  Semiflexible polymers such as filamentous actin play a vital role in the
mechanical behavior of cells, yet the basic properties of cross-linked F-actin
networks remain poorly understood. To address this issue, we have performed
numerical studies of the linear response of homogeneous and isotropic
two-dimensional networks subject to an applied strain at zero temperature. The
elastic moduli are found to vanish for network densities at a rigidity
percolation threshold. For higher densities, two regimes are observed: one in
which the deformation is predominantly affine and the filaments stretch and
compress; and a second in which bending modes dominate. We identify a
dimensionless scalar quantity, being a combination of the material length
scales, that specifies to which regime a given network belongs. A scaling
argument is presented that approximately agrees with this crossover variable.
By a direct geometric measure, we also confirm that the degree of affinity
under strain correlates with the distinct elastic regimes. We discuss the
implications of our findings and suggest possible directions for future
investigations.
