Failure of one-dimensional Smoluchowski diffusion models to describe the duration of conformational rearrangements in floppy, diffusive molecular systems: A case study of polymer cyclization

Motivated by recent experimental efforts to measure the duration of individual foldingunfolding transitions in proteins and RNA, here we use simulations to study the duration of a simple transition mimicking an elementary step in biopolymer folding: the closure of a loop in a long polymer chain. While the rate of such a transition is well approximated by a one-dimensional Smoluchowski model that views the end-to-end distance dynamics of a polymer chain as diffusion governed by the one-dimensional potential of mean force, the same model fails rather dramatically to describe the duration of such transitions. Instead, the latter timescale is well described by a model where the chain ends diffuse freely, uninfluenced by the average entropic force imposed by the polymer chain. The effective diffusion coefficient then depends on the length scale of the loop closure transition. Our findings suggest that simple one-dimensional models, when applied to estimate the duration of reactive events in complex molecular systems, should be used with caution.