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

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Directed motion emerging from two coupled random processes: translocation of a chain through a membrane nanopore driven by binding proteins. / Ambjörnsson, Tobias; Lomholt, Michael A; Metzler, Ralf.

In: Journal of Physics: Condensed Matter, Vol. 17, No. 47, 30.11.2005, p. S3945-S3964.

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T1 - Directed motion emerging from two coupled random processes: translocation of a chain through a membrane nanopore driven by binding proteins

AU - Ambjörnsson, Tobias

AU - Lomholt, Michael A

AU - Metzler, Ralf

PY - 2005/11/30

Y1 - 2005/11/30

N2 - 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.

AB - 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.

U2 - 10.1088/0953-8984/17/47/021

DO - 10.1088/0953-8984/17/47/021

M3 - Article

VL - 17

SP - S3945-S3964

JO - Journal of Physics: Condensed Matter

JF - Journal of Physics: Condensed Matter

SN - 1361-648X

IS - 47

ER -