Physics of collective cell migration.

Movement of cell clusters along extracellular matrices (ECM) during tissue development, wound healing, and early stage of cancer invasion involve various inter-connected migration modes such as: (1) cell movement within clusters, (2) cluster extension (wetting) and compression (de-wetting), and (3) directional cluster movement. It has become increasingly evident that dilational and volumetric viscoelasticity of cell clusters and their surrounding substrate significantly influence these migration modes through physical parameters such as: tissue and matrix surface tensions, interfacial tension between cells and substrate, gradients of surface and interfacial tensions, as well as, the accumulation of cell and matrix residual stresses. Inhomogeneous distribution of tissue surface tension along the cell-matrix biointerface can appear as a consequence of different contractility of various cluster regions. While the directional cell migration caused by the matrix stiffness gradient (i.e., durotaxis) has been widely elaborated, the structural changes of matrix surface caused by cell tractions which lead to the generation of the matrix surface tension gradient has not been considered yet. The main goal of this theoretical consideration is to clarify the roles of various physical parameters in collective cell migration based on the formulation of a biophysical model. This complex phenomenon is discussed with the help of model systems such as the movement of cell clusters on a collagen I gel matrix, simultaneously reviewing various experimental data with and without cells.