Competing polymerization of actin skeleton explains the relation between network polarity and cell movements

Abstract

Based on experimental observations it is known that various biological cells exhibit a persistent random walk during migration on flat substrates. The persistent random walk is characterized by 'stop-and-go' movements : unidirectional motions over distances of the order of several cell diameter are separated by localized short time erratic movements. Using computer simulations the reasons for this phenomena had been unveiled and shown to be attributed to two antagonistic nucleation processes during the polymerization of the cell's actin cytoskeleton : the (ordinary) spontaneous nucleation and the dendritic nucleation processes. Whereas spontaneous nucleations generate actin filaments growing in different directions and hence create motions in random directions, dendritic nucleations provide a unidirectional growth. Since dendritic growth exhibits stochastic fluctuations, spontaneous nucleation may eventually compete or even dominate, which results in a reorientation of filament growth and hence a new direction of cell motion. The event of reorientation takes place at instants of vanishing polarity of the actin skeleton.

Crawling of a driven adherent membrane

“…Assuming furthermore that association, p + , and dissociation, p − , at plus and minus ends, respectively, take place with the same rate 0 < p ≡ p + = p − ≤ 1, then we have the case of "treadmilling" filaments. Neglecting nucleation of actin filaments, 40,41 we have to assume that the length N F of each filament is always N F ≥ 2. Since the successful attempts of association at the plus ends are limited by the repulsion of the membrane, which is in contrast to the minus end where depolymerization is not limited, the length of the filaments shrinks to an average size N F ≈ 3.…”

Steady state dynamics of a moving model cell

“…In our model cell, we neglect the cell nucleus and other organelles and simulate a continuously remodeling actin network confined inside a fluctuating membrane. Following several previous successful attempts to model the cell membrane [10][11][12], we consider the cell membrane to be a flexible ring embedded on a square lattice. The size of the ring is characterized by its perimeter L, the number of segments of the ring.…”

“…We characterized the values of N and L for which the cell exhibits motility. A similar study characterized the persistent random walk of the model cell in terms of the competition between de novo nucleation and bidirectional Arp2/3-induced branching nucleation of new filaments [12]. In the present work, we have chosen the values of membrane size L = 200 and number of G actin N = 300 as they correspond to the motile regime of the model cell [10].…”