Many-body effects on tracer particle diffusion with applications for single-protein dynamics on DNA
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30% of the DNA in E. coli bacteria is covered by proteins. Such a high degree of crowding affects 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 D (after many unbinding events) depends on (i) the unbinding rate of crowder particles k(off), and (ii) crowder particle line density rho, from simulations (using the Gillespie algorithm) and analytical calculations. For small k(off), we find D similar to k(off)/rho(2) when crowder particles do not diffuse on the line, and D similar to root Dk(off)/rho when they are diffusing; D is the free particle diffusion constant. For large k(off), we find agreement with mean-field results which do not depend on k(off). From literature values of k(off) and D, we show that the small k(off) -limit is relevant for in vivo protein diffusion on crowded DNA. Our results apply to single-molecule tracking experiments.