  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
trap strength while the distance between the two walls as trap length to make
contact with the experimental optical trap apparatus. For an ideal solution of
reactive filaments and free monomers at fixed free monomers chemical potential,
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 Factin persistence length, subject to discrete contour
length variations to model single monomer (de)polymerization steps. Rigid
filaments, either isolated or in bundles, all provide average values of the
stalling force in agreement with Hill's predictions, independent of the average
trap length. Flexible filaments 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 and the single filament
buckling force.
