Stretching of a Fractal Polymer around a Disc Reveals Kardar-Parisi-Zhang Scaling.

While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting open question. We use scaling analysis and computer simulations to examine stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius R. We reveal that the typical excursions of the polymer away from the surface and curvature-induced correlation length scale as Δ∼R^{β} and S^{*}∼R^{1/z}, respectively, with the Kardar-Parisi-Zhang (KPZ) growth β=1/3 and dynamic exponents z=3/2.

On predicting regulatory genes by analysis of functional networks in C. elegans.

Background: Connectivity networks, which reflect multiple interactions between genes and proteins, possess not only a descriptive but also a predictive value, as new connections can be extrapolated and tested by means of computational analysis. Integration of different types of connectivity data (such as co-expression and genetic interactions) in one network has proven to benefit 'guilt by association' analysis. However predictive values of connectives of different types, that had their specific functional meaning and topological characteristics were not obvious, and have been addressed in this analysis.

A statistical model of intra-chromosome contact maps.

A statistical model describing a fine structure of the intra-chromosome maps obtained by a genome-wide chromosome conformation capture method (Hi-C) is proposed. The model combines hierarchical chain folding with a quenched heteropolymer structure of primary chromatin sequences. It is conjectured that the observed Hi-C maps are statistical averages over many different ways of hierarchical genome folding.

Effects of topological constraints on globular polymers.

Topological constraints can affect both equilibrium and dynamic properties of polymer systems and can play a role in the organization of chromosomes. Despite many theoretical studies, the effects of topological constraints on the equilibrium state of a single compact polymer have not been systematically studied. Here we use simulations to address this longstanding problem.

Fractal globules: a new approach to artificial molecular machines.

The over-damped relaxation of elastic networks constructed by contact maps of hierarchically folded fractal (crumpled) polymer globules was investigated in detail. It was found that the relaxation dynamics of an anisotropic fractal globule is very similar to the behavior of biological molecular machines like motor proteins. When it is perturbed, the system quickly relaxes to a low-dimensional manifold, M, with a large basin of attraction and then slowly approaches equilibrium, not escaping M.

Phase transition in random planar diagrams and RNA-type matching.

We study the planar matching problem, defined by a symmetric random matrix with independent identically distributed entries, taking values zero and one. We show that the existence of a perfect planar matching structure is possible only above a certain critical density, p(c), of allowed contacts (i.e.