187 research outputs found
Geometry and topology of knotted ring polymers in an array of obstacles
We study knotted polymers in equilibrium with an array of obstacles which
models confinement in a gel or immersion in a melt. We find a crossover in both
the geometrical and the topological behavior of the polymer. When the polymers'
radius of gyration, , and that of the region containing the knot,
, are small compared to the distance b between the obstacles, the knot
is weakly localised and scales as in a good solvent with an amplitude
that depends on knot type. In an intermediate regime where ,
the geometry of the polymer becomes branched. When exceeds b, the
knot delocalises and becomes also branched. In this regime, is
independent of knot type. We discuss the implications of this behavior for gel
electrophoresis experiments on knotted DNA in weak fields.Comment: 4 pages, 6 figure
Unbinding of mutually avoiding random walks and two dimensional quantum gravity
We analyze the unbinding transition for a two dimensional lattice polymer in
which the constituent strands are mutually avoiding random walks. At low
temperatures the strands are bound and form a single self-avoiding walk. We
show that unbinding in this model is a strong first order transition. The
entropic exponents associated to denaturated loops and end-segments
distributions show sharp differences at the transition point and in the high
temperature phase. Their values can be deduced from some exact arguments
relying on a conformal mapping of copolymer networks into a fluctuating
geometry, i.e. in the presence of quantum gravity. An excellent agreement
between analytical and numerical estimates is observed for all cases analized.Comment: 9 pages, 11 figures, revtex
Fractional Brownian motion and the critical dynamics of zipping polymers
We consider two complementary polymer strands of length attached by a
common end monomer. The two strands bind through complementary monomers and at
low temperatures form a double stranded conformation (zipping), while at high
temperature they dissociate (unzipping). This is a simple model of DNA (or RNA)
hairpin formation. Here we investigate the dynamics of the strands at the
equilibrium critical temperature using Monte Carlo Rouse dynamics. We
find that the dynamics is anomalous, with a characteristic time scaling as
, exceeding the Rouse time . We
investigate the probability distribution function, the velocity autocorrelation
function, the survival probability and boundary behaviour of the underlying
stochastic process. These quantities scale as expected from a fractional
Brownian motion with a Hurst exponent . We discuss similarities and
differences with unbiased polymer translocation.Comment: 7 pages, 8 figure
Stiffness dependence of critical exponents of semiflexible polymer chains situated on two-dimensional compact fractals
We present an exact and Monte Carlo renormalization group (MCRG) study of
semiflexible polymer chains on an infinite family of the plane-filling (PF)
fractals. The fractals are compact, that is, their fractal dimension is
equal to 2 for all members of the fractal family enumerated by the odd integer
(). For various values of stiffness parameter of the
chain, on the PF fractals (for ) we calculate exactly the critical
exponents (associated with the mean squared end-to-end distances of
polymer chain) and (associated with the total number of different
polymer chains). In addition, we calculate and through the MCRG
approach for up to 201. Our results show that, for each particular ,
critical exponents are stiffness dependent functions, in such a way that the
stiffer polymer chains (with smaller values of ) display enlarged values of
, and diminished values of . On the other hand, for any specific
, the critical exponent monotonically decreases, whereas the critical
exponent monotonically increases, with the scaling parameter . We
reflect on a possible relevance of the criticality of semiflexible polymer
chains on the PF family of fractals to the same problem on the regular
Euclidean lattices.Comment: 22 pages, 6 figure
Stretching of a single-stranded DNA: Evidence for structural transition
Recent experiments have shown that the force-extension (F-x) curve for
single-stranded DNA (ssDNA) consisting only of adenine [poly(dA)] is
significantly different from thymine [poly(dT)]. Here, we show that the base
stacking interaction is not sufficient to describe the F-x curves as seen in
the experiments. A reduction in the reaction co-ordinate arising from the
formation of helix at low forces and an increase in the distance between
consecutive phosphates of unstacked bases in the stretched state at high force
in the proposed model, qualitatively reproduces the experimentally observed
features. The multi-step plateau in the F-x curve is a signature of structural
change in ssDNA.Comment: 10 pages, 4 figure
Does changing the pulling direction give better insight into biomolecules?
Single molecule manipulation techniques reveal that the mechanical resistance
of a protein depends on the direction of the applied force. Using a lattice
model of polymers, we show that changing the pulling direction leads to
different phase diagrams. The simple model proposed here indicates that in one
case the system undergoes a transition akin to the unzipping of a
sheet, while in the other case the transition is of a shearing (slippage)
nature. Our results are qualitatively similar to experimental results. This
demonstrates the importance of varying the pulling direction since this may
yield enhanced insights into the molecular interactions responsible for the
stability of biomolecules.Comment: RevTeX v4, 10 pages with 6 eps figure
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