  Constructing physical models of living cells and tissues is an extremely
challenging task because of the high complexities of both intra- and
intercellular processes. In addition, the force that a single cell generates
vanishes in total due to the law of action and reaction. The typical mechanics
of cell crawling involve periodic changes in the cell shape and in the adhesion
characteristics of the cell to the substrate. However, the basic physical
mechanisms by which a single cell coordinates these processes cooperatively to
achieve autonomous migration are not yet well understood. To obtain a clearer
grasp of how the intracellular force is converted to directional motion, we
develop a basic mechanochemical model of a crawling cell based on subcellular
elements with the focus on the dependence of the protrusion and contraction as
well as the adhesion and deadhesion processes on intracellular biochemical
signals. By introducing reaction-diffusion equations that reproduce traveling
waves of local chemical concentrations, we clarify that the chemical dependence
of the cell-substrate adhesion dynamics determines the crawling direction and
distance with one chemical wave. Finally, we also perform multipole analysis of
the traction force to compare it with the experimental results. To our
knowledge, our present work is the first study that accomplishes fully
force-free migration utilizing intracellular chemical reactions. Although the
detailed mechanisms of actual cells are far more complicated than our simple
model, we believe that this mechanochemical model is a good prototype for more
realistic models.
