Predicting scale-dependent chromatin polymer properties from systematic coarse-graining

Bridging spatial and temporal scales of developmental gene regulation

The development of multicellular organisms relies on the precise coordination of molecular events across multiple spatial and temporal scales. Understanding how information flows from molecular interactions to cellular processes and tissue organization during development is crucial for explaining the remarkable reproducibility of complex organisms. This review explores how chromatin-encoded information is transduced from localized transcriptional events to global gene expression patterns, highlighting the challenge of bridging these scales. We discuss recent experimental findings and theoretical frameworks, emphasizing polymer physics as a tool for describing the relationship between chromatin structure and dynamics across scales. By integrating these perspectives, we aim to clarify how gene regulation is coordinated across levels of biological organization and suggest strategies for future experimental approaches.

Binder and monomer valencies determine the extent of collapse and reswelling of chromatin

Multivalent DNA-bridging protein-mediated collapse of chromatin polymers have long been established as one of the driving factors in chromatin organization inside cells. These multivalent proteins can bind to distant binding sites along the chromatin backbone and bring them together in spatial proximity, leading to collapsed conformations. Recently, it has been suggested that these proteins not only drive the collapse of the chromatin polymer but also reswelling at higher concentrations. In this study, we investigate the physical mechanisms underlying this unexpected reswelling behavior. We use the Langevin dynamics simulation of a coarse-grained homopolymer to investigate the effects of the valencies of both the binders and the monomers on the polymer conformations. We find that while the extent of collapse of the polymer is strongly dependent on the binder valency, the extent of reswelling is largely determined by the monomer valency. Furthermore, we also discovered two different physical mechanisms that drive the reswelling of the polymer-excluded volume effects and loss of long-range loops. Finally, we obtain a classification map to determine the regimes in which each of these mechanisms is the dominant factor leading to polymer reswelling.

Toward decoding the mechanisms that shape sub-megabase-scale genome organization

Understanding genome organization at the kilobase to megabase scale is critical, as it encompasses genes and regulatory elements. Improvements in the resolution of experimental techniques have revealed novel structural motifs at this scale, including micro-compartments, nucleosome clutches, microdomains, and packing domains. Here we review recent progress on developing theories to explain these observations. Key advances include elucidating the role of nucleosome positioning and epigenetic modifications, the role and mechanisms of compartmentalization in local structure, and the interplay between loop extrusion and phase separation. This work has revealed probable mechanisms by which the observed structures emerge, but it remains unclear how these factors act together in the cell. To this end, recent studies have used chromatin conformation capture data in concert with diverse genomics datasets to create native-like models of chromatin at nucleosome resolution and below. While several roadblocks remain, this strategy promises to decode how molecular forces sum to shape chromatin structure and ultimately regulate transcription.

Chromatin structures from integrated AI and polymer physics model

The physical organization of the genome in three-dimensional space regulates many biological processes, including gene expression and cell differentiation. Three-dimensional characterization of genome structure is critical to understanding these biological processes. Direct experimental measurements of genome structure are challenging; computational models of chromatin structure are therefore necessary. We develop an approach that combines a particle-based chromatin polymer model, molecular simulation, and machine learning to efficiently and accurately estimate chromatin structure from indirect measures of genome structure. More specifically, we introduce a new approach where the interaction parameters of the polymer model are extracted from experimental Hi-C data using a graph neural network (GNN). We train the GNN on simulated data from the underlying polymer model, avoiding the need for large quantities of experimental data. The resulting approach accurately estimates chromatin structures across all chromosomes and across several experimental cell lines despite being trained almost exclusively on simulated data. The proposed approach can be viewed as a general framework for combining physical modeling with machine learning, and it could be extended to integrate additional biological data modalities. Ultimately, we achieve accurate and high-throughput estimations of chromatin structure from Hi-C data, which will be necessary as experimental methodologies, such as single-cell Hi-C, improve.

The synergy between compartmentalization and motorization in chromatin architecture

High-resolution techniques capable of manipulating from single molecules to millions of cells are combined with three-dimensional modeling followed by simulation to comprehend the specific aspects of chromosomes. From the theoretical perspective, the energy landscape theory from protein folding inspired the development of the minimal chromatin model (MiChroM). In this work, two biologically relevant MiChroM energy terms were minimized under different conditions, revealing a competition between loci compartmentalization and motor-driven activity mechanisms in chromatin folding. Enhancing the motor activity energy baseline increased the lengthwise compaction and reduced the polymer entanglement. Concomitantly, decreasing compartmentalization-related interactions reduced the overall polymer collapse, although compartmentalization given by the microphase separation remained almost intact. For multiple chromosome simulations, increased motorization intensified the territory formation of the different chains and reduced compartmentalization strength lowered the probability of contact formation of different loci between multiple chains, approximating to the experimental inter-contacts of the human chromosomes. These findings have direct implications for experimental data-driven chromosome modeling, specially those involving multiple chromosomes. The interplay between phase-separation and territory formation mechanisms should be properly implemented in order to recover the genome architecture and dynamics, features that might play critical roles in regulating nuclear functions.

ChromoGen: Diffusion model predicts single-cell chromatin conformations

Breakthroughs in high-throughput sequencing and microscopic imaging technologies have revealed that chromatin structures vary considerably between cells of the same type. However, a thorough characterization of this heterogeneity remains elusive due to the labor-intensive and time-consuming nature of these experiments. To address these challenges, we introduce ChromoGen, a generative model based on state-of-the-art artificial intelligence techniques that efficiently predicts three-dimensional, single-cell chromatin conformations de novo with both region and cell type specificity. These generated conformations accurately reproduce experimental results at both the single-cell and population levels. Moreover, ChromoGen successfully transfers to cell types excluded from the training data using just DNA sequence and widely available DNase-seq data, thus providing access to chromatin structures in myriad cell types. These achievements come at a remarkably low computational cost. Therefore, ChromoGen enables the systematic investigation of single-cell chromatin organization, its heterogeneity, and its relationship to sequencing data, all while remaining economical.

Bridging spatial and temporal scales of developmental gene regulation

The development of multicellular organisms relies on the precise coordination of molecular events across multiple spatial and temporal scales. Understanding how information flows from molecular interactions to cellular processes and tissue organization during development is crucial for explaining the remarkable reproducibility of complex organisms. This review explores how chromatin-encoded information is transduced from localized transcriptional events to global gene expression patterns, highlighting the challenge of bridging these scales. We discuss recent experimental findings and theoretical frameworks, emphasizing polymer physics as a tool for describing the relationship between chromatin structure and dynamics across scales. By integrating these perspectives, we aim to clarify how gene regulation is coordinated across levels of biological organization and suggest strategies for future experimental approaches.

Topology-mediated organization of Escherichia coli chromosome in fast-growth conditions

The mechanism underlying the spatiotemporal chromosome organization in Escherichia coli cells remains an open question, though experiments have been able to visually see the evolving chromosome organization in fast- and slow-growing cells. We had proposed [D. Mitra et al., Soft Matter 18, 5615 (2022)1744-683X10.1039/D2SM00734G] that the DNA ring polymer adopts a specific polymer topology as it goes through its cell cycle, which in turn self-organizes the chromosome by entropic forces during slow growth. The fast-growing E. coli cells have four (or more) copies of the replicating DNA, with overlapping rounds of replication going on simultaneously. This makes the spatial segregation and the subsequent organization of the multiple generations of DNA a complex task. Here, we establish that the same simple principles of entropic repulsion between polymer segments which provided an understanding of self-organization of DNA in slow-growth conditions also explains the organization of chromosomes in the much more complex scenario of fast-growth conditions. Repulsion between DNA-polymer segments through entropic mechanisms is harnessed by modifying polymer topology. The ring-polymer topology is modified by introducing crosslinks (emulating the effects of linker proteins) between specific segments. Our simulation reproduces the emergent evolution of the organization of chromosomes as seen in vivo in fluorescent in situ hybridization experiments. Furthermore, we reconcile the mechanism of longitudinal organization of the chromosomes arms in fast-growth conditions by a suitable adaptation of the model. Thus, polymer physics principles, previously used to understand chromosome organization in slow-growing E. coli cells also resolve DNA organization in more complex scenarios with multiple rounds of replication occurring in parallel.

Phase separation in soft repulsive polymer mixtures: foundation and implication for chromatin organization

Given the wide range of length scales, the analysis of polymer systems often requires coarse-graining, for which various levels of description may be possible depending on the phenomenon under consideration. Here, we provide a super-coarse grained description, where polymers are represented as a succession of mesosopic soft beads which are allowed to overlap with others. We then investigate the phase separation behaviors in a mixture of such homopolymers based on mean-field theory, and discuss universal aspects of the miscibility phase diagram in comparison with the numerical simulation. We also discuss an extension of our analysis to mixtures involving random copolymers, which might be interesting in the context of chromatin organization in a cell nucleus.

OpenNucleome for high-resolution nuclear structural and dynamical modeling

The intricate structural organization of the human nucleus is fundamental to cellular function and gene regulation. Recent advancements in experimental techniques, including high-throughput sequencing and microscopy, have provided valuable insights into nuclear organization. Computational modeling has played significant roles in interpreting experimental observations by reconstructing high-resolution structural ensembles and uncovering organization principles. However, the absence of standardized modeling tools poses challenges for furthering nuclear investigations. We present OpenNucleome-an open-source software designed for conducting GPU-accelerated molecular dynamics simulations of the human nucleus. OpenNucleome offers particle-based representations of chromosomes at a resolution of 100 KB, encompassing nuclear lamina, nucleoli, and speckles. This software furnishes highly accurate structural models of nuclear architecture, affording the means for dynamic simulations of condensate formation, fusion, and exploration of non-equilibrium effects. We applied OpenNucleome to uncover the mechanisms driving the emergence of 'fixed points' within the nucleus-signifying genomic loci robustly anchored in proximity to specific nuclear bodies for functional purposes. This anchoring remains resilient even amidst significant fluctuations in chromosome radial positions and nuclear shapes within individual cells. Our findings lend support to a nuclear zoning model that elucidates genome functionality. We anticipate OpenNucleome to serve as a valuable tool for nuclear investigations, streamlining mechanistic explorations and enhancing the interpretation of experimental observations.

From Nucleosomes to Compartments: Physicochemical Interactions Underlying Chromatin Organization

Chromatin organization plays a critical role in cellular function by regulating access to genetic information. However, understanding chromatin folding is challenging due to its complex, multiscale nature. Significant progress has been made in studying in vitro systems, uncovering the structure of individual nucleosomes and their arrays, and elucidating the role of physicochemical forces in stabilizing these structures. Additionally, remarkable advancements have been achieved in characterizing chromatin organization in vivo, particularly at the whole-chromosome level, revealing important features such as chromatin loops, topologically associating domains, and nuclear compartments. However, bridging the gap between in vitro and in vivo studies remains challenging. The resemblance between in vitro and in vivo chromatin conformations and the relevance of internucleosomal interactions for chromatin folding in vivo are subjects of debate. This article reviews experimental and computational studies conducted at various length scales, highlighting the significance of intrinsic interactions between nucleosomes and their roles in chromatin folding in vivo.

Topological Spectra and Entropy of Chromatin Loop Networks

The 3D folding of a mammalian gene can be studied by a polymer model, where the chromatin fiber is represented by a semiflexible polymer which interacts with multivalent proteins, representing complexes of DNA-binding transcription factors and RNA polymerases. This physical model leads to the natural emergence of clusters of proteins and binding sites, accompanied by the folding of chromatin into a set of topologies, each associated with a different network of loops. Here, we combine numerics and analytics to first classify these networks and then find their relative importance or statistical weight, when the properties of the underlying polymer are those relevant to chromatin. Unlike polymer networks previously studied, our chromatin networks have finite average distances between successive binding sites, and this leads to giant differences between the weights of topologies with the same number of edges and nodes but different wiring. These weights strongly favor rosettelike structures with a local cloud of loops with respect to more complicated nonlocal topologies. Our results suggest that genes should overwhelmingly fold into a small fraction of all possible 3D topologies, which can be robustly characterized by the framework we propose here.

A mean-field theory for predicting single polymer collapse induced by neutral crowders

Macromolecular crowding can induce the collapse of a single long polymer into a globular form due to depletion forces of entropic nature. This phenomenon has been shown to play a significant role in compacting the genome within the bacterium Escherichia coli into a well-defined region of the cell known as the nucleoid. Motivated by the biological significance of this process, numerous theoretical and computational studies have searched for the primary determinants of the behavior of polymer-crowder phases. However, our understanding of this process remains incomplete and there is debate on a quantitatively unified description. In particular, different simulation studies with explicit crowders have proposed different order parameters as potential predictors for the collapse transition. In this work, we present a comprehensive analysis of published simulation data obtained from different sources. Based on the common behavior we find in this data, we develop a unified phenomenological model that we show to be predictive. Finally, to further validate the accuracy of the model, we conduct new simulations on polymers of various sizes, and investigate the role of jamming of the crowders.

OpenNucleome for high resolution nuclear structural and dynamical modeling

The intricate structural organization of the human nucleus is fundamental to cellular function and gene regulation. Recent advancements in experimental techniques, including high-throughput sequencing and microscopy, have provided valuable insights into nuclear organization. Computational modeling has played significant roles in interpreting experimental observations by reconstructing high-resolution structural ensembles and uncovering organization principles. However, the absence of standardized modeling tools poses challenges for furthering nuclear investigations. We present OpenNucleome-an open-source software designed for conducting GPU-accelerated molecular dynamics simulations of the human nucleus. OpenNucleome offers particle-based representations of chromosomes at a resolution of 100 KB, encompassing nuclear lamina, nucleoli, and speckles. This software furnishes highly accurate structural models of nuclear architecture, affording the means for dynamic simulations of condensate formation, fusion, and exploration of non-equilibrium effects. We applied OpenNucleome to uncover the mechanisms driving the emergence of "fixed points" within the nucleus-signifying genomic loci robustly anchored in proximity to specific nuclear bodies for functional purposes. This anchoring remains resilient even amidst significant fluctuations in chromosome radial positions and nuclear shapes within individual cells. Our findings lend support to a nuclear zoning model that elucidates genome functionality. We anticipate OpenNucleome to serve as a valuable tool for nuclear investigations, streamlining mechanistic explorations and enhancing the interpretation of experimental observations.

Regulation of chromatin architecture by transcription factor binding

Transcription factors (TF) bind to chromatin and regulate the expression of genes. The pair Myc:Max binds to E-box regulatory DNA elements throughout the genome to control the transcription of a large group of specific genes. We introduce an implicit modeling protocol for Myc:Max binding to mesoscale chromatin fibers at nucleosome resolution to determine TF effect on chromatin architecture and shed light into its mechanism of gene regulation. We first bind Myc:Max to different chromatin locations and show how it can direct fiber folding and formation of microdomains, and how this depends on the linker DNA length. Second, by simulating increasing concentrations of Myc:Max binding to fibers that differ in the DNA linker length, linker histone density, and acetylation levels, we assess the interplay between Myc:Max and other chromatin internal parameters. Third, we study the mechanism of gene silencing by Myc:Max binding to the Eed gene loci. Overall, our results show how chromatin architecture can be regulated by TF binding. The position of TF binding dictates the formation of microdomains that appear visible only at the ensemble level. At the same time, the level of linker histone and tail acetylation, or different linker DNA lengths, regulates the concentration-dependent effect of TF binding. Furthermore, we show how TF binding can repress gene expression by increasing fiber folding motifs that help compact and occlude the promoter region. Importantly, this effect can be reversed by increasing linker histone density. Overall, these results shed light on the epigenetic control of the genome dictated by TF binding.