Abstract
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 (after many unbinding events) depends on (i) the unbinding rate of crowder particles , and (ii) crowder particle line density ρ, from simulations (using the Gillespie algorithm) and analytical calculations. For small , we find when crowder particles do not diffuse on the line, and when they are diffusing; D is the free particle diffusion constant. For large , we find agreement with mean-field results which do not depend on . From literature values of and D, we show that the small -limit is relevant for in vivo protein diffusion on crowded DNA. Our results apply to single-molecule tracking experiments.
Highlights
There is not much doubt that macromolecular crowding has severe consequences for biological processes inside living cells [1]
We theoretically address the diffusion constant of attribution to the a tracer particle in a one-dimensional system surrounded by impenetrable crowder particles
D, we show that the small koff -limit is relevant for in vivo protein diffusion on crowded DNA
Summary
30% of the DNA in E. coli bacteria is covered by proteins Such a high degree of crowding affects the licence. We theoretically address the diffusion constant of attribution to the a tracer particle in a one-dimensional system surrounded by impenetrable crowder particles. Rebind at another, or the same, location In this scenario we determine how the long time diffusion constant (after many unbinding events) depends on (i) the unbinding rate of crowder particles koff , and (ii) crowder particle line density ρ, from simulations (using the Gillespie algorithm) and analytical calculations. For small koff , we find ∼ koff ρ2 when crowder particles do not diffuse on the line, and ∼ Dkoff ρ when they are diffusing; D is the free particle diffusion constant. D, we show that the small koff -limit is relevant for in vivo protein diffusion on crowded DNA.
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