Stochastic model of elongation-shortening-switching kinetics of a polymeric filament: Critical slowing down of first-passage and finite-size regularization

Several filamentous biopolymers exhibit unusual polymerization-depolymerization kinetics where continued elongation (shortening) is possible only in an `active' (`inactive') state while occasional random transition (switching) between the active and inactive states takes place. Here, we present a mi