Loops determine the mechanical properties of mitotic chromosomes

Steric repulsion introduced by loop constraints modulates the microphase separation of chromatins

Within the confines of a densely populated cell nucleus, chromatin undergoes intricate folding, forming loops, domains, and compartments under the governance of topological constraints and phase separation. This coordinated process inevitably introduces interference between different folding strategies. In this study, we model interphase chromatins as block copolymers with hetero-hierarchical loops within a confined system. Employing dissipative particle dynamics simulations and scaling analysis, we aim to explain how the structure and distribution of loop domains modulate the microphase separation of chromatins. Our results highlight the correlation between the microphase separation of the copolymer and the length, heterogeneity, and hierarchically nested levels of the loop domains. This correlation arises from steric repulsion intrinsic to loop domains. The steric repulsion induces variations in chain stiffness (including local orientation correlations and the persistence length), thereby influencing the degree of phase separation. Through simulations of block copolymers with distinct groups of hetero-hierarchical loop anchors, we successfully reproduce changes in phase separation across diverse cell lines, under fixed interaction parameters. These findings, in qualitative alignment with Hi-C data, suggest that the variations of loop constraints alone possess the capacity to regulate higher-order structures and the gene expressions of interphase chromatins.

Structural reorganization and relaxation dynamics of axially stressed chromosomes

Chromosomes endure mechanical stresses throughout the cell cycle; for example, resulting from the pulling of chromosomes by spindle fibers during mitosis or deformation of the nucleus during cell migration. The response to physical stress is closely related to chromosome structure and function. Micromechanical studies of mitotic chromosomes have revealed them to be remarkably extensible objects and informed early models of mitotic chromosome organization. We use a data-driven, coarse-grained polymer modeling approach to explore the relationship between the spatial organization of individual chromosomes and their emergent mechanical properties. In particular, we investigate the mechanical properties of our model chromosomes by axially stretching them. Simulated stretching led to a linear force-extension curve for small strain, with mitotic chromosomes behaving about 10-fold stiffer than interphase chromosomes. Studying their relaxation dynamics, we found that chromosomes are viscoelastic solids with a highly liquid-like, viscous behavior in interphase that becomes solid-like in mitosis. This emergent mechanical stiffness originates from lengthwise compaction, an effective potential capturing the activity of loop-extruding SMC complexes. Chromosomes denature under large strains via unraveling, which is characterized by opening of large-scale folding patterns. By quantifying the effect of mechanical perturbations on the chromosome's structural features, our model provides a nuanced understanding of in vivo mechanics of chromosomes.

Lattice simulation-based diffusion modelling of 3D chromatin structure

Eukaryotic nuclear genome is extensively folded in the nuclei, and the chromatin structure experiences dramatic changes, i.e., condensation and decondensation, during the cell cycle. However, a model to persuasively explain the preserved chromatin interactions during cell cycle remains lacking. In this paper, we developed two simple, lattice-based models that mimic polymer fiber decondensation from initial fractal or anisotropic condensed status, using Markov Chain Monte Carlo (MCMC) methods. By simulating the dynamic decondensation process, we observed about 8.17% and 2.03% of the interactions preserved in the condensation to decondensation transition, in the fractal diffusion and anisotropic diffusion models, respectively. Intriguingly, although interaction hubs, as a physical locus where a certain number of monomers inter-connected, were observed in diffused polymer models in both simulations, they were not associated with the preserved interactions. Our simulation demonstrated that there might exist a small portion of chromatin interactions that preserved during the diffusion process of polymers, while the interacted hubs were more dynamically formed and additional regulatory factors were needed for their preservation.

The mechanics of mitotic chromosomes

Condensation and faithful separation of the genome are crucial for the cellular life cycle. During chromosome segregation, mechanical forces generated by the mitotic spindle pull apart the sister chromatids. The mechanical nature of this process has motivated a lot of research interest into the mechanical properties of mitotic chromosomes. Although their fundamental mechanical characteristics are known, it still remains unclear how these characteristics emerge from the structure of the mitotic chromosome. Recent advances in genomics, computational and super-resolution microscopy techniques have greatly promoted our understanding of the chromosomal structure and have motivated us to review the mechanical characteristics of chromosomes in light of the current structural insights. In this review, we will first introduce the current understanding of the chromosomal structure, before reviewing characteristic mechanical properties such as the Young's modulus and the bending modulus of mitotic chromosomes. Then we will address the approaches used to relate mechanical properties to the structure of chromosomes and we will also discuss how mechanical characterization can aid in elucidating their structure. Finally, future challenges, recent developments and emergent questions in this research field will be discussed.

Many facades of CTCF unified by its coding for three-dimensional genome architecture

CCCTC-binding factor (CTCF) is a multifunctional zinc finger protein that is conserved in metazoan species. CTCF is consistently found to play an important role in many diverse biological processes. CTCF/cohesin-mediated active chromatin 'loop extrusion' architects three-dimensional (3D) genome folding. The 3D architectural role of CTCF underlies its multifarious functions, including developmental regulation of gene expression, protocadherin (Pcdh) promoter choice in the nervous system, immunoglobulin (Ig) and T-cell receptor (Tcr) V(D)J recombination in the immune system, homeobox (Hox) gene control during limb development, as well as many other aspects of biology. Here, we review the pleiotropic functions of CTCF from the perspective of its essential role in 3D genome architecture and topological promoter/enhancer selection. We envision the 3D genome as an enormous complex architecture, with tens of thousands of CTCF sites as connecting nodes and CTCF proteins as mysterious bonds that glue together genomic building parts with distinct articulation joints. In particular, we focus on the internal mechanisms by which CTCF controls higher order chromatin structures that manifest its many façades of physiological and pathological functions. We also discuss the dichotomic role of CTCF sites as intriguing 3D genome nodes for seemingly contradictory 'looping bridges' and 'topological insulators' to frame a beautiful magnificent house for a cell's nuclear home.

Loop extrusion: theory meets single-molecule experiments

Chromosomes are organized as chromatin loops that promote segregation, enhancer-promoter interactions, and other genomic functions. Loops were hypothesized to form by 'loop extrusion,' by which structural maintenance of chromosomes (SMC) complexes, such as condensin and cohesin, bind to chromatin, reel it in, and extrude it as a loop. However, such exotic motor activity had never been observed. Following an explosion of indirect evidence, recent single-molecule experiments directly imaged DNA loop extrusion by condensin and cohesin in vitro. These experiments observe rapid (kb/s) extrusion that requires ATP hydrolysis and stalls under pN forces. Surprisingly, condensin extrudes loops asymmetrically, challenging previous models. Extrusion by cohesin is symmetric but requires the protein Nipbl. We discuss how SMC complexes may perform their functions on chromatin in vivo.

Polymer models for the mechanisms of chromatin 3D folding: review and perspective

In this perspective paper, classical physical models for mammalian interphase chromatin folding are reviewed.

Heterogeneous Loop Model to Infer 3D Chromosome Structures from Hi-C

Adapting a well-established formalism in polymer physics, we develop a minimalist approach to infer three-dimensional folding of chromatin from Hi-C data. The three-dimensional chromosome structures generated from our heterogeneous loop model (HLM) are used to visualize chromosome organizations that can substantiate the measurements from fluorescence in situ hybridization, chromatin interaction analysis by paired-end tag sequencing, and RNA-seq signals. We demonstrate the utility of the HLM with several case studies. Specifically, the HLM-generated chromosome structures, which reproduce the spatial distribution of topologically associated domains from fluorescence in situ hybridization measurement, show the phase segregation between two types of topologically associated domains explicitly. We discuss the origin of cell-type-dependent gene-expression level by modeling the chromatin globules of α-globin and SOX2 gene loci for two different cell lines. We also use the HLM to discuss how the chromatin folding and gene-expression level of Pax6 loci, associated with mouse neural development, are modulated by interactions with two enhancers. Finally, HLM-generated structures of chromosome 19 of mouse embryonic stem cells, based on single-cell Hi-C data collected over each cell-cycle phase, visualize changes in chromosome conformation along the cell-cycle. Given a contact frequency map between chromatic loci supplied from Hi-C, HLM is a computationally efficient and versatile modeling tool to generate chromosome structures that can complement interpreting other experimental data.

Chromosome Compaction by Active Loop Extrusion

During cell division, chromosomes are compacted in length by more than a 100-fold. A wide range of experiments demonstrated that in their compacted state, mammalian chromosomes form arrays of closely stacked consecutive ∼100 kb loops. The mechanism underlying the active process of chromosome compaction into a stack of loops is unknown. Here we test the hypothesis that chromosomes are compacted by enzymatic machines that actively extrude chromatin loops. When such loop-extruding factors (LEF) bind to chromosomes, they progressively bridge sites that are further away along the chromosome, thus extruding a loop. We demonstrate that collective action of LEFs leads to formation of a dynamic array of consecutive loops. Simulations and an analytically solved model identify two distinct steady states: a sparse state, where loops are highly dynamic but provide little compaction; and a dense state, where there are more stable loops and dramatic chromosome compaction. We find that human chromosomes operate at the border of the dense steady state. Our analysis also shows how the macroscopic characteristics of the loop array are determined by the microscopic properties of LEFs and their abundance. When the number of LEFs are used that match experimentally based estimates, the model can quantitatively reproduce the average loop length, the degree of compaction, and the general loop-array morphology of compact human chromosomes. Our study demonstrates that efficient chromosome compaction can be achieved solely by an active loop-extrusion process.

Compaction and segregation of sister chromatids via active loop extrusion

The mechanism by which chromatids and chromosomes are segregated during mitosis and meiosis is a major puzzle of biology and biophysics. Using polymer simulations of chromosome dynamics, we show that a single mechanism of loop extrusion by condensins can robustly compact, segregate and disentangle chromosomes, arriving at individualized chromatids with morphology observed in vivo. Our model resolves the paradox of topological simplification concomitant with chromosome 'condensation', and explains how enzymes a few nanometers in size are able to control chromosome geometry and topology at micron length scales. We suggest that loop extrusion is a universal mechanism of genome folding that mediates functional interactions during interphase and compacts chromosomes during mitosis.

Pulled Polymer Loops as a Model for the Alignment of Meiotic Chromosomes

During recombination, the DNA of parents exchange their genetic information to give rise to a genetically unique offspring. For recombination to occur, homologous chromosomes need to find each other and align with high precision. Fission yeast solves this problem by folding chromosomes in loops and pulling them through the viscous nucleoplasm. We propose a theory of pulled polymer loops to quantify the effect of drag forces on the alignment of chromosomes. We introduce an external force field to the concept of a Brownian bridge and thus solve for the statistics of loop configurations in space.

A simple biophysical model emulates budding yeast chromosome condensation

Mitotic chromosomes were one of the first cell biological structures to be described, yet their molecular architecture remains poorly understood. We have devised a simple biophysical model of a 300 kb-long nucleosome chain, the size of a budding yeast chromosome, constrained by interactions between binding sites of the chromosomal condensin complex, a key component of interphase and mitotic chromosomes. Comparisons of computational and experimental (4C) interaction maps, and other biophysical features, allow us to predict a mode of condensin action. Stochastic condensin-mediated pairwise interactions along the nucleosome chain generate native-like chromosome features and recapitulate chromosome compaction and individualization during mitotic condensation. Higher order interactions between condensin binding sites explain the data less well. Our results suggest that basic assumptions about chromatin behavior go a long way to explain chromosome architecture and are able to generate a molecular model of what the inside of a chromosome is likely to look like.

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 distinct three-dimensional folding states of the human genome. We show that the highly compartmentalized and cell type-specific organization described previously for nonsynchronous cells is restricted to interphase. In metaphase, we identified a homogenous folding state that is locus-independent, common to all chromosomes, and consistent among cell types, suggesting a general principle of metaphase chromosome organization. Using polymer simulations, we found that metaphase Hi-C data are inconsistent with classic hierarchical models and are instead best described by a linearly organized longitudinally compressed array of consecutive chromatin loops.

Topological constraints and chromosome organization in eukaryotes: a physical point of view

New experimental tools capable of probing the three-dimensional organization of eukaryotic genomes with an unprecedented level of detail have been developed in the last few years. In the quest for a quantitative understanding of experimental results, several polymer models for chromatin organization were introduced and critically evaluated. In the present article, I give a brief introduction to the physical basis of chromosome organization, and recall the experimental evidence in favour of the importance of topological constraints for the description of chromosome conformations in eukaryotes.

Zinc finger proteins and the 3D organization of chromosomes

Zinc finger domains are one of the most common structural motifs in eukaryotic cells, which employ the motif in some of their most important proteins (including TFIIIA, CTCF, and ZiF268). These DNA binding proteins contain up to 37 zinc finger domains connected by flexible linker regions. They have been shown to be important organizers of the 3D structure of chromosomes and as such are called the master weaver of the genome. Using NMR and numerical simulations, much progress has been made during the past few decades in understanding their various functions and their ways of binding to the DNA, but a large knowledge gap remains to be filled. One problem of the hitherto existing theoretical models of zinc finger protein DNA binding in this context is that they are aimed at describing specific binding. Furthermore, they exclusively focus on the microscopic details or approach the problem without considering such details at all. We present the Flexible Linker Model, which aims explicitly at describing nonspecific binding. It takes into account the most important effects of flexible linkers and allows a qualitative investigation of the effects of these linkers on the nonspecific binding affinity of zinc finger proteins to DNA. Our results indicate that the binding affinity is increased by the flexible linkers by several orders of magnitude. Moreover, they show that the binding map for proteins with more than one domain presents interesting structures, which have been neither observed nor described before, and can be interpreted to fit very well with existing theories of facilitated target location. The effect of the increased binding affinity is also in agreement with recent experiments that until now have lacked an explanation. We further explore the class of proteins with flexible linkers, which are unstructured until they bind. We have developed a methodology to characterize these flexible proteins. Employing the concept of barcodes, we propose a measure to compare such flexible proteins in terms of a similarity measure. This measure is validated by a comparison between a geometric similarity measure and the topological similarity measure that takes geometry as well as topology into account.

Structure of metaphase chromosomes: a role for effects of macromolecular crowding

In metaphase chromosomes, chromatin is compacted to a concentration of several hundred mg/ml by mechanisms which remain elusive. Effects mediated by the ionic environment are considered most frequently because mono- and di-valent cations cause polynucleosome chains to form compact ~30-nm diameter fibres in vitro, but this conformation is not detected in chromosomes in situ. A further unconsidered factor is predicted to influence the compaction of chromosomes, namely the forces which arise from crowding by macromolecules in the surrounding cytoplasm whose measured concentration is 100-200 mg/ml. To mimic these conditions, chromosomes were released from mitotic CHO cells in solutions containing an inert volume-occupying macromolecule (8 kDa polyethylene glycol, 10.5 kDa dextran, or 70 kDa Ficoll) in 100 µM K-Hepes buffer, with contaminating cations at only low micromolar concentrations. Optical and electron microscopy showed that these chromosomes conserved their characteristic structure and compaction, and their volume varied inversely with the concentration of a crowding macromolecule. They showed a canonical nucleosomal structure and contained the characteristic proteins topoisomerase IIα and the condensin subunit SMC2. These observations, together with evidence that the cytoplasm is crowded in vivo, suggest that macromolecular crowding effects should be considered a significant and perhaps major factor in compacting chromosomes. This model may explain why ~30-nm fibres characteristic of cation-mediated compaction are not seen in chromosomes in situ. Considering that crowding by cytoplasmic macromolecules maintains the compaction of bacterial chromosomes and has been proposed to form the liquid crystalline chromosomes of dinoflagellates, a crowded environment may be an essential characteristic of all genomes.