Theoretical study of the role of dynamic bulk crowders in the protein search for targets on DNA

Abstract

The facilitated diffusion mechanism that involves the combination of one-dimensional and three-dimensional (3D) diffusion for recognition of a DNA target site by its protein is affected by the crowded cellular environment. Dynamic crowders can provide a better description of real processes in living cells. We develop a theoretical method based on a discrete state stochastic approach to understand the mechanism of the protein search on DNA in the presence of crowders that are moving around in the cellular medium. We obtain approximate analytical expressions for all dynamic properties. Our theoretical findings show that macromolecules present in the cellular volume and acting as dynamic crowders can influence 3D diffusion. The target search dynamics of proteins on DNA in the crowded cellular medium depend on the size and mobility of the macromolecular crowders. Highly mobile crowders do not affect the search dynamics, while slow moving crowders can significantly slow down the search process. Our theoretical results are discussed using physical explanations and they are also tested with extensive Monte Carlo computer simulations. Our theoretical predictions provide a physical understanding of the experimental observations and simulation results.