Pattern formation on dynamic membranes.

Abstract

Pattern formation defines cell identities and plays a crucial role in arguably all membrane functionality such are cell division, motility, communication, adhesion, etc. Cell often evolves by changing their shape, which translates to membrane dynamics, hence leading to pattern formation on dynamic surfaces. While pattern formation on static shapes has been intensively studied both theoretically and experimentally, the understanding of patterning on moving shapes remains largely elusive. We study force distribution on dynamic but initially spherical or cylindrical shapes by our surface dynamics equations. For simplicity, we consider small deformation of incompressible sphere and cylinder and show that shape dynamics induce nonuniform force distributions, therefore clarifying spontaneous polarisation, symmetry breaking, and rich static and moving pattern formations. Based on surface dynamics equations we derive a generic Young-Laplace equation which indicates that practically any static and dynamic patterns are possible in incompressible systems and if so, the question is what is the underlying mechanism that controls cell identity? The answer to the problem is again a surface dynamics equation that guarantees mass conservation. In other words, dynamic surfaces induce dynamic surface mass density that is governed by a generic mass balance equation and the last one controls the identity. While mass balance itself is regulated by an active or passive influx of material particles on the surface. The last statement for cell membrane means that membrane mass balance is in full correlation with cell-governed reaction, synthesis, and diffusion. The same statement can be reached for the charge balance equation which is also part of surface dynamics equations.