How proteins find their target on DNA? Delbruck model revisited

Alexander Grosberg
University of Minnesota, Twin Cities
School of Physics and Astronomy

It is known since the early days of molecular biology that proteins locate their specific targets on DNA two orders of magnitude faster than the Smoluchowski 3D diffusion rate. It was the idea due to Delbruck that they are non-specifically absorbed on DNA, and sliding along DNA provides for the faster 1D search. Surprisingly, the role of DNA conformation was
never considered in this context. For instance, if the DNA is a Gaussian coil, then over time t protein diffuses distance about square root of t along DNA, which translates into only forth root of t in space! How possibly can this slow
sub-diffusion be beneficial? We found that there exists a wealth of different scaling regimes, and show that the cells do face a problem here and do have the avenue to solve it. We also discuss possible roles of molecular motors in the light of our findings.

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