Transcription dynamics stabilizes nucleus-like layer structure in chromatin brush

Elasticity control of entangled chromosomes: Crosstalk between condensin complexes and nucleosomes

Condensin-mediated loop extrusion is now considered as the main driving force of mitotic chromosome assembly. Recent experiments have shown, however, that a class of mutant condensin complexes deficient in loop extrusion can assemble chromosome-like structures in Xenopus egg extracts, although these structures are somewhat different from those assembled by wild-type condensin complexes. In the absence of topoisomerase II (topo II), the mutant condensin complexes produce an unusual round-shaped structure termed a bean, which consists of a DNA-dense central core surrounded by a DNA-sparse halo. The mutant condensin complexes accumulate in the core, whereas histones are more concentrated in the halo than in the core. We consider that this peculiar structure serves as a model system to study how DNA entanglements, nucleosomes, and condensin functionally crosstalk with each other. To gain insight into how the bean structure is formed, here we construct a theoretical model. Our theory predicts that the core is formed by attractive interactions between mutant condensin complexes, whereas the halo is stabilized by the energy reduction through the selective accumulation of nucleosomes. The formation of the halo increases the elastic free energy due to the DNA entanglement in the core, but the latter free energy is compensated by condensin complexes that suppress the assembly of nucleosomes.

Polymeric nature of tandemly repeated genes enhances assembly of constitutive heterochromatin in fission yeast

Motivated by our recent experiments that demonstrate that the tandemly repeated genes become heterochromatin, here we show a theory of heterochromatin assembly by taking into account the connectivity of these genes along the chromatin in the kinetic equations of small RNA production and histone methylation, which are the key biochemical reactions involved in the heterochromatin assembly. Our theory predicts that the polymeric nature of the tandemly repeated genes ensures the steady production of small RNAs because of the stable binding of nascent RNAs produced from the genes to RDRC/Dicers at the surface of nuclear membrane. This theory also predicts that the compaction of the tandemly repeated genes suppresses the production of small RNAs, consistent with our recent experiments. This theory can be extended to the small RNA-dependent gene silencing in higher organisms.

Polymer brush inspired by ribosomal RNA transcription

Pre-ribosomal RNAs are synthesized during the transcription by RNA polymerase I molecules localized at the surfaces of a nucleolus subcompartment. Inspired by the ribosomal RNA transcription, we here develop a scaling theory of a brush of polymers, where monomers are added to their grafted ends in the steady state. Our theory predicts that monomers newly added to the polymers stay at the vicinity of the surface due to the slow dynamics of the polymers and thus the polymer volume fraction increases with increasing the polymerization rate. The excluded volume interaction between polymers and reactant monomers suppresses the diffusion of reactant monomers and thus decreases the polymerization rate. The extent of the suppression of monomer diffusion increases with increasing the polymerization rate because the diffusion length decreases, rather than the condensation of polymers due to their slow dynamics.

Phase separation driven by production of architectural RNA transcripts

We here use an extension of the Flory-Huggins theory to predict that phase separation is driven by the production of architectural RNA (arcRNA) at a DNA locus with a constant rate. The arcRNA molecules diffuse in the nucleoplasm and show attractive interactions via proteins that are bound to the arcRNA. Our theory predicts that when the Flory interaction parameter is larger than the value at the critical point, the volume fraction of arcRNA jumps between the two values corresponding to the volume fraction of the two coexisting phases at equilibrium at a distance from the DNA locus due to the local equilibrium condition. The distance defines the radius of the condensate that is assembled by the phase separation. When the interaction parameter is large, the volume of the condensates is proportional to the production rate of arcRNA and inversely proportional to the degradation rate of arcRNA. These results imply that most arcRNA molecules are degraded before they diffuse out from the condensates due to the strong segregation of arcRNA.

Dilution of contact frequency between superenhancers by loop extrusion at interfaces

The loop extrusion theory predicts that cohesin acts as a molecular motor that extrudes chromatin fibers to produce loops. Hi-C experiments have detected relatively high contact frequencies between superenhancers. These probably result from the fact that superenhancers are localized at condensates of transcriptional activators and coactivators. The contact frequency between superenhancers is enhanced by auxin treatment that removes cohesin from chromatin. Motivated by these experimental results, we here treat chromatin at the surface of a condensate as a loop extruding polymer brush. Our theory predicts that the lateral pressure generated by the brush decreases with decreasing the loading rate of cohesin. This is because loop extrusion actively transfers chain segments at the vicinity of the interface. Our theory thus predicts that the increase of contact frequency by auxin treatment results from the fact that suppressing the loop extrusion process induces the dissolution of molecular components to the nucleoplasm, decreasing the average distance between superenhancers.

The biology and polymer physics underlying large-scale chromosome organization

Chromosome large-scale organization is a beautiful example of the interplay between physics and biology. DNA molecules are polymers and thus belong to the class of molecules for which physicists have developed models and formulated testable hypotheses to understand their arrangement and dynamic properties in solution, based on the principles of polymer physics. Biologists documented and discovered the biochemical basis for the structure, function and dynamic spatial organization of chromosomes in cells. The underlying principles of chromosome organization have recently been revealed in unprecedented detail using high-resolution chromosome capture technology that can simultaneously detect chromosome contact sites throughout the genome. These independent lines of investigation have now converged on a model in which DNA loops, generated by the loop extrusion mechanism, are the basic organizational and functional units of the chromosome.