A mathematical framework for linked, interacting cytoskeletal domains

In multicellular biophysical systems, cells are mechanically linked by adhesion molecules such as E-cadherin. These molecules couple cells' internal states and dynamics by directly coupling together their cytoskeletons; they are also known to contribute to the overall mechanics of multicellular systems. Even though adhesion molecules interact directly with the internal states and cytoskeletons of adjacent cells, many existing multicellular models do not capture this interaction. To understand how multicellular systems behave and how forces are propagated between cells, we present a model of cell-cell coupling that takes into explicit account the dynamics of adhesion molecules and their interaction with the cytoskeleton. We describe a framework that solves a kinetic problem on the edges between adjacent cells in order to describe cellular adhesions as a dynamic one-dimensional field that interacts with two-dimensional, cytoskeletal fields internal to the cells. Our framework can capture a variety of models for force exerted between adhesions and cytoskeleton, for turnover of adhesions or cytoskeleton, for cytoskeletal activity, and for the dynamics of adhesions binding and unbinding to actin. Importantly, in collectives of cells coupled this way, we find global patterns of polarization as well as formation of spontaneous cortical actin rings; we additionally find exotic collective states such as alternating polarization and transient stress chains.