Crowding and hopping in a protein’s diffusive transport on DNA

Abstract

Diffusion is a ubiquitous phenomenon that impacts virtually all processes that involve random fluctuations, and as such, the foundational work of Smoluchowski has proven to be instrumental in addressing innumerable problems. Here, we focus on a critical biological problem that relies on diffusive transport and is analyzed using a probabilistic treatment originally developed by Smoluchowski. The search of a DNA binding protein for its specific target site is believed to rely on non-specific binding to DNA with transient hops along the chain. In this work, we address the impact of protein crowding along the DNA on the transport of a DNA-binding protein. The crowders dramatically alter the dynamics of the protein while bound to the DNA, resulting in single-file transport that is subdiffusive in nature. However, transient unbinding and hopping results in a long-time behavior (shown to be superdiffusive) that is qualitatively unaffected by the crowding on the DNA. Thus, hopping along the chain mitigates the role that protein crowding has in restricting the translocation dynamics along the chain. The superdiffusion coefficient is influenced by the quantitative values of the effective binding rate, which is influenced by protein crowding. We show that vacancy fraction and superdiffusion coefficient exhibits a non-monotonic relationship under many circumstances. We leverage analytical theory and dynamic Monte Carlo simulations to address this problem. With several additional contributions, the core of our modeling work adopts a reaction-diffusion framework that is based on Smoluchowski’s original work.