Condensation of actin filaments pushing against a barrier

Abstract

We develop a model to describe the force generated by the polymerization of an array of parallel biofilaments. The filaments are assumed to be coupled only through mechanical contact with a movable barrier. We calculate the filament density distribution and the force-velocity relation with a mean-field approach combined with simulations. We identify two regimes: a non-condensed regime at low force in which filaments are spread out spatially, and a condensed regime at high force in which filaments accumulate near the barrier. We confirm a result previously known from other related studies, namely that the stall force is equal to N times the stall force of a single filament. In the model studied here, the approach to stalling is very slow, and the velocity is practically zero at forces significantly lower than the stall force.

Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

“…[26,28,31,50,80,81]. Similar to the filaments, motors also work against load and have been modelled in several studies [32-34, 75, 76].…”

“…In the presence of a resisting force f , the polymerization rates (forwardhopping rate) decreases, and the depolymerization rate (backward-hopping rate) increases according to the following rules: u(f ) = ue −f δ and w(f ) = we f (1−δ) . Here, the parameter δ ∈ [0, 1] is commonly known as force distribution factor [28] [cite for motors also].…”

“…Many dynein motors attach to molecular cargo and generate force for cellular transportation [24,25], while myosin motors primarily work together to generate forces in stress fibres and muscle tissues. Hence, study of such systems, which are involved in a wide range of biological processes, requires understanding of the generation of collective force by multiple cytoskeletal filaments or motors [26][27][28][29][30][31][32][33][34][35][36][37][38].…”

“…On the theoretical and computational front, there are a number of very detailed models for understanding the force-velocity dynamics of a single biofilament [50][51][52][53], as well as a few that try to model the dynamics of multiple biofilaments [26,[28][29][30][31][54][55][56]. Some of these theoretical studies have demonstrated that the stall force of multiple, non-interacting filaments without ATP/GTP dynamics, scales linearly with the number of filaments [26,[28][29][30]54].…”

“…Some of these theoretical studies have demonstrated that the stall force of multiple, non-interacting filaments without ATP/GTP dynamics, scales linearly with the number of filaments [26,[28][29][30]54]. In contrast, a few other recent papers quite clearly report that inclusion of ATP/GTP hydrolysis can lead to either enhanced or reduced cooperativity in the maximum force generated by multiple growing filaments; the stall forces need not always scale with the number of filaments [31,[56][57][58].…”