  Myosin motor proteins drive vigorous steady-state fluctuations in the actin
cytoskeleton of cells. Endogenous embedded semiflexible filaments such as
microtubules, or added filaments such as single-walled carbon nanotubes are
used as novel tools to non-invasively track equilibrium and non-equilibrium
fluctuations in such biopolymer networks. Here we analytically calculate shape
fluctuations of semiflexible probe filaments in a viscoelastic environment,
driven out of equilibrium by motor activity. Transverse bending fluctuations of
the probe filaments can be decomposed into dynamic normal modes. We find that
these modes no longer evolve independently under non-equilibrium driving. This
effective mode coupling results in non-zero circulatory currents in a
conformational phase space, reflecting a violation of detailed balance. We
present predictions for the characteristic frequencies associated with these
currents and investigate how the temporal signatures of motor activity
determine mode correlations, which we find to be consistent with recent
experiments on microtubules embedded in cytoskeletal networks.
