A survey on random walk-based stochastic modeling in eukaryotic cell migration with emphasis on its application in cancer

The Eukaryotic cell migration, a complicated process, which is highly regulated by molecular pathways, plays a significant role in organogenesis and tissue development. Most cells demonstrate oriented or random migration in vitro, although they may have been extracted from tissue composed of immobile cells [1]. Cell migration disorders in developed organisms are mostly associated with impairments, such as cancer cell metastasis, immune diso-rders, and wound healing deficiency. Particularly in cancer, cell migration depends on the incidences of specific mutations [2] where extensive movement occurs in metastatic cells [3]. In addition, some studies have indi-cated that patients developing tumors with the elevated levels of tumor-infiltrating cytotoxic T lymphocytes have improved response to the treatment. In this regard, one of the main goals of cancer immunotherapy is to control tumor-immune system interactions [4]. The leading studies on cell migration process are focused on fibroblasts, keratinocytes, and myoblasts. Despite some differences in the migration process of various eukaryotic cells, studies have revealed basic similarities in the mechanisms involved in morphogenesis, wound healing, immune response, and cancer cell metastasis [5]. The quantification of these similarities and differences helps in categorizing and modeling of the process. These models predict the migration properties and help in understanding the speed of cell motion-dependent processes, such as metastasis, the characteristics of an optimum migration behavior for effective interaction between lymphocytes and infectious cells and tumor, and the migration ability of tumor cells considering the spatial heterogeneity of tumor. At present, mathematical modeling and numerical simulations are abundantly applied as complementary to in vitro investigations. Despite the perpetual necessity of experimental approaches for understanding biological processes, in silico experiments can complement these assays by limiting the measuring space and reducing the experiment cost [6–8]. The main advantage of in silico computational models is the simultaneous analysis of several dependent variables that presently seems unatt-ainable experimentally. The evaluation of the relationships of systems’ variables, in spite of non-linear dynamics, facilitates more compreh-ensive and accurate analyses of experimental observations. In addition, mathematical models can identify key parameters, determining the ultimate behavior of the system and suggest the most precise experiments for system assessment [9]. The processes associated with cell migration are inAbstract Impairments in cell migration processes may cause various diseases, among which cancer cell metastasis, tumor angiogenesis, and the disability of immune cells to infiltrate into tumors are prominent ones. Mathematical modeling has been widely used to analyze the cell migration process. Cell migration is a complicated process and requires statistical methods such as random walk for proper analysis. In this study, we reviewed the studies conducted on the random walk-based stochastic modeling of the eukaryotic cell migration. This statistical modeling can open some perspectives on more detailed modeling approaches and ultimately lead to more comprehensive knowledge about the biophysical and biochemical foundations of cell migration process.