Enhancement of target location rates by stochastic modulation of Brownian motion

Abstract

The binding of proteins to target sites on DNA, an important trigger of regulatory changes in a cell’s life cycle, is a complex biophysical process that is sensitive to details of the surroundings in which it takes place. It is affected, in particular, and among other factors, by thermal noise, by the random binding and unbinding of the protein to the polynucleotide chain, by fluctuations in the chain’s conformations, and by the degree of molecular crowding around the reacting species. In this paper, using a model based on dynamically disordered Brownian motion (a model previously introduced to explain the occasional occurrence of non-Gaussian effects in simple random walk behaviour), we show that one such factor—the internal dynamics of DNA—can enhance the rate at which a target on the chain is located by a particle moving randomly along its contour. The enhancement of the target location rate is reminiscent of the phenomenon of stochastic resonance, in that it occurs when the timescale characteristic of the chain’s relaxation matches the timescale of the particle’s motion. This finding is in qualitative agreement with the few experimental and numerical results to which it can be loosely compared.