Modeling of chromosome intermingling by partially overlapping uniform random polygons

State Transitions and Crystalline Structures of Single Polyethylene Rings: MD Simulations

This study investigates the structural changes of cyclic polyethylene (PE) single chains during cooling through molecular dynamics simulations. The influence of topological constraint on a ring is examined by comparing it with the results of its linear counterpart. A pseudo phase diagram of state transition for PE rings based on length and temperature is constructed, revealing a consistent chain-folding transition during cooling. The shape anisotropy of short crystallized cyclic chains exhibits oscillations with chain length, leading to a more pronounced odd-even effect in single cyclic chains compared with the linear ones. A honeycomb model is proposed to elucidate the odd-even effect of chain folding in crystalline structures of single linear and cyclic chains, and we discuss its potential to predict surface tension. Analyses of the tight folding model and the re-entry modes demonstrate that a cyclic chain possesses a shorter average crystalline stem length and a more compact folded structure than its linear counterpart. The findings highlight the impact of topological change on crystallization and the odd-even effect of chain length, providing valuable insights for understanding polymer crystallization with different topologies.

Conformation and dynamics of ring polymers under symmetric thin film confinement

Understanding the structure and dynamics of polymers under confinement has been of widespread interest, and one class of polymers that have received comparatively little attention under confinement is that of ring polymers. The properties of non-concatenated ring polymers can also be important in biological fields because ring polymers have been proven to be a good model to study DNA organization in the cell nucleus. From our previous study, linear polymers in a cylindrically confined polymer melt were found to segregate from each other as a result of the strong correlation hole effect that is enhanced by the confining surfaces. By comparison, our subsequent study of linear polymers in confined thin films at similar levels of confinements found only the onset of segregation. In this study, we use molecular dynamics simulation to investigate the chain conformations and dynamics of ring polymers under planar (1D) confinement as a function of film thickness. Our results show that conformations of ring polymers are similar to the linear polymers under planar confinement, except that ring polymers are less compressed in the direction normal to the walls. While we find that the correlation hole effect is enhanced under confinement, it is not as pronounced as the linear polymers under 2D confinement. Finally, we show that chain dynamics far above Tg are primarily affected by the friction from walls based on the monomeric friction coefficient we get from the Rouse mode analysis.

The Rabl configuration limits topological entanglement of chromosomes in budding yeast

The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers.

Interchromosomal interactions: A genomic love story of kissing chromosomes

Nuclei require a precise three- and four-dimensional organization of DNA to establish cell-specific gene-expression programs. Underscoring the importance of DNA topology, alterations to the nuclear architecture can perturb gene expression and result in disease states. More recently, it has become clear that not only intrachromosomal interactions, but also interchromosomal interactions, a less studied feature of chromosomes, are required for proper physiological gene-expression programs. Here, we review recent studies with emerging insights into where and why cross-chromosomal communication is relevant. Specifically, we discuss how long noncoding RNAs (lncRNAs) and three-dimensional gene positioning are involved in genome organization and how low-throughput (live-cell imaging) and high-throughput (Hi-C and SPRITE) techniques contribute to understand the fundamental properties of interchromosomal interactions.

Inter-chromosomal Contact Properties in Live-Cell Imaging and in Hi-C

Imaging (fluorescence in situ hybridization [FISH]) and genome-wide chromosome conformation capture (Hi-C) are two major approaches to the study of higher-order genome organization in the nucleus. Intra-chromosomal and inter-chromosomal interactions (referred to as non-homologous chromosomal contacts [NHCCs]) have been observed by several FISH-based studies, but locus-specific NHCCs have not been detected by Hi-C. Due to crosslinking, neither of these approaches assesses spatiotemporal properties. Toward resolving the discrepancies between imaging and Hi-C, we sought to understand the spatiotemporal properties of NHCCs in living cells by CRISPR/Cas9 live-cell imaging (CLING). In mammalian cells, we find that NHCCs are stable and occur as frequently as intra-chromosomal interactions, but NHCCs occur at farther spatial distance that could explain their lack of detection in Hi-C. By revealing the spatiotemporal properties in living cells, our study provides fundamental insights into the biology of NHCCs.

Systems-level chromosomal parameters represent a suprachromosomal basis for the non-random chromosomal arrangement in human interphase nuclei

Forty-six chromosome territories (CTs) are positioned uniquely in human interphase nuclei, wherein each of their positions can range from the centre of the nucleus to its periphery. A non-empirical basis for their non-random arrangement remains unreported. Here, we derive a suprachromosomal basis of that overall arrangement (which we refer to as a CT constellation), and report a hierarchical nature of the same. Using matrix algebra, we unify intrinsic chromosomal parameters (e.g., chromosomal length, gene density, the number of genes per chromosome), to derive an extrinsic effective gene density matrix, the hierarchy of which is dominated largely by extrinsic mathematical coupling of HSA19, followed by HSA17 (human chromosome 19 and 17, both preferentially interior CTs) with all CTs. We corroborate predicted constellations and effective gene density hierarchy with published reports from fluorescent in situ hybridization based microscopy and Hi-C techniques, and delineate analogous hierarchy in disparate vertebrates. Our theory accurately predicts CTs localised to the nuclear interior, which interestingly share conserved synteny with HSA19 and/or HSA17. Finally, the effective gene density hierarchy dictates how permutations among CT position represents the plasticity within its constellations, based on which we suggest that a differential mix of coding with noncoding genome modulates the same.

Current theoretical models fail to predict the topological complexity of the human genome

Understanding the folding of the human genome is a key challenge of modern structural biology. The emergence of chromatin conformation capture assays (e.g., Hi-C) has revolutionized chromosome biology and provided new insights into the three dimensional structure of the genome. The experimental data are highly complex and need to be analyzed with quantitative tools. It has been argued that the data obtained from Hi-C assays are consistent with a fractal organization of the genome. A key characteristic of the fractal globule is the lack of topological complexity (knotting or inter-linking). However, the absence of topological complexity contradicts results from polymer physics showing that the entanglement of long linear polymers in a confined volume increases rapidly with the length and with decreasing volume. In vivo and in vitro assays support this claim in some biological systems. We simulate knotted lattice polygons confined inside a sphere and demonstrate that their contact frequencies agree with the human Hi-C data. We conclude that the topological complexity of the human genome cannot be inferred from current Hi-C data.

From a melt of rings to chromosome territories: the role of topological constraints in genome folding

We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both.