Chromosome dynamics, molecular crowding, and diffusion in the interphase cell nucleus: a Monte Carlo lattice simulation study

The Material Properties of the Cell Nucleus: A Matter of Scale

Chromatin regulatory processes physically take place in the environment of the cell nucleus, which is filled with the chromosomes and a plethora of smaller biomolecules. The nucleus contains macromolecular assemblies of different sizes, from nanometer-sized protein complexes to micrometer-sized biomolecular condensates, chromosome territories, and nuclear bodies. This multiscale organization impacts the transport processes within the nuclear interior, the global mechanical properties of the nucleus, and the way the nucleus senses and reacts to mechanical stimuli. Here, we discuss recent work on these aspects, including microrheology and micromanipulation experiments assessing the material properties of the nucleus and its subcomponents. We summarize how the properties of multiscale media depend on the time and length scales probed in the experiment, and we reconcile seemingly contradictory observations made on different scales. We also revisit the concept of liquid-like and solid-like material properties for complex media such as the nucleus. We propose that the nucleus can be considered a multiscale viscoelastic medium composed of three major components with distinct properties: the lamina, the chromatin network, and the nucleoplasmic fluid. This multicomponent organization enables the nucleus to serve its different functions as a reaction medium on the nanoscale and as a mechanosensor and structural scaffold on the microscale.

A polymer chain with dipolar active forces in connection to spatial organization of chromatin

A living cell is an active environment where the organization and dynamics of chromatin are affected by different forms of activity. Optical experiments report that loci show subdiffusive dynamics and the chromatin fiber is seen to be coherent over micrometer-scale regions. Using a bead-spring polymer chain with dipolar active forces, we study how the subdiffusive motion of the loci generate large-scale coherent motion of the chromatin. We show that in the presence of extensile (contractile) activity, the dynamics of the loci grows faster (slower) and the spatial correlation length increases (decreases) compared to the case with no dipolar forces. Hence, both the dipolar active forces modify the elasticity of the chain. Interestingly in our model, the dynamics and organization of such dipolar active chains largely differ from the passive chain with renormalized elasticity.

Out of the Randomness: Correlating Noise in Biological Systems

The study of the dynamics of biological systems requires one to follow relaxation processes in time with micron-size spatial resolution. This need has led to the development of different fluorescence correlation techniques with high spatial resolution and a tremendous (from nanoseconds to seconds) temporal dynamic range. Spatiotemporal information can be obtained even on complex dynamic processes whose time evolution is not forecast by simple Brownian diffusion. Our discussion of the most recent applications of image correlation spectroscopy to the study of anomalous sub- or superdiffusion suggests that this field still requires the development of multidimensional image analyses based on analytical models or numerical simulations. We focus in particular on the framework of spatiotemporal image correlation spectroscopy and examine the critical steps in getting information on anomalous diffusive processes from the correlation maps. We point out how a dual space-time correlative analysis, in both the direct and the Fourier space, can provide quantitative information on superdiffusional processes when these are analyzed through an empirical model based on intermittent active dynamics. We believe that this dual space-time analysis, potentially amenable to mathematical treatment and to the exact fit of experimental data, could be extended to include the rich phenomenology of subdiffusive processes, thereby quantifying relevant parameters for the various motivating biological problems of interest.

Random Motion of Chromatin Is Influenced by Lamin A Interconnections

Using fluorescence correlation spectroscopy in single-plane illumination microscopy, we investigated the dynamics of chromatin in interphase mouse adult fibroblast cell nuclei under the influence of the intermediate filament protein lamin A. We find that 1) lamin A-eGFP and histone H2A-mRFP show significant comobility, indicating that their motions are clearly interconnected in the nucleus, and 2) that the random motion of histones H2A within the chromatin network is subdiffusive, i.e., the effective diffusion coefficient decreases for slow timescales. Knocking out lamin A changes the diffusion back to normal. Thus, lamin A influences the dynamics of the entire chromatin network. Our conclusion is that lamin A plays a central role in determining the viscoelasticity of the chromatin network and helping to maintain local ordering of interphase chromosomes.

Uniform Contraction-Expansion Description of Relative Centromere and Telomere Motion

Internal organization and dynamics of the eukaryotic nucleus have been at the front of biophysical research in recent years. It is believed that both dynamics and location of chromatin segments are crucial for genetic regulation. Here we study the relative motion between centromeres and telomeres at various distances and at times relevant for genetic activity. Using live-imaging fluorescent microscopy coupled to stochastic analysis of relative trajectories, we find that the interlocus motion is distance-dependent with a varying fractional memory. In addition to short-range constraining, we also observe long-range anisotropic-enhanced parallel diffusion, which contradicts the expectation for classic viscoelastic systems. This motion is linked to uniform expansion and contraction of chromatin in the nucleus, and leads us to define and measure a new (to our knowledge) uniform contraction-expansion diffusion coefficient that enriches the contemporary picture of nuclear behavior. Finally, differences between loci types suggest that different sites along the genome experience distinctive coupling to the nucleoplasm environment at all scales.

Elastic model for dinucleosome structure and energy

The equilibrium structure of a dinucleosome is studied using an elastic model that takes into account the force and torque balance conditions. Using the proper boundary conditions, it is found that the conformational energy of the problem does not depend on the length of the linker DNA. In addition it is shown that the two histone octamers are almost perpendicular to each other, and the linker DNA in short lengths is almost straight. These findings could shed some light on the role of DNA elasticity in the chromatin structure.

The interphase mammalian chromosome as a structural system based on tensegrity

Each mammalian chromosome is constituted by a DNA fiber of macroscopic length that needs to be fitted in a microscopic nucleus. The DNA fiber is subjected at physiological temperature to random thermal bending and looping that must be constrained so as achieve structural stability thus avoiding spontaneous rupturing of the fiber. Standard textbooks assume that chromatin proteins are primarily responsible for the packaging of DNA and so of its protection against spontaneous breakage. Yet the dynamic nature of the interactions between chromatin proteins and DNA is unlikely to provide the necessary long-term structural stability for the chromosomal DNA. On the other hand, longstanding evidence indicates that stable interactions between DNA and constituents of a nuclear compartment commonly known as the nuclear matrix organize the chromosomal DNA as a series of topologically constrained, supercoiled loops during interphase. This results in a primary level of DNA condensation and packaging within the nucleus, as well as in protection against spontaneous DNA breakage, independently of chromatin proteins which nevertheless increase and dynamically modulate the degree of DNA packaging and its role in the regulation of DNA function. Thus current evidence, presented hereunder, supports a model for the organization of the interphase chromosome as resilient system that satisfies the principles of structural tensegrity.

Loss of lamin A function increases chromatin dynamics in the nuclear interior

Chromatin is organized in a highly ordered yet dynamic manner in the cell nucleus, but the principles governing this organization remain unclear. Similarly, it is unknown whether, and how, various proteins regulate chromatin motion and as a result influence nuclear organization. Here by studying the dynamics of different genomic regions in the nucleus of live cells, we show that the genome has highly constrained dynamics. Interestingly, depletion of lamin A strikingly alters genome dynamics, inducing a dramatic transition from slow anomalous diffusion to fast and normal diffusion. In contrast, depletion of LAP2α, a protein that interacts with lamin A and chromatin, has no such effect on genome dynamics. We speculate that chromosomal inter-chain interactions formed by lamin A throughout the nucleus contribute to chromatin dynamics, and suggest that the molecular regulation of chromatin diffusion by lamin A in the nuclear interior is critical for the maintenance of genome organization.

Anomalous diffusion in fractal globules

The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by ⟨X(2)(t)⟩∼t(αF) with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing.

The physical size of transcription factors is key to transcriptional regulation in chromatin domains

Genetic information, which is stored in the long strand of genomic DNA as chromatin, must be scanned and read out by various transcription factors. First, gene-specific transcription factors, which are relatively small (∼50 kDa), scan the genome and bind regulatory elements. Such factors then recruit general transcription factors, Mediators, RNA polymerases, nucleosome remodellers, and histone modifiers, most of which are large protein complexes of 1-3 MDa in size. Here, we propose a new model for the functional significance of the size of transcription factors (or complexes) for gene regulation of chromatin domains. Recent findings suggest that chromatin consists of irregularly folded nucleosome fibres (10 nm fibres) and forms numerous condensed domains (e.g., topologically associating domains). Although the flexibility and dynamics of chromatin allow repositioning of genes within the condensed domains, the size exclusion effect of the domain may limit accessibility of DNA sequences by transcription factors. We used Monte Carlo computer simulations to determine the physical size limit of transcription factors that can enter condensed chromatin domains. Small gene-specific transcription factors can penetrate into the chromatin domains and search their target sequences, whereas large transcription complexes cannot enter the domain. Due to this property, once a large complex binds its target site via gene-specific factors it can act as a 'buoy' to keep the target region on the surface of the condensed domain and maintain transcriptional competency. This size-dependent specialization of target-scanning and surface-tethering functions could provide novel insight into the mechanisms of various DNA transactions, such as DNA replication and repair/recombination.

The viscoelastic properties of chromatin and the nucleoplasm revealed by scale-dependent protein mobility

The eukaryotic cell nucleus harbours the DNA genome that is organized in a dynamic chromatin network and embedded in a viscous crowded fluid. This environment directly affects enzymatic reactions and target search processes that access the DNA sequence information. However, its physical properties as a reaction medium are poorly understood. Here, we exploit mobility measurements of differently sized inert green fluorescent tracer proteins to characterize the viscoelastic properties of the nuclear interior of a living human cell. We find that it resembles a viscous fluid on small and large scales but appears viscoelastic on intermediate scales that change with protein size. Our results are consistent with simulations of diffusion through polymers and suggest that chromatin forms a random obstacle network rather than a self-similar structure with fixed fractal dimensions. By calculating how long molecules remember their previous position in dependence on their size, we evaluate how the nuclear environment affects search processes of chromatin targets.

A statistical model of intra-chromosome contact maps

A statistical model describing a fine structure of the intra-chromosome maps obtained by a genome-wide chromosome conformation capture method (Hi-C) is proposed. The model combines hierarchical chain folding with a quenched heteropolymer structure of primary chromatin sequences. It is conjectured that the observed Hi-C maps are statistical averages over many different ways of hierarchical genome folding. It is shown that the existence of a quenched primary structure coupled with hierarchical folding induces a full range of features observed in experimental Hi-C maps: hierarchical elements, chess-board intermittency and large-scale compartmentalization.

Effects of physiological self-crowding of DNA on shape and biological properties of DNA molecules with various levels of supercoiling

DNA in bacterial chromosomes and bacterial plasmids is supercoiled. DNA supercoiling is essential for DNA replication and gene regulation. However, the density of supercoiling in vivo is circa twice smaller than in deproteinized DNA molecules isolated from bacteria. What are then the specific advantages of reduced supercoiling density that is maintained in vivo? Using Brownian dynamics simulations and atomic force microscopy we show here that thanks to physiological DNA–DNA crowding DNA molecules with reduced supercoiling density are still sufficiently supercoiled to stimulate interaction between cis-regulatory elements. On the other hand, weak supercoiling permits DNA molecules to modulate their overall shape in response to physiological changes in DNA crowding. This plasticity of DNA shapes may have regulatory role and be important for the postreplicative spontaneous segregation of bacterial chromosomes.

Effects of supercoiling on enhancer-promoter contacts

Using Brownian dynamics simulations, we investigate here one of possible roles of supercoiling within topological domains constituting interphase chromosomes of higher eukaryotes. We analysed how supercoiling affects the interaction between enhancers and promoters that are located in the same or in neighbouring topological domains. We show here that enhancer–promoter affinity and supercoiling act synergistically in increasing the fraction of time during which enhancer and promoter stay in contact. This stabilizing effect of supercoiling only acts on enhancers and promoters located in the same topological domain. We propose that the primary role of recently observed supercoiling of topological domains in interphase chromosomes of higher eukaryotes is to assure that enhancers contact almost exclusively their cognate promoters located in the same topological domain and avoid contacts with very similar promoters but located in neighbouring topological domains.

Chromatin as dynamic 10-nm fibers

Since Flemming described a nuclear substance in the nineteenth century and named it “chromatin,” this substance has fascinated biologists. What is the structure of chromatin? DNA is wrapped around core histones, forming a nucleosome fiber (10-nm fiber). This fiber has long been assumed to fold into a 30-nm chromatin fiber and subsequently into helically folded larger fibers or radial loops. However, several recent studies, including our cryo-EM and X-ray scattering analyses, demonstrated that chromatin is composed of irregularly folded 10-nm fibers, without 30-nm chromatin fibers, in interphase chromatin and mitotic chromosomes. This irregular folding implies a chromatin state that is physically less constrained, which could be more dynamic compared with classical regular helical folding structures. Consistent with this, recently, we uncovered by single nucleosome imaging large nucleosome fluctuations in living mammalian cells (∼50 nm/30 ms). Subsequent computational modeling suggested that nucleosome fluctuation increases chromatin accessibility, which is advantageous for many “target searching” biological processes such as transcriptional regulation. Therefore, this review provides a novel view on chromatin structure in which chromatin consists of dynamic and disordered 10-nm fibers.

Relevance and limitations of crowding, fractal, and polymer models to describe nuclear architecture

Chromosome architecture plays an essential role for all nuclear functions, and its physical description has attracted considerable interest over the last few years among the biophysics community. These researches at the frontiers of physics and biology have been stimulated by the demand for quantitative analysis of molecular biology experiments, which provide comprehensive data on chromosome folding, or of live cell imaging experiments that enable researchers to visualize selected chromosome loci in living or fixed cells. In this review our goal is to survey several nonmutually exclusive models that have emerged to describe the folding of DNA in the nucleus, the dynamics of proteins in the nucleoplasm, or the movements of chromosome loci. We focus on three classes of models, namely molecular crowding, fractal, and polymer models, draw comparisons, and discuss their merits and limitations in the context of chromosome structure and dynamics, or nuclear protein navigation in the nucleoplasm. Finally, we identify future challenges in the roadmap to a unified model of the nuclear environment.

Models that include supercoiling of topological domains reproduce several known features of interphase chromosomes

Understanding the structure of interphase chromosomes is essential to elucidate regulatory mechanisms of gene expression. During recent years, high-throughput DNA sequencing expanded the power of chromosome conformation capture (3C) methods that provide information about reciprocal spatial proximity of chromosomal loci. Since 2012, it is known that entire chromatin in interphase chromosomes is organized into regions with strongly increased frequency of internal contacts. These regions, with the average size of ∼1 Mb, were named topological domains. More recent studies demonstrated presence of unconstrained supercoiling in interphase chromosomes. Using Brownian dynamics simulations, we show here that by including supercoiling into models of topological domains one can reproduce and thus provide possible explanations of several experimentally observed characteristics of interphase chromosomes, such as their complex contact maps.

Flexible and dynamic nucleosome fiber in living mammalian cells

Genomic DNA is organized three dimensionally within cells as chromatin and is searched and read by various proteins by an unknown mechanism; this mediates diverse cell functions. Recently, several pieces of evidence, including our cryomicroscopy and synchrotron X-ray scattering analyses, have demonstrated that chromatin consists of irregularly folded nucleosome fibers without a 30-nm chromatin fiber (i.e., a polymer melt-like structure). This melt-like structure implies a less physically constrained and locally more dynamic state, which may be crucial for protein factors to scan genomic DNA. Using a combined approach of fluorescence correlation spectroscopy, Monte Carlo computer simulations, and single nucleosome imaging, we demonstrated the flexible and dynamic nature of the nucleosome fiber in living mammalian cells. We observed local nucleosome fluctuation (~50 nm movement per 30 ms) caused by Brownian motion. Our in vivo-in silico results suggest that local nucleosome dynamics facilitate chromatin accessibility and play a critical role in the scanning of genome information.

Influences of excluded volume of molecules on signaling processes on the biomembrane

We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins, and crowders on the cell membrane. The signaling proteins are activated by receptors, and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activated. If the target proteins bind frequently, the volume fraction of molecules on the membrane becomes so large that the excluded volume of the molecules for the reaction and diffusion dynamics cannot be negligible. We find that such excluded volume effects of the molecules induce non-trivial variations of the signal flow, defined as the activation frequency of target proteins, as follows. With an increase in the binding rate of target proteins, the signal flow varies by monotonically increasing; increasing then decreasing in a bell-shaped curve; or increasing, decreasing, then increasing in an S-shaped curve. We further demonstrate that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits a large signal flow, the signaling proteins tend to surround the receptors to form receptor-signaling protein clusters, and the target proteins tend to become distributed around such clusters. To explain these phenomena, we analyze the stochastic model of the local motions of molecules around the receptor.

Kinetic lattice Monte Carlo simulation of viscoelastic subdiffusion

We propose a kinetic Monte Carlo method for the simulation of subdiffusive random walks on a cartesian lattice. The random walkers are subject to viscoelastic forces which we compute from their individual trajectories via the fractional Langevin equation. At every step the walkers move by one lattice unit, which makes them differ essentially from continuous time random walks, where the subdiffusive behavior is induced by random waiting. To enable computationally inexpensive simulations with n-step memories, we use an approximation of the memory and the memory kernel functions with a complexity O(log n). Eventual discretization and approximation artifacts are compensated with numerical adjustments of the memory kernel functions. We verify with a number of analyses that this new method provides binary fractional random walks that are fully consistent with the theory of fractional brownian motion.

Local nucleosome dynamics facilitate chromatin accessibility in living mammalian cells

Genome information, which is three-dimensionally organized within cells as chromatin, is searched and read by various proteins for diverse cell functions. Although how the protein factors find their targets remains unclear, the dynamic and flexible nature of chromatin is likely crucial. Using a combined approach of fluorescence correlation spectroscopy, single-nucleosome imaging, and Monte Carlo computer simulations, we demonstrate local chromatin dynamics in living mammalian cells. We show that similar to interphase chromatin, dense mitotic chromosomes also have considerable chromatin accessibility. For both interphase and mitotic chromatin, we observed local fluctuation of individual nucleosomes (~50 nm movement/30 ms), which is caused by confined Brownian motion. Inhibition of these local dynamics by crosslinking impaired accessibility in the dense chromatin regions. Our findings show that local nucleosome dynamics drive chromatin accessibility. We propose that this local nucleosome fluctuation is the basis for scanning genome information.

Different patterns of Robertsonian fusion pairing in Bovidae and the house mouse: the relationship between chromosome size and nuclear territories

Using a dataset of karyotypic changes reported for bovids and the house mouse (Mus musculus domesticus) together with information from the cattle (Bos taurus) and mouse genomes, we examined two principal variables that have been proposed to predict chromosomal positioning in the nucleus, chromosome size and GC content. These were expected to influence the distribution of Robertsonian (Rb) fusions, the predominant mode of chromosomal change in both taxa. We found the largest chromosomes to be most frequently involved in fusions in bovids, and confirm earlier reports that chromosomes of intermediate size were the most frequent fusers in mice. We then tested whether chromosomal positioning can explain Rb fusion frequencies. We classified chromosomes into groups by size and considered the frequency of interactions between specific groups. Among the interactions, mouse chromosomes showed a slight tendency to fuse with neighbouring chromosomes, in line with expectations of chromosomal positioning, but also resembling predictions from meiotic spindle-induced bias. Bovids, on the other hand, showed no trend in interactions, with small chromosomes being the least frequent partner for all size classes. We discuss the results in terms of nuclear organization at various cell cycle stages and the proposed mechanisms of Rb fusion formation, and note that the difference can be explained by (i) considering bovid species generally to be characterized by a greater intermingling of chromosomal size classes than the house mouse, or (ii) by the vastly different timescales underpinning their evolutionary histories.

Cell cycle-dependent mobility of Cdc45 determined in vivo by fluorescence correlation spectroscopy

Eukaryotic DNA replication is a dynamic process requiring the co-operation of specific replication proteins. We measured the mobility of eGFP-Cdc45 by Fluorescence Correlation Spectroscopy (FCS) in vivo in asynchronous cells and in cells synchronized at the G1/S transition and during S phase. Our data show that eGFP-Cdc45 mobility is faster in G1/S transition compared to S phase suggesting that Cdc45 is part of larger protein complex formed in S phase. Furthermore, the size of complexes containing Cdc45 was estimated in asynchronous, G1/S and S phase-synchronized cells using gel filtration chromatography; these findings complemented the in vivo FCS data. Analysis of the mobility of eGFP-Cdc45 and the size of complexes containing Cdc45 and eGFP-Cdc45 after UVC-mediated DNA damage revealed no significant changes in diffusion rates and complex sizes using FCS and gel filtration chromatography analyses. This suggests that after UV-damage, Cdc45 is still present in a large multi-protein complex and that its mobility within living cells is consistently similar following UVC-mediated DNA damage.

Interphase chromatin organisation in Arabidopsis nuclei: constraints versus randomness

The spatial chromatin organisation and molecular interactions within and between chromatin domains and chromosome territories (CTs) are essential for fundamental processes such as replication, transcription and DNA repair via homologous recombination. To analyse the distribution and interaction of whole CTs, centromeres, (sub)telomeres and ~100-kb interstitial chromatin segments in endopolyploid nuclei, specific FISH probes from Arabidopsis thaliana were applied to 2-64C differentiated leaf nuclei. Whereas CTs occupy a distinct and defined volume of the nucleus and do not obviously intermingle with each other in 2-64C nuclei, ~100-kb sister chromatin segments within these CTs become more non-cohesive with increasing endopolyploidy. Centromeres, preferentially located at the nuclear periphery, may show ring- or half-moon like shapes in 2C and 4C nuclei. Sister centromeres tend to associate up to the 8C level. From 16C nuclei on, they become progressively separated. The higher the polyploidy level gets, the more separate chromatids are present. Due to sister chromatid separation in highly endopolyploid nuclei, the centromeric histone variant CENH3, the 180-bp centromeric repeats and pericentromeric heterochromatin form distinct subdomains at adjacent but not intermingling positions. The (sub)telomeres are frequently associated with each other and with the nucleolus and less often with centromeres. The extent of chromatid separation and of chromatin decondensation at subtelomeric chromatin segments varies between chromosome arms. A mainly random distribution and similar shapes of CTs even at higher ploidy levels indicate that in general no substantial CT reorganisation occurs during endopolyploidisation. Non-cohesive sister chromatid regions at chromosome arms and at the (peri)centromere are accompanied by a less dense chromatin conformation in highly endopolyploid nuclei. We discuss the possible function of this conformation in comparison to transcriptionally active regions at insect polytene chromosomes.