A Multiscale Perspective on Chromatin Architecture through Polymer Physics

Abstract

The spatial organization of chromatin within the eukaryotic nucleus is critical in regulating key cellular functions, such as gene expression, and its disruption can lead to disease. Advances in experimental techniques, such as Hi-C and microscopy, have significantly enhanced our understanding of chromatin’s intricate and dynamic architecture, revealing complex patterns of interaction at multiple scales. Along with experimental methods, physics-based computational models, including polymer phase separation and loop-extrusion mechanisms, have been developed to explain chromatin structure in a principled manner. Here, we illustrate genome-wide applications of these models, highlighting their ability to predict chromatin contacts across different scales and to spread light on the underlying molecular determinants. Additionally, we discuss how these models provide a framework for understanding alterations in chromosome folding associated with disease states, such as SARS-CoV-2 infection and pathogenic structural variants, providing valuable insights into the role of chromatin architecture in health and disease.

1. Introduction

The three-dimensional (3D) organization of the genome within the nucleus of eukaryotic cells is fundamental to its functionality and regulation. This intricate spatial arrangement, from the scale of entire chromosomes to that of individual nucleosomes, plays crucial roles in processes such as gene expression, DNA replication, and genome stability (1–7) and its aberrant conformation can lead to phenotypical disorders (1, 8). Recent advancements in experimental techniques, including Hi-C (9), Genome Architecture Mapping (GAM) (10, 11), and super-resolution microscopy (12–19), have revealed the hierarchical and dynamic nature of chromatin organization. These approaches have provided unprecedented insights into how the linear DNA sequence folds and interacts in 3D space, revealing a complex landscape of genomic domains that are crucial for cellular function and identity. Chromatin architecture is characterized by hierarchical levels of organization that span from whole chromosomes to sub-megabase (Mb) scales. At the largest scale, chromatin forms chromosome territories within the nucleus (20). Across these territories, chromatin is partitioned into 10-Mb sized A/B compartments, which segregate active (A) and inactive (B) chromatin regions (9). These compartments are further organized into topologically associated domains (TADs), self-interacting regions of DNA typically spanning from hundreds of kilobases to a few Mb (21–24). TADs play a critical role in gene regulation by facilitating enhancer-promoter interactions while insulating neighboring regulatory elements from each other (2, 3, 25, 26). Advancements in microscopy and single-cell genomics have provided additional layers of complexity to our understanding of chromatin organization (12, 27–29). Single-cell imaging techniques have revealed significant heterogeneity in chromatin folding patterns among individual cells within a population (12, 30, 31). These studies have highlighted the dynamic nature of chromatin folding, which can vary across different cell types, developmental stages, and physiological conditions (12, 32, 33). Moreover, diseases like SARS-CoV-2 and genomic mutations such as Structural Variants (SVs) can induce significant alterations in chromatin architecture across different scales, ranging from gene regulatory interactions to TADs and compartments (4, 6, 34–41). Such a proliferation of innovative experimental data required the development of theoretical models that could help to deconvolve their complexity and understand the mechanisms of chromatin organization and its changes due to disease. Several physics-based models have been developed (31, 34, 42–56), which can be divided in two main categories based on the underlying mechanisms: loop extrusion (LE) and phase separation. In parallel, data-driven models attempt to approach the chromatin 3D conformation problem, in healthy and disease-affected cells, simply by computational inference techniques from experimental data (57–59), taking advantage of deep learning methods (60). In this review, we provide an overview of the main polymer physics models of chromatin organization and examine their predictions across different length scales. We also discuss how these models can elucidate the interplay between chromatin organization and epigenetic states (53). Finally, we summarize recent advances in chromatin conformation modeling in healthy and diseases states, with a particular focus on the effects of SARS-CoV-2 (39) and genomic mutations (34).

2. Results

2.1. Polymer physics models of chromatin organization

To decipher the molecular mechanisms driving chromatin architecture, computational models rooted in polymer physics have become indispensable tools. These models aim to integrate experimental data with theoretical frameworks to elucidate the physical principles governing chromatin folding.

A first category of polymer models, which includes the Strings and Binders (SBS) model (42–45), relies on phase-separation mechanisms (Figure 1a). These models are based on the concept that chromatin can undergo phase separation driven by interactions between different types of chromatin binding sites and associated cognate molecules (binders) (42–45). This process causes chromatin to spontaneously assemble into phase-separated clusters of sites with enriched levels of self-interactions. The type-specificity of binding sites is represented by different colors. The SBS and similar models have been instrumental in explaining the formation of distinct chromatin domains across genomic scales, such as TADs and compartments observed in Hi-C maps and other genomic interaction datasets(43, 45–48). By simulating the thermodynamic properties of chromatin folding, these models have provided insights into how molecular interactions can drive the phase separation of chromatin into distinct domains enriched in specific binding factors. The locations of binding sites in phase-separation-based polymer models can be identified by different approaches. One strategy is to set the model binding sites based on prior knowledge of epigenetic marks and binding molecules, such as proteins. This approach is particularly useful for testing molecular hypotheses (61–65). A complementary strategy infers binding sites from chromatin contact data, without prior epigenetic information. This approach is particularly useful to discover new molecular factors shaping chromatin architecture. An example of this second strategy is the polymer-based recursive statistical inference method (PRISMR) (34), sketched in Figure 1b, which infers the optimal SBS polymer model to best fit input pairwise contact data, such as Hi-C (34) or GAM (66).

Figure 1. Physics models of chromatin contact formation.

a) In the Strings and Binders (SBS) model, chromatin is modeled as a self-avoiding polymer chain, presenting different types of binding sites (represented by different colors) to cognate diffusing molecules (binders). The binders can loop the chain by bridging their cognate binding sites, thus driving phase separation of distinct clusters of sites with enriched levels of self-interactions. b) The PRISMR method infers the minimal number of SBS binding sites required to explain a genomic region’s experimental contact matrix by iteratively minimizing the difference between model and experimental contact matrices. c) In the LE+SBS model, polymer phase separation acts concurrently with loop-extrusion, an active mechanism in which extruding motors translocate along the chromatin chain and extrude loops until they find anchor points such as CTCF sites with opposite orientation.

In parallel, models based on the loop-extrusion (LE) mechanism have gained traction in explaining the formation and maintenance of TADs and other chromatin structures such as loops and stripes (50–52, 54). Loop-extrusion models propose that structural maintenance of chromosomes (SMC) complexes, such as Cohesin, dynamically extrude loops of chromatin fiber by sliding along the DNA strand until they are halted by convergent CTCF binding sites or other structural barriers. This active process, fueled by ATP hydrolysis, has been implicated in establishing and maintaining TAD boundaries and facilitating long-range DNA interactions critical for gene regulation (50, 51). Hybrid models (51, 67–70) that integrate phase separation with LE can offer a sophisticated framework for simulating chromatin dynamics. One example is the LE+SBS model (31), in which CTCF anchor sites for extruding motors are present in the polymer model as well as the SBS binding sites (Figure 1c). Polymer simulations incorporating this mechanism have successfully replicated the structural heterogeneity of chromatin architecture observed in populations of cells through multiplexed FISH experiments, and provided mechanistic insights into the functional implications of chromatin structure. These results demonstrate that both of phase separation and loop extrusion mechanisms can work together to shape chromatin folding at the single-cell level (31).

2.2. Polymer models of chromosomes and molecular determinants of folding

The chromatin folding machinery operates on a wide range of scales, from single genes to entire chromosomes (7, 24). Polymer models at the chromosome level are therefore essential for assessing the underlying physical mechanisms. Notably, the SBS model can be applied genome-wide to identify the locations and combinations of putative binding sites that recapitulate chromatin contacts. Additionally, it provides an initial characterization of their molecular attributes (53). The ability of the SBS model to describe folding on large genomic scales has been validated, for instance, using high-resolution (5 kb) in situ Hi-C data for whole chromosomes from the human lymphoblastoid cell line GM12878 (71). For each chromosome, the PRISMR algorithm (34, 53) has been used to deduce the SBS polymer that best reproduces its contact matrix. Notably, PRISMR relies solely on Hi-C data without requiring prior knowledge of binding factors. For example, Figure 2a depicts the results of the PRISMR method for chromosome 20, where experimental and model contact patterns exhibit a significant degree of similarity (Pearson correlation r=0.97, distance corrected Pearson correlation r’ = 0.85). Distributions of the inferred binding site types (binding domains) along the chromosome are also depicted (Figure 2a, middle panel). Interestingly, the binding domains have a complex spatial arrangement along the polymer chain: they overlap with each other and extend across multiple megabases, capturing contacts on the chromosomal scale (53). Moreover, although derived from chromosome-wide contact matrices, the SBS models do not miss shorter-scale structures at the TAD and sub-TAD level, including loops: as an example, Figure 2b shows a zoom-in of results for two 2-Mb long genomic regions along chromosome 20. These findings suggest that fundamental molecular components of the SBS model are sufficient to explain with a good accuracy contact patterns across different genomic scales.

Figure 2. SBS model of chromosomes and epigenetic barcode of binding domains.

a) SBS model of chromosome 20 in GM12878 cell line (71). Hi-C data (top) for the entire chromosome 20 at 5 kb resolution is well recapitulated by the SBS model (bottom, r=0.97; r’=0.85). The model binding domains (middle) overlap with each other along the chromosome. Similar results are found across other chromosomes. b) Zoom-in from panel a of the Hi-C (top) and model (bottom) matrices for two 2-Mb regions along chromosome 20, highlighting that the model inferred for the entire chromosome also captures genomic contacts at short ranges, e.g. at TAD scales. c) The model binding domains cluster in nine main epigenetic classes based on their correlations with epigenetic marks. The centroid of each class represents the combinatorial barcode displayed in the heatmap. d) The epigenetic barcode can predict de novo chromatin contacts: SBS binding domains are identified for a test set of independent chromosomes by correlating their epigenetic signals with the epigenetic classes in panel c. Subsequently, the contact matrices are predicted using the SBS model. As an example, de novo predicted contact matrices and their comparison to independent Hi-C matrices (71)for chromosomes 19 (r=0.91, r’=0.47) and 21 (r=0.91, r’=0.63) of GM12878 cell line are shown. Adapted from (53).

Binding sites have been characterized post hoc by cross-referencing their genomic positions with independent epigenetic data. Specifically, five key histone marks from the ENCODE database in GM12878 cell line (72) were analyzed, and the correlation between their genomic signals and the locations of model binding domains was computed, yielding an epigenetic signature for each domain. By clustering the histone profiles of the binding domains across chromosomes using hierarchical algorithms, nine statistically distinct groups (or epigenetic classes) were identified (53). Figure 2c shows the average histone profile for each class. Notably, each class correlates with a specific combination of different epigenetic factors rather than with a single one. For instance, while there are three classes that strongly correlate with active chromatin marks (Active 1, Active 2, and Active 3 in Figure 2c), class 1 is enriched solely for active marks, whereas classes 2 and 3 are enriched in H3K9me3 (typically found in heterochromatin), and class 3, in particular, shows a stronger correlation with H3K4me1, a histone mark linked to active enhancer regions (73).

Epigenetic classes closely align with chromatin states identified in epigenetic genome segmentation studies (13, 53, 73–76). However, the SBS binding domains are derived solely from Hi-C data without any prior epigenetic information, thereby integrating independent architectural and epigenetic data. A key characteristic of these model binding domains in explaining contact data is the overlapping nature of different types along the genome. Consequently, each DNA segment is endowed with a unique set of binding site types. This contrasts with 1D epigenetic segmentation classes, which, by definition, do not overlap genomically, resulting in each DNA segment being associated with only one such class. To validate the identified epigenetic barcode, we tested its ability to predict de-novo chromatin contacts on a set of independent chromosomes, not utilized to produce the code itself. Specifically, the test set contains odd-indexed chromosomes, while the training set, whose binding domains have been inferred by PRISMR and used to derive the epigenetic barcode, contains the even-indexed ones. In a reverse approach, binding domains are identified for odd-indexed chromosomes starting from only epigenetic data through the derived epigenetic barcode. Next, their contact matrices are predicted via polymer physics, leading to a satisfying prediction of chromatin contacts, even without using PRISMR. As an example, Figure 2d shows de novo predicted contact matrices and their comparison to the corresponding Hi-C data (71) for chromosomes 19 (r=0.91, r’=0.47) and 21 (r=0.91, r’=0.63) of GM12878.

In summary, the genome-wide inferred binding domains possess specific histone mark signatures falling into epigenetic classes that align well with the chromatin states identified in previous segmentation studies (13, 73–76). However, unlike these segmentation studies which define non-overlapping segments, the binding domains identified here do overlap along the genome, endowing each DNA region with a unique set of binding site types that can be interpreted as a combinatorial code linking 1D and 3D chromatin organization, which can also be used to perform de novo predictions on chromatin contacts, with a prior knowledge of epigenetic signals only (53).

2.3. Models of chromatin organization at multiple scales in SARS-CoV-2 infected cells

The polymer-physics based models described here can be used not only to explain genome-wide 3D chromatin contacts in healthy cells but also to study how these interactions are altered by diseases, such as SARS-CoV-2 (39).(40, 41)(4, 6) Recent findings (40, 41, 77) indicate that SARS-CoV-2 significantly affects genome organization at various length scales, from A/B compartments to TADs and specific regulatory interactions of critical genes involved in the immune response such as interferon (INF) response and pro-inflammatory genes. The SBS and LE+SBS models have been recently applied to quantitatively examine the multiscale chromatin re-arrangements resulting from SARS-CoV-2 infection (39), based on published Hi-C (40) data in control conditions (A549 mock infected cells) and in A549 cells 24 hours post-SARS-CoV-2 infection.

One of the main structural reorganizations in chromatin architecture caused by SARS-CoV-2 infection occurs at the A/B compartment level. Specifically, as schematically illustrated in Figure 3a, Hi-C data (40) indicate that viral infection leads to a general weakening of the A-compartment and enhanced A/B compartment mixing. At the A/B compartment level, chromatin can be represented in the SBS framework by a block co-polymer (45, 78), where the A and B compartments are modeled as two distinct types of binding sites (colors) that phase-separate within the same compartment by homotypically interacting with cognate molecular binders with affinities E_A-A and E_B-B (Figure 3b). Binders can also mediate heterotypic interactions, with a general affinity E_A-B. Ensuring E_A-A > E_A-B and E_B-B > E_A-B guarantees the micro-phase separation of the A and B blocks. Interestingly, while Mock Hi-C data are predominantly explained by balanced homotypic interactions (E_A-A = E_B-B), indicating a substantial similarity in the A and B compartmentalization level and consistent with existing models of A/B compartmentalization (79), data from infected cells are best described by unbalanced interactions (E_B-B > E_A-A), reflecting the general weakening of the A compartment and increased A/B mixing. Those results indicate that the restructuring of A/B compartments in infected cells can be explained by a remodulation of intra-compartment homotypic affinities, which influences the propensity of compartments to undergo microphase separation.

Figure 3. Chromatin is reshaped at A/B compartments and TADs scales in SARS-CoV-2 infected cells.

a) Sketch of the overall A-compartment weakening and increased A/B mixing in the infected genome found from Hi-C data (40). b) Block co-polymer model of chromatin at the A/B compartement level: binders mediate homotypic interactions with affinities E_A-A and E_B-B and heterotypic interactions with affinity E_A-B. c) Hi-C data (40) show intra-TAD contacts weakening in SARS-CoV-2 infected genome with respect to the mock case, together with a general reduction of Cohesin level (40). d) SBS+LE model used to study the effects of SARS-CoV-2 infection at the TAD scale. e) Mock Hi-C data (top) of the genomic region (Chr9:32,3–32,7 Mb, hg19) centered around the interferon response DDX58 gene are well reproduced by the model simulated contact map (bottom). Between the matrices CTCF signal (40) and both anchor point probability and binding domains for the LE+SBS model are shown. f) As in panel e, for SARS-CoV-2 infection case. The viral infection causes structural re-arrangements of the IFN DDX58 locus. Adapted from (39) (Creative Commons CCBY license).

At the TAD level, Hi-C data (40) show that SARS-CoV-2 infection causes a general weakening of intra-TAD contacts and a slight increase in inter-TAD interactions, as sketched in Figure 3c, along with a reduction in Cohesin levels, suggesting decreased loop-extrusion activity. To explore these effects at the TAD scale, a combined LE+SBS model has been employed (Figure 3d) and the key model parameters have been set to best fit the experimental data (31). The best model for Mock data reveals an average distance between extruders of approximately 100–150 kb, consistent with previous estimations obtained from independent Hi-C datasets (54). In contrast, the best model for SARS-CoV-2 infected data shows a significantly decreased number of extruders (approximately halved), consistent with experimental observations of reduced Cohesin levels (40). Moreover, fitting Hi-C data in infected cells requires reduced interaction affinity (around 15–20%) between binders and chromatin, affecting chromatin spatial localization and contributing to the weakening of intra-TAD contacts. Therefore, the model traces back the observed reduction in intra-TAD contacts in infected genomes to a combined alteration in both phase separation (marked by decreased interaction affinity) and loop extrusion (characterized by a reduced number of extruders).

To understand how structural rearrangements within TADs affect gene regulation, genomic regions relevant to viral infection have been modeled. Loci containing interferon (IFN) response genes are typically upregulated upon interferon stimulus and commonly expressed in response to viral infection (80). As an example, the DDX58 gene locus (chr9: 32.3–32.7 Mb, hg19 assembly) is analyzed. In Mock conditions, DDX58 is contained in a well-defined domain limited by convergent CTCF sites (Figure 3e), while in infected cells, a general weakening of intra-TAD interactions is observed, although CTCF peaks remain largely unchanged (Figure 3f). To explore these effects, a realistic LE+SBS polymer model has been built by using experimental CTCF ChIP-seq data to set extruder anchor points and Hi-C data to optimize the SBS binding site positions. The model generates ensembles of 3D structures capturing the differences in the DDX58 locus between Mock (Figure 3e) and SARS-CoV-2 (Figure 3f) conditions, with simulated contact maps highly correlating with experimental data in both cases (r > 0.9, r’ = 0.67). Importantly, the generated 3D structures can be used to explore architectural differences in Mock and SARS-CoV-2-infected cells at the single-molecule level. To this aim several physical observables have been examined such as the 3D distance between the DDX58 promoter and its enhancer (40). In Mock cells, this distance was significantly shorter, while in infected cells, the distribution was more variable, with a 30% higher standard deviation. These results suggests that viral infection disrupts regulatory contacts by altering the coherence of 3D structures, likely through changes in Cohesin and other factors.

To summarize, the polymer-physics-based 3D reconstruction of SARS-CoV-2 infected cells provides mechanistic insights into genome architecture disruption and resulting gene misregulation (39), highlighting the value of polymer physics models for studying 3D chromatin alterations in disease contexts, such as those caused by SARS-CoV-2 infection.

2.4. Predictive models of the impact of SVs on chromatin 3D architecture

A crucial aspect of polymer physics models is their application as predictive tools for chromatin architecture rearrangements upon genomic mutations. In particular, large genomic mutations, such as deletions, duplications and inversions, collectively referred to as Structural Variants (SVs), can disrupt the three-dimensional organization of chromatin, leading to changes in gene expression that underlie various diseases such as congenital disorders and cancer (8, 35, 38, 81–84). Recent research has demonstrated the efficacy of the SBS polymer model in predicting the 3D chromatin structure changes caused by disease-related SVs. This predictive ability aids in understanding how SVs contribute to disease mechanisms (34, 53, 85). Other studies have demonstrated that the LE model can effectively predict the effects of small mutations such alterations of individual CTCF binding sites (50). Interestingly, a combined model that integrates the SBS with specific interactions between CTCF sites enhances the predictions of the SVs effects, reinforcing the idea that the combination of phase separation and LE offers a more comprehensive framework for understanding chromatin folding, even in disease contexts (34).

Here we discuss the application of the SBS model to predict and analyze the impact of SVs on chromatin architecture, as successfully tested in different mutations, including deletions, inversions and duplications at key genomic loci in murine and human cells (34, 53, 85). In this approach, PRISMR is first applied to Hi-C data from wild-type (WT) cells to infer the baseline WT polymer model describing the input contact map. Next, by implementing a SV into the WT polymer model, the resulting changes in the contact map are predicted in-silico from polymer physics only, without any fitting parameters, offering insights into how SVs reshape chromatin architecture, as sketched in Figure 4a. Here we use as an illustrative example, (34)(34). cHi-C data in human skin fibroblasts WT cells reveal a pattern of several TADs, with interactions predominantly occurring within TAD boundaries. PRISMR accurately recapitulates this pattern (Figure 4b), with a high correlation between experimental and model inferred contact maps (r=0.93, r’=0.69). As shown in Figure 4c, the model predicts significant alterations in chromatin architecture upon deletion, and the prediction has been successfully validated against independent cHi-C data (34) performed on cultured human skin fibroblasts carrying this mutation (r=0.93, r’=0.61). The predicted ectopic pattern consents to interpret the deletion from a functional point of view, in terms of rewiring of promoter-enhancer contacts. The deletion disrupts existing TAD boundaries, leading to the formation of new interactions between previously separated regions. Specifically, increased contacts are observed between the EPHA4 enhancers and the gene PAX3, resulting in PAX3 misexpression and disease (34).

Figure 4. Chromatin is reshaped at TADs scale under the effect of SVs.

a) By informing the SBS model inferred from WT contact data with a specific rearrangement (e.g. a deletion), the effects of genomic mutations on chromatin architecture can be predicted from only polymer physics. b) Contact matrices from WT cHi-C data (top) (34) and SBS model (bottom) for a 6-Mb long region in human skin fibroblasts around the EPHA4 gene. The model well recapitulates the locus architecture (r=0.93, r’=0.69). c) The model predicts the effects of DelB, a 1.6-Mb heterozygous deletion at the EPHA4 locus (top), as validated by independent cHi-C data (bottom) in human skin fibroblasts carrying this mutation (34) (r=0.93, r’=0.61). Increased interaction is detected between the EPHA4 enhancer region and the gene PAX3 (blue bars), leading to PAX3 misexpression and brachydactyly. The locus genes (rectangles), TAD boundaries (hexagons), enhancers (ovals), and the deletion (gray box) are displayed between the matrices. Adapted from (34).

In summary, SVs have profound effects on chromatin architecture and gene regulation, often leading to developmental disorders and diseases. Polymer physics-based models offer powerful tools to predict how these variants reshape the three-dimensional genome. By leveraging high-resolution chromosome conformation data, these models can provide detailed insights into the mechanisms by which SVs disrupt chromatin organization and gene expression.

3. Discussion

Polymer physics models provide compelling insights into the multi-scale organization of chromatin and the molecular mechanisms driving it. In this review, we focused on the LE and SBS polymer models, which capture two fundamental and complementary mechanisms of chromosome folding: loop extrusion and phase separation. LE models posit that molecular motors, such as SMC proteins, actively extrude DNA loops, consuming cellular energy (51, 52, 54). Conversely, phase-separation models like SBS suggest that chromatin structures emerge from the spontaneous interaction of diffusing binders, which bridge distal DNA sites via equilibrium polymer thermodynamics (42, 43, 45), a process driven by phase transitions and emergent complex behaviors common to biological systems and soft-matter physics (86–100). The combination of SBS and LE models at the single-molecule level closely aligns with single-cell imaging data, indicating how chromatin contacts at the megabase-scale arise from both active and passive processes (31).

At the genomic level, we showed that the SBS model effectively explains chromatin contacts across various scales, from large chromosomes to TADs and loops. Notably, the molecular nature of the model binding domains has been investigated by correlating their locations with key histone marks (53). This approach revealed that domains fall into major epigenetic classes aligning with known chromatin states (13, 53, 73–76) However, unlike linear segmentations, the binding domains show broad overlaps across the genome, that are necessary to accurately explain Hi-C data. The identified epigenetic classes provide a first, simplified description of these domains, and future models of chromosomes could integrate additional molecular factors, such as CTCF, Pol-II and other histone marks, and additional mechanisms of chromosome folding, such as LE.

Next, we explored applications of polymer physics models in disease contexts. A study applying LE+SBS models to SARS-CoV-2 infected cells effectively explained significant alterations in A/B compartmentalization and TAD structures (40, 77), providing mechanistic insights into how viral infection disrupts chromatin architecture, impacting the expression of genes that are crucial for immune response regulation (39). Polymer models have been also applied to enable quantitative predictions on the effects of disease-linked genomic mutations on chromatin structures, that can be tested against independent experiments. For instance, the SBS model has been shown to successfully predict how specific SVs at key loci, like the EPHA4 locus, perturb 3D chromatin structure, producing ectopic contacts that lead to limb malformations (34). Such predictive capabilities are crucial for interpreting human genetic variants in the context of diseases, such as congenital disorders and cancers, where understanding chromatin organization can inform clinical outcomes. Despite these advancements, accurately simulating the variety of genomic rearrangements caused by SVs remains challenging, especially in case of complex SVs as those emerging in the cancer context (38, 81–84).

Furthermore, the search for the mechanisms controlling chromosome architecture remains an ongoing and debated endeavor. Many questions, such as the molecular rules shaping enhancer-promoter communication, are only partially addressed by current models. Emerging models of long-range transcriptional control propose various mechanisms, such as longer-lived promoter states (26), “activity-by-contact” models based on chromatin state measurements (101), and transcription factor (TF)-grounded activity models relying on local 3D gradients of chemical signals (102). However, a comprehensive molecular understanding is still far from being achieved. Validated theories from polymer physics, based on robust organizing principles, are crucial for elucidating the relationship between genome architecture and function. Additionally, validated models can serve as benchmarks for experimental technologies, expanding their applications in silico (103, 104). Continued advancements in integrating diverse data modalities and refining predictive models will propel the field towards personalized genomic medicine and precision therapies targeting chromatin-mediated diseases.