Modeling the mechanobioelectricity of cell clusters.

We propose a continuum finite strain theory for the interplay between the bioelectricity and the poromechanics of a cell cluster. Specifically, we refer to a cluster of closely packed cells, whose mechanics is governed by a polymer network of cytoskeletal filaments joined by anchoring junctions, modeled through compressible hyperelasticity. The cluster is saturated with a solution of water and ions. We account for water and ion transport in the intercellular spaces, between cells through gap junctions, and across cell membranes through aquaporins and ion channels. Water fluxes result from the contributions due to osmosis, electro-osmosis, and water pressure, while ion fluxes encompass electro-diffusive and convective terms. We consider both the cases of permeable and impermeable cluster boundary, the latter simulating the presence of sealing tight junctions. We solve the coupled governing equations for a one-dimensional axisymmetric benchmark through finite elements, thus determining the spatiotemporal evolution of the intracellular and extracellular ion concentrations, setting the membrane potential, and water concentrations, establishing the cluster deformation. When suitably complemented with genetic, biochemical, and growth dynamics, we expect this model to become a useful instrument for investigating specific aspects of developmental mechanobioelectricity.