Fully-coupled mathematical modeling of actomyosin-cytosolic two-phase flow in a highly deformable moving Keratocyte cell.

Interaction between intracellular dynamics and extracellular matrix (ECM) generally occurred into very thin fragment of moving cell, namely lamellipodia, enables all movable cells to crawl on ECM. In fast-moving cells such as fish Keratocytes, Lamellipodia including most cell area finds a fan-like shape during migration, with a variety of aspect ratio function of fish type. In this work, our purpose is to present a novel and more complete two-dimensional continuum mathematical model of actomyosin-cytosolic two-phase flow of a self-deforming Keratocyte with circular spreaded to steady fan-like shape. In the new approach, in addition to the two-phase flow of the F-actin and cytosol, the G-actin transport was spatiotemporally modeled. We also for the first time modeled the effect of variable volume fraction of the moving F-actin porous network on solute transport in the cytosolic fluid. Our novel fully-coupled mathematical model provides a better understanding of intracellular dynamics of fast-migrating Keratocytes; such as the F-actin centripetal and cytosolic fountain-like flows, free-active myosin distribution, distribution sequence of the G-actin, F-actin, and myosin, and myosin-induced pressure flied of cytoplasm as well as the map of intracellular forces like myosin contraction and adhesion traction. All these results are qualitatively and quantitatively in good agreement with experimental observations. According to a range of value of parameters used in this model, our steady state of moving Keratocyte finds fan-like shape with the same aspect ratio as wide category of fish Keratocytes. This new model can predict shape of Keratocytes in other range of parameter values.