Session Q38: Genome Organization & Subnuclear Phenomena I: Organizational Principles

The three-dimensional architecture of the human genome: understanding the physical mechanisms controlling gene expression

In vivo, the human genome folds into a characteristic ensemble of 3D structures. The mechanism driving the folding process remains unknown. A theoretical model for chromatin (the minimal chromatin model) explains the folding of interphase chromosomes and generates chromosome conformations consistent with experimental data is presented. The energy landscape of the model was derived by using the maximum entropy principle and relies on two experimentally derived inputs: a classification of loci into chromatin types and a catalog of the positions of chromatin loops. This model was generalized by utilizing a neural network to infer these chromatin types using epigenetic marks present at a locus, as assayed by ChIP-Seq. The ensemble of structures resulting from these simulations completely agree with HI-C data and exhibits unknotted chromosomes, phase separation of chromatin types, and a tendency for open chromatin to lie at the periphery of chromosome territories. Although this theoretical methodology was trained in one cell line, the human GM12878 lymphoblastoid cells, it has successfully predicted the structural ensembles of multiple human cell lines. Finally, going beyond Hi-C, our predicted structures are also consistent with microscopy measurements. Analysis of both structures from simulation and microscopy reveals that short segments of chromatin make two-state transitions between closed conformations and open dumbbell conformations. For gene active segments, the vast majority of genes appear clustered in the linker region of the chromatin segment, allowing us to speculate possible mechanisms by which chromatin structure and dynamics may be involved in controlling gene expression.

* Supported by the NSF

 

    

Machine learning-based parametrization of a chromatin polymer model

The physical organization of the genome in three-dimensional space regulates many biological processes, including gene expression and cell differentiation. In order to fully understand the complexity of these processes, sophisticated computational models of chromatin structure will be essential. Given an experimental Hi-C contact map, we seek to estimate the interaction parameters of a polymer model such that the polymer model reproduces the underlying chromatin structure. We show that a graph neural network (GNN) can learn a mapping from an experimental contact map to a set of interaction parameters that is empirically competitive with parameters estimated using traditional methods but can be computed an order of magnitude faster. We develop an approach to train the GNN using exclusively simulated data from the polymer model, avoiding the need for large quantities of experimental data. We demonstrate that our approach generalizes across experimental cell lines and is robust to the range of sequencing read depths seen in bulk Hi-C data. We anticipate our method to be particularly useful in the single-cell setting, as single-cell Hi-C variants can generate tens of thousands of contact maps.   

From Effective Interactions Extracted Using Hi-C Data to Chromosome Structures in Conventional and Inverted Nuclei

Contact probabilities between loci, separated by arbitrary genomic distance, for a number of cell types have been reported using genome-wide chromosome conformation capture (Hi-C) experiments. How to extract the effective interaction energies between active euchromatin (A) and inactive heterochromatin (B) directly from the experimental data, without an underlying polymer model, is unsolved. Here, we first calculate the pairwise effective interaction energies (A-A, B-B, or A-B) for interphase chromosomes based on Hi-C data by using the concept of statistical potential (SP), which assumes that the interaction energy between two loci is proportional to the logarithm of the frequency with which they interact. Polymer simulations, using the extracted interaction energy values without any parameters, reproduce the segregation between A and B type loci (compartments), and the emergence of topologically associating domains, features that are prominent in the Hi-C data for interphase chromosomes. Remarkably, the values of the SP automatically satisfy the Flory-Huggins phase separation criterion for all the chromosomes, which explains the mechanism of compartment formation in interphase chromosomes. Strikingly, simulations using the SP that accounts for pericentromeric constitutive heterochromatin (C-type) show hierarchical structuring with the high density of C-type loci in the nuclear center, followed by localization of the B-type loci, with euchromatin being confined to the nuclear periphery, which differs from the expected nuclear organization of conventional interphase chromosomes, but is in accord with imaging data. Such an unusual organization of chromosomes is found in the inverted nuclei of photoreceptor rods in nocturnal mammals. The proposed method without free parameters and its applications show that compartment formation in conventional and inverted nuclei is best explained by the inequality between the effective interaction energies, with heterochromatin attraction being the dominant driving force.   

Illuminating the link between nuclear geometry and chromatin structure dynamics through 4D nucleus modeling

Eukaryotic nucleus confines nearly meter-long polymeric chromatin folding chains within its micron-sized membrane bounds while remaining dynamic and accessible for gene regulation. The chromatin structures in the nucleus form through microphase separation of epigenetically decorated chromatin types. The 3D structures and dynamical aspects of chromatin is believed to be strongly coupled with genetic processes. Investigating the principles underlying the nuclear architectures and dynamics could pave the way to identifying the relationship between chromatin structures, gene expression, and regulation machinery. The chromatin capture and imaging techniques have revealed a much more dynamic and stochastic nature of chromatin structures which is reminiscent of multiphase fluid behavior. The recent findings show that the nuclear geometry and presence of membrane-bound lamina globally shapes nuclear architectures and dynamical aspects of chromatin organization. The link between nuclear geometry and the dynamics of phase-separated chromatin domains is imperative to be considered for revealing features of the nucleus and its biological functions. Here, we present a mesoscale liquid model of the nucleus called MELON-4D, which describes the state of the nucleus as a mixture of incompressible multiphase liquid-like chromatin types. Our model disentangles the complex interplay of nuclear geometry and driving forces that contribute to the emergent patterns of chromatin organization and dynamics. Our results indicate that the liquid-liquid phase separation, together with surface tension effects, are sufficient to recapitulate much of the structural and dynamical aspects of nuclear chromatin architectures along the life cycle of cells. We also shed light on the dynamical heterogeneity and coherent motions of chromatin compartments which are fully captured by an interplay of micro-phase separation of chromatin types and lamina binding.   

Data-Driven Simulation of Chromatin Structure and the Epigenetic Code

The interplay between epigenetic marks and chromatin structure is increasingly appreciated as crucial to biological function. However, the full features of chromatin organization in three dimensoins are not fully understood and are actively being investigated in both theory and experiment. Here we present a chromosome scale model to study the relationship between one-dimensional epigenetic sequences and three-dimensional chromatin structure. The sequence-structure relationship presents some similarities to conventional block copolymers, as described by previous models, but also departs from a purely synthetic polymer due to the overlapping and interacting nature of epigenetic marks and machinery. Understanding these unique features of the epigenetic code will be crutial to future diagnostic and therapeudic efforts to modulate chromatin organization by way of targeted epigenetic engineering.   

A wave pinning model for spread of chromosomal inactivation

X chromosome inactivation (XCI) is a crucial process essential for achieving dosage compensation of X-linked genes in females. During XCI, most genes in the X chromosome are inactivated in a progressive manner following the transcription of the X-linked long noncoding RNA XIST. Recent experiments with transgenes showed that the spread of chromosomal inactivation can be restricted in autosomes even in the presence of XIST synthesis in cis, but the mechanism of controlling the spread remains unclear. In this work, we formulated a wave pinning model that elucidates chromosomal inactivation through a bistable reaction-diffusion system. In addition, we have developed an approach for integrating the discrete three-dimensional spatial arrangement of the X chromosome and autosomes into a continuous reaction-diffusion model. This method enables the investigation of spatiotemporal dynamics pertaining to the inactivation of the X chromosome and autosomes with varying degrees for spread of inactivation.   

Activity-driven chromatin organization during interphase: compaction, segregation, and overlap suppression

In mammalian cells, the cohesin protein complex is believed to translocate along chromatin during interphase to form dynamic loops through a process known as active loop extrusion. We develop a theory demonstrating that active loop extrusion causes the apparent fractal dimension of chromatin to cross over between two and four at contour lengths on the order of 30 kilo-base pairs (kbp). The anomalously high fractal dimension of D=4 is due to the inability of extruded chromatin loops to fully relax during active extrusion. Compaction on longer contour length scales extends within topologically associated domains (TADs), facilitating gene regulation by distal elements. Furthermore, cohesin motion couples to chromatin conformation formed by other extruding cohesins. Extrusion-induced compaction suppresses overlaps such that 400 kbp TADs are mostly segregated and the genomic length of entangled chromatin sections increases to be on the order of Mega-base pairs. We validate our results with hybrid molecular dynamics – Monte Carlo simulations and show that our theory is consistent with experimental data. This work provides a theoretical basis for the compact organization of interphase chromatin explaining the physical reason for segregation of TADs and suppression of chromatin entanglements which contribute to efficient gene regulation.   

Cohesin distribution encodes chromatin 3D organization via conserved-current loop extrusion

Inhomogeneous patterns of enhanced DNA-DNA contacts at mesoscale of the genome are a generic feature of chromatin spatial organization. These features, termed topologically associating domains (TADs), have led to the loop extrusion factor (LEF) model, where TADs arise from loop extrusion by cohesin complexes. Currently, our ability to model TADs relies on the observation that in vertebrate the TAD boundaries are correlated with DNA sequence that binds CTCF, which therefore is inferred to block loop extrusion. However, although TADs feature prominently in their Hi-C maps, non-vertebrate organisms either do not express CTCF or show few TAD boundaries that correlate with CTCF sites. In all of these organisms, the counterpart of CTCF remains unknown, frustrating the comparisons between Hi-C data and simulation. To extend the LEF model across the tree of life, we propose the conserved-current loop extrusion (CCLE) model that interprets loop-extruding cohesin as a nearly-conserved probability current. By solely utilizing the cohesin ChIP-seq data, the CCLE model allows us to derive a position-dependent loop extrusion velocity and to simulate dynamic steady-state loop configurations. To demonstrate its utility across the tree of life, we apply the CCLE model to the Hi-C maps of S. pombe, S. cerevisiae, M. musculus, D. melanogaster, and C. elegans. In all cases, the model accurately predicts the TAD-scale Hi-C maps, suggesting that loop extrusion by cohesin is a highly-conserved mechanism underlying TADs.   

Loop extrusion with dynamic barriers explains genome folding for long-lived cohesin mutants

Loop extrusion performed by molecular motors is a universal mechanism governing genome folding across various cell types and organisms. In this process, a loop extrusion complex binds to DNA, and processively enlarges DNA loops until it dissociates. In mammalian interphase cells, extrusion is performed by the cohesin complex limited by CTCF-mediated boundaries at specific genomic locations. Strong evidence for loop extrusion comes from chromosome conformation capture techniques (e.g. Hi-C), which use high-throughput sequencing to generate genome-wide contact maps. Extrusion manifests in distinct features of contact maps at intermediate scales (kb-mb), including domains with peaks at their corners. While existing polymer physics models successfully reproduce certain features of contact maps, they do not account for recent observations of CTCF binding dynamics. Motivated by these findings, we propose a model where boundary elements dynamically switch between bound and unbound states, with rates parametrized from recent biophysical data. Using this model, we investigated how the characteristics of boundary elements impact features observable in experimental genomic and imaging datasets, including ChIPseq, Hi-C, and immunofluorescence microscopy. Our analysis highlights the importance of multiple timescales. Beyond the occupancy of the boundary elements, their average binding lifetime relative to the average cohesin binding lifetime is a pivotal factor. At a fixed occupancy, the ratio of boundary lifetime to extruder lifetime greatly alters simulated ChIPseq and simulated Hi-C. Our simulations suggest that CTCF clusters may thus be crucial for reconciling experimentally-observed rapid CTCF binding dynamics. Importantly, when time spent in the bound state becomes very high, the dynamic barrier model transitions to a stalling regime, with similar behavior to models that do not account for CTCF dynamics. Collectively, our biophysical model identifies a specific range of CTCF binding and unbinding times which are consistent with experimental observations from ChIP-Seq measurements and Hi-C data. More generally, we illustrate how the integration of dynamic biophysical measurements into genomics models will sharpen our understanding of genome regulation.   

Polymer loop extrusion with motor-motor bypassing can explain mitotic chromosome elasticity

During mitosis, chromosomes are rapidly folded into an array of polymer loops to form mitotic chromosomes. This process is largely governed by condensins, protein motors that collectively and dynamically structure chromosomes. To do this, each condensin performs 'loop extrusion', by binding the chromatin fiber and subsequently reeling it in and extruding it as a loop. Currently, the loop extrusion model explains mesoscale chromosome structure, but not the mechanical properties of chromosomes. We performed polymer simulations to investigate the chromosomal mechanical properties that emerge from loop extrusion. We focused on the consequences of the ability of condensins to bypass each other while extruding, as seen in vitro. As in experiments with isolated chromosomes, condensins contribute to the stiffness of chromosomes in simulations, with differential contributions depending on condensin extrusion dynamics. Simulated chromosomes that are randomly cut, as by restriction enzymes, can maintain their mechanical integrity as observed in experiments, if condensins can bypass each other while extruding loops. Thus, the condensins generate gel-like structure in simulated mitotic chromosomes. The model suggests how different extrusion dynamics can generate specific signatures in the mechanical response and structure of chromosomes.