  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
smaller values of 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.
