Topological interactions between ring polymers: Implications for chromatin loops.

Loops Determine the Mechanical Properties of Mitotic Chromosomes

We introduce a new polymer model for mitotic chromosomes. The key assumption of the model is the ability of the chromatin fibre to cross-link to itself due to binding proteins. These protein-chromatin interactions are included by a probabilistic and dynamic mechanism. The hypothesis is motivated by the observation of high repulsive forces between ring polymers. We performed computer simulations...

Chromatin organization: from polymer loops to topological domains

Statistical and Dynamical Properties of Topological Polymers with Graphs and Ring Polymers with Knots

We review recent theoretical studies on the statistical and dynamical properties of polymers with nontrivial structures in chemical connectivity and those of polymers with a nontrivial topology, such as knotted ring polymers in solution. We call polymers with nontrivial structures in chemical connectivity expressed by graphs “topological polymers”. Graphs with no loop have only trivial topology...

Topological signatures of globular polymers.

Simulations in which a globular ring polymer with delocalized knots is separated in two interacting loops by a slipping link, or in two noninteracting globuli by a wall with a hole, show how the minimal crossing number of the knots controls the equilibrium statistics. With slipping link the ring length is divided between the loops according to a simple law, but with unexpectedly large fluctuati...

Expression-Dependent Folding of Interphase Chromatin

Multiple studies suggest that chromatin looping might play a crucial role in organizing eukaryotic genomes. To investigate the interplay between the conformation of interphase chromatin and its transcriptional activity, we include information from gene expression profiles into a polymer model for chromatin that incorporates genomic loops. By relating loop formation to transcriptional activity, ...