119 research outputs found
Facilitated diffusion of DNA-binding proteins
The diffusion-controlled limit of reaction times for site-specific
DNA-binding proteins is derived from first principles. We follow the generally
accepted concept that a protein propagates via two competitive modes, a
three-dimensional diffusion in space and a one-dimensional sliding along the
DNA. However, our theoretical treatment of the problem is new. The accuracy of
our analytical model is verified by numerical simulations. The results confirm
that the unspecific binding of protein to DNA, combined with sliding, is
capable to reduce the reaction times significantly.Comment: 4 pages, 2 figures Nov 22 2005 - accepted for PR
Multiscale entanglement in ring polymers under spherical confinement
The interplay of geometrical and topological entanglement in semiflexible
knotted polymer rings confined inside a spherical cavity is investigated using
advanced numerical methods. By using stringent and robust algorithms for
locating knots, we characterize how the knot length lk depends on the ring
contour length, Lc and the radius of the confining sphere, Rc . In the no- and
strong- confinement cases we observe weak knot localization and complete knot
delocalization, respectively. We show that the complex interplay of lk, Lc and
Rc that seamlessly bridges these two limits can be encompassed by a simple
scaling argument based on deflection theory. The same argument is used to
rationalize the multiscale character of the entanglement that emerges with
increasing confinement.Comment: 9 pages 9 figure
The two-angle model and the phase diagram for Chromatin
We have studied the phase diagram for chromatin within the framework of the
two-angle model. Rather than improving existing models with finer details our
main focus of the work is getting mathematically rigorous results on the
structure, especially on the excluded volume effects and the effects on the
energy due to the long-range forces and their screening. Thus we present a
phase diagram for the allowed conformations and the Coulomb energies
Scattering functions of knotted ring polymers
We discuss the scattering function of a Gaussian random polygon with N nodes
under a given topological constraint through simulation. We obtain the Kratky
plot of a Gaussian polygon of N=200 having a fixed knot for some different
knots such as the trivial, trefoil and figure-eight knots. We find that some
characteristic properties of the different Kratky plots are consistent with the
distinct values of the mean square radius of gyration for Gaussian polygons
with the different knots.Comment: 4pages, 3figures, 3table
Fluctuating semiflexible polymer ribbon constrained to a ring
Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer
bundle is captured by the elastic ribbon model. We investigate the effects a
ring geometry induces to a thermally fluctuating ribbon, finding bend-bend
coupling in addition to twist-bend coupling. Furthermore, due to the geometric
constraint the polymer's effective bending stiffness increases. A new parameter
for experimental investigations of polymer bundles is proposed: the mean square
diameter of a ribbonlike ring, which is determined analytically in the
semiflexible limit. Monte Carlo simulations are performed which affirm the
model's prediction up to high flexibility.Comment: 6 pages, 3 figures, Version as published in Eur. Phys. J.
Modeling Bacterial DNA: Simulation of Self-avoiding Supercoiled Worm-Like Chains Including Structural Transitions of the Helix
Under supercoiling constraints, naked DNA, such as a large part of bacterial
DNA, folds into braided structures called plectonemes. The double-helix can
also undergo local structural transitions, leading to the formation of
denaturation bubbles and other alternative structures. Various polymer models
have been developed to capture these properties, with Monte-Carlo (MC)
approaches dedicated to the inference of thermodynamic properties. In this
chapter, we explain how to perform such Monte-Carlo simulations, following two
objectives. On one hand, we present the self-avoiding supercoiled Worm-Like
Chain (ssWLC) model, which is known to capture the folding properties of
supercoiled DNA, and provide a detailed explanation of a standard MC simulation
method. On the other hand, we explain how to extend this ssWLC model to include
structural transitions of the helix.Comment: Book chapter to appear in The Bacterial Nucleoid, Methods and
Protocols, Springer serie
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
Characteristic length of random knotting for cylindrical self-avoiding polygons
We discuss the probability of random knotting for a model of self-avoiding
polygons whose segments are given by cylinders of unit length with radius .
We show numerically that the characteristic length of random knotting is
roughly approximated by an exponential function of the chain thickness .Comment: 5 pages, 4 figure
CRANKITE: a fast polypeptide backbone conformation sampler
Background: CRANKITE is a suite of programs for simulating backbone conformations of polypeptides and proteins. The core of the suite is an efficient Metropolis Monte Carlo sampler of backbone conformations in continuous three-dimensional space in atomic details.
Methods: In contrast to other programs relying on local Metropolis moves in the space of dihedral angles, our sampler utilizes local crankshaft rotations of rigid peptide bonds in Cartesian space.
Results: The sampler allows fast simulation and analysis of secondary structure formation and conformational changes for proteins of average length
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