Heterogeneous fluid-like movements of chromatin and their implications to transcription.

Eukaryotic chromatin is a complex of genome DNA and associated proteins, and its structure and dynamics play a crucial role in regulating DNA functions. Chromatin takes rather irregular structures in the nucleus and exhibits heterogeneous sub-diffusive movements as polymers fluctuating in a fluid state. Using genome-wide single-nucleosome tracking data, heterogeneity of movements was statistically analyzed, which categorized chromatin into two types: slow chromatin that moves under structurally constrained environments and fast chromatin that moves with less constraints. Interactions of chromatin to various protein factors determine the motional constraints. For example, loss of the cohesin complex that bundles the chromatin chains reduces the motional constraints and increases the population of fast chromatin. Another example is the transcriptional machinery. While it was previously thought that the transcriptional activity is associated with more open and dynamic chromatin structure, recent studies suggested a more nuanced role of transcription in chromatin dynamics: dynamic association/dissociation of active RNA polymerase II (RNAPII) and other transcription factors and Mediators (TF-Meds) transiently bridges transcriptionally active DNA regions, which forms a loose network of chromatin and constrains chromatin movement, enhancing the slow chromatin population. This new view on the dynamical effects of transcription urges a reflection on the traditional model of transcription factories and invites the more recent models of condensates/phase-separated liquid droplets of RNAPII, transcription factors, and Mediators. The combined procedure of genome-wide single-nucleosome tracking and its statistical analysis would unveil heterogeneity in the chromatin movement, which should provide a key to understanding the relations among chromatin dynamics, structure, and function.

Organization of fast and slow chromatin revealed by single-nucleosome dynamics.

Understanding chromatin organization and dynamics is important, since they crucially affect DNA functions. In this study, we investigate chromatin dynamics by statistically analyzing single-nucleosome movement in living human cells. Bimodal nature of the mean square displacement distribution of nucleosomes allows for a natural categorization of the nucleosomes as fast and slow. Analyses of the nucleosome-nucleosome correlation functions within these categories along with the density of vibrational modes show that the nucleosomes form dynamically correlated fluid regions (i.e., dynamic domains of fast and slow nucleosomes). Perturbed nucleosome dynamics by global histone acetylation or cohesin inactivation indicate that nucleosome-nucleosome interactions along with tethering of chromatin chains organize nucleosomes into fast and slow dynamic domains. A simple polymer model is introduced, which shows the consistency of this dynamic domain picture. Statistical analyses of single-nucleosome movement provide rich information on how chromatin is dynamically organized in a fluid manner in living cells.

Single nucleosome imaging reveals loose genome chromatin networks via active RNA polymerase II.

Although chromatin organization and dynamics play a critical role in gene transcription, how they interplay remains unclear. To approach this issue, we investigated genome-wide chromatin behavior under various transcriptional conditions in living human cells using single-nucleosome imaging. While transcription by RNA polymerase II (RNAPII) is generally thought to need more open and dynamic chromatin, surprisingly, we found that active RNAPII globally constrains chromatin movements. RNAPII inhibition or its rapid depletion released the chromatin constraints and increased chromatin dynamics. Perturbation experiments of P-TEFb clusters, which are associated with active RNAPII, had similar results. Furthermore, chromatin mobility also increased in resting G0 cells and UV-irradiated cells, which are transcriptionally less active. Our results demonstrated that chromatin is globally stabilized by loose connections through active RNAPII, which is compatible with models of classical transcription factories or liquid droplet formation of transcription-related factors. Together with our computational modeling, we propose the existence of loose chromatin domain networks for various intra-/interchromosomal contacts via active RNAPII clusters/droplets.

Effects of Collective Histone State Dynamics on Epigenetic Landscape and Kinetics of Cell Reprogramming.

Cell reprogramming is a process of transitions from differentiated to pluripotent cell states via transient intermediate states. Within the epigenetic landscape framework, such a process is regarded as a sequence of transitions among basins on the landscape; therefore, theoretical construction of a model landscape which exhibits experimentally consistent dynamics can provide clues to understanding epigenetic mechanism of reprogramming. We propose a minimal gene-network model of the landscape, in which each gene is regulated by an integrated mechanism of transcription-factor binding/unbinding and the collective chemical modification of histones. We show that the slow collective variation of many histones around each gene locus alters topology of the landscape and significantly affects transition dynamics between basins. Differentiation and reprogramming follow different transition pathways on the calculated landscape, which should be verified experimentally via single-cell pursuit of the reprogramming process. Effects of modulation in collective histone state kinetics on transition dynamics and pathway are examined in search for an efficient protocol of reprogramming.

Inherent structures, fragility, and jamming: insights from quasi-one-dimensional hard disks.

We study a quasi-one-dimensional system of hard disks confined between hard lines to explore the relationship between the inherent structure landscape, the thermodynamics, and the dynamics of the fluid. The transfer matrix method is used to obtain an exact description of the landscape, equation of state, and provide a mapping of configurations of the equilibrium fluid to their local jammed structures. This allows us to follow how the system samples the landscape as a function of occupied volume fraction ϕ. Configurations of the ideal gas map to the maximum in the distribution of inherent structures, with a jamming volume fraction ϕ(J)(*), and sample more dense basins with increasing ϕ. This suggests jammed states with a density below ϕ(J)(*) are inaccessible from the equilibrium fluid. The configurational entropy of the fluid decreases rapidly at intermediate ϕ before plateauing at a low value and going to zero as the most dense packing is approached. This leads to the appearance of a maximum in both the isobaric heat capacity and the inherent structure pressure. We also show that the system exhibits a crossover from fragile to strong fluid behavior, located at the heat capacity maximum. Structural relaxation in the fragile fluid is shown to be controlled by the presence of high order saddle points caused by neighboring defects that are unstable with respect to jamming and spontaneously rearrange to form a stable local environment. In the strong fluid, the defect concentration is low so that defects do not interact and relaxation occurs through the hopping of isolated defects between stable local packing environments.

Inherent structure landscape connection between liquids, granular materials, and the jamming phase diagram.

We provide a comprehensive picture of the jamming phase diagram by connecting the athermal, granular ensemble of jammed states and the equilibrium fluid through the inherent structure paradigm for a system of hard disks confined to a narrow channel. The J line is shown to be divided into packings that are either accessible or inaccessible from the equilibrium fluid. The J point itself is found to occur at the transition between these two sets of packings and is located at the maximum of the inherent structure distribution. We also present a general thermodynamic argument that suggests the density of the states at the maximum of the configurational entropy represents a lower bound on the J-point density in hard sphere systems. Finally, we show that the granular system, modeled using the Edwards ensemble, and the fluid sample the same set of thermodynamically accessible states over the full range of thermodynamic state points, but only occupy the same set of inherent structures, under the same thermodynamic conditions, at two points, corresponding to zero and infinite pressures, where they sample the J-point states and the most dense packing, respectively.

Calculations of the structure of basin volumes for mechanically stable packings.

Experimental and computational model systems composed of frictionless particles in a fixed geometry have a finite number of distinct mechanically stable (MS) packings. The frequency of occurrence for each MS packing is highly variable and depends strongly on preparation protocol. Despite intense work, it is extremely difficult to predict a priori the MS packing probabilities. We describe a novel computational method for calculating the volume and other geometrical properties of the "basin of attraction" for each MS packing. The basin of attraction for an MS packing contains all initial conditions in configuration space that map to that MS packing using a given preparation protocol. We find that the basin is a highly complex structure. For a compressive-quench-from-zero-density protocol, we show the existence of a small core volume of the basin around each MS packing for which all points map to that MS packing. However, in contrast to previous studies for supercooled liquids, glasses, and over-compressed jammed systems, we find that the MS packing probabilities are very weakly correlated with this core volume. Instead, MS packing probabilities obtained from compression protocols that use initially dilute configurations and do not allow particle overlaps (i.e., those relevant to granular media) are determined by complex geometric features of the basin of attraction that are distant from the MS packing. In particular, we find that the shape of the average basin profile function S(l), which gives the probability for a point on a hyperspherical shell a distance l from a given MS packing to map back to that packing, can be described by a Γ distribution with a peak that increases as the system size increases and as the quench rate decreases. We find a simple model which predicts S(l) for the extreme cases of very slow and fast quench rates.

Fragile-strong fluid crossover and universal relaxation times in a confined hard-disk fluid.

We show that a system of hard disks confined to a narrow channel exhibits a fragile-strong fluid crossover located at the maximum of the isobaric heat capacity and that the relaxation times for different channel widths fall onto a single master curve when rescaled by the relaxation times and temperatures of the crossover. Calculations of the configurational entropy and the inherent structure equation of state find that the crossover is related to properties of the jamming landscape for the model but that the Adam-Gibbs relation does not predict the relaxation behavior. We also show that a facilitated dynamics description of the system, where kinetically excited regions are identified with local packing arrangements of the disks, successfully describes the fragile-strong crossover.

Edwards entropy and compactivity in a model of granular matter.

Formulating a statistical mechanics for granular matter remains a significant challenge, in part due to the difficulty associated with a complete characterization of the systems under study. We present a fully characterized model of a granular material consisting of N two-dimensional, frictionless hard disks, confined between hard walls, including a complete enumeration of all possible jammed structures. We show that the properties of the jammed packings are independent of the distribution of defects within the system and that all the packings are isostatic. This suggests that the assumption of equal probability for states of equal volume, which provides one possible way of constructing the equivalent of a microcanonical ensemble, is likely to be valid for our model. An application of the second law of thermodynamics involving two subsystems in contact shows that the expected spontaneous equilibration of defects between the two is accompanied by an increase in entropy and that the equilibrium, obtained by entropy maximization, is characterized by the equality of compactivities. Finally, we explore the properties of the equivalent to the canonical ensemble for this system.

Complete jamming landscape of confined hard discs.

An exact description of the complete jamming landscape is developed for a system of hard discs of diameter sigma, confined between two lines separated by a distance 1+sqrt[3/4]

Metal-to-semimetal transition in supercooled liquid silicon.

Computer simulations, using the Stillinger-Weber potential, have previously been employed to demonstrate a liquid-liquid transition in supercooled silicon near 1060 K. From calculations of electronic structure using an empirical psuedopotential, we show that silicon undergoes an associated metal to semimetal transition with a resistivity jump of roughly 1 order of magnitude. We show that the electronic states near the Fermi energy become localized in the low temperature phase, and that changes in electronic structure between the two phases arise from a change in atomic structure, and not from a change in density.