Many-body effects in tracer particle diffusion with applications for single-protein dynamics on DNA

Abstract

30% of the DNA in E. coli bacteria is covered by proteins. Such high degree of crowding affect the dynamics of generic biological processes (e.g. gene regulation, DNA repair, protein diffusion etc.) in ways that are not yet fully understood. In this paper, we theoretically address the diffusion constant of a tracer particle in a one dimensional system surrounded by impenetrable crowder particles. While the tracer particle always stays on the lattice, crowder particles may unbind to a surrounding bulk and rebind at another or the same location. In this scenario we determine how the long time diffusion constant $\mathcal{D}$ (after many unbinding events) depends on (i) the unbinding rate of crowder particles $k_{\mathrm{off}}$, and (ii) crowder particle line density $\rho$, from simulations (Gillespie algorithm) and analytical calculations. For small $k_{\mathrm{off}}$, we find $\mathcal{D}\sim k_{\mathrm{off}}/{\rho }^2$ when crowder particles are immobile on the line, and $\mathcal{D}\sim \sqrt{D{k}_{\mathrm{off}}}/\rho$ when they are diffusing; $D$ is the free particle diffusion constant. For large $k_{\mathrm{off}}$, we find agreement with mean-field results which do not depend on $k_{\mathrm{off}}$. From literature values of $k_{\mathrm{off}}$ and $D$, we show that the small $k_{\mathrm{off}}$-limit is relevant for in vivo protein diffusion on a crowded DNA. Our results applies to single-molecule tracking experiments.

10 pages, 8 figures

References in corpus (12)

• Anomalous transport in the crowded world of biological cells
• Intermittent search strategies
• Optimal target search on a fast folding polymer chain with volume exchange
• Single-File Diffusion of Atomic and Colloidal Systems: Asymptotic Laws
• How do proteins search for their specific sites on coiled or globular DNA
• Non-universal tracer diffusion in crowded media of non-inert obstacles
• Single-File diffusion in a Box
• Theory of Single File Diffusion in a Force Field
• Biased diffusion in a one-dimensional adsorbed monolayer
• Fluctuations and correlations of a driven tracer in a hard-core lattice gas
• Dissimilar bouncy walkers
• First-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems

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