  We present a revised theoretical study of the affine assumption applied to
semiflexible networks. Drawing on simple models of semiflexible worm-like
chains we derive an expression for the probability distribution of crosslink
separations valid at all separations. This accounts for both entropic and
mechanical filament stretching. From this we obtain the free energy density of
such networks explicitly as a function of applied strain. We are therefore able
to calculate the elastic moduli of such networks for any imposed strain or
stress. We find that accounting for the distribution of cross-link separations
destroys the simple scaling of modulus with stress that is well known in single
chains, and that such scaling is sensitive to the mechanical stretch modulus of
individual filaments. We compare this model to three experimental data sets,
for networks of different types of filaments, and find that a properly treated
affine model can successfully account for the data. We find that for networks
of stiffer filaments, such as F-actin, to fit data we require a much smaller
effective persistence length than usually assumed to be characteristic of this
filament type. We propose that such an effectively reduced rigidity of
filaments might be a consequence of network formation.
