  Cytoskeletal gels are prototyped to reproduce the mechanical contraction of
the cytoskeleton in-vitro. They are composed of a polymer network (backbone),
swollen by the presence of a liquid solvent, and active molecules (molecular
motors, MMs) that transduce chemical energy into the mechanical work of
contraction. These motors attach to the polymer chains to shorten them and/or
act as dynamic crosslinks, thereby constraining the thermal fluctuation of the
chains. We describe both mechanisms thermodynamically as a microstructural
reconfiguration, where the backbone stiffens to motivate solvent (out)flow and
accommodate contraction. Via simple steady-state energetic analysis, under the
simplest case of isotropic contraction, we quantify the mechanical energy
required to achieve contraction as a function of polymer chain density and
molecular motor density. We identify two limit cases, (fm) fast MM activation
for which MMs provide all the available mechanical energy instantaneously and
leave the polymer in a stiffened state, i.e. their activity occurs at a time
scale that is much smaller than solvent diffusion, and (sm) slow MM activation
for which the MM activation timescale is much longer. To achieve the same final
contracted state, fm requires the largest amount of work per unit reference
volume, while sm requires the least. For all intermediate cases where the
timescale of MM activation is comparable with that of solvent flow, the
required work ranges between the two cases. We provide all these quantities as
a function of chain density and MM density. Finally, we compare our results
with experiments and observe good agreement.
