Subgroup Contributed Talks

Ryan John Murphy

Queensland University of Technology, Australia

"Mechanical cell competition in heterogeneous epithelial tissues"

Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. To study this phenomenon, we propose a one-dimensional mechanical model of cell migration in heterogeneous epithelial tissues that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are modelled in the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Applications we discuss include the evolution of homogeneous tissues experiencing proliferation and death, and cancer invasion with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mecha- nisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than by having some intrinsic proliferative advantage.

Aleksandra Ardaseva

University of Oxford, Oxford, UK

"Modelling evolutionary adaptation of cancer cells to fluctuating oxygen levels"

A major challenge in malignant tumours is cell heterogeneity, which has been proposed to arise due to temporal variations in nutrient supply caused by highly irregular vasculature. Such variability requires cells to adapt to potentially lethal variations in environmental conditions. Risk spreading (“bet-hedging”) through spontaneous phenotypic variations is an evolutionary strategy that allows species to survive in temporally varying environments. Individuals within a species diversify their phenotypes ensuring that at least some of them can survive in the face of sudden environmental change. We aim to investigate whether cancer cells may adopt this strategy when dealing with rapidly changing levels of nutrient due to temporally-varying blood flow. Here, we present a system of nonlocal partial differential equations modelling the evolutionary dynamics of phenotype-structured cancer cell populations exposed to fluctuating oxygen levels. In this model, the phenotypic state of every cell is described by a continuous variable that provides a simple representation of its metabolic phenotype, ranging from fully oxidative to fully glycolytic. The cells are grouped into two competing populations that undergo heritable, spontaneous, phenotypic variations at different rates. A combination of analysis and numerical simulations indicates that under certain conditions the cell-oxygen dynamics can lead to regions of chronic hypoxia (low oxygen level) and cycling hypoxia. Moreover, the model shows that under chronic-hypoxic conditions lower rates of phenotypic variation lead to a competitive advantage, whereas higher rates of phenotypic variation can confer a competitive advantage under cycling-hypoxic conditions. In the latter case, bet-hedging evolutionary strategies, whereby cells switch between oxidative and glycolytic phenotypes, can spontaneously emerge. These results shed light on the evolutionary processes that may underpin the emergence of phenotypic heterogeneity in vascularised tumours, and suggest potential therapeutic strategies.

Phillip J. Brown

The University of Adelaide, Australia

"Modelling colon cancer: Investigating serrated crypts using a new model for deformable membranes"

Serrated sessile polyps (SSPs) are a type of lesion found in the colon that are known to lead to colorectal cancer. They develop when there are disruptions in the processes controlling the function of colonic crypts - the test-tube shaped structures that make up the lining of colon. It is currently not clear what will cause a healthy crypt to become serrated. The crypt has been extensively modelled, owing to its relatively simple composition. However, little modelling work has focused on the formation of serrated crypts, perhaps because of the relatively difficult task of modelling the epithelial monolayer on a deformable supporting structure. In this talk, we will introduce new a modelling approach that allows us to build a deformable membrane, sidestepping the issues that made the predominant off lattice models less suitable. We will then present some preliminary findings on the potential causes behind the characteristic appearance of serrated crypts elucidated by this model.

Lisa C. Tucker-Kellog

Singapore

"During multi-drug combination therapy, the speed of evolving drug-resistance is affected by the uniformity of pairwise synergism, additivity, or antagonism between the drugs"

Introduction: The search for combination therapies against cancer has focused on studying synergistic combinations (drug combinations with greater-than-additive efficacy) because they exhibit enhanced therapeutic efficacy at lower doses. Although synergistic combinations are intuitively attractive, therapeutic success often depends on whether drug resistance develops. In computational modeling of drug-resistance evolution, our recent work (Saputra et. al, Cancer Res, 2018) delineated conditions under which synergistic pairs of drugs would have worse long-term performance than non-synergistic pairs of drugs, due to faster evolution of drug-resistance. In this work, we extend our modeling to three-drug combinations. In a multi-drug cocktail, some pairs of drugs may be synergistic while other pairs of drugs in the same cocktail may be additive or antagonistic (quantified using the combination index). Does this matter for evolution of drug-resistance? We develop theoretical generalizations about relative performance, for winning the race between cancer-killing efficacy versus drug-resistance evolution, using multi-drug cocktails with equal efficacy but different distributions of combination index (CI). Methods: We performed mathematical modeling of tumor cells evolving under selective pressure from synergistic, additive, and antagonistic three-drug combinations. Starting with small populations of drug-sensitive cells, we allowed rare mutational events to change a cell’s phenotype toward any single drug, which over time created potential for the presence or absence of drug-resistance against any or all drugs in the multi-drug therapy. Meanwhile, proliferation and death were simulated according to the combined cocktail efficacy toward each phenotype of cell. Results and Discussion: Longer duration of cancer control was achieved by multi-drug combinations having higher uniformity of pairwise CI (i.e., all pairs of drugs within the cocktail having similar levels of synergism, or all pairs having similar levels of antagonism), compared with multi-drug cocktails having equal initial efficacy and equal overall CI, but greater differences in the pairwise CI’s. In other words, treatment was more likely to fail sooner if the three drugs had non-uniform amounts of pairwise synergism, compared with cocktails that had more uniform CI between the drug-pairs within the cocktail. The difference in outcomes was due to partially resistant phenotypes that achieved greater competitive advantage (meaning greater clonal expansion and greater sabotage of therapy) by resisting the most synergistic aspects of the cocktail. This is because resisting one part of a synergistic group destroys not on

Yangjin Kim

Konkuk University, Republic of Korea

"How the surgery-induced transition of reactive astrocytes to stem cell-like phenotypes leads to recurrence of GBM by Cxcl5: hybrid multi-scale approaches"

Glioblastoma multiforme (GBM) is the most aggressive form of brain cancer with a short median survival time. GBM is characterized by the hallmarks of aggressive proliferation and cellular infiltration of normal brain tissue. Tumor cells also interact with many cells including astrocytes and immune cells, and extracellular matrix (ECM) in a tumor microenvironment (TME) via exchanging molecular signals in order to increase survival rates in response to biochemical and biomechanical challenges. miRNAs and their downstream molecules are known to play a pivotal role in regulation of the balance of proliferation and aggressive invasion in response to metabolic stress in the tumour microenvironment (TME). Surgery-induced transition in reactive astrocyte populations can dramatically change the growth and invasion dynamics of GBM cells. In this work, we develop a multi-scale mathematical model of the tumor astrocytes dynamics in response to surgical resection of the primary tumor in TME. The hybrid model takes into account miR-451-LKB1-AMPK-OCT1-mTOR pathway signalling (ODEs), individual cell dynamics of the tumour, reactive astrocytes, stem cell-like astrocytes (lattice-free individual model), and signal transport by diffusible molecules (PDEs). We show how the effects of fluctuating glucose on tumour cell dynamics need to be reprogrammed by taking into account the recent history of glucose variations and an LKB1/OCT1 reciprocal feedback loop, which then determines tumor cell proliferation and migration. The model shows that surgery-induced changes in TME are the important factors for inducing the critical transition from reactive astrocytes to stem cell-like phenotypes. The model illustrates how variations in glucose availability significantly affect the activity of signalling molecules and, in turn, lead to critical cell migration. The model also predicts that (i) microsurgery of a primary tumour induces phenotypical changes in reactive astrocytes and stem cell-like astrocytes promoting tumour cell proliferation and migration by Cxcl5, (ii) this critical transition essentially increases the recurrence potential of GBM and leads to the low survival rate of patients. Finally, we investigated a new anti-tumour strategy by Cxcl5-targeting drugs in order to prevent this critical recurrence of the tumor.