ONCO Subgroup Contributed Talks

Sabrina Neumaier

Technical University of Munich

"Introduction of an environmental stress level to model tumor cell growth and survival"

Survival of living cells underlies many influences such as nutrient saturation, oxygen level, drug concentrations or mechanical forces. Data-supported mathematical modeling can be a powerful tool to get a better understanding of cell behavior in different settings. However, under consideration of numerous environmental factors mathematical modeling can get challenging. We present an approach to model the separate influences of each environmental quantity on the cells in a collective manner by introducing the 'environmental stress level'. It is an artificial, immeasurable variable, which quantifies to what extent viable cells would get in a stressed state, if exposed to certain conditions. A high stress level can inhibit cell growth, promote cell death and influence cell movement. As a proof of concept, we compare two systems of ordinary differential equations, which model tumor cell dynamics under various nutrient saturations respectively with and without considering an environmental stress level. Particle-based Bayesian inversion methods are used to calibrate unknown model parameters with time resolved measurements of in vitro populations of liver cancer cells. While predictions of both calibrated models show good agreement with the data, the model considering the stress level yields a better fitting.

Mohit Kumar Jolly

Indian Institute of Science

"Topological signatures in regulatory network enable phenotypic heterogeneity in small cell lung cancer"

Phenotypic (non-genetic) heterogeneity has significant implications for development and evolution of organs, organisms, and populations. Recent observations in multiple cancers have unravelled the role of phenotypic heterogeneity in driving metastasis and therapy recalcitrance. However, the origins of such phenotypic heterogeneity are poorly understood in most cancers. Here, we investigate a regulatory network underlying phenotypic heterogeneity in small cell lung cancer, a devastating disease with no molecular targeted therapy. Discrete and continuous dynamical simulations of this network reveal its multistable behavior that can explain co-existence of four experimentally observed phenotypes. Analysis of the network topology uncovers that multistability emerges from two teams of players that mutually inhibit each other but members of a team activate one another, forming a 'toggle switch' between the two teams. Deciphering these topological signatures in cancer-related regulatory networks can unravel their 'latent' design principles and offer a rational approach to characterize phenotypic heterogeneity in a tumor.

Meghan Rhodes

University of Alberta

"Comparing the effects of linear and one-term Ogden elasticity in a model of glioblastoma invasion."

We present a model of glioblastoma (GBM) invasion which includes mass effects and tissue mechanics. Furthermore, we show how different brain tissue elasticity models affect the dynamics and invasion wave speed. Inspired by Budday et al. (2017) who mechanically tested brain tissue to determine an appropriate constitutive model of brain tissue mechanics, we explore two models: The linear elasticity model, and the one-term Ogden model. In a simplified 1D version of the model, we show the existence of travelling wave solutions. The traveling waves can be viewed as the invasion of GBM tumor cells into the surrounding healthy brain tissue. Thus, identifying the speed of the wave and how it is affected by model components and parameters is useful in determining what drives invasion. We show that although the wave speed is independent of the chosen mechanical model, the dynamics of GBM spread and the effects on surrounding brain tissue differ significantly between the linear and one-term Ogden elasticity models. Simulations predict opposite modes of GBM invasion depending on the mechanical model, with the linear and one-term Ogden models showing that GBM invades via either “pushing” or “pulling” on the surrounding tissue, respectively.

Matthias M. Fischer

Charite Universitaetsmedizin Berlin, Institut fuer Pathologie; IRI Life Sciences, Humboldt University, Berlin, Germany

"Mathematical modelling of colon epithelium population dynamics reveals conditions for maintaining tissue homoeostasis"

The intestinal epithelium is one of the fastest renewing tissues in mammals and shows a remarkable degree of stability towards external perturbations such as physical injuries or radiation damage. This process is driven by intestinal stem cells as well as by differentiated cells being able to revert back to a stem cell state in situations of tissue regeneration. Self-renewal and regeneration, however, require a tightly regulated balance to uphold tissue homoeostasis, as failures in maintaining this balance may lead to tissue extinction or to unbounded growth, thereby giving rise to cancerous lesions.Here, we present and analyze a mathematical model of intestinal epithelium population dynamics. The model allows to derive conditions for stability and thereby helps to identify mechanisms that lead to loss of homoeostasis, causing either regenerative failure or unbounded, malignant growth. One of the key results is the existence of specific thresholds in feedbacks after which unbounded growth occur, and a subsequent convergence of the system to a stable ratio of stem to non-stem cells. Additionally, we demonstrate how allowing for dedifferentiation enables the system to recover more gracefully after certain external perturbations from equilibrium, however opens up another way to malignant growth.