On the properties of a bundle of flexible actin filaments in an optical trap

We establish the statistical mechanics framework for a bundle of Nf living and uncrosslinked actin filaments in a supercritical solution of free monomers pressing against a mobile wall. The filaments are anchored normally to a fixed planar surface at one of their ends and, because of their limited flexibility, they grow almost parallel to each other. Their growing ends hit a moving obstacle, depicted as a second planar wall, parallel to the previous one and subjected to a harmonic compressive force. The force constant is denoted as the trap strength while the distance between the two walls as the trap length to make contact with the experimental optical trap apparatus. For an ideal solution of reactive filaments and free monomers at fixed free monomer chemical potential μ1, we obtain the general expression for the grand potential from which we derive averages and distributions of relevant physical quantities, namely, the obstacle position, the bundle polymerization force, and the number of filaments in direct contact with the wall. The grafted living filaments are modeled as discrete Wormlike chains, with F-actin persistence length lp, subject to discrete contour length variations ±d (the monomer size) to model single monomer (de)polymerization steps. Rigid filaments (lp = ∞), either isolated or in bundles, all provide average values of the stalling force in agreement with Hill’s predictions FsH = Nf kBT ln(ρ1/ρ1c)/d, independent of the average trap length. Here ρ1 is the density of free monomers in the solution and ρ1c its critical value at which the filament does not grow nor shrink in the absence of external forces. Flexible filaments (lp < ∞) instead, for values of the trap strength suitable to prevent their lateral escape, provide an average bundle force and an average trap length slightly larger than the corresponding rigid cases (few percents). Still the stalling force remains nearly independent on the average trap length, but results from the product of two strongly L-dependent contributions: the fraction of touching filaments ∝ (⟨L⟩O.T .)^2 and the single filament buckling force ∝ (⟨L⟩O.T .)^−2