DNA-Protein Binding Rates: Bending Fluctuation and Hydrodynamic Coupling Effects

TL;DR

This paper develops a theory for DNA-protein binding rates considering polymer bending fluctuations and hydrodynamic effects, showing these factors significantly influence reaction kinetics and can be tested experimentally.

Contribution

It introduces a combined theoretical framework accounting for shape fluctuations and hydrodynamic coupling in DNA-protein binding, validated by simulations.

Findings

Binding rate varies with polymer stiffness and particle size.

Rate can increase up to 100% over classical models.

Both effects are essential for accurate reaction rate estimates.

Abstract

We investigate diffusion-limited reactions between a diffusing particle and a target site on a semiflexible polymer, a key factor determining the kinetics of DNA-protein binding and polymerization of cytoskeletal filaments. Our theory focuses on two competing effects: polymer shape fluctuations, which speed up association, and the hydrodynamic coupling between the diffusing particle and the chain, which slows down association. Polymer bending fluctuations are described using a mean field dynamical theory, while the hydrodynamic coupling between polymer and particle is incorporated through a simple heuristic approximation. Both of these we validate through comparison with Brownian dynamics simulations. Neither of the effects has been fully considered before in the biophysical context, and we show they are necessary to form accurate estimates of reaction processes. The association rate depends on the stiffness of the polymer and the particle size, exhibiting a maximum for intermediate persistence length and a minimum for intermediate particle radius. In the parameter range relevant to DNA-protein binding, the rate increase is up to 100% compared to the Smoluchowski result for simple center-of-mass motion. The quantitative predictions made by the theory can be tested experimentally.