Directed motion emerging from two coupled random processes: translocation of a chain through a membrane nanopore driven by binding proteins
(2005) In Journal of Physics: Condensed Matter 17(47). p.3945-3964- Abstract
- We investigate the translocation of a stiff polymer consisting of M monomers
through a nanopore in a membrane, in the presence of binding particles
(chaperones) that bind onto the polymer, and partially prevent backsliding of
the polymer through the pore. The process is characterized by the rates: k
for the polymer to make a diffusive jump through the pore, q for unbinding of
a chaperone, and the rate qκ for binding (with a binding strength κ); except
for the case of no binding κ = 0 the presence of the chaperones gives rise
to an effective force that drives the translocation process. In more detail, we
develop a dynamical description of the process in terms of a (2+1)-variable
master equation for the... (More) - We investigate the translocation of a stiff polymer consisting of M monomers
through a nanopore in a membrane, in the presence of binding particles
(chaperones) that bind onto the polymer, and partially prevent backsliding of
the polymer through the pore. The process is characterized by the rates: k
for the polymer to make a diffusive jump through the pore, q for unbinding of
a chaperone, and the rate qκ for binding (with a binding strength κ); except
for the case of no binding κ = 0 the presence of the chaperones gives rise
to an effective force that drives the translocation process. In more detail, we
develop a dynamical description of the process in terms of a (2+1)-variable
master equation for the probability of having m monomers on the target side
of the membrane with n bound chaperones at time t. Emphasis is put on the
calculation of the mean first passage time as a function of total chain length M.
The transfer coefficients in the master equation are determined through detailed
balance, 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 two
rates determines, together with κ and λ, three limiting cases, for which analytic
results are derived: (i) for the case of slow binding (γ κ → 0), the motion is
purely diffusive, and M2 for large M; (ii) for fast binding (γ κ → ∞) but
slow 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 fast
variable n, and find that for a very long polymer M, but with a smaller
prefactor than for ratchet-like dynamics. We solve the general case numerically
as a function of the dimensionless parameters λ, κ and γ , and compare to the
three limiting cases. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/130fa085-f691-4eac-9e39-c7e3687a8584
- author
- Ambjörnsson, Tobias LU ; Lomholt, Michael A and Metzler, Ralf
- publishing date
- 2005-11-30
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Physics: Condensed Matter
- volume
- 17
- issue
- 47
- pages
- 3945 - 3964
- publisher
- IOP Publishing
- external identifiers
-
- scopus:27744597109
- ISSN
- 0953-8984
- DOI
- 10.1088/0953-8984/17/47/021
- language
- English
- LU publication?
- no
- id
- 130fa085-f691-4eac-9e39-c7e3687a8584
- date added to LUP
- 2019-05-03 11:44:01
- date last changed
- 2022-03-31 17:21:02
@article{130fa085-f691-4eac-9e39-c7e3687a8584,
abstract = {{We investigate the translocation of a stiff polymer consisting of M monomers<br/>through a nanopore in a membrane, in the presence of binding particles<br/>(chaperones) that bind onto the polymer, and partially prevent backsliding of<br/>the polymer through the pore. The process is characterized by the rates: k<br/>for the polymer to make a diffusive jump through the pore, q for unbinding of<br/>a chaperone, and the rate qκ for binding (with a binding strength κ); except<br/>for the case of no binding κ = 0 the presence of the chaperones gives rise<br/>to an effective force that drives the translocation process. In more detail, we<br/>develop a dynamical description of the process in terms of a (2+1)-variable<br/>master equation for the probability of having m monomers on the target side<br/>of the membrane with n bound chaperones at time t. Emphasis is put on the<br/>calculation of the mean first passage time as a function of total chain length M.<br/>The transfer coefficients in the master equation are determined through detailed<br/>balance, and depend on the relative chaperone size λ and binding strength κ,<br/>as well as the two rate constants k and q. The ratio γ = q/k between the two<br/>rates determines, together with κ and λ, three limiting cases, for which analytic<br/>results are derived: (i) for the case of slow binding (γ κ → 0), the motion is<br/>purely diffusive, and M2 for large M; (ii) for fast binding (γ κ → ∞) but<br/>slow unbinding (γ → 0), the motion is, for small chaperones λ = 1, ratchetlike, and M; (iii) for the case of fast binding and unbinding dynamics<br/>(γ → ∞ and γ κ → ∞), we perform the adiabatic elimination of the fast<br/>variable n, and find that for a very long polymer M, but with a smaller<br/>prefactor than for ratchet-like dynamics. We solve the general case numerically<br/>as a function of the dimensionless parameters λ, κ and γ , and compare to the<br/>three limiting cases.}},
author = {{Ambjörnsson, Tobias and Lomholt, Michael A and Metzler, Ralf}},
issn = {{0953-8984}},
language = {{eng}},
month = {{11}},
number = {{47}},
pages = {{3945--3964}},
publisher = {{IOP Publishing}},
series = {{Journal of Physics: Condensed Matter}},
title = {{Directed motion emerging from two coupled random processes: translocation of a chain through a membrane nanopore driven by binding proteins}},
url = {{http://dx.doi.org/10.1088/0953-8984/17/47/021}},
doi = {{10.1088/0953-8984/17/47/021}},
volume = {{17}},
year = {{2005}},
}