Premium
Polymer Translocation through a Nanopore: A Showcase of Anomalous Diffusion
Author(s) -
Milchev A.,
Dubbeldam Johan L. A.,
Rostiashvili Vakhtang G.,
Vilgis Thomas A.
Publication year - 2009
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.2008.04068.x
Subject(s) - exponent , nanopore , monte carlo method , statistical physics , scaling , physics , molecular dynamics , drag , polymer , anomalous diffusion , diffusion , thermodynamics , materials science , mathematics , nanotechnology , quantum mechanics , geometry , nuclear magnetic resonance , philosophy , linguistics , statistics , innovation diffusion , knowledge management , computer science
We investigate the translocation dynamics of a polymer chain threaded through a membrane nanopore by a chemical potential gradient that acts on the chain segments inside the pore. By means of diverse methods (scaling theory, fractional calculus, and Monte Carlo and molecular dynamics simulations), we demonstrate that the relevant dynamic variable, the transported number of polymer segments, s ( t ), displays an anomalous diffusive behavior, both with and without an external driving force being present. We show that in the absence of drag force the time τ, needed for a macromolecule of length N to thread from the cis into the trans side of a cell membrane, scales as τ N 2/α with the chain length. The anomalous dynamics of the translocation process is governed by a universal exponent α= 2/(2ν+ 2 −γ 1 ), which contains the basic universal exponents of polymer physics, ν (the Flory exponent) and γ 1 (the surface entropic exponent). A closed analytic expression for the probability to find s translocated segments at time t in terms of chain length N and applied drag force f is derived from the fractional Fokker–Planck equation, and shown to provide analytic results for the time variation of the statistical moments 〈 s ( t )〉 and 〈 s 2 ( t )〉. It turns out that the average translocation time scales as τ∝ f −1 N 2/α−1 . These results are tested and found to be in perfect agreement with extensive Monte Carlo and molecular dynamics computer simulations.