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. We find that sufficiently long unknotted polymers differ from knotted ones in the spatial and topological states of their subchains. The unknotted globule has subchains that are mostly unknotted and form asymptotically compact $R_G(s) \sim s^{1/3}$ crumples. However, crumples display high fractal dimension of the surface $d_b = 2.8$, forming excessive contacts and interpenetrating each other. We conclude that this topologically constrained equilibrium state resembles a conjectured crumpled globule [Grosberg et al., Journal de Physique, 1988, 49, 2095], but differs from its idealized hierarchy of self-similar, isolated and compact crumples

Chromosomal Architecture Changes upon Cell Differentiation

Physic

Modeling chromosomes: Beyond pretty pictures

Recently, Chromosome Conformation Capture (3C) based experiments have highlighted the importance of computational models for the study of chromosome organization. In this review, we propose that current computational models can be grouped into roughly four classes, with two classes of data-driven models: consensus structures and data-driven ensembles, and two classes of de novo models: structural ensembles and mechanistic ensembles. Finally, we highlight specific questions mechanistic ensembles can address.National Institutes of Health (U.S.) (Grant R01HG003143)National Institutes of Health (U.S.) (Grant R01 GM114190

Chromatin Loops as Allosteric Modulators of Enhancer-Promoter Interactions

The classic model of eukaryotic gene expression requires direct spatial contact between a distal enhancer and a proximal promoter. Recent Chromosome Conformation Capture (3C) studies show that enhancers and promoters are embedded in a complex network of looping interactions. Here we use a polymer model of chromatin fiber to investigate whether, and to what extent, looping interactions between elements in the vicinity of an enhancer-promoter pair can influence their contact frequency. Our equilibrium polymer simulations show that a chromatin loop, formed by elements flanking either an enhancer or a promoter, suppresses enhancer-promoter interactions, working as an insulator. A loop formed by elements located in the region between an enhancer and a promoter, on the contrary, facilitates their interactions. We find that different mechanisms underlie insulation and facilitation; insulation occurs due to steric exclusion by the loop, and is a global effect, while facilitation occurs due to an effective shortening of the enhancer-promoter genomic distance, and is a local effect. Consistently, we find that these effects manifest quite differently for in silico 3C and microscopy. Our results show that looping interactions that do not directly involve an enhancer-promoter pair can nevertheless significantly modulate their interactions. This phenomenon is analogous to allosteric regulation in proteins, where a conformational change triggered by binding of a regulatory molecule to one site affects the state of another site

Polymer Models of Topological Insulators

Physic

Chromatin organization by an interplay of loop extrusion and compartmental segregation

Mammalian chromatin is spatially organized at many scales showing two prominent features in interphase: (i) alternating regions (1–10 Mb) of active and inactive chromatin that spatially segregate into different compartments, and (II) domains (<1 Mb), that is, regions that preferentially interact internally [topologically associating domains (TADs)] and are central to gene regulation. There is growing evidence that TADs are formed by active extrusion of chromatin loops by cohesin, whereas compartmentalization is established according to local chromatin states. Here, we use polymer simulations to examine how loop extrusion and compartmental segregation work collectively and potentially interfere in shaping global chromosome organization. A model with differential attraction between euchromatin and heterochromatin leads to phase separation and reproduces compartmentalization as observed in Hi-C. Loop extrusion, essential for TAD formation, in turn, interferes with compartmentalization. Our integrated model faithfully reproduces Hi-C data from puzzling experimental observations where altering loop extrusion also led to changes in compartmentalization. Specifically, depletion of chromatin-associated cohesin reduced TADs and revealed finer compartments, while increased processivity of cohesin strengthened large TADs and reduced compartmentalization; and depletion of the TAD boundary protein CTCF weakened TADs while leaving compartments unaffected. We reveal that these experimental perturbations are special cases of a general polymer phenomenon of active mixing by loop extrusion. Our results suggest that chromatin organization on the megabase scale emerges from competition of nonequilibrium active loop extrusion and epigenetically defined compartment structure. Keywords: chromatin; genome architecture; Hi-C; polymer physics; active matterNational Science Foundation (U.S.) (Grant 1504942

Polymer Models of Yeast S. cerevisiae Genome Organization

Physic

S cerevisiae Genome as a Confined Equilibrium Polymer Brush

Physic

Organization of the Mitotic Chromosome

Mitotic chromosomes are among the most recognizable structures in the cell, yet for over a century their internal organization remains largely unsolved. We applied chromosome conformation capture methods, 5C and Hi-C, across the cell cycle and revealed two alternative three-dimensional folding states of the human genome. We show that the highly compartmentalized and cell-type-specific organization described previously for non-synchronous cells is restricted to interphase. In metaphase, we identify a homogenous folding state, which is locus-independent, common to all chromosomes, and consistent among cell types, suggesting a general principle of metaphase chromosome organization. Using polymer simulations, we find that metaphase Hi-C data are inconsistent with classic hierarchical models, and is instead best described by a linearly-organized longitudinally compressed array of consecutive chromatin loops.National Cancer Institute (U.S.) (Grant U54CA143874

Iterative Correction of Hi-C Data Reveals Hallmarks of Chromosome Organization

Extracting biologically meaningful information from chromosomal interactions obtained with genome-wide chromosome conformation capture (3C) analyses requires elimination of systematic biases. We present a pipeline that integrates a strategy for mapping of sequencing reads and a data-driven method for iterative correction of biases, yielding genome-wide maps of relative contact probabilities. We validate ICE (Iterative Correction and Eigenvector decomposition) on published Hi-C data, and demonstrate that eigenvector decomposition of the obtained maps provides insights into local chromatin states, global patterns of chromosomal interactions, and the conserved organization of human and mouse chromosomes