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Register a new userFacilitated diffusion of proteins on chromatin
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We present a theoretical model of facilitated diffusion of proteins in the cell nucleus. This model, which takes into account the successive binding/unbinding events of proteins to DNA, relies on a fractal description of the chromatin which has been recently evidenced experimentally. Facilitated diffusion is shown quantitatively to be favorable for a fast localization of a target locus by a transcription factor, and even to enable the minimization of the search time by tuning the affinity of the transcription factor with DNA. This study shows the robustness of the facilitated diffusion mechanism, invoked so far only for linear conformations of DNA.
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We study the impact of DNA coiling on the search rate of proteins moving along the DNA contour interspersed by three-dimensional (3D) bulk excursions. When the DNA is coiled proteins performing short 3D hops along a DNA segment can be captured by foreign DNA segments that have looped back close to the original segment. These intersegmental jumps are shown to enhance the search rate for a specific site on the DNA by lowering the tendency to resample previously visited sites on the DNA. The model developed here offers a quantitative description of recent single molecule experiments on facilitated diffusion of restriction enzymes EcoRV.
The diffusion-controlled limit of reaction times for site-specific DNA-binding proteins is derived from first principles. We follow the generally accepted concept that a protein propagates via two competitive modes, a three-dimensional diffusion in space and a one-dimensional sliding along the DNA. However, our theoretical treatment of the problem is new. The accuracy of our analytical model is verified by numerical simulations. The results confirm that the unspecific binding of protein to DNA, combined with sliding, is capable to reduce the reaction times significantly.
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 $rho$, from simulations (Gillespie algorithm) and analytical calculations. For small $k_{rm off}$, we find ${cal D}sim k_{rm off}/rho^2$ when crowder particles are immobile on the line, and ${cal D}sim sqrt{D k_{rm off}}/rho$ 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.
The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be calibrated in numerical simulations inside a test system of moderate size. Once this is done, reaction times of systems of arbitrary dimensions are derived by extrapolation, with an accuracy of 10 to 15 percent. The achieved speed up, when compared to explicit simulations of the reaction process, is increasing proportional to the extrapolated volume of the cell.
Experimental approaches have been applied to address questions in understanding three-dimensional chromatin organisation and function. As datasets increase in size and complexity, it becomes a challenge to reach a mechanistic interpretation of experimental results. Polymer simulations and mechanistic modelling have been applied to explain experimental observations, and the links to different aspects of genome function. Here, we provide a guide for biologists, explaining different simulation approaches and the contexts in which they have been used.
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