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Diffusion in correlated random potentials, with applications to DNA

2004; American Physical Society; Volume: 69; Issue: 6 Linguagem: Inglês

10.1103/physreve.69.061903

1550-2376

Michael Slutsky, Mehran Kardar, Leonid A. Mirny,

Nanopore and Nanochannel Transport Studies

Many biological processes involve one dimensional diffusion over a correlated inhomogeneous energy landscape with a correlation length $ξ_c$. Typical examples are specific protein target location on DNA, nucleosome repositioning, or DNA translocation through a nanopore, in all cases with $ξ_c\approx$ 10 nm. We investigate such transport processes by the mean first passage time (MFPT) formalism, and find diffusion times which exhibit strong sample to sample fluctuations. For a a displacement $N$, the average MFPT is diffusive, while its standard deviation over the ensemble of energy profiles scales as $N^{3/2}$ with a large prefactor. Fluctuations are thus dominant for displacements smaller than a characteristic $N_c \gg ξ_c$: typical values are much less than the mean, and governed by an anomalous diffusion rule. Potential biological consequences of such random walks, composed of rapid scans in the vicinity of favorable energy valleys and occasional jumps to further valleys, is discussed.