2,769 research outputs found
Pore-blockade Times for Field-Driven Polymer Translocation
We study pore blockade times for a translocating polymer of length ,
driven by a field across the pore in three dimensions. The polymer performs
Rouse dynamics, i.e., we consider polymer dynamics in the absence of
hydrodynamical interactions. We find that the typical time the pore remains
blocked during a translocation event scales as ,
where is the Flory exponent for the polymer. In line with our
previous work, we show that this scaling behaviour stems from the polymer
dynamics at the immediate vicinity of the pore -- in particular, the memory
effects in the polymer chain tension imbalance across the pore. This result,
along with the numerical results by several other groups, violates the lower
bound suggested earlier in the literature. We discuss why
this lower bound is incorrect and show, based on conservation of energy, that
the correct lower bound for the pore-blockade time for field-driven
translocation is given by , where is the viscosity of
the medium surrounding the polymer.Comment: 14 pages, 6 figures, slightly shorter than the previous version; to
appear in J. Phys.: Cond. Ma
Probabilistic Phase Space Trajectory Description for Anomalous Polymer Dynamics
It has been recently shown that the phase space trajectories for the
anomalous dynamics of a tagged monomer of a polymer --- for single polymeric
systems such as phantom Rouse, self-avoiding Rouse, Zimm, reptation, and
translocation through a narrow pore in a membrane; as well as for
many-polymeric system such as polymer melts in the entangled regime --- is
robustly described by the Generalized Langevin Equation (GLE). Here I show that
the probability distribution of phase space trajectories for all these
classical anomalous dynamics for single polymers is that of a fractional
Brownian motion (fBm), while the dynamics for polymer melts between the
entangled regime and the eventual diffusive regime exhibits small, but
systematic deviations from that of a fBm.Comment: 8 pages, two figures, 3 eps figure files, minor changes,
supplementary material included moved to the appendix, references expanded,
to appear in J. Phys.: Condens. Matte
Dynamical Eigenmodes of a Polymerized Membrane
We study the bead-spring model for a polymerized phantom membrane in the
overdamped limit, which is the two-dimensional generalization of the well-known
Rouse model for polymers. We derive the {\it exact} eigenmodes of the membrane
dynamics (the "Rouse modes"). This allows us to obtain exact analytical
expressions for virtually any equilibrium or dynamical quantity for the
membrane. As examples we determine the radius of gyration, the mean square
displacement of a tagged bead, and the autocorrelation function of the
difference vector between two tagged beads. Interestingly, even in the presence
of tensile forces of any magnitude the Rouse modes remain the exact eigenmodes
for the membrane. With stronger forces the membrane becomes essentially flat,
and does not get the opportunity to intersect itself; in such a situation our
analysis provides a useful and exactly soluble approach to the dynamics for a
realistic model flat membrane under tension.Comment: 17 pages, 4 figures, minor changes, references updated, to appear in
JSTA
Dynamical Eigenmodes of Star and Tadpole Polymers
The dynamics of phantom bead-spring chains with the topology of a symmetric
star with arms and tadpoles (, a special case) is studied, in the
overdamped limit. In the simplified case where the hydrodynamic radius of the
central monomer is times as heavy as the other beads, we determine their
dynamical eigenmodes exactly, along the lines of the Rouse modes for linear
bead-spring chains. These eigenmodes allow full analytical calculations of
virtually any dynamical quantity. As examples we determine the radius of
gyration, the mean square displacement of a tagged monomer, and, for star
polymers, the autocorrelation function of the vector that spans from the center
of the star to a bead on one of the arms.Comment: 21 pages in double spacing preprint format, 5 figures, minor changes
in the "Discussion" section, to appear in JSTA
Through the Eye of the Needle: Recent Advances in Understanding Biopolymer Translocation
In recent years polymer translocation, i.e., transport of polymeric molecules
through nanometer-sized pores and channels embedded in membranes, has witnessed
strong advances. It is now possible to observe single-molecule polymer dynamics
during the motion through channels with unprecedented spatial and temporal
resolution. These striking experimental studies have stimulated many
theoretical developments. In this short theory-experiment review, we discuss
recent progress in this field with a strong focus on non-equilibrium aspects of
polymer dynamics during the translocation process.Comment: 29 pages, 6 figures, 3 tables, to appear in J. Phys.: Condens. Matter
as a Topical Revie
Simulations of Two-Dimensional Unbiased Polymer Translocation Using the Bond Fluctuation Model
We use the Bond Fluctuation Model (BFM) to study the pore-blockade times of a
translocating polymer of length in two dimensions, in the absence of
external forces on the polymer (i.e., unbiased translocation) and hydrodynamic
interactions (i.e., the polymer is a Rouse polymer), through a narrow pore.
Earlier studies using the BFM concluded that the pore-blockade time scales with
polymer length as , with , whereas some
recent studies with different polymer models produce results consistent with
, originally predicted by us. Here is the Flory exponent of
the polymer; in 2D. In this paper we show that for the BFM if the
simulations are extended to longer polymers, the purported scaling ceases to hold. We characterize the finite-size effects, and study
the mobility of individual monomers in the BFM. In particular, we find that in
the BFM, in the vicinity of the pore the individual monomeric mobilities are
heavily suppressed in the direction perpendicular to the membrane. After a
modification of the BFM which counters this suppression (but possibly
introduces other artifacts in the dynamics), the apparent exponent
increases significantly. Our conclusion is that BFM simulations do not rule out
our theoretical prediction for unbiased translocation, namely .Comment: minor proofreading corrections, 23 pages (double spacing), 7 figures,
published versio
Rouse Modes of Self-avoiding Flexible Polymers
Using a lattice-based Monte Carlo code for simulating self-avoiding flexible
polymers in three dimensions in the absence of explicit hydrodynamics, we study
their Rouse modes. For self-avoiding polymers, the Rouse modes are not expected
to be statistically independent; nevertheless, we demonstrate that numerically
these modes maintain a high degree of statistical independence. Based on
high-precision simulation data we put forward an approximate analytical
expression for the mode amplitude correlation functions for long polymers. From
this, we derive analytically and confirm numerically several scaling properties
for self-avoiding flexible polymers, such as (i) the real-space end-to-end
distance, (ii) the end-to-end vector correlation function, (iii) the
correlation function of the small spatial vector connecting two nearby monomers
at the middle of a polymer, and (iv) the anomalous dynamics of the middle
monomer. Importantly, expanding on our recent work on the theory of polymer
translocation, we also demonstrate that the anomalous dynamics of the middle
monomer can be obtained from the forces it experiences, by the use of the
fluctuation-dissipation theorem.Comment: 16 pages (double spaced), 5 figures, small changes and corrections,
to appear in J. Chem. Phy
Critical Dynamical Exponent of the Two-Dimensional Scalar Model with Local Moves
We study the scalar one-component two-dimensional (2D) model by
computer simulations, with local Metropolis moves. The equilibrium exponents of
this model are well-established, e.g. for the 2D model
and . The model has also been conjectured to belong to the Ising
universality class. However, the value of the critical dynamical exponent
is not settled. In this paper, we obtain for the 2D model using
two independent methods: (a) by calculating the relative terminal exponential
decay time for the correlation function ,
and thereafter fitting the data as , where is the system
size, and (b) by measuring the anomalous diffusion exponent for the order
parameter, viz., the mean-square displacement (MSD) as , and from the numerically
obtained value , we calculate . For different values of the
coupling constant , we report that and
for the two methods respectively. Our results indicate that
is independent of , and is likely identical to that for the 2D
Ising model. Additionally, we demonstrate that the Generalised Langevin
Equation (GLE) formulation with a memory kernel, identical to those applicable
for the Ising model and polymeric systems, consistently capture the observed
anomalous diffusion behavior.Comment: 14 pages, 4 figures, 6 figure files, to appear in Phys. Rev.
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