Active fluctuations, driven by processes that consume ATP, are prevalent in living cells and are mostly driven by different forms of molecular motors. Such motors often move and transmit forces along biopolymers, which in general can be treated as semiflexible chains. We present a theoretical analysis of the active (out of thermal equilibrium) fluctuation of semiflexible polymers, using both analytical and simulation methods. We find that enhanced diffusion, even superdiffusive, occurs in a well-defined temporal regime, defined by the thermal modes of the chain and the typical timescale of the activity. In addition, we find a dynamic resonance-like condition between the elastic modes of the chain and the duration of the active force, which leads to enhanced spatial correlation of local displacements. These results are in qualitative agreement with observations of cytoskeletal biopolymers, and were recently observed for the dynamics of chromatin in interphase cells. We therefore propose that the interplay between elasticity and activity is driving long-range correlations in our model system, and may also be manifest inside living cells.
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