Correlated random walks inside a cell: actin branching and microtubule dynamics

Correlated random walks (CRW) have been explored in many settings, most notably in the motion of individuals in a swarm or flock. But some subcellular systems such as growth or disassembly of bio-polymers can also be described with similar models and understood using related mathematical methods. Here we consider two examples of growing cytoskeletal elements, actin and microtubules. We use CRW or generalized CRW-like PDEs to model their spatial distributions. In each case, the linear models can be reduced to a Telegrapher's equation. A combination of explicit solutions (in one case) and numerical solutions (in the other) demonstrates that the approach to steady state can be accompanied by (decaying) waves.