Instabilities and oscillations in isotropic active gels

We present a generic formulation of the continuum elasticity of an isotropic crosslinked active gel. The gel is described by a two-component model consisting of an elastic network coupled frictionally to a permeating fluid. Activity is induced by active crosslinkers that undergo an ATP-activated cycle and transmit forces to the network. The on/off dynamics of the active crosslinkers is described via rate equations for unbound and bound motors. For large activity motors yield a contractile instability of the network. At intermediate activity, the on/off motor dynamics provides an effective inertial drag on the network that opposes elastic restoring forces, resulting in spontaneous oscillations. Our work provides a continuum formulation that unifies earlier microscopic models of oscillations in muscle sarcomeres and a generic framework for the description of the large scale properties of isotropic active solids.