Stochastic motion and transcriptional dynamics of pairs of distal DNA loci on a compacted chromosome

Node features of chromosome structure networks and their connections to genome annotation

The 3D conformations of chromosomes can encode biological significance, and the implications of such structures have been increasingly appreciated recently. Certain chromosome structural features, such as A/B compartmentalization, are frequently extracted from Hi-C pairwise genome contact information (physical association between different regions of the genome) and compared with linear annotations of the genome, such as histone modifications and lamina association. We investigate how additional properties of chromosome structure can be deduced using an abstract graph representation of the contact heatmap, and describe specific network properties that can have a strong connection with some of these biological annotations. We constructed chromosome structure networks (CSNs) from bulk Hi-C data and calculated a set of site-resolved (node-based) network properties. These properties are useful for characterizing certain aspects of chromosomal structure. We examined the ability of network properties to differentiate several scenarios, such as haploid vs diploid cells, partially inverted nuclei vs conventional architecture, depletion of chromosome architectural proteins, and structural changes during cell development. We also examined the connection between network properties and a series of other linear annotations, such as histone modifications and chromatin states including poised promoter and enhancer labels. We found that semi-local network properties exhibit greater capability in characterizing genome annotations compared to diffusive or ultra-local node features. For example, the local square clustering coefficient can be a strong classifier of lamina-associated domains. We demonstrated that network properties can be useful for highlighting large-scale chromosome structure differences that emerge in different biological situations.

Cell type- and transcription-independent spatial proximity between enhancers and promoters

Cell type-specific enhancers are critically important for lineage specification. The mechanisms that determine cell-type specificity of enhancer activity, however, are not fully understood. Most current models for how enhancers function invoke physical proximity between enhancer elements and their target genes. Here, we use an imaging-based approach to examine the spatial relationship of cell type-specific enhancers and their target genes with single-cell resolution. Using high-throughput microscopy, we measure the spatial distance from target promoters to their cell type-specific active and inactive enhancers in individual pancreatic cells derived from distinct lineages. We find increased proximity of all promoter-enhancer pairs relative to non-enhancer pairs separated by similar genomic distances. Strikingly, spatial proximity between enhancers and target genes was unrelated to tissue-specific enhancer activity. Furthermore, promoter-enhancer proximity did not correlate with the expression status of target genes. Our results suggest that promoter-enhancer pairs exist in a distinctive chromatin environment but that genome folding is not a universal driver of cell-type specificity in enhancer function.

Dynamic microenvironments shape nuclear organization and gene expression

Live imaging has revealed that the regulation of gene expression is largely driven by transient interactions. For example, many regulatory proteins bind chromatin for just seconds, and loop-like genomic contacts are rare and last only minutes. These discoveries have been difficult to reconcile with our canonical models that are predicated on stable and hierarchical interactions. Proteomic microenvironments that concentrate nuclear factors may explain how brief interactions can still mediate gene regulation by creating conditions where reactions occur more frequently. Here, we summarize new imaging technologies and recent discoveries implicating microenvironments as a potential driver of nuclear function. Finally, we propose that key properties of proteomic microenvironments, such as their size, enrichment, and lifetimes, are directly linked to regulatory function.

Tracking pairwise genomic loci by the ParB-ParS and Noc-NBS systems in living cells

The dynamics of genomic loci pairs and their interactions are essential for transcriptional regulation and genome organization. However, a robust method for tracking pairwise genomic loci in living cells is lacking. Here we developed a multicolor DNA labeling system, mParSpot (multicolor ParSpot), to track pairs of genomic loci and their interactions in living cells. The mParSpot system is derived from the ParB/ParS in the parABS system and Noc/NBS in its paralogous nucleoid occlusion system. The insertion of 16 base-pair palindromic ParSs or NBSs into the genomic locus allows the cognate binding protein ParB or Noc to spread kilobases of DNA around ParSs or NBSs for loci-specific visualization. We tracked two loci with a genomic distance of 53 kilobases and measured their spatial distance over time. Using the mParSpot system, we labeled the promoter and terminator of the MSI2 gene span 423 kb and measured their spatial distance. We also tracked the promoter and terminator dynamics of the MUC4 gene in living cells. In sum, the mParSpot is a robust and sensitive DNA labeling system for tracking genomic interactions in space and time under physiological or pathological contexts.

Activity-driven chromatin organization during interphase: Compaction, segregation, and entanglement suppression

In mammalian cells, the cohesin protein complex is believed to translocate along chromatin during interphase to form dynamic loops through a process called active loop extrusion. Chromosome conformation capture and imaging experiments have suggested that chromatin adopts a compact structure with limited interpenetration between chromosomes and between chromosomal sections. We developed 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. The anomalously high fractal dimension [Formula: see text] is due to the inability of extruded 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. Extrusion-induced compaction segregates TADs such that overlaps between TADs are reduced to less than 35% and increases the entanglement strand of chromatin by up to a factor of 50 to several Mega-base pairs. Furthermore, active loop extrusion couples cohesin motion to chromatin conformations formed by previously extruding cohesins and causes the mean square displacement of chromatin loci during lag times ([Formula: see text]) longer than tens of minutes to be proportional to [Formula: see text]. 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 TAD segregation and suppression of chromatin entanglements which contribute to efficient gene regulation.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Toward a comprehensive view of gene architecture during transcription

The activation of genes within the nucleus of eukaryotic cells is a tightly regulated process, orchestrated by a complex interplay of various physical properties and interacting factors. Studying the multitude of components and features that collectively contribute to gene activation has proven challenging due to the complexities of simultaneously visualizing the dynamic and transiently interacting elements that coalesce within the small space occupied by each individual gene. However, various labeling and imaging advances are now starting to overcome this challenge, enabling visualization of gene activation at different lengths and timescales. In this review, we aim to highlight these microscopy-based advances and suggest how they can be combined to provide a comprehensive view of the mechanisms regulating gene activation.

Transcription-induced active forces suppress chromatin motion

The organization of interphase chromosomes in a number of species is starting to emerge thanks to advances in a variety of experimental techniques. However, much less is known about the dynamics, especially in the functional states of chromatin. Some experiments have shown that the motility of individual loci in human interphase chromosome decreases during transcription and increases upon inhibiting transcription. This is a counterintuitive finding because it is thought that the active mechanical force (F) on the order of ten piconewtons, generated by RNA polymerase II (RNAPII) that is presumably transmitted to the gene-rich region of the chromatin, would render it more open, thus enhancing the mobility. We developed a minimal active copolymer model for interphase chromosomes to investigate how F affects the dynamical properties of chromatin. The movements of the loci in the gene-rich region are suppressed in an intermediate range of F and are enhanced at small F values, which has also been observed in experiments. In the intermediate F, the bond length between consecutive loci increases, becoming commensurate with the distance at the minimum of the attractive interaction between nonbonded loci. This results in a transient disorder-to-order transition, leading to a decreased mobility during transcription. Strikingly, the F-dependent change in the locus dynamics preserves the organization of the chromosome at [Formula: see text]. Transient ordering of the loci, which is not found in the polymers with random epigenetic profiles, in the gene-rich region might be a plausible mechanism for nucleating a dynamic network involving transcription factors, RNAPII, and chromatin.

Enhancer selectivity in space and time: from enhancer-promoter interactions to promoter activation

The primary regulators of metazoan gene expression are enhancers, originally functionally defined as DNA sequences that can activate transcription at promoters in an orientation-independent and distance-independent manner. Despite being crucial for gene regulation in animals, what mechanisms underlie enhancer selectivity for promoters, and more fundamentally, how enhancers interact with promoters and activate transcription, remain poorly understood. In this Review, we first discuss current models of enhancer-promoter interactions in space and time and how enhancers affect transcription activation. Next, we discuss different mechanisms that mediate enhancer selectivity, including repression, biochemical compatibility and regulation of 3D genome structure. Through 3D polymer simulations, we illustrate how the ability of 3D genome folding mechanisms to mediate enhancer selectivity strongly varies for different enhancer-promoter interaction mechanisms. Finally, we discuss how recent technical advances may provide new insights into mechanisms of enhancer-promoter interactions and how technical biases in methods such as Hi-C and Micro-C and imaging techniques may affect their interpretation.

Multi-dimensional condensation of intracellular biomolecules

Liquid-liquid phase separation has been recognized as universal mechanisms in living cells for the formation of RNA-protein condensates and ordered lipid domains. These biomolecular condensates or domains nucleate, diffuse and interact with each other across physical dimensions to perform their biological functions. Here we summarize key features of biophysical principles underlying the multi-dimensional condensation of RNA-protein condensates and ordered lipid domains, which are related to nuclear transcription, and signaling on cell membranes. Uncovering physicochemical factors that govern the spatiotemporal coupling of those condensates presents a new avenue in their functions and associated human diseases.

Power-law behavior of transcriptional bursting regulated by enhancer-promoter communication

Revealing how transcriptional bursting kinetics are genomically encoded is challenging because genome structures are stochastic at the organization level and are suggestively linked to gene transcription. To address this challenge, we develop a generic theoretical framework that integrates chromatin dynamics, enhancer-promoter (E-P) communication, and gene-state switching to study transcriptional bursting. The theory predicts that power law can be a general rule to quantitatively describe bursting modulations by E-P spatial communication. Specifically, burst frequency and burst size are up-regulated by E-P communication strength, following power laws with positive exponents. Analysis of the scaling exponents further reveals that burst frequency is preferentially regulated. Bursting kinetics are down-regulated by E-P genomic distance with negative power-law exponents, and this negative modulation desensitizes at large distances. The mutual information between burst frequency (or burst size) and E-P spatial distance further reveals essential characteristics of the information transfer from E-P communication to transcriptional bursting kinetics. These findings, which are in agreement with experimental observations, not only reveal fundamental principles of E-P communication in transcriptional bursting but also are essential for understanding cellular decision-making.

Internal friction as a factor in the anomalous chain length dependence of DNA transcriptional dynamics

Recent experiments by Brückner et al. [Science 380, 1357 (2023)] have observed an anomalous chain length dependence of the time of near approach of widely separated pairs of genomic elements on transcriptionally active chromosomal DNA. In this paper, I suggest that the anomaly may have its roots in internal friction between neighboring segments on the DNA backbone. The basis for this proposal is a model of chain dynamics formulated in terms of a continuum scaled Brownian walk (sBw) of polymerization index N. The sBw is an extension of the simple Brownian walk model widely used in path integral calculations of polymer properties, differing from it in containing an additional parameter H (the Hurst index) that can be tuned to produce varying degrees of correlation between adjacent monomers. A calculation using the sBw of the mean time τc for chain closure predicts-under the Wilemski-Fixman approximation for diffusion-controlled reactions-that at early times, τc varies as the 2/3 power of N, in close agreement with the findings of the Brückner et al. study. Other scaling relations of that study, including those related to the probability of loop formation and the mean square displacements of terminal monomers, are also satisfactorily accounted for by the model.

The searchable chromosome

To date, genome structure and dynamics have been studied mostly independently; their interplay is a notable blind spot of the field. Brückner, Chen, et al. recently demonstrated an integrated experimental approach sensitive to both, uncovering a striking robustness of enhancer-promoter search times (dynamics) to changes in genomic separation (structure).

Connecting Chromatin Structures to Gene Regulation Using Dynamic Polymer Simulations

The transfer of regulatory information between distal loci on chromatin is thought to involve physical proximity, but key biophysical features of these contacts remain unclear. For instance, it is unknown how close and for how long two loci need to be in order to productively interact. The main challenge is that it is currently impossible to measure chromatin dynamics with high spatiotemporal resolution at scale. Polymer simulations provide an accessible and rigorous way to test biophysical models of chromatin regulation, yet there is a lack of simple and general methods for extracting the values of model parameters. Here we adapt the Nelder-Mead simplex optimization algorithm to select the best polymer model matching a given Hi-C dataset, using the MYC locus as an example. The model's biophysical parameters predict a compartmental rearrangement of the MYC locus in leukemia, which we validate with single-cell measurements. Leveraging trajectories predicted by the model, we find that loci with similar Hi-C contact frequencies can exhibit widely different contact dynamics. Interestingly, the frequency of productive interactions between loci exhibits a non-linear relationship with their Hi-C contact frequency when we enforce a specific capture radius and contact duration. These observations are consistent with recent experimental observations and suggest that the dynamic ensemble of chromatin configurations, rather than average contact matrices, is required to fully predict long-range chromatin interactions.

Gene Activity as the Predictive Indicator for Transcriptional Bursting Dynamics

Transcription commonly occurs in bursts, with alternating productive (ON) and quiescent (OFF) periods, governing mRNA production rates. Yet, how transcription is regulated through bursting dynamics remains unresolved. In this study, we conduct real-time measurements of endogenous transcriptional bursting with single-mRNA sensitivity. Leveraging the diverse transcriptional activities in early fly embryos, we uncover stringent relationships between bursting parameters. Specifically, we find that the durations of ON and OFF periods are linked. Regardless of the developmental stage or body-axis position, gene activity levels predict the average ON and OFF periods of individual alleles. Lowly transcribing alleles predominantly modulate OFF durations (burst frequency), while highly transcribing alleles primarily tune ON durations (burst size). Importantly, these relationships persist even under perturbation of cis-regulatory elements or trans-factors. This suggests a novel mechanistic constraint governing bursting dynamics rather than a modular control of distinct parameters by distinct regulatory processes. Our study provides a foundation for future investigations into the molecular mechanisms underpinning spatiotemporal transcriptional control.

Technological advances in probing 4D genome organization

The last two decades of work on chromosome conformation in eukaryotic nuclei have revealed a complex and highly regulated hierarchy of architectural features, from self-associating domains and compartmental interactions to locus-specific loops. Recent findings have shown that these structures are dynamic and heterogeneous, with emerging insights into the factors that shape them and implications for the control of transcription and other nuclear processes. Here, we review the latest advances in the DNA sequencing- and microscopy-based technologies for probing these features in space and time (4D) and discuss how they have been combined with complementary approaches such as genetic perturbations, protein and RNA measurements, and modeling to gain mechanistic insights about genome regulation across space and time.

Model chromatin flows: numerical analysis of linear and nonlinear hydrodynamics inside a sphere

We solve a hydrodynamic model of active chromatin dynamics, within a confined geometry simulating the cell nucleus. Using both analytical and numerical methods, we describe the behavior of the chromatin polymer driven by the activity of motors having polar symmetry, both in the linear response regime as well as in the long-term, fully nonlinear regime of the flows. The introduction of a boundary induces a particular geometry in the flows of chromatin, which we describe using vector spherical harmonics, a tool which greatly simplifies both our analytical and numerical approaches. We find that the long-term behavior of this model in confinement is dominated by steady, transverse flows of chromatin which circulate around the spherical domain. These circulating flows are found to be robust to perturbations, and their characteristic size is set by the size of the domain. This gives us further insight into active chromatin dynamics in the cell nucleus, and provides a foundation for development of further, more complex models of active chromatin dynamics.

Spatial and temporal organization of the genome: Current state and future aims of the 4D nucleome project

The four-dimensional nucleome (4DN) consortium studies the architecture of the genome and the nucleus in space and time. We summarize progress by the consortium and highlight the development of technologies for (1) mapping genome folding and identifying roles of nuclear components and bodies, proteins, and RNA, (2) characterizing nuclear organization with time or single-cell resolution, and (3) imaging of nuclear organization. With these tools, the consortium has provided over 2,000 public datasets. Integrative computational models based on these data are starting to reveal connections between genome structure and function. We then present a forward-looking perspective and outline current aims to (1) delineate dynamics of nuclear architecture at different timescales, from minutes to weeks as cells differentiate, in populations and in single cells, (2) characterize cis-determinants and trans-modulators of genome organization, (3) test functional consequences of changes in cis- and trans-regulators, and (4) develop predictive models of genome structure and function.