Cancer associated fibroblasts and alectinib switch the evolutionary games that non-small cell lung cancer plays

Artem Kaznatcheev, Jeffrey Peacock, David Basanta, Andriy Marusyk, Jacob G. Scott

doi: https://doi.org/10.1101/179259

This article is a preprint and has not been peer-reviewed [what does this mean?].

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Abstract

Tumors are heterogeneous, evolving ecosystems, composed of sub-populations of neoplastic cells that follow distinct strategies for survival and propagation. The success of a strategy defining any single neoplastic sub-population is dependent on the distribution of other strategies, and on various components of the tumour microenvironment like cancer associated fibroblasts (CAFs). The rules mapping the population's strategy distribution to the fitness of individual strategies can be represented as an evolutionary game. In four different environments, we measure the games between treatment naive (Alectinib therapy sensitive) cells and a derivative line in which resistance was previously evolved. We find that the games are not only qualitatively different between different environments, but that targeted therapy and the presence of CAFs qualitatively switch the type of game being played. This provides the first empirical confirmation for the theoretical postulate of evolutionary game theory (EGT) in mathematical oncology that we can treat not just the player, but also the game. Although we concentrate on measuring games played by cancer cells, the measurement methodology we develop can be used to advance the study of games in other microscopic systems.

http://www.biorxiv.org/content/early/2017/08/21/179259

Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature

Artem Kaznatcheev, Robert Vander Velde, Jacob G Scott, David Basanta

 

Abstract

Background: Tumours are diverse ecosystems with persistent heterogeneity in various cancer hallmarks like self-sufficiency of growth factor production for angiogenesis and reprogramming of energy-metabolism for aerobic glycolysis. This heterogeneity has consequences for diagnosis, treatment, and disease progression. Methods: We introduce the double goods game to study the dynamics of these traits using evolutionary game theory. We model glycolytic acid production as a public good for all tumour cells and oxygen from vascularization via VEGF production as a club good benefiting non-glycolytic tumour cells. This results in three viable phenotypic strategies: glycolytic, angiogenic, and aerobic non-angiogenic. Results: We classify the dynamics into three qualitatively distinct regimes: (1) fully glycolytic, (2) fully angiogenic, or (3) polyclonal in all three cell types. The third regime allows for dynamic heterogeneity even with linear goods, something that was not possible in prior public good models that considered glycolysis or growth-factor production in isolation. Conclusion: The cyclic dynamics of the polyclonal regime stress the importance of timing for anti-glycolysis treatments like lonidamine. The existence of qualitatively different dynamic regimes highlights the order effects of treatments. In particular, we consider the potential of vascular renormalization as a neoadjuvant therapy before follow up with interventions like buffer therapy.

Link: doi: http://dx.doi.org/10.1101/067488

 

 

Cell-cell interactions and evolution using evolutionary game theory

David Basanta

Cancers arise from genetic aberrations but also consistently display high levels of intra-tumor heterogeneity and evolve according to Darwinian dynamics. This makes evolutionary game theory an ideal tool in which to mathematically capture these cell-cell interactions and in which to investigate how they impact evolutionary dynamics. In this chapter we present some examples of how evolutionary game theory can elucidate cancer evolution.

Link: http://dx.doi.org/10.1101/028746

 

Edge effects in game theoretic dynamics of spatially structured tumors

Edge effects in game theoretic dynamics of spatially structured tumours

Artem Kaznatcheev, Jacob G Scott, DavidBasanta

doi: http://dx.doi.org/10.1101/014233

Abstract

Background: Analysing tumour architecture for metastatic potential usually focuses on phenotypic differences due to cellular morphology or specific genetic mutations, but often ignore the cell's position within the heterogeneous substructure. Similar disregard for local neighborhood structure is common in mathematical models. Methods: We view the dynamics of disease progression as an evolutionary game between cellular phenotypes. A typical assumption in this modeling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard local heterogeneities. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go vs. grow game. Results: We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary -- such as a blood-vessel, organ capsule, or basement membrane -- we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (EMT positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Interpretation: Pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. We expect our approach to extend to other evolutionary game models where interaction neighborhoods change at fixed system boundaries.

Link: http://biorxiv.org/content/early/2015/01/23/014233

Spatial evolutionary games with small selection coefficients

Spatial evolutionary games with small selection coefficients

Rick Durrett May 5, 2014

Abstract
Here we will use results of Cox, Durrett, and Perkins [56] for voter model perturba- tions to study spatial evolutionary games on Zd, d ≥ 3 when the interaction kernel is finite range, symmetric, and has covariance matrix σ2I. The games we consider have payoff matrices of the form 1 + wG where 1 is matrix of all 1’s and w is small and positive. Since our population size N = ∞, we call our selection small rather than weak which usually means w = O(1/N). We prove that the effect of space is equiv- alent to replacing the replicator ODE by a related PDE where the reaction term is the replicator equation for a game matrix with some of the entries changed. The first idea is well known in the theory of stochastic spatial processes [58, 16, 62, 63]. The second is inspired by work of Ohtsuki and Nowak [28] (for the pair approximation). A remarkable aspect of our result is that the modifications of the game matrix depend on the interaction kernel only through the values of two simple probabilities for an associated coalescing random walk. 

link: http://www.math.duke.edu/~rtd/evog/spaceg.pdf

Edge effects in game theoretic dynamics of spatially structured tumours

 Edge effects in game theoretic dynamics of spatially structured tumours

Authors: +Artem Kaznatcheev , +Jacob Scott and +David Basanta

Abstract:
Evolutionary game theory has been used to model many situations in ecology
where different species, or different phenotypes within one species, compete
against one another. Of late, this has extended to cancer biology to understand
the dynamics of disease progression as a game between competing cellular
phenotypes. A major assumption in this modeling paradigm is that the population
is inviscid: the probability of a player with a given phenotypic strategy
interacting with another depends exclusively on the respective abundance of
those strategies in the population. While there are scenarios where this
assumption might be useful, in solid tumours, where the populations have
spatial structure, this assumption can yield misleading results. In this study
we use a recently developed mathematical tool, the Ohtsuki-Nowak transform, to
study the effect of interaction neighborhood size on a canonical evolutionary
cancer game: go vs. grow. We show that spatial structure promotes invasive (go)
strategy. By considering the change in neighbourhood size at a boundary we show
an edge effect in solid tumours. This edge effect allows a tumour with no
invasive phenotypes expressed internally to have a polyclonal boundary with
both invasive and non-invasive cells. We focus on evolutionary game dynamics
between competing cancer cells, but we anticipate that our approach can be
extended to games between other types of players where interaction
neighborhoods change at the system boundary.

Manuscript in arXiv [link].

Interesting review about how game theory (including game theory on networks) can be used to study the interactions between cells in a homeostatic tissue (made of cooperators) and how defectors (cancer cells) can disrupt that homeostasis.

Cooperation and competition in the dynamics of tissue architecture during homeostasis and tumorigenesis

Attila Csikász-Nagy, Luis M. Escudero, Martial Guillaud, Sean Sedwards, Buzz Baum, Matteo Cavaliere

Abstract: The construction of a network of cell-to-cell contacts makes it possible to characterize the patterns and spatial organisation of tissues. Such networks are highly dynamic, depending on the changes of the tissue architecture caused by cell division, death and migration. Local competitive and cooperative cell-to-cell interactions influence the choices cells make. We review the literature on quantitative data of epithelial tissue topology and present a dynamical network model that can be used to explore the evolutionary dynamics of a two dimensional tissue architecture with arbitrary cell-to-cell interactions. In particular, we show that various forms of experimentally observed types of interactions can be modelled using game theory. We discuss a model of cooperative and non-cooperative cell-to-cell communication that can capture the interplay between cellular competition and tissue dynamics. We conclude with an outlook on the possible uses of this approach in modelling tumorigenesis and tissue homeostasis. 

Preprint: http://arxiv.org/abs/1305.7478