  The interplay between cytoskeletal architecture and the nonlinearity of the
interactions due to bucklable filaments plays a key role in modulating the
cell's mechanical stability and affecting its structural rearrangements. We
study a model of cytoskeletal structure treating it as an amorphous network of
hard centers rigidly cross-linked by nonlinear elastic strings, neglecting the
effects of motorization. Using simulations along with a self-consistent phonon
method, we show that this minimal model exhibits diverse thermodynamically
stable mechanical phases that depend on excluded volume, crosslink
concentration, filament length and stiffness. Within the framework set by the
free energy functional formulation and making use of the random first order
transition theory of structural glasses, we further estimate the characteristic
densities for a kinetic glass transition to occur in this model system. Network
connectivity strongly modulates the transition boundaries between various
equilibrium phases, as well as the kinetic glass transition density.
