Directed motion emerging from two coupled random processes: translocation of a chain through a membrane nanopore driven by binding proteins

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@article{130fa085f6914eac9e39c7e3687a8584,
title = "Directed motion emerging from two coupled random processes: translocation of a chain through a membrane nanopore driven by binding proteins",
abstract = "We investigate the translocation of a stiff polymer consisting of M monomersthrough a nanopore in a membrane, in the presence of binding particles(chaperones) that bind onto the polymer, and partially prevent backsliding ofthe polymer through the pore. The process is characterized by the rates: kfor the polymer to make a diffusive jump through the pore, q for unbinding ofa chaperone, and the rate qκ for binding (with a binding strength κ); exceptfor the case of no binding κ = 0 the presence of the chaperones gives riseto an effective force that drives the translocation process. In more detail, wedevelop a dynamical description of the process in terms of a (2+1)-variablemaster equation for the probability of having m monomers on the target sideof the membrane with n bound chaperones at time t. Emphasis is put on thecalculation of the mean first passage time as a function of total chain length M.The transfer coefficients in the master equation are determined through detailedbalance, and depend on the relative chaperone size λ and binding strength κ,as well as the two rate constants k and q. The ratio γ = q/k between the tworates determines, together with κ and λ, three limiting cases, for which analyticresults are derived: (i) for the case of slow binding (γ κ → 0), the motion ispurely diffusive, and M2 for large M; (ii) for fast binding (γ κ → ∞) butslow unbinding (γ → 0), the motion is, for small chaperones λ = 1, ratchetlike, and M; (iii) for the case of fast binding and unbinding dynamics(γ → ∞ and γ κ → ∞), we perform the adiabatic elimination of the fastvariable n, and find that for a very long polymer M, but with a smallerprefactor than for ratchet-like dynamics. We solve the general case numericallyas a function of the dimensionless parameters λ, κ and γ , and compare to thethree limiting cases.",
author = "Tobias Ambj{\"o}rnsson and Lomholt, {Michael A} and Ralf Metzler",
year = "2005",
month = "11",
day = "30",
doi = "10.1088/0953-8984/17/47/021",
language = "English",
volume = "17",
pages = "S3945--S3964",
journal = "Journal of Physics: Condensed Matter",
issn = "1361-648X",
publisher = "IOP Publishing",
number = "47",

}