876 research outputs found
Adsorption of a random heteropolymer at a potential well revisited: location of transition point and design of sequences
The adsorption of an ideal heteropolymer loop at a potential point well is
investigated within the frameworks of a standard random matrix theory. On the
basis of semi-analytical/semi-numerical approach the histogram of transition
points for the ensemble of quenched heteropolymer structures with bimodal
symmetric distribution of types of chain's links is constructed. It is shown
that the sequences having the transition points in the tail of the histogram
display the correlations between nearest-neighbor monomers.Comment: 11 pages (revtex), 3 figure
Ring polymers in melts and solutions: scaling and crossover
We propose a simple mean-field theory for the structure of ring polymer
melts. By combining the notion of topological volume fraction and a classical
van der Waals theory of fluids, we take into account many body effects of
topological origin in dense systems. We predict that although the compact
statistics with the Flory exponent is realized for very long chains,
most practical cases fall into the crossover regime with the apparent exponent
during which the system evolves toward a topological dense-packed
limit.Comment: 4 pages, 3 figure
Metastable tight knots in a worm-like polymer
Based on an estimate of the knot entropy of a worm-like chain we predict that
the interplay of bending energy and confinement entropy will result in a
compact metastable configuration of the knot that will diffuse, without
spreading, along the contour of the semi-flexible polymer until it reaches one
of the chain ends. Our estimate of the size of the knot as a function of its
topological invariant (ideal aspect ratio) agrees with recent experimental
results of knotted dsDNA. Further experimental tests of our ideas are proposed.Comment: 4 pages, 3 figure
A coil-globule transition of a semiflexible polymer driven by the addition of spherical particles
The phase behaviour of a single large semiflexible polymer immersed in a
suspension of spherical particles is studied. All interactions are simple
excluded volume interactions and the diameter of the spherical particles is an
order of magnitude larger than the diameter of the polymer. The spherical
particles induce a quite long ranged depletion attraction between the segments
of the polymer and this induces a continuous coil-globule transition in the
polymer. This behaviour gives an indication of the condensing effect of
macromolecular crowding on DNA.Comment: 12 pages, 4 figure
How long does it take to pull an ideal polymer into a small hole?
We present scaling estimates for characteristic times and
of pulling ideal linear and randomly branched polymers of
monomers into a small hole by a force . We show that the absorbtion process
develops as sequential straightening of folds of the initial polymer
configuration. By estimating the typical size of the fold involved into the
motion, we arrive at the following predictions: and , and we also confirm them by
the molecular dynamics experiment.Comment: 4 pages, 3 figure
Collapsed 2-Dimensional Polymers on a Cylinder
Single partially confined collapsed polymers are studied in two dimensions.
They are described by self-avoiding random walks with nearest-neighbour
attractions below the -point, on the surface of an infinitely long
cylinder. For the simulations we employ the pruned-enriched-Rosenbluth method
(PERM). The same model had previously been studied for free polymers (infinite
lattice, no boundaries) and for polymers on finite lattices with periodic
boundary conditions. We verify the previous estimates of bulk densities, bulk
free energies, and surface tensions. We find that the free energy of a polymer
with fixed length has, for , a minimum at a finite cylinder
radius which diverges as . Furthermore, the surface
tension vanishes roughly as for with
. The density in the interior of a globule scales as
with .Comment: 4 pages, 8 figure
Error-proof programmable self-assembly of DNA-nanoparticle clusters
We study theoretically a new generic scheme of programmable self-assembly of
nanoparticles into clusters of desired geometry. The problem is motivated by
the feasibility of highly selective DNA-mediated interactions between colloidal
particles. By analyzing both a simple generic model and a more realistic
description of a DNA-colloidal system, we demonstrate that it is possible to
suppress the glassy behavior of the system, and to make the self-assembly
nearly error-proof. This regime requires a combination of stretchable
interparticle linkers (e.g. sufficiently long DNA), and a soft repulsive
potential. The jamming phase diagram and the error probability are computed for
several types of clusters. The prospects for the experimental implementation of
our scheme are also discussed. PACS numbers: 81.16.Dn, 87.14.Gg, 36.40.EiComment: 6 pages, 4 figures, v2: substantially revised version, added journal
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Entropically driven transition to a liquid-crystalline polymer globule
A self-consistent-field theory (SCFT) in the grand canonical ensemble
formulation is used to study transitions in a helix-coil multiblock copolymer
globule. The helices are modeled as stiff rods. In addition to the established
coil-globule transition we show for the first time that, even without explicit
rod-rod alignment interaction, the system undergoes a transition to a nematic
liquid-crystalline (LC) globular state. The LC-globule formation is driven by
the hydrophobic helical segment attraction and the anisotropy of the globule
surface energy. The full phase diagram of the copolymer was calculated. It
discriminates between an open chain, amorphous globule and LC-globule. This
model provides a relatively simple example of the interplay between secondary
and tertiary structures in homopolypeptides. Moreover, it gives a simple
explanation for the formation of helix bundles in certain globular proteins.Comment: 5 pages, 5 figures, submitted to Europhys. Let
Localization in simple multiparticle catalytic absorption model
We consider the phase transition in the system of n simultaneously developing
random walks on the halfline x>=0. All walks are independent on each others in
all points except the origin x=0, where the point well is located. The well
depth depends on the number of particles simultaneously staying at x=0. We
consider the limit n>>1 and show that if the depth growth faster than 3/2 n
ln(n) with n, then all random walks become localized simultaneously at the
origin. In conclusion we discuss the connection of that problem with the phase
transition in the copolymer chain with quenched random sequence of monomers
considered in the frameworks of replica approach.Comment: 17 pages in LaTeX, 5 PostScript figures; submitted to J.Phys.(A):
Math. Ge
On the Limits of Analogy Between Self-Avoidance and Topology-Driven Swelling of Polymer Loops
The work addresses the analogy between trivial knotting and excluded volume
in looped polymer chains of moderate length, , where the effects of
knotting are small. A simple expression for the swelling seen in trivially
knotted loops is described and shown to agree with simulation data. Contrast
between this expression and the well known expression for excluded volume
polymers leads to a graphical mapping of excluded volume to trivial knots,
which may be useful for understanding where the analogy between the two
physical forms is valid. The work also includes description of a new method for
the computational generation of polymer loops via conditional probability.
Although computationally intensive, this method generates loops without
statistical bias, and thus is preferable to other loop generation routines in
the region .Comment: 10 pages, 5 figures, supplementary tex file and datafil
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