Anisotropic nucleation growth of actin bundle: a model for determining the well-defined thickness of bundles

Biopolymers such as DNA, F-actins, and microtubules, which are highly charged, rodlike polyelectrolytes, are assembled into architectures with defined morphology and size by electrostatic interaction with multivalent cations (or polycations) in vivo and in vitro. The physical origin to determine their morphology and size is not clearly understood yet. Our results show that the actin bundle formation consists of two stages: the thickness of actin bundles is determined nearly at the initial stage, while the length of actin bundles is determined later on. It is also found that the thickness of actin bundles decreases with the increase of polycation-mediated attraction between F-actins. From these results, we propose the anisotropic nucleation-growth mechanism, in which the thickness of actin bundles is determined by critical nucleus size, whereas the length of actin bundles is determined by the concentration of free actins relative to nucleus concentration. Observing that polycations are concentrated in some sites of actin bundles, which are thought to be nucleation sites to initiate the formation of actin bundles, supports this model. This anisotropic nucleation-growth mechanism of actin bundles can be broadly applied to the self-assembly of rodlike polyelectrolytes.