A maximum-entropy model to predict 3D structural ensembles of chromatin from pairwise distances with applications to interphase chromosomes and structural variants

Multiscale molecular modeling of chromatin with MultiMM: From nucleosomes to the whole genome

Motivation: We present a user-friendly 3D chromatin simulation model for the human genome based on OpenMM, addressing the challenges posed by existing models with use-specific implementations. Our approach employs a multi-scale energy minimization strategy, capturing chromatin's hierarchical structure. Initiating with a Hilbert curve-based structure, users can input files specifying nucleosome positioning, loops, compartments, or subcompartments. Results: The model utilizes an energy minimization approach with a large choice of numerical integrators, providing the entire genome's structure within minutes. Output files include the generated structures for each chromosome, offering a versatile and accessible tool for chromatin simulation in bioinformatics studies. Furthermore, MultiMM is capable of producing nucleosome-resolution structures by making simplistic geometric assumptions about the structure and the density of nucleosomes on the DNA. Code availability: Open-source software and the manual are freely available on https://github.com/SFGLab/MultiMM or via pip https://pypi.org/project/MultiMM/.

Genome structural dynamics: insights from Gaussian network analysis of Hi-C data

Characterization of the spatiotemporal properties of the chromatin is essential to gaining insights into the physical bases of gene co-expression, transcriptional regulation and epigenetic modifications. The Gaussian network model (GNM) has proven in recent work to serve as a useful tool for modeling chromatin structural dynamics, using as input high-throughput chromosome conformation capture data. We focus here on the exploration of the collective dynamics of chromosomal structures at hierarchical levels of resolution, from single gene loci to topologically associating domains or entire chromosomes. The GNM permits us to identify long-range interactions between gene loci, shedding light on the role of cross-correlations between distal regions of the chromosomes in regulating gene expression. Notably, GNM analysis performed across diverse cell lines highlights the conservation of the global/cooperative movements of the chromatin across different types of cells. Variations driven by localized couplings between genomic loci, on the other hand, underlie cell differentiation, underscoring the significance of the four-dimensional properties of the genome in defining cellular identity. Finally, we demonstrate the close relation between the cell type-dependent mobility profiles of gene loci and their gene expression patterns, providing a clear demonstration of the role of chromosomal 4D features in defining cell-specific differential expression of genes.

Hi-C-guided many-polymer model to decipher 3D genome organization

We propose a high-throughput chromosome conformation capture data-based many-polymer model that allows us to generate an ensemble of multi-scale genome structures. We demonstrate the efficacy of our model by validating the generated structures against experimental measurements and employ them to address key questions regarding genome organization. Our model first confirms a significant correlation between chromosome size and nuclear positioning. Specifically, smaller chromosomes are distributed at the core region, whereas larger chromosomes are at the periphery, interacting with the nuclear envelope. The spatial distribution of A- and B-type compartments, which is nontrivial to infer from the corresponding high-throughput chromosome conformation capture maps alone, can also be elucidated using our model, accounting for an issue such as the effect of chromatin-lamina interaction on the compartmentalization of conventional and inverted nuclei. In accordance with imaging data, the overall shape of the 3D genome structures generated from our model displays significant variation. As a case study, we apply our method to the yellow fever mosquito genome, finding that the predicted morphology displays, on average, a more globular shape than the previously suggested spindle-like organization and that our prediction better aligns with the fluorescence in situ hybridization data. Our model has great potential to be extended to investigate many outstanding issues concerning 3D genome organization.

Footprints of loop extrusion in statistics of intra-chromosomal distances: An analytically solvable model

Active loop extrusion-the process of formation of dynamically growing chromatin loops due to the motor activity of DNA-binding protein complexes-is a firmly established mechanism responsible for chromatin spatial organization at different stages of a cell cycle in eukaryotes and bacteria. The theoretical insight into the effect of loop extrusion on the experimentally measured statistics of chromatin conformation can be gained with an appropriately chosen polymer model. Here, we consider the simplest analytically solvable model of an interphase chromosome, which is treated as an ideal chain with disorder of sufficiently sparse random loops whose conformations are sampled from the equilibrium ensemble. This framework allows us to arrive at the closed-form analytical expression for the mean-squared distance between pairs of genomic loci, which is valid beyond the one-loop approximation in diagrammatic representation. In addition, we analyze the loop-induced deviation of chain conformations from the Gaussian statistics by calculating kurtosis of probability density of the pairwise separation vector. The presented results suggest the possible ways of estimating the characteristics of the loop extrusion process based on the experimental data on the scale-dependent statistics of intra-chromosomal pair-wise distances.

Replicating Chromosomes in Whole-Cell Models of Bacteria

Computational models of cells cannot be considered complete unless they include the most fundamental process of life, the replication of genetic material. In a recent study, we presented a computational framework to model systems of replicating bacterial chromosomes as polymers at 10 bp resolution with Brownian dynamics. This approach was used to investigate changes in chromosome organization during replication and extend the applicability of an existing whole-cell model (WCM) for a genetically minimal bacterium, JCVI-syn3A, to the entire cell cycle. To achieve cell-scale chromosome structures that are realistic, we modeled the chromosome as a self-avoiding homopolymer with bending and torsional stiffnesses that capture the essential mechanical properties of dsDNA in Syn3A. Additionally, the polymer interacts with ribosomes distributed according to cryo-electron tomograms of Syn3A. The polymer model was further augmented by computational models of loop extrusion by structural maintenance of chromosomes (SMC) protein complexes and topoisomerase action, and the modeling and analysis of multi-fork replication states.

Dynamics of chromosome organization in a minimal bacterial cell

Computational models of cells cannot be considered complete unless they include the most fundamental process of life, the replication and inheritance of genetic material. By creating a computational framework to model systems of replicating bacterial chromosomes as polymers at 10 bp resolution with Brownian dynamics, we investigate changes in chromosome organization during replication and extend the applicability of an existing whole-cell model (WCM) for a genetically minimal bacterium, JCVI-syn3A, to the entire cell-cycle. To achieve cell-scale chromosome structures that are realistic, we model the chromosome as a self-avoiding homopolymer with bending and torsional stiffnesses that capture the essential mechanical properties of dsDNA in Syn3A. In addition, the conformations of the circular DNA must avoid overlapping with ribosomes identitied in cryo-electron tomograms. While Syn3A lacks the complex regulatory systems known to orchestrate chromosome segregation in other bacteria, its minimized genome retains essential loop-extruding structural maintenance of chromosomes (SMC) protein complexes (SMC-scpAB) and topoisomerases. Through implementing the effects of these proteins in our simulations of replicating chromosomes, we find that they alone are sufficient for simultaneous chromosome segregation across all generations within nested theta structures. This supports previous studies suggesting loop-extrusion serves as a near-universal mechanism for chromosome organization within bacterial and eukaryotic cells. Furthermore, we analyze ribosome diffusion under the influence of the chromosome and calculate in silico chromosome contact maps that capture inter-daughter interactions. Finally, we present a methodology to map the polymer model of the chromosome to a Martini coarse-grained representation to prepare molecular dynamics models of entire Syn3A cells, which serves as an ultimate means of validation for cell states predicted by the WCM.

Identification of Two Subsets of Subcompartment A1 Associated with High Transcriptional Activity and Frequent Loop Extrusion

Three-dimensional genome organization has been increasingly recognized as an important determinant of the precise regulation of gene expression in mammalian cells, yet the relationship between gene transcriptional activity and spatial subcompartment positioning is still not fully comprehended. Here, we first utilized genome-wide Hi-C data to infer eight types of subcompartment (labeled A1, A2, A3, A4, B1, B2, B3, and B4) in mouse embryonic stem cells and four primary differentiated cell types, including thymocytes, macrophages, neural progenitor cells, and cortical neurons. Transitions of subcompartments may confer gene expression changes in different cell types. Intriguingly, we identified two subsets of subcompartments defined by higher gene density and characterized by strongly looped contact domains, named common A1 and variable A1, respectively. We revealed that common A1, which includes highly expressed genes and abundant housekeeping genes, shows a ~2-fold higher gene density than the variable A1, where cell type-specific genes are significantly enriched. Thus, our study supports a model in which both types of genomic loci with constitutive and regulatory high transcriptional activity can drive the subcompartment A1 formation. Special chromatin subcompartment arrangement and intradomain interactions may, in turn, contribute to maintaining proper levels of gene expression, especially for regulatory non-housekeeping genes.

Structural changes in chromosomes driven by multiple condensin motors during mitosis

We create a computational framework that utilizes loop extrusion (LE) by multiple condensin I/II motors to predict changes in chromosome organization during mitosis. The theory accurately reproduces the experimental contact probability profiles for the mitotic chromosomes in HeLa and DT40 cells. The LE rate is smaller at the start of mitosis and increases as the cells approach metaphase. Condensin II-mediated mean loop size is about six times larger than loops because of condensin I. The loops, which overlap each other, are stapled to a central dynamically changing helical scaffold formed by the motors during the LE process. A polymer physics-based data-driven method that uses the Hi-C contact map as the only input shows that the helix is characterized as random helix perversions (RHPs) in which the handedness changes randomly along the scaffold. The theoretical predictions, which are testable using imaging experiments, do not contain any parameters.