  Within the cell, biopolymers are often situated in constrained, fluid
environments, e.g., cytoskeletal networks, stretched DNAs in chromatin. It is
of paramount importance to understand quantitatively how they, utilizing their
flexibility, optimally respond to a minute signal, which is, in general,
temporally fluctuating far away from equilibrium. To this end, we analytically
study viscoelastic response and associated stochastic resonance in a stretched
single semi-flexible chain to an oscillatory force or electric field. Including
hydrodynamic interactions between chain segments, we evaluate dynamics of the
polymer extension in coherent response to the force or field. We find power
amplification factor of the response at a noise-strength (temperature) can
attain the maximum that grows as the chain length increases, indicative of an
entropic stochastic resonance (ESR). In particular for a charged chain under an
electric field, we find that the maximum also occurs at an optimal chain
length, a new feature of ESR. The hydrodynamic interaction is found to enhance
the power amplification, representing unique polymer cooperativity which the
fluid background imparts despite its overdamping nature. For the slow
oscillatory force, the resonance behavior is explained by the chain undulation
of the longest wavelength. This novel ESR phenomenon suggests how a biopolymer
self-organizes in an overdamping environment, utilizing its flexibility and
thermal fluctuations.
