A fractal model for nuclear organization: current evidence and biological implications

Diffusive lensing as a mechanism of intracellular transport and compartmentalization

While inhomogeneous diffusivity has been identified as a ubiquitous feature of the cellular interior, its implications for particle mobility and concentration at different length scales remain largely unexplored. In this work, we use agent-based simulations of diffusion to investigate how heterogeneous diffusivity affects the movement and concentration of diffusing particles. We propose that a nonequilibrium mode of membrane-less compartmentalization arising from the convergence of diffusive trajectories into low-diffusive sinks, which we call 'diffusive lensing,' is relevant for living systems. Our work highlights the phenomenon of diffusive lensing as a potentially key driver of mesoscale dynamics in the cytoplasm, with possible far-reaching implications for biochemical processes.

Formamide denaturation of double-stranded DNA for fluorescence in situ hybridization (FISH) distorts nanoscale chromatin structure

As imaging techniques rapidly evolve to probe nanoscale genome organization at higher resolution, it is critical to consider how the reagents and procedures involved in sample preparation affect chromatin at the relevant length scales. Here, we investigate the effects of fluorescent labeling of DNA sequences within chromatin using the gold standard technique of three-dimensional fluorescence in situ hybridization (3D FISH). The chemical reagents involved in the 3D FISH protocol, specifically formamide, cause significant alterations to the sub-200 nm (sub-Mbp) chromatin structure. Alternatively, two labeling methods that do not rely on formamide denaturation, resolution after single-strand exonuclease resection (RASER)-FISH and clustered regularly interspaced short palindromic repeats (CRISPR)-Sirius, had minimal impact on the three-dimensional organization of chromatin. We present a polymer physics-based analysis of these protocols with guidelines for their interpretation when assessing chromatin structure using currently available techniques.

Correlative single molecule lattice light sheet imaging reveals the dynamic relationship between nucleosomes and the local chromatin environment

In the nucleus, biological processes are driven by proteins that diffuse through and bind to a meshwork of nucleic acid polymers. To better understand this interplay, we present an imaging platform to simultaneously visualize single protein dynamics together with the local chromatin environment in live cells. Together with super-resolution imaging, new fluorescent probes, and biophysical modeling, we demonstrate that nucleosomes display differential diffusion and packing arrangements as chromatin density increases whereas the viscoelastic properties and accessibility of the interchromatin space remain constant. Perturbing nuclear functions impacts nucleosome diffusive properties in a manner that is dependent both on local chromatin density and on relative location within the nucleus. Our results support a model wherein transcription locally stabilizes nucleosomes while simultaneously allowing for the free exchange of nuclear proteins. Additionally, they reveal that nuclear heterogeneity arises from both active and passive processes and highlight the need to account for different organizational principles when modeling different chromatin environments.

From Cell States to Cell Fates: Control of Cell State Transitions

We examine the coordinated behavior of thousands of genes in cell fate transitions through genome expression as an integrated dynamical system using the concepts of self-organized criticality and coherent stochastic behavior. To quantify the effects of the collective behavior of genes, we adopted the flux balance approach and developed it in a new tool termed expression flux analysis (EFA). Here we describe this tool and demonstrate how its application to specific experimental genome-wide expression data provides new insights into the dynamics of the cell-fate transitions. Particularly, we show that in cell fate change, specific stochastic perturbations can spread over the entire system to guide distinct cell fate transitions through switching cyclic flux flow in the genome engine. Utilization of EFA enables us to elucidate a unified genomic mechanism for when and how cell-fate change occurs through critical transitions.

Correlative single molecule lattice light sheet imaging reveals the dynamic relationship between nucleosomes and the local chromatin environment

In the nucleus, biological processes are driven by proteins that diffuse through and bind to a meshwork of nucleic acid polymers. To better understand this interplay, we developed an imaging platform to simultaneously visualize single protein dynamics together with the local chromatin environment in live cells. Together with super-resolution imaging, new fluorescent probes, and biophysical modeling, we demonstrated that nucleosomes display differential diffusion and packing arrangements as chromatin density increases whereas the viscoelastic properties and accessibility of the interchromatin space remain constant. Perturbing nuclear functions impacted nucleosome diffusive properties in a manner that was dependent on local chromatin density and supportive of a model wherein transcription locally stabilizes nucleosomes while simultaneously allowing for the free exchange of nuclear proteins. Our results reveal that nuclear heterogeneity arises from both active and passive process and highlights the need to account for different organizational principals when modeling different chromatin environments.

Morphological profiling by high-throughput single-cell biophysical fractometry

Complex and irregular cell architecture is known to statistically exhibit fractal geometry, i.e., a pattern resembles a smaller part of itself. Although fractal variations in cells are proven to be closely associated with the disease-related phenotypes that are otherwise obscured in the standard cell-based assays, fractal analysis with single-cell precision remains largely unexplored. To close this gap, here we develop an image-based approach that quantifies a multitude of single-cell biophysical fractal-related properties at subcellular resolution. Taking together with its high-throughput single-cell imaging performance (~10,000 cells/sec), this technique, termed single-cell biophysical fractometry, offers sufficient statistical power for delineating the cellular heterogeneity, in the context of lung-cancer cell subtype classification, drug response assays and cell-cycle progression tracking. Further correlative fractal analysis shows that single-cell biophysical fractometry can enrich the standard morphological profiling depth and spearhead systematic fractal analysis of how cell morphology encodes cellular health and pathological conditions.

First-passage statistics of colloids on fractals: Theory and experimental realization

In nature and technology, particle dynamics frequently occur in complex environments, for example in restricted geometries or crowded media. These dynamics have often been modeled invoking a fractal structure of the medium although the fractal structure was only indirectly inferred through the dynamics. Moreover, systematic studies have not yet been performed. Here, colloidal particles moving in a laser speckle pattern are used as a model system. In this case, the experimental observations can be reliably traced to the fractal structure of the underlying medium with an adjustable fractal dimension. First-passage time statistics reveal that the particles explore the speckle in a self-similar, fractal manner at least over four decades in time and on length scales up to 20 times the particle radius. The requirements for fractal diffusion to be applicable are laid out, and methods to extract the fractal dimension are established.

Bifractal structure of chromatin in rat lymphocyte nuclei

The small-angle neutron scattering (SANS) on the rat lymphocyte nuclei demonstrates the bifractal nature of the chromatin structural organization. The scattering intensity from rat lymphocyte nuclei is described by power law Q^{-D} with fractal dimension approximately 2.3 on smaller scales and 3 on larger scales. The crossover between two fractal structures is detected at momentum transfer near 10^{-1}nm^{-1}. The use of contrast variation (D_{2}O-H_{2}O) in SANS measurements reveals clear similarity in the structural organizations of nucleic acids (NA) and proteins. Both chromatin components show bifractal behavior with logarithmic fractal structure on the large scale and volume fractal with slightly smaller than 2.5 structure on the small scale. Scattering intensities from chromatin, protein component, and NA component demonstrate an extremely extensive range of logarithmic fractal behavior (from 10^{-3} to approximately 10^{-1}nm^{-1}). We compare the fractal arrangement of rat lymphocyte nuclei with that of chicken erythrocytes and the immortal HeLa cell line. We conclude that the bifractal nature of the chromatin arrangement is inherent in the nuclei of all these cells. The details of the fractal arrangement-its range and correlation/interaction between nuclear acids and proteins are specific for different cells and is related to their functionality.

Observation of nucleic acid and protein correlation in chromatin of HeLa nuclei using small-angle neutron scattering with D_{2}O-H_{2}O contrast variation

The small-angle neutron scattering (SANS) on HeLa nuclei demonstrates the bifractal nature of the chromatin structural organization. The border line between two fractal structures is detected as a crossover point at Q_{c}≈4×10^{-2}nm^{-1} in the momentum transfer dependence Q^{-D}. The use of contrast variation (D_{2}O-H_{2}O) in SANS measurements reveals clear similarity in the large scale structural organizations of nucleic acids (NA) and proteins. Both NA and protein structures have a mass fractal arrangement with the fractal dimension of D≈2.5 at scales smaller than 150 nm down to 20 nm. Both NA and proteins show a logarithmic fractal behavior with D≈3 at scales larger than 150 nm up to 6000 nm. The combined analysis of the SANS and atomic force microscopy data allows one to conclude that chromatin and its constitutes (DNA and proteins) are characterized as soft, densely packed, logarithmic fractals on the large scale and as rigid, loosely packed, mass fractals on the smaller scale. The comparison of the partial cross sections from NA and proteins with one from chromatin as a whole demonstrates spatial correlation of two chromatin's components in the range up to 900 nm. Thus chromatin in HeLa nuclei is built as the unified structure of the NA and proteins entwined through each other. Correlation between two components is lost upon scale increases toward 6000 nm. The structural features at the large scale, probably, provide nuclei with the flexibility and chromatin-free space to build supercorrelations on the distance of 10^{3} nm resembling cycle cell activity, such as an appearance of nucleoli and a DNA replication.

Stochastic chromatin packing of 3D mitotic chromosomes revealed by coherent X-rays

DNA molecules are atomic-scale information storage molecules that promote reliable information transfer via fault-free repetitions of replications and transcriptions. Remarkable accuracy of compacting a few-meters-long DNA into a micrometer-scale object, and the reverse, makes the chromosome one of the most intriguing structures from both physical and biological viewpoints. However, its three-dimensional (3D) structure remains elusive with challenges in observing native structures of specimens at tens-of-nanometers resolution. Here, using cryogenic coherent X-ray diffraction imaging, we succeeded in obtaining nanoscale 3D structures of metaphase chromosomes that exhibited a random distribution of electron density without characteristics of high-order folding structures. Scaling analysis of the chromosomes, compared with a model structure having the same density profile as the experimental results, has discovered the fractal nature of density distributions. Quantitative 3D density maps, corroborated by molecular dynamics simulations, reveal that internal structures of chromosomes conform to diffusion-limited aggregation behavior, which indicates that 3D chromatin packing occurs via stochastic processes.

Neutron Scattering Techniques and Complementary Methods for Structural and Functional Studies of Biological Macromolecules and Large Macromolecular Complexes

Abstract

The review describes the application of small-angle scattering (SAS) of neutrons and complementary methods to study the structures of biomacromolecules. Here we cover SAS techniques, such as the contrast variation, the neutron spin-echo, and the solution of direct and inverse problems of three-dimensional reconstruction of the structures of macromolecules from SAS spectra by means of molecular modeling. A special section is devoted to specific objects of research, such as supramolecular complexes, influenza virus nucleoprotein, and chromatin.

Dynamic asymmetry and why chromatin defies simple physical definitions

Recent experiments have demonstrated a nucleus where chromatin is molded into stable, interwoven loops. Yet, many of the proteins, which shape chromatin structure, bind only transiently. In those brief encounters, these dynamic proteins temporarily crosslink chromatin loops. While, on the average, individual crosslinks do not persist, in the aggregate, they are sufficient to create and maintain stable chromatin domains. Owing to the asymmetry in size and speed of molecules involved, this type of organization imparts unique biophysical properties-the slow (chromatin) component can exhibit gel-like behaviors, whereas the fast (protein) component allows domains to respond with liquid-like characteristics.

Switch of fractal properties of DNA in chicken erythrocytes nuclei by mechanical stress

The small-angle neutron scattering (SANS) on the chicken erythrocyte nuclei demonstrates the bifractal nature of the chromatin structural organization. Use of the contrast variation (D_{2}O-H_{2}O) in SANS measurements reveals the differences in the DNA and protein arrangements inside the chromatin substance. It is the DNA that serves as a framework that constitutes the bifractal behavior showing the mass fractal properties with D=2.22 at a smaller scale and the logarithmic fractal behavior with D≈3 at a larger scale. The protein spatial organization shows the mass fractal properties with D≈2.34 throughout the whole nucleus. The borderline between two fractal levels can be significantly shifted toward smaller scales by centrifugation of the nuclei disposed on the dry substrate, since nuclei suffer from mechanical stress transforming them to a disklike shape. The height of this disk measured by atomic force microscopy (AFM) coincides closely with the fractal borderline, thus characterizing two types of the chromatin with the soft (at larger scale) and rigid (at smaller scale) properties. The combined SANS and AFM measurements demonstrate the stress induced switch of the DNA fractal properties from the rigid, but loosely packed, mass fractal to the soft, but densely packed, logarithmic fractal.

The Complexity and Fractal Geometry of Nuclear Medicine Images

Irregularity in shape and behavior is the main feature of every anatomical system, including human organs, tissues, cells, and sub-cellular entities. It has been shown that this property cannot be quantified by means of the classical Euclidean geometry, which is only able to describe regular geometrical objects. In contrast, fractal geometry has been widely applied in several scientific fields. This rapid growth has also produced substantial insights in the biomedical imaging. Consequently, particular attention has been given to the identification of pathognomonic patterns of "shape" in anatomical entities and their changes from natural to pathological states. Despite the advantages of fractal mathematics and several studies demonstrating its applicability to oncological research, many researchers and clinicians remain unaware of its potential. Therefore, this review aims to summarize the complexity and fractal geometry of nuclear medicine images.

Computing 3D Chromatin Configurations from Contact Probability Maps by Inverse Brownian Dynamics

The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state-accessibility and amount of gene expression-of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.

Chromatin Compaction Multiscale Modeling: A Complex Synergy Between Theory, Simulation, and Experiment

Understanding the mechanisms that trigger chromatin compaction, its patterns, and the factors they depend on, is a fundamental and still open question in Biology. Chromatin compacts and reinforces DNA and is a stable but dynamic structure, to make DNA accessible to proteins. In recent years, computational advances have provided larger amounts of data and have made large-scale simulations more viable. Experimental techniques for the extraction and reconstitution of chromatin fibers have improved, reinvigorating theoretical and experimental interest in the topic and stimulating debate on points previously considered as certainties regarding chromatin. A great assortment of approaches has emerged, from all-atom single-nucleosome or oligonucleosome simulations to various degrees of coarse graining, to polymer models, to fractal-like structures and purely topological models. Different fiber-start patterns have been studied in theory and experiment, as well as different linker DNA lengths. DNA is a highly charged macromolecule, making ionic and electrostatic interactions extremely important for chromatin topology and dynamics. Indeed, the repercussions of varying ionic concentration have been extensively examined at the computational level, using all-atom, coarse-grained, and continuum techniques. The presence of high-curvature AT-rich segments in DNA can cause conformational variations, attesting to the fact that the role of DNA is both structural and electrostatic. There have been some tentative attempts to describe the force fields governing chromatin conformational changes and the energy landscapes of these transitions, but the intricacy of the system has hampered reaching a consensus. The study of chromatin conformations is an intrinsically multiscale topic, influenced by a wide range of biological and physical interactions, spanning from the atomic to the chromosome level. Therefore, powerful modeling techniques and carefully planned experiments are required for an overview of the most relevant phenomena and interactions. The topic provides fertile ground for interdisciplinary studies featuring a synergy between theoretical and experimental scientists from different fields and the cross-validation of respective results, with a multi-scale perspective. Here, we summarize some of the most representative approaches, and focus on the importance of electrostatics and solvation, often overlooked aspects of chromatin modeling.

Scale Trotter: Illustrative Visual Travels Across Negative Scales

We present ScaleTrotter, a conceptual framework for an interactive, multi-scale visualization of biological mesoscale data and, specifically, genome data. ScaleTrotter allows viewers to smoothly transition from the nucleus of a cell to the atomistic composition of the DNA, while bridging several orders of magnitude in scale. The challenges in creating an interactive visualization of genome data are fundamentally different in several ways from those in other domains like astronomy that require a multi-scale representation as well. First, genome data has intertwined scale levels-the DNA is an extremely long, connected molecule that manifests itself at all scale levels. Second, elements of the DNA do not disappear as one zooms out-instead the scale levels at which they are observed group these elements differently. Third, we have detailed information and thus geometry for the entire dataset and for all scale levels, posing a challenge for interactive visual exploration. Finally, the conceptual scale levels for genome data are close in scale space, requiring us to find ways to visually embed a smaller scale into a coarser one. We address these challenges by creating a new multi-scale visualization concept. We use a scale-dependent camera model that controls the visual embedding of the scales into their respective parents, the rendering of a subset of the scale hierarchy, and the location, size, and scope of the view. In traversing the scales, ScaleTrotter is roaming between 2D and 3D visual representations that are depicted in integrated visuals. We discuss, specifically, how this form of multi-scale visualization follows from the specific characteristics of the genome data and describe its implementation. Finally, we discuss the implications of our work to the general illustrative depiction of multi-scale data.

Disordered chromatin packing regulates phenotypic plasticity

Three-dimensional supranucleosomal chromatin packing plays a profound role in modulating gene expression by regulating transcription reactions through mechanisms such as gene accessibility, binding affinities, and molecular diffusion. Here, we use a computational model that integrates disordered chromatin packing (CP) with local macromolecular crowding (MC) to study how physical factors, including chromatin density, the scaling of chromatin packing, and the size of chromatin packing domains, influence gene expression. We computationally and experimentally identify a major role of these physical factors, specifically chromatin packing scaling, in regulating phenotypic plasticity, determining responsiveness to external stressors by influencing both intercellular transcriptional malleability and heterogeneity. Applying CPMC model predictions to transcriptional data from cancer patients, we identify an inverse relationship between patient survival and phenotypic plasticity of tumor cells.

Guided nuclear exploration increases CTCF target search efficiency

The enormous size of mammalian genomes means that for a DNA-binding protein, the number of non-specific, off-target sites vastly exceeds the number of specific, cognate sites. How mammalian DNA-binding proteins overcome this challenge to efficiently locate their target sites is not known. Here through live-cell single-molecule tracking, we show that CCCTC-binding factor, CTCF, is repeatedly trapped in small zones that likely correspond to CTCF clusters, in a manner that is largely dependent on an internal RNA-binding region (RBR_i). We develop a new theoretical model, Anisotropic Diffusion through transient Trapping in Zones (ADTZ), to explain CTCF dynamics. Functionally, transient RBR_i-mediated trapping increases the efficiency of CTCF target search by ~2.5 fold. Overall, our results suggest a “guided” mechanism where CTCF clusters concentrate diffusing CTCF proteins near cognate binding sites, thus increasing the local ON-rate. We suggest that local guiding may allow DNA-binding proteins to more efficiently locate their target sites.

Small-angle neutron scattering (SANS) and spin-echo SANS measurements reveal the logarithmic fractal structure of the large-scale chromatin organization in HeLa nuclei

This paper reports on the two-scale fractal structure of chromatin organization in the nucleus of the HeLa cell. Two neutron scattering methods, small-angle neutron scattering (SANS) and spin-echo SANS, are used to unambiguously identify the large-scale structure as being a logarithmic fractal with the correlation function γ(r) ∼ ln(r/ξ). The smaller-scale structural level is shown to be a volume fractal with dimension D F = 2.41. By definition, the volume fractal is self-similar at different scales, while the logarithmic fractal is hierarchically changed upon scaling. As a result, the logarithmic fractal is more compact than the volume fractal but still has a rather high surface area, which provides accessibility at all length scales. Apparently such bi-fractal chromatin organization is the result of an evolutionary process of optimizing the compactness and accessibility of gene packing. As they are in a water solution, the HeLa nuclei tend to agglomerate over time. The large-scale logarithmic fractal structure of chromatin provides the HeLa nucleus with the possibility of penetrating deeply into the adjacent nucleus during the agglomeration process. The interpenetration phenomenon of the HeLa nuclei shows that the chromatin-free space of one nucleus is not negligible but is as large as the volume occupied by chromatin itself. It is speculated that it is the logarithmic fractal architecture of chromatin that provides a comfortable compartment for this most important function of the cell.

Chromatin fiber structural motifs as regulatory hubs of genome function?

Nucleosomes cover eukaryotic genomes like beads on a string and play a central role in regulating genome function. Isolated strings of nucleosomes have the potential to compact and form higher order chromatin structures, such as the well-characterized 30-nm fiber. However, despite tremendous advances in observing chromatin fibers in situ it has not been possible to confirm that regularly ordered fibers represent a prevalent structural level in the folding of chromosomes. Instead, it appears that folding at a larger scale than the nucleosome involves a variety of random structures with fractal characteristics. Nevertheless, recent progress provides evidence for the existence of structural motifs in chromatin fibers, potentially localized to strategic sites in the genome. Here we review the current understanding of chromatin fiber folding and the emerging roles that oligonucleosomal motifs play in the regulation of genome function.

Transmission Electron Microscopy Imaging to Analyze Chromatin Density Distribution at the Nanoscale Level

Transmission electron microscopy (TEM) is used to study the fine ultrastructural organization of cells. Delicate specimen preparation is required for results to reflect the "native" ultrastructural organization of subcellular features such as the nucleus. Despite the advent of high-resolution, fluorescent imaging of chromatin components, TEM still provides a unique and complementary level of resolution capturing chromatin organization at the nanoscale level. Here, we describe the workflow, from tissue preparation, TEM image acquisition and image processing, for obtaining a quantitative description of chromatin density distribution in plant cells, informing on local fluctuations and periodicity. Comparative analyses then allow to elucidate the structural changes induced by developmental or environmental cues, or by mutations affecting specific chromatin modifiers at the nanoscale level. We argue that this approach remains affordable and merits a renewed interest by the plant chromatin community.

Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects

We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to such system details. By contrast, we verify that the fractal dimension d_{f} is a universal quantity and unaffected by the choice of metric. We also show that for weak correlations, its value coincides with that for the uncorrelated system. In two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength, approaching d_{f}→2. The onset of this change does not seem to be determined by the extended Harris criterion.

Measuring Nanoscale Chromatin Heterogeneity with Partial Wave Spectroscopic Microscopy

Despite extensive research in the area, current understanding of the structural organization of higher-order chromatin topology (between 20 and 200 nm) is limited due to a lack of proper imaging techniques at these length scales. The organization of chromatin at these scales defines the physical context (nanoenvironment) in which many important biological processes occur. Improving our understanding of the nanoenvironment is crucial because it has been shown to play a critical functional role in the regulation of chemical reactions. Recent progress in partial wave spectroscopic (PWS) microscopy enables real-time measurement of higher-order chromatin organization within label-free live cells. Specifically, PWS quantifies the nanoscale variations in mass density (heterogeneity) within the cell. These advancements have made it possible to study the functional role of chromatin topology, such as its regulation of the global transcriptional state of the cell and its role in the development of cancer. In this chapter, the importance of studying chromatin topology is explained, the theory and instrumentation of PWS are described, the measurements and analysis processes for PWS are laid out in detail, and common issues, troubleshooting steps, and validation techniques are provided.

The 10-nm chromatin fiber and its relationship to interphase chromosome organization

A chromosome is a single long DNA molecule assembled along its length with nucleosomes and proteins. During interphase, a mammalian chromosome exists as a highly organized supramolecular globule in the nucleus. Here, we discuss new insights into how genomic DNA is packaged and organized within interphase chromosomes. Our emphasis is on the structural principles that underlie chromosome organization, with a particular focus on the intrinsic contributions of the 10-nm chromatin fiber, but not the regular 30-nm fiber. We hypothesize that the hierarchical globular organization of an interphase chromosome is fundamentally established by the self-interacting properties of a 10-nm zig-zag array of nucleosomes, while histone post-translational modifications, histone variants, and chromatin-associated proteins serve to mold generic chromatin domains into specific structural and functional entities.

Macrogenomic engineering via modulation of the scaling of chromatin packing density

Many human diseases result from the dysregulation of the complex interactions between tens to thousands of genes. However, approaches for the transcriptional modulation of many genes simultaneously in a predictive manner are lacking. Here, through the combination of simulations, systems modelling and in vitro experiments, we provide a physical regulatory framework based on chromatin packing-density heterogeneity for modulating the genomic information space. Because transcriptional interactions are essentially chemical reactions, they depend largely on the local physical nanoenvironment. We show that the regulation of the chromatin nanoenvironment allows for the predictable modulation of global patterns in gene expression. In particular, we show that the rational modulation of chromatin density fluctuations can lead to a decrease in global transcriptional activity and intercellular transcriptional heterogeneity in cancer cells during chemotherapeutic responses to achieve near-complete cancer cell killing in vitro. Our findings represent a 'macrogenomic engineering' approach to modulating the physical structure of chromatin for whole-scale transcriptional modulation.

Postnatal Developmental Changes in Fractal Complexity of Giemsa-Stained Chromatin in Mice Spleen Follicular Cells

Although there are numerous recent works focusing on fractal properties of DNA and chromatin, many issues regarding changes in chromatin fractality during physiological aging remain unclear. In this study, we present results indicating that in mice, there is an age-related reduction of chromatin fractal complexity in a population of spleen follicular cells (SFCs). Spleen tissue was obtained from 16 mice and fixated in Carnoy solution. The youngest animal was newborn, and each animal was exactly 1 month older than the previous. We performed fractal analysis of SFC chromatin structure, stained using Giemsa technique. Fractal analysis was done in a plugin algorithm of ImageJ software. We also performed gray-level co-occurrence matrix (GLCM) analysis of all chromatin structures with the calculation of parameters such as angular second moment and inverse difference moment. Giemsa-stained SFC chromatin exhibited an age-dependent reduction of fractal dimension with statistically significant (p<0.01) linear trend. Moreover, there was a statistically significant increase of SFC chromatin lacunarity. The chromatin GLCM parameters did not significantly change. To our knowledge, this is the first study to perform fractal and GLCM analyses of SFC chromatin and to investigate potential changes of fractal parameters during postnatal development.

Unravelling the complexity of signalling networks in cancer: A review of the increasing role for computational modelling

Cancer induction is a highly complex process involving hundreds of different inducers but whose eventual outcome is the same. Clearly, it is essential to understand how signalling pathways and networks generated by these inducers interact to regulate cell behaviour and create the cancer phenotype. While enormous strides have been made in identifying key networking profiles, the amount of data generated far exceeds our ability to understand how it all "fits together". The number of potential interactions is astronomically large and requires novel approaches and extreme computation methods to dissect them out. However, such methodologies have high intrinsic mathematical and conceptual content which is difficult to follow. This review explains how computation modelling is progressively finding solutions and also revealing unexpected and unpredictable nano-scale molecular behaviours extremely relevant to how signalling and networking are coherently integrated. It is divided into linked sections illustrated by numerous figures from the literature describing different approaches and offering visual portrayals of networking and major conceptual advances in the field. First, the problem of signalling complexity and data collection is illustrated for only a small selection of known oncogenes. Next, new concepts from biophysics, molecular behaviours, kinetics, organisation at the nano level and predictive models are presented. These areas include: visual representations of networking, Energy Landscapes and energy transfer/dissemination (entropy); diffusion, percolation; molecular crowding; protein allostery; quinary structure and fractal distributions; energy management, metabolism and re-examination of the Warburg effect. The importance of unravelling complex network interactions is then illustrated for some widely-used drugs in cancer therapy whose interactions are very extensive. Finally, use of computational modelling to develop micro- and nano- functional models ("bottom-up" research) is highlighted. The review concludes that computational modelling is an essential part of cancer research and is vital to understanding network formation and molecular behaviours that are associated with it. Its role is increasingly essential because it is unravelling the huge complexity of cancer induction otherwise unattainable by any other approach.

Measuring the Autocorrelation Function of Nanoscale Three-Dimensional Density Distribution in Individual Cells Using Scanning Transmission Electron Microscopy, Atomic Force Microscopy, and a New Deconvolution Algorithm

Essentially all biological processes are highly dependent on the nanoscale architecture of the cellular components where these processes take place. Statistical measures, such as the autocorrelation function (ACF) of the three-dimensional (3D) mass-density distribution, are widely used to characterize cellular nanostructure. However, conventional methods of reconstruction of the deterministic 3D mass-density distribution, from which these statistical measures can be calculated, have been inadequate for thick biological structures, such as whole cells, due to the conflict between the need for nanoscale resolution and its inverse relationship with thickness after conventional tomographic reconstruction. To tackle the problem, we have developed a robust method to calculate the ACF of the 3D mass-density distribution without tomography. Assuming the biological mass distribution is isotropic, our method allows for accurate statistical characterization of the 3D mass-density distribution by ACF with two data sets: a single projection image by scanning transmission electron microscopy and a thickness map by atomic force microscopy. Here we present validation of the ACF reconstruction algorithm, as well as its application to calculate the statistics of the 3D distribution of mass-density in a region containing the nucleus of an entire mammalian cell. This method may provide important insights into architectural changes that accompany cellular processes.

Iron oxide nanoparticles decrease nuclear fractal dimension of buccal epithelial cells in a time-dependent manner

In this paper, we present results that iron oxide nanoparticles (IONPs) induce time-dependent structural changes in nuclei of buccal epithelial cells. The cells were treated with magnetite, Fe₃ O₄ nanoparticles (spherical shape, diameter 80-100 nanometres). The digital micrographs of the nuclei were made in 3 different time points: 15, 30 and 60 min after the treatment with IONPs, as well as in the control cells. A total of 120 nuclear structures (30 per sample) were analysed. Fractal analysis of nuclei was done in ImageJ software of the National Institutes of Health, (Bethesda, MD, USA). For each nuclear structure, the values of fractal dimension and lacunarity were calculated. There was a time-dependent reduction of nuclear fractal dimension in buccal epithelial cells after exposure to magnetite iron oxide nanoparticles. Negative trend was observed (p < 0.01). Nuclear lacunarity, as another fractal parameter was shown to increase, also in a time-dependent manner, after the treatment with IONPs. To our knowledge, this is the first study to investigate effects of magnetite nanomaterial on nuclear fractal complexity, and also the first to apply fractal analysis method in testing of the interaction between nanoparticles and cell nucleus in this experimental setting.

Stochastic fluorescence switching of nucleic acids under visible light illumination

We report detailed characterizations of stochastic fluorescence switching of unmodified nucleic acids under visible light illumination. Although the fluorescent emission from nucleic acids under the visible light illumination has long been overlooked due to their apparent low absorption cross section, our quantitative characterizations reveal the high quantum yield and high photon count in individual fluorescence emission events of nucleic acids at physiological concentrations. Owing to these characteristics, the stochastic fluorescence switching of nucleic acids could be comparable to that of some of the most potent exogenous fluorescence probes for localization-based super-resolution imaging. Therefore, utilizing the principle of single-molecule photon-localization microscopy, native nucleic acids could be ideal candidates for optical label-free super-resolution imaging.

Review of interferometric spectroscopy of scattered light for the quantification of subdiffractional structure of biomaterials

Optical microscopy is the staple technique in the examination of microscale material structure in basic science and applied research. Of particular importance to biology and medical research is the visualization and analysis of the weakly scattering biological cells and tissues. However, the resolution of optical microscopy is limited to ? 200 ?? nm due to the fundamental diffraction limit of light. We review one distinct form of the spectroscopic microscopy (SM) method, which is founded in the analysis of the second-order spectral statistic of a wavelength-dependent bright-field far-zone reflected-light microscope image. This technique offers clear advantages for biomedical research by alleviating two notorious challenges of the optical evaluation of biomaterials: the diffraction limit of light and the lack of sensitivity to biological, optically transparent structures. Addressing the first issue, it has been shown that the spectroscopic content of a bright-field microscope image quantifies structural composition of samples at arbitrarily small length scales, limited by the signal-to-noise ratio of the detector, without necessarily resolving them. Addressing the second issue, SM utilizes a reference arm, sample arm interference scheme, which allows us to elevate the weak scattering signal from biomaterials above the instrument noise floor.

The Global Relationship between Chromatin Physical Topology, Fractal Structure, and Gene Expression

Most of what we know about gene transcription comes from the view of cells as molecular machines: focusing on the role of molecular modifications to the proteins carrying out transcriptional reactions at a loci-by-loci basis. This view ignores a critical reality: biological reactions do not happen in an empty space, but in a highly complex, interrelated, and dense nanoenvironment that profoundly influences chemical interactions. We explored the relationship between the physical nanoenvironment of chromatin and gene transcription in vitro. We analytically show that changes in the fractal dimension, D, of chromatin correspond to simultaneous increases in chromatin accessibility and compaction heterogeneity. Using these predictions, we demonstrate experimentally that nanoscopic changes to chromatin D within thirty minutes correlate with concomitant enhancement and suppression of transcription. Further, we show that the increased heterogeneity of physical structure of chromatin due to increase in fractal dimension correlates with increased heterogeneity of gene networks. These findings indicate that the higher order folding of chromatin topology may act as a molecular-pathway independent code regulating global patterns of gene expression. Since physical organization of chromatin is frequently altered in oncogenesis, this work provides evidence pairing molecular function to physical structure for processes frequently altered during tumorigenesis.

Dynamic properties of independent chromatin domains measured by correlation spectroscopy in living cells

Background

Genome organization into subchromosomal topologically associating domains (TADs) is linked to cell-type-specific gene expression programs. However, dynamic properties of such domains remain elusive, and it is unclear how domain plasticity modulates genomic accessibility for soluble factors.

Results

Here, we combine and compare a high-resolution topology analysis of interacting chromatin loci with fluorescence correlation spectroscopy measurements of domain dynamics in single living cells. We identify topologically and dynamically independent chromatin domains of ~1 Mb in size that are best described by a loop-cluster polymer model. Hydrodynamic relaxation times and gyration radii of domains are larger for open (161 ± 15 ms, 297 ± 9 nm) than for dense chromatin (88 ± 7 ms, 243 ± 6 nm) and increase globally upon chromatin hyperacetylation or ATP depletion.

Conclusions

Based on the domain structure and dynamics measurements, we propose a loop-cluster model for chromatin domains. It suggests that the regulation of chromatin accessibility for soluble factors displays a significantly stronger dependence on factor concentration than search processes within a static network.

Electronic supplementary material

The online version of this article (doi:10.1186/s13072-016-0093-1) contains supplementary material, which is available to authorized users.

Active diffusion of model chromosomal loci driven by athermal noise

Active diffusion, i.e., fluctuating dynamics driven by athermal noise, is found in various out-of-equilibrium systems. Here we discuss the nature of the active diffusion of tagged monomers in a flexible polymer. A scaling argument based on the notion of tension propagation clarifies how the polymeric effect is reflected in the anomalous diffusion exponent, which may be of relevance to the dynamics of chromosomal loci in living cells.

Chromatin Fractal Organization, Textural Patterns, and Circularity of Nuclear Envelope in Adrenal Zona Fasciculata Cells

Despite previous research efforts in the fields of histology and cell physiology, the relationship between chromatin structural organization and nuclear shape remains unclear. The aim of this research was to test the existence and strength of correlations between mathematical parameters of chromatin microarchitecture and roundness of the nuclear envelope. On a sample of 240 nuclei of adrenal zona fasciculata cells stained using the DNA-specific Feulgen method, we quantified fractal parameters such as fractal dimension and lacunarity, as well as textural parameters such as angular second moment (ASM), entropy, inverse difference moment, contrast, and variance. Circularity of the nuclear envelope was determined from the nuclear area and perimeter. The results indicate that there is a statistically significant negative correlation between chromatin ASM and circularity. Moreover, there was a statistically significant positive correlation between chromatin fractal dimension and envelope circularity. This is the first study to demonstrate these relationships in adrenal tissue, and also one of the first studies to test the connection between circularity and fractal and gray-level co-occurrence matrix parameters in DNA-specific Feulgen stain. The results could be useful both as an addition to the current knowledge on chromatin/nuclear envelope interactions, and for design of future computer-assisted research software for evaluation of nuclear morphology.

Label-free imaging of the native, living cellular nanoarchitecture using partial-wave spectroscopic microscopy

The organization of chromatin is a regulator of molecular processes including transcription, replication, and DNA repair. The structures within chromatin that regulate these processes span from the nucleosomal (10-nm) to the chromosomal (>200-nm) levels, with little known about the dynamics of chromatin structure between these scales due to a lack of quantitative imaging technique in live cells. Previous work using partial-wave spectroscopic (PWS) microscopy, a quantitative imaging technique with sensitivity to macromolecular organization between 20 and 200 nm, has shown that transformation of chromatin at these length scales is a fundamental event during carcinogenesis. As the dynamics of chromatin likely play a critical regulatory role in cellular function, it is critical to develop live-cell imaging techniques that can probe the real-time temporal behavior of the chromatin nanoarchitecture. Therefore, we developed a live-cell PWS technique that allows high-throughput, label-free study of the causal relationship between nanoscale organization and molecular function in real time. In this work, we use live-cell PWS to study the change in chromatin structure due to DNA damage and expand on the link between metabolic function and the structure of higher-order chromatin. In particular, we studied the temporal changes to chromatin during UV light exposure, show that live-cell DNA-binding dyes induce damage to chromatin within seconds, and demonstrate a direct link between higher-order chromatin structure and mitochondrial membrane potential. Because biological function is tightly paired with structure, live-cell PWS is a powerful tool to study the nanoscale structure-function relationship in live cells.

Chromatin fibers: from classical descriptions to modern interpretation

The first description of intrachromosomal fibers was made by Baranetzky in 1880. Since that time, a plethora of fibrillar substructures have been described inside the mitotic chromosomes, and published data indicate that chromosomes may be formed as a result of the hierarchical folding of chromatin fibers. In this review, we examine the evolution and the current state of research on the morphological organization of mitotic chromosomes.

Fractal Characterization of Chromatin Decompaction in Live Cells

Chromatin organization has a fundamental impact on the whole spectrum of genomic functions. Quantitative characterization of the chromatin structure, particularly at submicron length scales where chromatin fractal globules are formed, is critical to understanding this structure-function relationship. Such analysis is currently challenging due to the diffraction-limited resolution of conventional light microscopy. We herein present an optical approach termed inverse spectroscopic optical coherence tomography to characterize the mass density fractality of chromatin, and we apply the technique to observe chromatin decompaction in live cells. The technique makes it possible for the first time, to our knowledge, to sense intracellular morphology with length-scale sensitivity from ∼30 to 450 nm, thus primarily probing the higher-order chromatin structure, without resolving the actual structures. We used chromatin decompaction due to inhibition of histone deacytelases and measured the subsequent changes in the fractal dimension of the intracellular structure. The results were confirmed by transmission electron microscopy and confocal fluorescence microscopy.

High resolution imaging reveals heterogeneity in chromatin states between cells that is not inherited through cell division

Background

Genomes of eukaryotes exist as chromatin, and it is known that different chromatin states can influence gene regulation. Chromatin is not a static structure, but is known to be dynamic and vary between cells. In order to monitor the organisation of chromatin in live cells we have engineered fluorescent fusion proteins which recognize specific operator sequences to tag pairs of syntenic gene loci. The separation of these loci was then tracked in three dimensions over time using fluorescence microscopy.

Results

We established a work flow for measuring the distance between two fluorescently tagged, syntenic gene loci with a mean measurement error of 63 nm. In general, physical separation was observed to increase with increasing genomic separations. However, the extent to which chromatin is compressed varies for different genomic regions. No correlation was observed between compaction and the distribution of chromatin markers from genomic datasets or with contacts identified using capture based approaches. Variation in spatial separation was also observed within cells over time and between cells. Differences in the conformation of individual loci can persist for minutes in individual cells. Separation of reporter loci was found to be similar in related and unrelated daughter cell pairs.

Conclusions

The directly observed physical separation of reporter loci in live cells is highly dynamic both over time and from cell to cell. However, consistent differences in separation are observed over some chromosomal regions that do not correlate with factors known to influence chromatin states. We conclude that as yet unidentified parameters influence chromatin configuration. We also find that while heterogeneity in chromatin states can be maintained for minutes between cells, it is not inherited through cell division. This may contribute to cell-to-cell transcriptional heterogeneity.

Electronic supplementary material

The online version of this article (doi:10.1186/s12860-016-0111-y) contains supplementary material, which is available to authorized users.

Large Scale Chromosome Folding Is Stable against Local Changes in Chromatin Structure

Characterizing the link between small-scale chromatin structure and large-scale chromosome folding during interphase is a prerequisite for understanding transcription. Yet, this link remains poorly investigated. Here, we introduce a simple biophysical model where interphase chromosomes are described in terms of the folding of chromatin sequences composed of alternating blocks of fibers with different thicknesses and flexibilities, and we use it to study the influence of sequence disorder on chromosome behaviors in space and time. By employing extensive computer simulations, we thus demonstrate that chromosomes undergo noticeable conformational changes only on length-scales smaller than 10⁵ basepairs and time-scales shorter than a few seconds, and we suggest there might exist effective upper bounds to the detection of chromosome reorganization in eukaryotes. We prove the relevance of our framework by modeling recent experimental FISH data on murine chromosomes.

A key determining factor in many important cellular processes as DNA transcription, for instance, the specific composition of the chromatin fiber sequence has a major influence on chromosome folding during interphase. Yet, how this is achieved in detail remains largely elusive. In this work, we explore this link by means of a novel quantitative computational polymer model for interphase chromosomes where the associated chromatin filaments are composed of mixtures of fibers with heterogeneous physical properties. Our work suggests a scenario where chromosomes undergo only limited reorganization, namely on length-scales below 10⁵ basepairs and time-scales shorter than a few seconds. Our conclusions are supported by recent FISH data on murine chromosomes.

Unique fractal evaluation and therapeutic implications of mitochondrial morphology in malignant mesothelioma

Malignant mesothelioma (MM), is an intractable disease with limited therapeutic options and grim survival rates. Altered metabolic and mitochondrial functions are hallmarks of MM and most other cancers. Mitochondria exist as a dynamic network, playing a central role in cellular metabolism. MM cell lines display a spectrum of altered mitochondrial morphologies and function compared to control mesothelial cells. Fractal dimension and lacunarity measurements are a sensitive and objective method to quantify mitochondrial morphology and most importantly are a promising predictor of response to mitochondrial inhibition. Control cells have high fractal dimension and low lacunarity and are relatively insensitive to mitochondrial inhibition. MM cells exhibit a spectrum of sensitivities to mitochondrial inhibitors. Low mitochondrial fractal dimension and high lacunarity correlates with increased sensitivity to the mitochondrial inhibitor metformin. Lacunarity also correlates with sensitivity to Mdivi-1, a mitochondrial fission inhibitor. MM and control cells have similar sensitivities to cisplatin, a chemotherapeutic agent used in the treatment of MM. Neither oxidative phosphorylation nor glycolytic activity, correlated with sensitivity to either metformin or mdivi-1. Our results suggest that mitochondrial inhibition may be an effective and selective therapeutic strategy in mesothelioma, and identifies mitochondrial morphology as a possible predictor of response to targeted mitochondrial inhibition.

GMOL: An Interactive Tool for 3D Genome Structure Visualization

It has been shown that genome spatial structures largely affect both genome activity and DNA function. Knowing this, many researchers are currently attempting to accurately model genome structures. Despite these increased efforts there still exists a shortage of tools dedicated to visualizing the genome. Creating a tool that can accurately visualize the genome can aid researchers by highlighting structural relationships that may not be obvious when examining the sequence information alone. Here we present a desktop application, known as GMOL, designed to effectively visualize genome structures so that researchers may better analyze genomic data. GMOL was developed based upon our multi-scale approach that allows a user to scale between six separate levels within the genome. With GMOL, a user can choose any unit at any scale and scale it up or down to visualize its structure and retrieve corresponding genome sequences. Users can also interactively manipulate and measure the whole genome structure and extract static images and machine-readable data files in PDB format from the multi-scale structure. By using GMOL researchers will be able to better understand and analyze genome structure models and the impact their structural relations have on genome activity and DNA function.

Nuclear Fractal Dimensions as a Tool for Prognostication of Oral Squamous Cell Carcinoma

BACKGROUND

Carcinogenesis follows complex molecular alterations, which are triggered by subtle chromatin architectural changes that are imperceptible to the human eye. As the treatment decisions in Oral Squamous Cell Carcinoma (OSCC) are hindered by the imprecise clinical stage determination and inter-observer variability in histological grading, focus in recent years has shifted to discovering identifiers related to neoplastic cell morphology studied through computer-aided image analysis. One such approach is the assessment of fractal geometry, a technique first described by Mandelbrot, which aids in precise assessment of architecture of natural objects. Assessment and quantification of degree of complexity of these fractal objects (self-similarities in structural complexity at different magnifying scales) is described as fractal dimension (FD).

AIM

To evaluate the nuclear fractal dimension (NFD) in OSCC using computer-aided image analysis.

MATERIALS AND METHODS

Histological sections of 14 selected cases of Oral Squamous Cell Carcinoma (OSCC) and 6 samples of normal buccal mucosa (as control) were stained with Haematoxylin-Eosin and Feulgen stain for histopathological examination and evaluation of nuclear complexity respectively. Fifteen HPF at Invasive Tumour Front (ITF) and Tumour Proper (TP) of Feulgen-stained sections were selected and photographed in test and control samples. At ITF, TP and normal buccal mucosa 200 nuclei each were selected and analyzed using Image J software to quantify FD. The test and control groups were compared statistically using Independent sample t-test and One-way ANOVA.

RESULTS

Nuclear FD increased progressively towards worst tumour staging as compared to normal buccal mucosa.

CONCLUSION

Nuclear FD can be considered for quantification of nuclear architectural changes as a prognostic indicator in OSCC.