Modeling Invasion Dynamics with Spatial Random-Fitness Due to Micro-Environment.
Numerous experimental studies have demonstrated that the microenvironment is a key regulator influencing the proliferative and migrative potentials of species. Spatial and temporal disturbances lead to adverse and hazardous microenvironments for cellular systems that is reflected in the phenotypic heterogeneity within the system. In this paper, we study the effect of microenvironment on the invasive capability of species, or mutants, on structured grids (in particular, square lattices) under the influence of site-dependent random proliferation in addition to a migration potential. We discuss both continuous and discrete fitness distributions. Our results suggest that the invasion probability is negatively correlated with the variance of fitness distribution of mutants (for both advantageous and neutral mutants) in the absence of migration of both types of cells. A similar behaviour is observed even in the presence of a random fitness distribution of host cells in the system with neutral fitness rate. In the case of a bimodal distribution, we observe zero invasion probability until the system reaches a (specific) proportion of advantageous phenotypes. Also, we find that the migrative potential amplifies the invasion probability as the variance of fitness of mutants increases in the system, which is the exact opposite in the absence of migration. Our computational framework captures the harsh microenvironmental conditions through quenched random fitness distributions and migration of cells, and our analysis shows that they play an important role in the invasion dynamics of several biological systems such as bacterial micro-habitats, epithelial dysplasia, and metastasis. We believe that our results may lead to more experimental studies, which can in turn provide further insights into the role and impact of heterogeneous environments on invasion dynamics.
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada.
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Manem
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada.
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Kaveh
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada.
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Kohandel
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada; Centre for Mathematical Medicine, Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada.
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Sivaloganathan
D008954:Models, Biological; D011157:Population Dynamics