  Recent experiments have demonstrated that the nonlinear elasticity of in
vitro networks of the biopolymer actin is dramatically altered in the presence
of a flexible cross-linker such as the abundant cytoskeletal protein filamin.
The basic principles of such networks remain poorly understood. Here we
describe an effective medium theory of flexibly cross-linked stiff polymer
networks. We argue that the response of the cross-links can be fully attributed
to entropic stiffening, while softening due to domain unfolding can be ignored.
The network is modeled as a collection of randomly oriented rods connected by
flexible cross-links to an elastic continuum. This effective medium is treated
in a linear elastic limit as well as in a more general framework, in which the
medium self-consistently represents the nonlinear network behavior. This model
predicts that the nonlinear elastic response sets in at strains proportional to
cross-linker length and inversely proportional to filament length. Furthermore,
we find that the differential modulus scales linearly with the stress in the
stiffening regime. These results are in excellent agreement with bulk rheology
data.
