Regulation of Migration of Chemotactic Tumor Cells by the Spatial Distribution of the Collagen Fibers' Orientation

Collagen fibers, an important component of the extracellular matrix (ECM), can both inhibit and promote cellular migration. {\it In-vitro} studies have revealed that the fibers' orientations are crucial to cellular invasion, while {\it in-vivo} investigations have led to the development of tumor-associated collagen signatures (TACS) as an important prognostic factor. Studying biophysical regulation of cell invasion and the effect of the fibers' oritentation not only deepens our understanding of the phenomenon, but also helps classifying the TACSs precisely, which is currently lacking. We present a stochastic model for random/chemotactic migration of cells in fibrous ECM, and study the role of the various factors in it. The model provides a framework, for the first time to our knowledge, for quantitative classification of the TACSs, and reproduces quantitatively recent experimental data for cell motility. It also indicates that the spatial distribution of the fibers' orientations and extended correlations between them, hitherto ignored, as well as dynamics of cellular motion all contribute to regulation of the cells' invasion length, which represents a measure of metastatic risk. Although the fibers' orientations trivially affect randomly moving cells, their effect on chemotactic cells is completely nontrivial and unexplored, which we study in this paper.