Mechanical perspective on chemotaxis

Abstract

Cell motion in response to external chemical cues (chemotaxis) is a fundamental step in many physiological and pathological phenomena. The ability of cells to move onto two-dimensional flat substrates requires the activation of numerous intracellular mechanical and chemical mechanisms to achieve cell polarization and dynamic assembly and reorganization of the actin network. In this work we aim to bridge the gap between the mathematical models focusing on the mechanics of cell motion and the one describing the final motion of the cell in response to the external chemical field. We thus develop a one-dimensional continuous model representing cell migration, taking into account the mechanical stress inside the cell, the intracellular signaling molecules triggered by external factors, such as an external chemical field, and the actin dynamics during polymerization and depolymerization. The proposed model is solved numerically to simulate cell behavior during biologically relevant conditions and to study different mechanisms of conversion of the external field onto the intracellular chemical messenger, here called the polymerizing factor. The model is able to reproduce the transitions from the nonmigrating to the migrating regime, possibly triggered by the external chemotactic gradient, which is amplified by the internal chemical dynamics. More complex migratory behaviors can be described, as well, by including intracellular regulatory pathways of the polymerizing factor. Thus, the proposed model, even though kept as simple as possible, provides an interesting insight onto possible mathematical laws defining cell migratory velocity inside external chemical field gradients.