A semi-flexible model prediction for the polymerization force exerted by a living F-actin filament on a fixed wall

We consider a single living semi-flexible filament with persistence length l_p in chemical equilibrium with a solution of free monomers at fixed monomer chemical potential mu_1 and fixed temperature T. While one end of the filament is chemically active with single monomer (de)polymerization steps, the other end is grafted normally to a rigid wall to mimick a rigid network from which the filament under consideration emerges. A second rigid wall, parallel to the grafting wall, is fixed at distance L<<l_p from the filament seed. In supercritical conditions the filament tends to grow and impinges onto the second surface which, in suitable conditions (non-escaping filament regime) stops the filament growth. We first establish the grand-potential and derive some general properties, in particular the filament size distribution and the force exerted by the living filament on the obstacle wall. We apply this formalism to the semi-flexible, living, discrete Wormlike chain (d-WLC) model with step size d and persistence length l_p, hitting a hard wall. By original Monte-Carlo calculations we justify the use of the weak bending universal expressions of Gholami et al. (Phys.Rev.E. 74,(2006), 041803) over the whole non escaping filament regime. Employing this universal form for living filaments, we find that the average force exerted by a living filament on a wall at distance L is in practice L independent and very close to the value predicted by Hill, his expression being strictly valid in the rigid filament limit. The average filament force results from the product of the cumulative size fraction x, where the filament is in contact with the wall, times the buckling force on a filament of size L_c ~ L. We discuss several consequences of the L independence of the stalling force for our specific filament model.
Comment: 22 pages, 9 figures, regular article accepted for publication by The Journal of Chemical Physics on 21 Sept 2015