 Reaction-limited polymerization Brownian ratchet

When load-gap equilibration is fast compared with chemical events, an opposing force gives an exponential gap distribution. The probability of room for an addition is $e^{-Fa/(k_{B}T)}$. With unloaded addition rate $u$ and removal rate $w$, assumed force-independent except for this steric gating, the velocity is the displayed expression. For $u>w$, stall occurs at $F_s=(k_{B}T/a)\log (u/w)$. Concentration is included in $u=k_{\mathrm{on}}c$ if the on-rate constant is bimolecular.