192 research outputs found
Monte Carlo Results for Projected Self-Avoiding Polygons: A Two-dimensional Model for Knotted Polymers
We introduce a two-dimensional lattice model for the description of knotted
polymer rings. A polymer configuration is modeled by a closed polygon drawn on
the square diagonal lattice, with possible crossings describing pairs of
strands of polymer passing on top of each other. Each polygon configuration can
be viewed as the two- dimensional projection of a particular knot. We study
numerically the statistics of large polygons with a fixed knot type, using a
generalization of the BFACF algorithm for self-avoiding walks. This new
algorithm incorporates both the displacement of crossings and the three types
of Reidemeister transformations preserving the knot topology. Its ergodicity
within a fixed knot type is not proven here rigorously but strong arguments in
favor of this ergodicity are given together with a tentative sketch of proof.
Assuming this ergodicity, we obtain numerically the following results for the
statistics of knotted polygons: In the limit of a low crossing fugacity, we
find a localization along the polygon of all the primary factors forming the
knot. Increasing the crossing fugacity gives rise to a transition from a
self-avoiding walk to a branched polymer behavior.Comment: 36 pages, 30 figures, latex, epsf. to appear in J.Phys.A: Math. Ge
Probing the entanglement and locating knots in ring polymers: a comparative study of different arc closure schemes
The interplay between the topological and geometrical properties of a polymer
ring can be clarified by establishing the entanglement trapped in any portion
(arc) of the ring. The task requires to close the open arcs into a ring, and
the resulting topological state may depend on the specific closure scheme that
is followed. To understand the impact of this ambiguity in contexts of
practical interest, such as knot localization in a ring with non trivial
topology, we apply various closure schemes to model ring polymers. The rings
have the same length and topological state (a trefoil knot) but have different
degree of compactness. The comparison suggests that a novel method, termed the
minimally-interfering closure, can be profitably used to characterize the arc
entanglement in a robust and computationally-efficient way. This closure method
is finally applied to the knot localization problem which is tackled using two
different localization schemes based on top-down or bottom-up searches.Comment: 9 pages, 7 figures. Submitted to Progress of Theoretical Physic
Nos\'e-Hoover and Langevin thermostats do not reproduce the nonequilibrium behavior of long-range Hamiltonians
We compare simulations performed using the Nos\'e-Hoover and the Langevin
thermostats with the Hamiltonian dynamics of a long-range interacting system in
contact with a reservoir. We find that while the statistical mechanics
equilibrium properties of the system are recovered by all the different
methods, the Nos\'e-Hoover and the Langevin thermostats fail in reproducing the
nonequilibrium behavior of such Hamiltonian.Comment: Contribution to the proceeding of the "International Conference on
the Frontiers of Nonlinear and Complex Systems" in honor of Prof. Bambi Hu,
Hong Kong, May 200
Phase Ordering in Nematic Liquid Crystals
We study the kinetics of the nematic-isotropic transition in a
two-dimensional liquid crystal by using a lattice Boltzmann scheme that couples
the tensor order parameter and the flow consistently. Unlike in previous
studies, we find the time dependences of the correlation function, energy
density, and the number of topological defects obey dynamic scaling laws with
growth exponents that, within the numerical uncertainties, agree with the value
1/2 expected from simple dimensional analysis. We find that these values are
not altered by the hydrodynamic flow. In addition, by examining shallow
quenches, we find that the presence of orientational disorder can inhibit
amplitude ordering.Comment: 21 pages, 14 eps figures, revte
The entropic cost to tie a knot
We estimate by Monte Carlo simulations the configurational entropy of
-steps polygons in the cubic lattice with fixed knot type. By collecting a
rich statistics of configurations with very large values of we are able to
analyse the asymptotic behaviour of the partition function of the problem for
different knot types. Our results confirm that, in the large limit, each
prime knot is localized in a small region of the polygon, regardless of the
possible presence of other knots. Each prime knot component may slide along the
unknotted region contributing to the overall configurational entropy with a
term proportional to . Furthermore, we discover that the mere existence
of a knot requires a well defined entropic cost that scales exponentially with
its minimal length. In the case of polygons with composite knots it turns out
that the partition function can be simply factorized in terms that depend only
on prime components with an additional combinatorial factor that takes into
account the statistical property that by interchanging two identical prime knot
components in the polygon the corresponding set of overall configuration
remains unaltered. Finally, the above results allow to conjecture a sequence of
inequalities for the connective constants of polygons whose topology varies
within a given family of composite knot types
Interplay between writhe and knotting for swollen and compact polymers
The role of the topology and its relation with the geometry of biopolymers
under different physical conditions is a nontrivial and interesting problem.
Aiming at understanding this issue for a related simpler system, we use Monte
Carlo methods to investigate the interplay between writhe and knotting of ring
polymers in good and poor solvents. The model that we consider is interacting
self-avoiding polygons on the simple cubic lattice. For polygons with fixed
knot type we find a writhe distribution whose average depends on the knot type
but is insensitive to the length of the polygon and to solvent conditions.
This "topological contribution" to the writhe distribution has a value that is
consistent with that of ideal knots. The standard deviation of the writhe
increases approximately as in both regimes and this constitutes a
geometrical contribution to the writhe. If the sum over all knot types is
considered, the scaling of the standard deviation changes, for compact
polygons, to . We argue that this difference between the two
regimes can be ascribed to the topological contribution to the writhe that, for
compact chains, overwhelms the geometrical one thanks to the presence of a
large population of complex knots at relatively small values of . For
polygons with fixed writhe we find that the knot distribution depends on the
chosen writhe, with the occurrence of achiral knots being considerably
suppressed for large writhe. In general, the occurrence of a given knot thus
depends on a nontrivial interplay between writhe, chain length, and solvent
conditions.Comment: 10 pages, accepted in J.Chem.Phy
Linking in domain-swapped protein dimers
The presence of knots has been observed in a small fraction of single-domain
proteins and related to their thermodynamic and kinetic properties. The
exchanging of identical structural elements, typical of domain-swapped
proteins, make such dimers suitable candidates to validate the possibility that
mutual entanglement between chains may play a similar role for protein
complexes. We suggest that such entanglement is captured by the linking number.
This represents, for two closed curves, the number of times that each curve
winds around the other. We show that closing the curves is not necessary, as a
novel parameter , termed Gaussian entanglement, is strongly correlated with
the linking number. Based on non redundant domain-swapped dimers, our
analysis evidences a high fraction of chains with a significant intertwining,
that is with . We report that Nature promotes configurations with
negative mutual entanglement and surprisingly, it seems to suppress
intertwining in long protein dimers. Supported by numerical simulations of
dimer dissociation, our results provide a novel topology-based classification
of protein-swapped dimers together with some preliminary evidence of its impact
on their physical and biological properties.Comment: v2: some new paragraphs and new abstrac
A Lattice Boltzmann Model of Binary Fluid Mixture
We introduce a lattice Boltzmann for simulating an immiscible binary fluid
mixture. Our collision rules are derived from a macroscopic thermodynamic
description of the fluid in a way motivated by the Cahn-Hilliard approach to
non-equilibrium dynamics. This ensures that a thermodynamically consistent
state is reached in equilibrium. The non-equilibrium dynamics is investigated
numerically and found to agree with simple analytic predictions in both the
one-phase and the two-phase region of the phase diagram.Comment: 12 pages + 4 eps figure
Exploring the correlation between the folding rates of proteins and the entanglement of their native states
The folding of a protein towards its native state is a rather complicated
process. However there are empirical evidences that the folding time correlates
with the contact order, a simple measure of the spatial organisation of the
native state of the protein. Contact order is related to the average length of
the main chain loops formed by amino acids which are in contact. Here we argue
that folding kinetics can be influenced also by the entanglement that loops may
undergo within the overall three dimensional protein structure. In order to
explore such possibility, we introduce a novel descriptor, which we call
"maximum intrachain contact entanglement". Specifically, we measure the maximum
Gaussian entanglement between any looped portion of a protein and any other
non-overlapping subchain of the same protein, which is easily computed by
discretized line integrals on the coordinates of the atoms. By
analyzing experimental data sets of two-state and multistate folders, we show
that also the new index is a good predictor of the folding rate. Moreover,
being only partially correlated with previous methods, it can be integrated
with them to yield more accurate predictions.Comment: 8 figures. v2: new titl
Zipping and collapse of diblock copolymers
Using exact enumeration methods and Monte Carlo simulations we study the
phase diagram relative to the conformational transitions of a two dimensional
diblock copolymer. The polymer is made of two homogeneous strands of monomers
of different species which are joined to each other at one end. We find that
depending on the values of the energy parameters in the model, there is either
a first order collapse from a swollen to a compact phase of spiral type, or a
continuous transition to an intermediate zipped phase followed by a first order
collapse at lower temperatures. Critical exponents of the zipping transition
are computed and their exact values are conjectured on the basis of a mapping
onto percolation geometry, thanks to recent results on path-crossing
probabilities.Comment: 12 pages, RevTeX and 14 PostScript figures include
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