Dynamics of Motile Populations in Heterogeneous Environments.

Movement behavior of biological entities plays a crucial role in their destiny through regulating their intraspecific and interspecific interactions as well as their interaction with surrounding environment. In spite of various models for population dynamics, the effect of movement behavior and heterogeneity of environment on population dynamics has remained poorly understood. We introduced an extended version of Kolmogorov equation which captures movement behavior and translated our model to a biased random walk on percolation lattice. Then we explored the effect of mentioned topic on population dynamics, especially for intratumor heterogeneity, metastasis and immune surveillance. In the case of tumor, our result reveals that communication between cell colons and the structure of host tissue together regulate the intratumor heterogeneity. For metastasis, our model predicts that the interplay between the structure of metastatic niche and interactions between metastatic cells arrived from different colons determines that which kind of seeds, polyclonal or monoclonal, can successfully metastasized there. Finally, studying the immune cells-tumor cells interaction in this context reveals the negative effect of the heterogeneous structure of host tissue on immune surveillance. These findings deepen our understanding of cancer biology and may have applications in Immunotherapy.