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arXiv 1502.02164cond-mat.stat-mechq-bio.SC
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示踪粒子扩散中的多体效应及其在DNA单蛋白动力学中的应用

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

Sebastian Ahlberg, Tobias Ambjörnsson, Ludvig Lizana

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10 pages, 8 figures
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摘要：

E.大肠杆菌被蛋白质覆盖。这种高度拥挤影响了一般生物过程的动力学（例如基因调节、DNA修复、蛋白质扩散等）。以一种尚未被完全理解的方式。本文从理论上讨论了示踪粒子在被不可穿透的拥挤粒子包围的一维系统中的扩散常数。虽然示踪粒子总是停留在晶格上，但拥挤粒子可能会与周围的块体解除绑定，并在另一个或相同的位置重新绑定。在这种情况下，我们确定长时间扩散常数${\cal D}$（在许多解结合事件之后）如何取决于（i）拥挤粒子的解结合速率$k_{\rm off}$和（ii）拥挤粒子线密度$ρ$，来自模拟（Gillespie算法）和分析计算。对于小$k_{\rm off}$，我们发现${\cal D}\sim k_{\rm off}/ρ^2$时，拥挤的粒子是固定的线上，和${\cal D}\sim \sqrt{D k_{\rm off}}/ρ$时，他们扩散; $D$是自由粒子扩散常数。对于大的$k_{\rm off}$，我们发现协议与平均场的结果不依赖于$k_{\rm off}$。从文献值的$k_{\rm off}$和$D$，我们表明，小的$k_{\rm off}$限制是相关的在拥挤的DNA在体内蛋白质扩散。我们的结果适用于单分子跟踪实验。

英文摘要：

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 ${\cal D}$ (after many unbinding events) depends on (i) the unbinding rate of crowder particles $k_{\rm off}$, and (ii) crowder particle line density $ρ$, from simulations (Gillespie algorithm) and analytical calculations. For small $k_{\rm off}$, we find ${\cal D}\sim k_{\rm off}/ρ^2$ when crowder particles are immobile on the line, and ${\cal D}\sim \sqrt{D k_{\rm off}}/ρ$ when they are diffusing; $D$ is the free particle diffusion constant. For large $k_{\rm off}$, we find agreement with mean-field results which do not depend on $k_{\rm off}$. From literature values of $k_{\rm off}$ and $D$, we show that the small $k_{\rm off}$-limit is relevant for in vivo protein diffusion on a crowded DNA. Our results applies to single-molecule tracking experiments.

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