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Non-Markovian effects in the first-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems.

Forsling, Robin; Sanders, Lloyd LU ; Ambjörnsson, Tobias LU and Lizana, Ludvig (2014) In Journal of Chemical Physics 141(9).
Abstract
The standard setup for single-file diffusion is diffusing particles in one dimension which cannot overtake each other, where the dynamics of a tracer (tagged) particle is of main interest. In this article, we generalize this system and investigate first-passage properties of a tracer particle when flanked by identical crowder particles which may, besides diffuse, unbind (rebind) from (to) the one-dimensional lattice with rates koff (kon). The tracer particle is restricted to diffuse with rate kD on the lattice and the density of crowders is constant (on average). The unbinding rate koff is our key parameter and it allows us to systematically study the non-trivial transition between the completely Markovian case (koff ≫ kD) to the... (More)
The standard setup for single-file diffusion is diffusing particles in one dimension which cannot overtake each other, where the dynamics of a tracer (tagged) particle is of main interest. In this article, we generalize this system and investigate first-passage properties of a tracer particle when flanked by identical crowder particles which may, besides diffuse, unbind (rebind) from (to) the one-dimensional lattice with rates koff (kon). The tracer particle is restricted to diffuse with rate kD on the lattice and the density of crowders is constant (on average). The unbinding rate koff is our key parameter and it allows us to systematically study the non-trivial transition between the completely Markovian case (koff ≫ kD) to the non-Markovian case (koff ≪ kD) governed by strong memory effects. This has relevance for several quasi one-dimensional systems. One example is gene regulation where regulatory proteins are searching for specific binding sites on a crowded DNA. We quantify the first-passage time distribution, f (t) (t is time), numerically using the Gillespie algorithm, and estimate f (t) analytically. In terms of koff (keeping kD fixed), we study the transition between the two known regimes: (i) when koff ≫ kD the particles may effectively pass each other and we recover the single particle result f (t) ∼ t(-3/2), with a reduced diffusion constant; (ii) when koff ≪ kD unbinding is rare and we obtain the single-file result f (t) ∼ t(-7/4). The intermediate region displays rich dynamics where both the characteristic f (t) - peak and the long-time power-law slope are sensitive to koff. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Chemical Physics
volume
141
issue
9
publisher
American Institute of Physics
external identifiers
  • pmid:25194389
  • wos:000342207400036
  • scopus:84907054893
ISSN
0021-9606
DOI
10.1063/1.4894117
language
English
LU publication?
yes
id
268d40a6-7918-4419-ab62-69bf1bd8472d (old id 4692171)
date added to LUP
2014-10-06 10:16:39
date last changed
2017-08-27 03:09:59
@article{268d40a6-7918-4419-ab62-69bf1bd8472d,
  abstract     = {The standard setup for single-file diffusion is diffusing particles in one dimension which cannot overtake each other, where the dynamics of a tracer (tagged) particle is of main interest. In this article, we generalize this system and investigate first-passage properties of a tracer particle when flanked by identical crowder particles which may, besides diffuse, unbind (rebind) from (to) the one-dimensional lattice with rates koff (kon). The tracer particle is restricted to diffuse with rate kD on the lattice and the density of crowders is constant (on average). The unbinding rate koff is our key parameter and it allows us to systematically study the non-trivial transition between the completely Markovian case (koff ≫ kD) to the non-Markovian case (koff ≪ kD) governed by strong memory effects. This has relevance for several quasi one-dimensional systems. One example is gene regulation where regulatory proteins are searching for specific binding sites on a crowded DNA. We quantify the first-passage time distribution, f (t) (t is time), numerically using the Gillespie algorithm, and estimate f (t) analytically. In terms of koff (keeping kD fixed), we study the transition between the two known regimes: (i) when koff ≫ kD the particles may effectively pass each other and we recover the single particle result f (t) ∼ t(-3/2), with a reduced diffusion constant; (ii) when koff ≪ kD unbinding is rare and we obtain the single-file result f (t) ∼ t(-7/4). The intermediate region displays rich dynamics where both the characteristic f (t) - peak and the long-time power-law slope are sensitive to koff.},
  articleno    = {094902},
  author       = {Forsling, Robin and Sanders, Lloyd and Ambjörnsson, Tobias and Lizana, Ludvig},
  issn         = {0021-9606},
  language     = {eng},
  number       = {9},
  publisher    = {American Institute of Physics},
  series       = {Journal of Chemical Physics},
  title        = {Non-Markovian effects in the first-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems.},
  url          = {http://dx.doi.org/10.1063/1.4894117},
  volume       = {141},
  year         = {2014},
}