  We report on the nonlinear mechanical properties of a statistically
homogeneous, isotropic semiflexible network cross-linked by polymers containing
numerous small unfolding domains, such as the ubiquitous F-actin cross-linker
Filamin.
  We show that the inclusion of such proteins has a dramatic effect on the
large strain behavior of the network. Beyond a strain threshold, which depends
on network density, the unfolding of protein domains leads to bulk shear
softening. Past this critical strain, the network spontaneously organizes
itself so that an appreciable fraction of the Filamin cross-linkers are at the
threshold of domain unfolding. We discuss via a simple mean-field model the
cause of this network organization and suggest that it may be the source of
power-law relaxation observed in in vitro and in intracellular microrheology
experiments. We present data which fully justifies our model for a simplified
network architecture.
