356 research outputs found
DNA uptake into nuclei: Numerical and analytical results
The dynamics of polymer translocation through a pore has been the subject of
recent theoretical and experimental works. We have considered theoretical
estimates and performed computer simulations to understand the mechanism of DNA
uptake into the cell nucleus, a phenomenon experimentally investigated by
attaching a small bead to the free end of the double helix and pulling this
bead with the help of an optical trap. The experiments show that the uptake is
monotonous and slows down when the remaining DNA segment becomes very short.
Numerical and analytical studies of the entropic repulsion between the DNA
filament and the membrane wall suggest a new interpretation of the experimental
observations. Our results indicate that the repulsion monotonically decreases
as the uptake progresses. Thus, the DNA is pulled in (i) either by a small
force of unknown origin, and then the slowing down can be interpreted only
statistically; (ii) or by a strong but slow ratchet mechanism, which would
naturally explain the observed monotonicity, but then the slowing down requires
additional explanations. Only further experiments can unambiguously distinguish
between these two mechanisms.Comment: 12 pages, 6 figures, submitted to J. Phys. Cond. Ma
Microscopic theory of network glasses
A molecular theory of the glass transition of network forming liquids is
developed using a combination of self-consistent phonon and liquid state
approaches. Both the dynamical transition and the entropy crisis characteristic
of random first order transitions are mapped out as a function of the degree of
bonding and the density. Using a scaling relation for a soft-core model to
crudely translate the densities into temperatures, the theory predicts that the
ratio of the dynamical transition temperature to the laboratory transition
temperature rises as the degree of bonding increases, while the Kauzmann
temperature falls relative to the laboratory transition. These results indicate
why highly coordinated liquids should be "strong" while van der Waals liquids
without coordination are "fragile".Comment: slightly revised version that has been accepted for publication in
Phys. Rev. Let
Elasticity model of a supercoiled DNA molecule
Within a simple elastic theory, we study the elongation versus force
characteristics of a supercoiled DNA molecule at thermal equilibrium in the
regime of small supercoiling. The partition function is mapped to the path
integral representation for a quantum charged particle in the field of a
magnetic monopole with unquantized charge.
We show that the theory is singular in the continuum limit and must be
regularised at an intermediate length scale. We find good agreement with
existing experimental data, and point out how to measure the twist rigidity
accurately.Comment: Latex, 4 pages. The figure contains new experimental data, giving a
new determination of the twist rigidit
Elasticity of Semiflexible Biopolymer Networks
We develop a model for gels and entangled solutions of semiflexible
biopolymers such as F-actin. Such networks play a crucial structural role in
the cytoskeleton of cells. We show that the rheologic properties of these
networks can result from nonclassical rubber elasticity. This model can explain
a number of elastic properties of such networks {\em in vitro}, including the
concentration dependence of the storage modulus and yield strain.Comment: Uses RevTeX, full postscript with figures available at
http://www.umich.edu/~fcm/preprints/agel/agel.htm
Diffusion with random distribution of static traps
The random walk problem is studied in two and three dimensions in the
presence of a random distribution of static traps. An efficient Monte Carlo
method, based on a mapping onto a polymer model, is used to measure the
survival probability P(c,t) as a function of the trap concentration c and the
time t. Theoretical arguments are presented, based on earlier work of Donsker
and Varadhan and of Rosenstock, why in two dimensions one expects a data
collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda
t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects
a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of
t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both
data collapses show a clear crossover from the early-time Rosenstock behavior
to Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure
Improving signal-to-noise resolution in single molecule experiments using molecular constructs with short handles
We investigate unfolding/folding force kinetics in DNA hairpins exhibiting
two and three states with newly designed short dsDNA handles (29 bp) using
optical tweezers. We show how the higher stiffness of the molecular setup
moderately enhances the signal-to-noise ratio (SNR) in hopping experiments as
compared to conventional long handles constructs (approximately 700 bp). The
shorter construct results in a signal of higher SNR and slower
folding/unfolding kinetics, thereby facilitating the detection of otherwise
fast structural transitions. A novel analysis of the elastic properties of the
molecular setup, based on high-bandwidth measurements of force fluctuations
along the folded branch, reveals that the highest SNR that can be achieved with
short handles is potentially limited by the marked reduction of the effective
persistence length and stretch modulus of the short linker complex.Comment: Main paper: 20 pages and 6 figures. Supplementary Material: 25 page
Conformations of Linear DNA
We examine the conformations of a model for under- and overwound DNA. The
molecule is represented as a cylindrically symmetric elastic string subjected
to a stretching force and to constraints corresponding to a specification of
the link number. We derive a fundamental relation between the Euler angles that
describe the curve and the topological linking number. Analytical expressions
for the spatial configurations of the molecule in the infinite- length limit
were obtained. A unique configuraion minimizes the energy for a given set of
physical conditions. An elastic model incorporating thermal fluctuations
provides excellent agreement with experimental results on the plectonemic
transition.Comment: 5 pages, RevTeX; 6 postscript figure
Colloid-Induced Polymer Compression
We consider a model mixture of hard colloidal spheres and non-adsorbing
polymer chains in a theta solvent. The polymer component is modelled as a
polydisperse mixture of effective spheres, mutually noninteracting but excluded
from the colloids, with radii that are free to adjust to allow for
colloid-induced compression. We investigate the bulk fluid demixing behaviour
of this model system using a geometry-based density-functional theory that
includes the polymer size polydispersity and configurational free energy,
obtained from the exact radius-of-gyration distribution for an ideal
(random-walk) chain. Free energies are computed by minimizing the free energy
functional with respect to the polymer size distribution. With increasing
colloid concentration and polymer-to-colloid size ratio, colloidal confinement
is found to increasingly compress the polymers. Correspondingly, the demixing
fluid binodal shifts, compared to the incompressible-polymer binodal, to higher
polymer densities on the colloid-rich branch, stabilizing the mixed phase.Comment: 14 pages, 4 figure
Corrections to scaling in 2--dimensional polymer statistics
Writing for the mean
square end--to--end length of a self--avoiding polymer chain of
links, we have calculated for the two--dimensional {\em continuum}
case from a new {\em finite} perturbation method based on the ground state of
Edwards self consistent solution which predicts the (exact) exponent.
This calculation yields . A finite size scaling analysis of data
generated for the continuum using a biased sampling Monte Carlo algorithm
supports this value, as does a re--analysis of exact data for two--dimensional
lattices.Comment: 10 pages of RevTex, 5 Postscript figures. Accepted for publication in
Phys. Rev. B. Brief Reports. Also submitted to J. Phys.
Elasticity of semiflexible polymers with and without self-interactions
A {\it new} formula for the force vs extension relation is derived from the
discrete version of the so called {\it worm like chain} model. This formula
correctly fits some recent experimental data on polymer stretching and some
numerical simulations with pairwise repulsive potentials. For a more realistic
Lennard-Jones potential the agreement with simulations is found to be good when
the temperature is above the temperature. For lower temperatures a
plateau emerges, as predicted by some recent experimental and theoretical
results, and our formula gives good results only in the high force regime. We
briefly discuss how other kinds of self-interactions are expected to affect the
elasticity of the polymer.Comment: 8 pages, 10 figure
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