Decoding the spatial organizations of chromosomes has crucial on the relationship between complex chromatin structure and its regulatory functions in controlling genomic activities (1–4). Computing a trust region step. However, relation between large-scale order of chromosome positioning and gene .. This work was supported by grants from the Wellcome Trust /04/ Z. How do chromosomes, DNA and genes all fit together? We can use the analogy of a city to better understand the relationship between DNA molecules.
The Global Relationship between Chromatin Physical Topology, Fractal Structure, and Gene Expression
In 19an expectation-maximization based algorithm was proposed to infer the 3D chromatin organizations under a Bayesian like framework. Several stochastic sampling based methods, such as Markov chain Monte Carlo MCMC and simulated annealing 32were also used in a probabilistic framework to compute chromatin structures that satisfy the spatial distances derived from Hi-C data.
In addition, a shortest-path algorithm was used in ShRec3D 18 to interpolate the spatial distance matrix obtained from Hi-C data, based on which the MDS algorithm was then applied to reconstruct the 3D coordinates of genomic loci. Despite the significant progress made in the methodology development of 3D chromatin structure reconstruction, most of existing reconstruction methods still suffer from several limitations.
For example, few methods integrate the experimental Hi-C data with the previously known biophysical energy model of 3D chromatin structure, raising potential concerns about the biophysical feasibility and structural stability of the reconstructed 3D structures. More importantly, as mentioned previously, most of existing chromatin structure modeling methods 57111315—242627 heavily rely on the underlying assumptions about the explicit relationships between interaction frequencies derived from 3C-based data and spatial distances between genomic loci.
If the specific forms of hypothetical functions or distributions are not sufficiently accurate, they will mislead the optimization process and cause bias during the modeling process. Thus, the accuracy of the chromatin structures reconstructed by these methods is heavily dependent on the goodness of the assumed relationships between interaction frequencies and spatial distances.
Recently, manifold learning, such as t-SNE 33has been successfully applied as a general framework for nonlinear dimensionality reduction in machine learning and pattern recognition 3134— It aims to reconstruct the underlying low-dimensional manifolds from the abstract representations in the high-dimensional space.
In this work, to address the aforementioned issues in 3D chromatin structure reconstruction, we propose a novel manifold learning based framework, called GEM Genomic organization reconstructor based on conformational Eenergy and Manifold learningwhich directly embeds the neighboring affinities from Hi-C space into 3D Euclidean space using an optimization process that considers both Hi-C data and the conformational energy derived from our current biophysical knowledge about the polymer model.
From the perspective of manifold learning, the spatial organizations of chromosomes can be interpreted as the geometry of manifolds in 3D Euclidean space.
The Global Relationship between Chromatin Physical Topology, Fractal Structure, and Gene Expression
Here, the Hi-C interaction frequency data can be regarded as a specific representation of the neighboring affinities reflecting the spatial arrangements of genomic loci, which is intrinsically determined by the underlying manifolds embedded in Hi-C space. Based on this rationale, manifold learning can be applied here to uncover the intrinsic 3D geometry of the underlying manifolds from Hi-C data.
In mitotic chromosomes, scaffold proteins fold the chromatin fibre into loops along its length. Chromosomes are very dynamic structures and take several forms, but the basic organisation is always related to the structure of mitotic chromosomes. The location of chromosomes in the nucleus, the nature of the loops and modifications to the chromatin fibre are thought to be important in determining which DNA sequences are made available for transcription and other processes.
Chromosomes and Chromatin
In eukaryotic cells, genes are located in chromosomes in the cell nucleus. Before the DNA has been replicated, a chromosome consists of a single very long DNA double helix that is highly coiled and folded by proteins. Transcriptional activation of genes, or readiness for transcriptional activation, is associated with histone acetylation, and inactivation is generally associated with histone methylation.
In mitotic chromosomes, the chromatin fibre is folded into loops by attachment to a scaffold of nonhistone proteins. Mitotic chromosome condensation appears to involve two components: The various chromosome forms that are seen throughout the cell cycle or the life cycle of the organism have closely related structures.
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Chromosome banding and chromosome painting are medically important for detecting chromosome abnormalities such as breaks, fusions, translocations and aneuploidy and can be used to track chromosomal rearrangements that have occurred during evolution. Reproduced with permission from Luger et al.
Reproduced from Thoma et al. Mitotic chromosomes, scaffolds and loops. The scaffold has a diffuse, fibrous texture except in i where part of one arm appears to have become artefactually condensed during spreading and dehydration. Micrograph in a reproduced with permission from DuPraw ; be and f reproduced from Marsden and Laemmli with permission from Elsevier; c and d reproduced from Paulson and Laemmli with permission from Elsevier; g reproduced from Roth and Gall with permission from The Rockefeller University Press; h and i reproduced from Paulson with permission from Springer.
Condensin regulates the structure of the vertebrate mitotic chromosome. The condensin complex is present in the axial region of each chromatid. In turn, the fractal properties of chromatin topology may have profound effects on the spatial arrangement of chromatin density. Therefore in this work, we quantitatively analyzed the effects of changes in fractal dimension D on the accessible surface area and the variations in focal compaction.
In this model, we show that as D increases, both the accessible surface area and the variations of local compaction within chromatin increase.
As the increase of accessible surface area and focal compaction will have competing effects on gene expression globally, we hypothesized that a competition would occur in vitro between activation and suppression of expression as D increases.
Likewise, we hypothesized that increases in the variations of density would in turn produce a heterogeneity in gene expression. To test these effects, we utilized microarray analysis to measure changes in gene expression and PWS microscopy to measure the changes in chromatin heterogeneity in colonic HT cells under different growth conditions.Genes vs. DNA vs. Chromosomes - Instant Egghead #19
Using newly developed live cell PWS microscopy, we further show that these physical changes in chromatin structure precede the observed transformation in transcription with topological changes occurring within 30 minutes. In agreement with this model, our results show that as D increases a competition between gene activation and repression occurs.
Additionally, the results demonstrate that increases in D produced an increase in transcriptional heterogeneity for critical processes such as cellular proliferation and apoptosis. Further, to understand if these changes in genes sensitive to physical topology could have a functional significance in gene expression related to oncology, we analyzed the ontologies of genes correlated with D.
Significantly, we show that genes highly correlated with D are more likely to regulate cellular metabolism than genes uncorrelated with D — with activation of genes regulating glucose metabolism and a suppression of mitochondrial genes maintaining oxidative metabolism, indicating a shift toward glycolytic metabolism as D increases.
Finally, by analyzing gene expression data within the Cancer Genome Atlas TCGAwe show that colon cancer patients with mutations in genes correlated D have a shorter mean survival than patients without mutations in those genes. In total, this work provides the first quantitative functional model that shows an integration between the physical structure of chromatin, transcriptional homeostasis, and colon cancer.
Results and Discussion In cells, there are several potential mechanisms through which changes in the physical topology of chromatin can broadly and nonspecifically regulate gene expression.
For example, an overall increase in the surface area of chromatin may facilitate global gene transcription due to an improved access of transcription factors to DNA.
In comparison, increasing the average mass-density i.
- Associated Data
- Chromosomes and Chromatin
Therefore, increasing access globally may have an associated cost that cannot be captured by qualitative models of chromatin organization. Evidence for this non-linearity between the accessible surface area and variations in focal chromatin compaction has been shown within a few tens of nanometers near the site of active transcription, suggesting that increased accessibility for some genes is paired to tightly packing neighboring genes 2633 Consequently, understanding this relation globally requires a quantitative model of chromatin physical structure.
To understand this structure-function relation in the context of human disease, we first consider the alterations that occur in the physical structure of chromatin during carcinogenesis. It is widely accepted that the physical structure of the nucleus is altered in tumor cells at the time of diagnosis. While histological identification of physical alterations in tumor cells shows evidence of micron-scale transformation in topology, the question naturally arises if this transformation extends to the earliest stages of tumor formation at the nanoscale.
Previous studies using TEM and PWS have shown nanoscopic physical transformation in chromatin organization at these earliest stages even in histologically normal tissue 1819212235 The fractal nature of chromatin folding has been observed by a variety of techniques including transmission electron microscopy TEM 18high throughput chromatin conformation capture HiC 2STORM microscopy 26DNA photon localization microscopy 37neutron scattering 23Partial Wave Spectroscopic microscopy 38and fluorescence correlation spectroscopy