Spatial stochastic models of cancer: Fitness, migration, invasion

Natalia L. Komarova

doi:10.3934/mbe.2013.10.761

Article Contents

2013, Volume 10, Issue 3: 761-775. Doi: 10.3934/mbe.2013.10.761

This issue Previous Article Calcium waves with mechano-chemical couplings Next Article Equilibrium solutions for microscopic stochastic systems in population dynamics

Spatial stochastic models of cancer: Fitness, migration, invasion

Natalia L. Komarova^1,

1.
Department of Mathematics, University of California Irvine, Irvine CA 92697

Received: June 30, 2012

Revised: October 31, 2012

Published: March 2013

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Abstract

Cancer progression is driven by genetic and epigenetic events giving rise to heterogeneity of cell phenotypes, and by selection forces that shape the changing composition of tumors. The selection forces are dynamic and depend on many factors. The cells favored by selection are said to be more ``fit'' than others. They tend to leave more viable offspring and spread through the population. What cellular characteristics make certain cells more fit than others? What combinations of the mutant characteristics and ``background'' characteristics make the mutant cells win the evolutionary competition? In this review we concentrate on two phenotypic characteristics of cells: their reproductive potential and their motility. We show that migration has a direct positive impact on the ability of a single mutant cell to invade a pre-existing colony. Thus, a decrease in the reproductive potential can be compensated by an increase in cell migration. We further demonstrate that the neutral ridges (the set of all types with the invasion probability equal to that of the host cells) remain invariant under the increase of system size (for large system sizes), thus making the invasion probability a universal characteristic of the cells' selection status. We list very general conditions under which the optimal phenotype is just one single strategy (thus leading to a nearly-homogeneous type invading the colony), or a large set of strategies that differ by their reproductive potentials and migration characteristics, but have a nearly-equal fitness. In the latter case the evolutionary competition will result in a highly heterogeneous population.

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Mathematics Subject Classification: 92B05, 92C17, 92C50, 92D25.

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