microenvironmental influences present in tumors. TICs are enriched under low nutrient conditions due to the cooption of the high affinity GLUT3 transporter normally expressed by neurons (Flavahan et al. Nature Neuroscience 2013). We have now extended these findings to demonstrate that cellular metabolism is differentially regulated within the tumor hierarchy at several levels to provide resources for sustained self-renewal and proliferation (Xie et al. Nature Neuroscience 2015). We also recently found that TICs have basal genotoxic stress activating PARP permitting radiosensitization (Venere et al. Cell Death Differentiation 2014). To discover novel TIC targets, we are using several technologies, including aptamers (Kim et al. Cancer Research 2013), flow cytometry (Lathia et al. Cell Reports 2014), and phage display (Liu et al. Cell Death Diff. 2014), showing that TICs manifest nodes of fragility mediating cell survival and invasion (e.g. JAM-A, VAV3, and CD97). Combining TIC models from patients with non-neoplastic progenitors from epilepsy resections, we are interrogating additional molecular regulators of the cellular hierarchy that can be distinguished from normal stem cells to minimize toxicity. The conventional pyramidal unidirectional differentiation cascade with TICs at the apex has been called into question by studies demonstrating plasticity of the TIC phenotype (Cheng et al. Cell 2013), thus suggesting that targeting only TICs will likely fail to cure patients and require simultaneous targeting of TICs and the bulk tumor. Although the field of TIC biology is relatively young, continued elucidation of the tumor hierarchy holds promise for development of novel patient therapies.

Replicative Senescence as a Tumor Suppressor Pathway

Abstract not submitted.

Radiation-induced reprogramming of senescent mammary epithelial cells enriches CD44+/CD24low/- putative stem cell populations

The enrichment of CD44+/CD24low/- breast adenocarcinoma putative stem cell populations following exposure to ionizing radiation has been attributed their inherent radio resistance and an elevated frequency of asymmetric division during repopulation. However, recent studies demonstrating radiation induced reprogramming (the transition of non CD44+/CD24low/- cells into the CD44+/CD24low/- phenotype) as a potential mechanism of enrichment have raised the question of whether survival of existing CD44+/CD24low/- cells or their induced reprogramming is the primary mode of enrichment. To answer this question, we have combined a cellular automata model with in vitro experimental data using both non-tumorigenic (MCF-10a) and cancerous (MCF-7) mammary epithelial cell lines, with the aim of evaluating the enrichment of CD44+/CD24-/low cell populations in the context of radiation induced senescence. Modeling determined that the imperfect phenotypic reprogramming of radiation induced senescent cells (conveying the CD44+/CD24low/- phenotype, but with a more limited proliferation capability) could be a major driving force underlying CD44+/CD24low/- enrichment. Further the enrichment response of MCF-7 cells appears to be less regulated (occurring both at lower doses, earlier time points, and lasting longer) than that observed in MCF-10a cells, suggesting a potential role for such enrichment in radiation induced carcinogenesis. Together, these results suggest that reprogramming of senescent cells plays a significant role in the repopulation of cancer and non-cancer breast epithelial cells following exposure to ionizing radiation, a finding with important implications in radiation therapy.

Mathematical models for anisotropic glioma invasion: a multiscale approach

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main brain cells that can develop into neoplasms. Since they are highly invasive they are hard to remove by surgery, as the tumor margin it most often not precisely enough identifiable. The understanding of glioma spread patterns is hence essential for both radiological therapy as well as surgical treatment. We propose a multiscale framework for glioma growth includinginteractions of the cells with the underlying tissue network, along with proliferative effects. Relying on experimental findings, we assume that cancer cells use neuronal fibre tracts as invasive pathways. Hence, the individual structure of brain tissue seems to be decisive for the tumor spread. Diffusion tensor imaging (DTI) is able to provide such information, thus opening the way for patient specific modeling of glioma invasion. Starting from a multiscale model involving subcellular (microscopic) and individual (mesoscale) cell dynamics, we deduce on the macroscale effective equations characterizing the evolution of the tumor cell population and perform numerical simulations based on DTI data. Particular attention is payed on the modeling of proliferation terms on the mesoscale level, in order to deduce the corresponding source terms on the macroscale.

On a mathematical model of cancer stem cells with non-local terms

Abstract not submitted.

Mathematical modelling of multiple myeloma

Multiple myeloma is a malignant disease characterized by an abnormal proliferation of plasma cells in the bone marrow. Tumor growth prevents normal functioning of erythropoiesis and leads to anemia. In this lecture we will present the results of mathematical modelling of normal erythropoesis and of multiple myeloma development and treatment. Darwinian evolution of cancer cells will be discussed in a more general context.