Dynamical control of the shape and size of stereocilia and microvilli

We discuss theoretically the shape of actin-based protrusions such as stereocilia or microvilli that have important functions in many biological systems. These linear protrusions are dynamical structures continuously renewed by treadmilling: actin polymerizes at the tip of the cilium and depolymerizes in its bulk. They also often have a well-controlled length such as in the hair bundles of the inner ear cells where they appear in a graded staircase structure. Recent experimental results by another group of researchers show that the treadmilling velocity of the hair cell stereocilia is proportional to their length. We use generic arguments to describe the physics of stereocilia taking into account the effect of many individual proteins at a coarse-grained level by a few phenomenological parameters. At the tip of the cilium, we find that actin polymerization induces an effective pressure. Below the tip, the shape of the cilium is determined by depolymerization: Agreement with the observed shape requires that depolymerization occurs at least in two steps. Under these conditions, we calculate the cilium shape and provide physical grounds for the proportionality between treadmilling velocity and cilium length. We also calculate the penetration of the stereocilium in the actin cortical layer.