  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 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.
