Active Polymers Confer Fast Reorganization Kinetics

Many cytoskeletal biopolymers are "active," consuming energy in large quantities. In this Letter, we identify a fundamental difference between active polymers and passive, equilibrium polymers: for equal mean lengths, active polymers can reorganize faster than equilibrium polymers. We show that equilibrium polymers are intrinsically limited to linear scaling between mean lifetime and mean length, MFPT ~ <L>, by analogy to 1-d Potts models. By contrast, we present a simple active-polymer model that improves upon this scaling, such that MFPT ~ <L>^{1/2}. Since to be biologically useful, structural biopolymers must typically be many monomers long, yet respond dynamically to the needs of the cell, the difference in reorganization kinetics may help to justify active polymers' greater energy cost. PACS numbers: 87.10.Ed, 87.16.ad, 87.16.Ln