Mechanical and biochemical signals perceived at the cell membrane activate transcription factors, which are subsequently directed to the target site to modulate cell- or tissue-specific gene expression [248,249,250]. When cells are placed on a substrate with different topographies, the nuclei change their shape, which leads to the activation of different gene expressions [251]. Cells placed on a different topography can exhibit distinct behaviors of proliferation, differentiation, and apoptosis [252,253]. Systemic turning of the contact area between the cell and extracellular matrix leads to altered gene expression of the matrix protein collagen [254]. Fibroblasts plated on polarized geometry express more matrix- or cytoskeleton-associated genes, whereas on isotropic surfaces, they express more cell–cell-junction and cell-cycle genes [251]. Nuclear architecture greatly shapes dynamic activities and expression of transcription factors, and with many genes, transcription occurs in bursts [255]. The transcription level is controlled by the burst frequency rather than the burst size [256]. Enhancer and promoter contacts, even in distant genomic loci, correlate with transcription, whereas the size of polymerase II correlates with the number of transcripts produced in a burst [257,258]. The temporal order of spatial clustering is a crucial aspect of gene co-regulation, and is necessary for activating various gene expression programs in different cell types [259,260,261]. During gene expression, genes are physically brought together. It may also involve the recruitment of transcription factors at different target sites and their subsequent clustering with other supporting transcription factor machinery [33]. It is highly possible that the integration and translation of biochemical cues into different gene expressions are enabled by different cellular and mechanical states [33]. The spatial organization of the genome has been optimized for cell-type-specific transcription, mediated by numerous mechanical and biochemical signals. Defects in mechano-signaling can lead to cell-to-cell contacts or an impaired extracellular matrix, which can lead to the disruption of the cytoskeleton–nucleus interaction, resulting in impaired nuclear morphology [262,263].

The close interaction between the 3D interphase DNA structure and gene expression has made chromatin folding a rapidly developing field of study. Several previous reports have been continuously challenged by the progress of research. For example, in the solenoid model, chromatin is folded into a 30-nm fibre, which is assembled into higher-order structures [264]. However, this report has not been substantiated when studied using electron microscopy tomography, which has shown highly distorted chromatin polymers [232]. We have discussed the role of TADs and the genomic contact and loop extrusion hypothesis based on CTCF and cohesin. It was previously thought that condensin compacts chromosomes by randomly bridging the DNA segment or supercoiling or passively pushing to sites of convergent transcription by RNA polymerase [220]. However, direct observation of loop extrusion in a single molecule has been found in condensin motor activity when quantum-dot-tagged yeast condensin was translocated along double-tethered DNA curtains [265]. The loop extrusion in the naked DNA was reported to be faster than that in DNA polymerase. While the loop extrusion of naked DNA translocation proceeded at a speed of 0.5–2 kb/s, those of DNA and RNA polymerases proceeded at approximately 1 kb/s and 1 kb/min, respectively [266,267]. The SMC complex uses ATP hydrolysis to perform the loop extrusion at a rate of 0.1–2 s⁻¹ [220]. It has also been reported that cohesin- or condensin-binding factors possibly reduce the rate of chromatin loop extrusion. The major factors are the 11-nm nucleosome, RNA polymerase, protein complexes, and DNA structures [220]. However, the SMC complex can avoid these obstacles through nontopological binding, involving intermittent interactions with Nipbl1 and Pds5 proteins that alter the extrusion dynamics, where Nipbl1 possibly acts as a ‘dynamic safety belt’ for the cohesin protein [220]. A recent study has explored these aspects and reported the presence of TAD-like clusters even after cohesin knockout [268,269]. These results suggest that large cooperation of the architectural regulatory proteins, as well as the interplay of supercoiling, molecular binding, phase separation, crowding effect, and loop extrusion events, is needed. There are also questions regarding the functional units of chromatin and their hierarchy of folding, and the inner functional units of working TADs at the single-cell level. To understand all these intricate events, researchers have applied mathematical rules (stochastic, self-returning event) and studied a folding algorithm that can replicate experimental observations [270]. The most common type of chromatin interaction in the genome is that of the promoter and enhancer for transcriptional regulation and heterogeneous packing, which disperses local DNA accessibility and allows transcription and nuclear transport. From a polymer physics point of view, there is an apparent conflict between these two chromatin properties. It has been reported that chromatin resembles a fractal globule, which is a self-similar polymer in a collapsed state [271,272]. Although the fractal globule model observes high contact frequencies, it does not explain the spatial heterogeneity of chromatin packaging, which a 1D polymer cannot provide [270]. Therefore, researchers have provided a self-returning random walk (SRRW) mathematical model to address the contact-structure paradox [270]. It provides a non-branching topology of the 10-nm chromatin fiber and generates tree-like topological domains connected to an open chromatin backbone [270]. The SRRW model, presenting a new picture of genome organization, supports the hypothesis that local DNA density plays a critical role as a transcriptional regulator; the chromatin folds into a variety of minimally entangled hierarchical structures across the length from nanometers to micrometers without the necessity of a 30-nm fiber [270]. This model also explains the structure–function relationship of the interphase DNA with higher-order folding and a substantial reduction in dimension during genomic landscape exploration [270]. The model also predicts that the topological domains in single cells contain random-tree structures, where tree domains are regarded as nanoclusters and loops on a kilobase-to-megabase scale, serving as building blocks for large packaging domains. These tree domains are called ‘3D forests’ within the chromosome territory [270]. The size of a tree domain is positively correlated with the size of the genome, with considerable depression [270]. There is also a positive correlation between the tree domain size and packaging density, suggesting a size-dependent domain activity, where the nanodomain of the peak radius is approximately 70 nm [270]. Additionally, the model predicts a correlation between local DNA density and domain size, supporting the view that small domains are more active than large domains [270]. The first-order genome of a double helix DNA evolves to adopt a ‘virtual tree data structure’ for higher-order genome organization [270]. This tree-like topological domain is connected by an open functional backbone segment, which facilitates the proper organization of genomic contacts, package-based regulation of transcription, transport and accommodation of nuclear proteins, and transition between the interphase and mitosis [270].

A computational string and binder (SBS) model was proposed in polymer physics to understand the mechanism of chromosome compartmentalization, pattern formation, and chromatin folding [273]. According to the SBS model, chromatin folding can be driven thermodynamically by homotypic interactions between DNA sites that share compatible chromatin marks [273,274,275,276,277]. The chromatin filament acts as a self-avoiding walk string of beads, where specific beads function as binding sites for a cognate diffusing binder that can bridge them to allow folding [273]. The different binding sites can selectively interact with their cognate binder, and these binding activities can be computationally investigated by molecular dynamics simulations using Langevin dynamics with classical interaction potential [273,277]. This model explains chromatin folding thermodynamically by homotypic interactions between DNA sites sharing cognate chromatin [275,276,277,278,279]. This interaction takes place via protein binding to multiple sites, inducing phase separation of chromatin sub-compartments [280]. The association between chromatin sites and the nuclear lamina and speckles can also be inferred using the SBS model, with the help of the bridging protein transcription factor YY1, RNA polymerase II, and Polycomb repressive complex 1 [273,281].

The role of an enhancer that resides in the proximity of its target genes and the role of TADs are well known. The volume of the chromatin interaction data increases regularly, and efficient visualization and navigation of these data are the major bottlenecks for their interpretation. These factors make it a daunting task for an individual laboratory to store and explore them properly. To overcome these problems, several visualization tools have been developed, with unique features and limitations. The Hi-C data browser is reportedly the first web-based query tool to visualize Hi-C data as heat maps [152]. However, it does not support zoom functionalization and can hold only a limited number of datasets. The WashU epigenome browser visualizes Hi-C and ChIA-PET data, which also enables access to thousands of epigenome datasets from ENCODE and the Roadmap epigenome project (Figure 4) [286,287]. A Hi-C data matrix of files with large sizes up to hundreds of gigabytes tends to slow down the visualization process. Furthermore, it does not have the option to display inter-chromosomal interaction data as in a heat map. Hi-C data can also be explored using Juicebox [288] and Hi-Glass [289] at high speeds. However, none of these provides chromatin data, such as Capture Hi-C or ChIA-PET (Table 1, Figure 4). The Delta browser can display Hi-C data and a physical view of 3D genome modelling [290]. The 3D genome browser can help explore chromatin interaction data at the domain level and provide high-resolution promoter–enhancer interactions [291]. The 3D genome browser can facilitate zoom and traverse functions in real time, enabling queries using genomic loci, gene names, or SNPs (Figure 4) [291]. A user can also incorporate the UCSC genome browser with the WashU epigenome browser and query the chromatin interaction data with thousands of genetic, epigenetic, and phenotypic datasets, using the 3D genome browser [291]. Additionally, users can add or modify existing data or upload their genome or epigenome data, as well as view Hi-C data by converting the contract matrix into an indexed binary file called the ‘binary upper triangular matrix’ (BUTLR file). Users need to host a BUTLR file on an HTTP server and provide the URL to the 3D genome browser to obtain the full advantage of all the features of the 3D genome browser without the need to upload Hi-C data [291].