The dynamics of actin filaments in vitro and in vesicles

In the first part of the talk, I consider an equation that describes orientational aggregation of actin filaments by a jump process.

I show that a delta peak is a stable stationary solution if filaments attract each other. Then I study the bifurcation behaviour of the model. In particular, I show that when there is a generic bifurcation from the homogeneous distribution (i.e., exactly one of the eigenmodes changes stability), there is an analytic branch of stationary solutions emanating from the bifurcation point whose power series expansion can be computed explicitly. Moreover I show that our model can exhibit a wide variety of types of dynamical behaviour, for example travelling waves, periodic solutions not of travelling wave type, and solutions combining characteristics of both.

In the second part of the talk, I present two models for the cortex formation of actin filaments near the inner membrane of a vesicle. The first model is a partial differential equation that contains anisotropic spatial diffusion and reorientation of filaments. In the second model a system of partial differential equation mimics the dynamic processes that take place when actin polymerization is started at the boundary of the vesicle. Numerical simulations show that both models can lead to aggregation.