Analysis of stable two-dimensional patterns in contractile cytogel

Summary Contractile actomyosin systems play a central role in the generation of intracellular patterns. Models for pattern formation have benefited greatly from the application of mechanochemical theory. However, investigations of the patterns have been primarily qualitative in nature; the two-dimensional nature of the evolving patterns has not yet been addressed mathematically, nor has the evolution of stable heterogeneous steady-state solutions. We consider these issues, supporting our analytical predictions with numerical simulations in one and two spatial dimensions. We show how, for certain gels, the two and three-dimensional tensor equation which describes a balance of forces can be reduced to a reaction-diffusion equation.