Role of diffusion and reaction of the constituents in spreading of histone modification marks.

Cells switch genes ON or OFF by altering the state of chromatin via histone modifications at specific regulatory locations along the chromatin polymer. These gene regulation processes are carried out by a network of reactions in which the histone marks spread to neighboring regions with the help of enzymes. In the literature, this spreading has been studied as a purely kinetic, non-diffusive process considering the interactions between neighboring nucleosomes. In this work, we go beyond this framework and study the spreading of modifications using a reaction-diffusion (RD) model accounting for the diffusion of the constituents. We quantitatively segregate the modification profiles generated from kinetic and RD models. The diffusion and degradation of enzymes set a natural length scale for limiting the domain size of modification spreading, and the resulting enzyme limitation is inherent in our model. We also demonstrate the emergence of confined modification domains without the explicit requirement of a nucleation site. We explore polymer compaction effects on spreading and show that single-cell domains may differ from averaged profiles. We find that the modification profiles from our model are comparable with existing H3K9me3 data of S. pombe.

Orc4 spatiotemporally stabilizes centromeric chromatin.

The establishment of centromeric chromatin and its propagation by the centromere-specific histone CENPA is mediated by epigenetic mechanisms in most eukaryotes. DNA replication origins, origin binding proteins, and replication timing of centromere DNA are important determinants of centromere function. The epigenetically regulated regional centromeres in the budding yeast Candida albicans have unique DNA sequences that replicate earliest in every chromosome and are clustered throughout the cell cycle. In this study, the genome-wide occupancy of the replication initiation protein Orc4 reveals its abundance at all centromeres in C. albicans Orc4 is associated with four different DNA sequence motifs, one of which coincides with tRNA genes (tDNA) that replicate early and cluster together in space. Hi-C combined with genome-wide replication timing analyses identify that early replicating Orc4-bound regions interact with themselves stronger than with late replicating Orc4-bound regions. We simulate a polymer model of chromosomes of C. albicans and propose that the early replicating and highly enriched Orc4-bound sites preferentially localize around the clustered kinetochores. We also observe that Orc4 is constitutively localized to centromeres, and both Orc4 and the helicase Mcm2 are essential for cell viability and CENPA stability in C. albicans Finally, we show that new molecules of CENPA are recruited to centromeres during late anaphase/telophase, which coincides with the stage at which the CENPA-specific chaperone Scm3 localizes to the kinetochore. We propose that the spatiotemporal localization of Orc4 within the nucleus, in collaboration with Mcm2 and Scm3, maintains centromeric chromatin stability and CENPA recruitment in C. albicans.

Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop.

Several types of molecular machines move along biopolymers like chromatin. However, the details about the microscopic activity of these machines and how to distinguish their modes of action are not well understood. We propose that the activity of such machines can be classified by studying looped chromatin under shear flow. Our simulations show that a chromatin-like polymer with two types of activities-constant (type-I) or local curvature-dependent tangential forces (type-II)-exhibits very different behavior under shear flow. We show that one can distinguish both activities by measuring the nature of a globule-to-extended coil transition, tank treading, and tumbling dynamics.

Nonequilibrium switching of segmental states can influence compaction of chromatin.

Knowledge about the dynamic nature of chromatin organization is essential to understand the regulation of processes like DNA transcription and repair. The existing models of chromatin assume that protein organization and chemical states along chromatin are static and the 3D organization is purely a result of protein-mediated intra-chromatin interactions. Here we present a new hypothesis that certain nonequilibrium processes, such as switching of chemical and physical states due to nucleosome assembly/disassembly or gene repression/activation, can also simultaneously influence chromatin configurations. To understand the implications of this inherent nonequilibrium switching, we present a block copolymer model of chromatin, with switching of its segmental states between two states, mimicking active/repressed or protein unbound/bound states. We show that competition between switching timescale Tt, polymer relaxation timescale τp, and segmental relaxation timescale τs can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when Tt ≈ τp and a maximum when Tt ≈ τs. We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate.

Continuous variable responses and signal gating form kinetic bases for pulsatile insulin signaling and emergence of resistance.

Understanding kinetic control of biological processes is as important as identifying components that constitute pathways. Insulin signaling is central for almost all metazoans, and its perturbations are associated with various developmental disorders, metabolic diseases, and aging. While temporal phosphorylation changes and kinetic constants have provided some insights, constant or variable parameters that establish and maintain signal topology are poorly understood. Here, we report kinetic parameters that encode insulin concentration and nutrient-dependent flow of information using iterative experimental and mathematical simulation-based approaches. Our results illustrate how dynamics of distinct phosphorylation events collectively contribute to selective kinetic gating of signals and maximum connectivity of the signaling cascade under normo-insulinemic but not hyper-insulinemic states. In addition to identifying parameters that provide predictive value for maintaining the balance between metabolic and growth-factor arms, we posit a kinetic basis for the emergence of insulin resistance. Given that pulsatile insulin secretion during a fasted state precedes a fed response, our findings reveal rewiring of insulin signaling akin to memory and anticipation, which was hitherto unknown. Striking disparate temporal behavior of key phosphorylation events that destroy the topology under hyper-insulinemic states underscores the importance of unraveling regulatory components that act as bandwidth filters. In conclusion, besides providing fundamental insights, our study will help in identifying therapeutic strategies that conserve coupling between metabolic and growth-factor arms, which is lost in diseases and conditions of hyper-insulinemia.

High fidelity epigenetic inheritance: Information theoretic model predicts threshold filling of histone modifications post replication.

During cell devision, maintaining the epigenetic information encoded in histone modification patterns is crucial for survival and identity of cells. The faithful inheritance of the histone marks from the parental to the daughter strands is a puzzle, given that each strand gets only half of the parental nucleosomes. Mapping DNA replication and reconstruction of modifications to equivalent problems in communication of information, we ask how well enzymes can recover the parental modifications, if they were ideal computing machines. Studying a parameter regime where realistic enzymes can function, our analysis predicts that enzymes may implement a critical threshold filling algorithm which fills unmodified regions of length at most k. This algorithm, motivated from communication theory, is derived from the maximum à posteriori probability (MAP) decoding which identifies the most probable modification sequence based on available observations. Simulations using our method produce modification patterns similar to what has been observed in recent experiments. We also show that our results can be naturally extended to explain inheritance of spatially distinct antagonistic modifications.

Role of non-specific interactions in the phase-separation and maturation of macromolecules.

Phase separation of biomolecules could be mediated by both specific and non-specific interactions. How the interplay between non-specific and specific interactions along with polymer entropy influences phase separation is an open question. We address this question by simulating self-associating molecules as polymer chains with a short core stretch that forms the specifically interacting functional interface and longer non-core regions that participate in non-specific/promiscuous interactions. Our results show that the interplay of specific (strength, ϵsp) and non-specific interactions (strength, ϵns) could result in phase separation of polymers and its transition to solid-like aggregates (mature state). In the absence of ϵns, the polymer chains do not dwell long enough in the vicinity of each other to undergo phase separation and transition into a mature state. On the other hand, in the limit of strong ϵns, the assemblies cannot transition into the mature state and form a non-specific assembly, suggesting an optimal range of interactions favoring mature multimers. In the scenario where only a fraction (Nfrac) of the non-core regions participate in attractive interactions, we find that slight modifications to either ϵns or Nfrac can result in dramatically altered self-assembled states. Using a combination of heterogeneous and homogeneous mix of polymers, we establish how this interplay between interaction energies dictates the propensity of biomolecules to find the correct binding partner at dilute concentrations in crowded environments.

Heterogeneous interactions and polymer entropy decide organization and dynamics of chromatin domains.

Chromatin is known to be organized into multiple domains of varying sizes and compaction. While these domains are often imagined as static structures, they are highly dynamic and show cell-to-cell variability. Since processes such as gene regulation and DNA replication occur in the context of these domains, it is important to understand their organization, fluctuation, and dynamics. To simulate chromatin domains, one requires knowledge of interaction strengths among chromatin segments. Here, we derive interaction-strength parameters from experimentally known contact maps and use them to predict chromatin organization and dynamics. Taking two domains on the human chromosome as examples, we investigate its three-dimensional organization, size/shape fluctuations, and dynamics of different segments within a domain, accounting for hydrodynamic effects. Considering different cell types, we quantify changes in interaction strengths and chromatin shape fluctuations in different epigenetic states. Perturbing the interaction strengths systematically, we further investigate how epigenetic-like changes can alter the spatio-temporal nature of the domains. Our results show that heterogeneous weak interactions are crucial in determining the organization of the domains. Computing effective stiffness and relaxation times, we investigate how perturbations in interactions affect the solid- and liquid-like nature of chromatin domains. Quantifying dynamics of chromatin segments within a domain, we show how the competition between polymer entropy and interaction energy influence the timescales of loop formation and maintenance of stable loops.

Irregular Chromatin: Packing Density, Fiber Width, and Occurrence of Heterogeneous Clusters.

How chromatin is folded on the length scale of a gene is an open question. Recent experiments have suggested that, in vivo, chromatin is folded in an irregular manner and not as an ordered fiber with a width of 30 nm that is expected from theories of higher order packaging. Using computational methods, we examine how the interplay between DNA-bending nonhistone proteins, histone tails, intrachromatin electrostatic, and other interactions decide the nature of the packaging of chromatin. We show that although the DNA-bending nonhistone proteins make the chromatin irregular, they may not alter the packing density and size of the fiber. We find that the length of the interacting region and intrachromatin electrostatic interactions influence the packing density, clustering of nucleosomes, and the width of the chromatin fiber. Our results suggest that the heterogeneity in the interaction pattern will play an important role in deciding the nature of the packaging of chromatin.

The Accidental Ally: Nucleosome Barriers Can Accelerate Cohesin-Mediated Loop Formation in Chromatin.

An important question in the context of the three-dimensional organization of chromosomes is the mechanism of formation of large loops between distant basepairs. Recent experiments suggest that the formation of loops might be mediated by loop extrusion factor proteins such as cohesin. Experiments on cohesin have shown that cohesins walk diffusively on the DNA and that nucleosomes act as obstacles to the diffusion, lowering the permeability and hence reducing the effective diffusion constant. An estimation of the times required to form the loops of typical sizes seen in Hi-C experiments using these low-effective-diffusion constants leads to times that are unphysically large. The puzzle then is the following: how does a cohesin molecule diffusing on the DNA backbone achieve speeds necessary to form the large loops seen in experiments? We propose a simple answer to this puzzle and show that although at low densities, nucleosomes act as barriers to cohesin diffusion, beyond a certain concentration they can reduce loop formation times because of a subtle interplay between the nucleosome size and the mean linker length. This effect is further enhanced on considering stochastic binding kinetics of nucleosomes on the DNA backbone and leads to predictions of lower loop formation times than might be expected from a naive obstacle picture of nucleosomes.

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.

Regulation of microtubule disassembly by spatially heterogeneous patterns of acetylation.

Microtubules (MTs) are bio-polymers, composed of tubulin proteins, involved in several functions such as cell division, transport of cargoes within cells, maintaining cellular structures etc. Their kinetics are often affected by chemical modifications on the filament known as Post Translational Modifications (PTMs). Acetylation is a PTM which occurs on the luminal surface of the MT lattice and has been observed to reduce the lateral interaction between tubulins on adjacent protofilaments. Depending on the properties of the acetylase enzyme αTAT1 and the structural features of MTs, the patterns of acetylation formed on MTs are observed to be quite diverse. In this study, we present a multi-protofilament model with spatially heterogeneous patterns of acetylation, and investigate how the local kinetic differences arising from heterogeneity affect the global kinetics of MT filaments. From the computational study we conclude that a filament with spatially uniform acetylation is least stable against disassembly, while ones with more clustered acetylation patterns may provide better resistance against disassembly. The increase in disassembly times for clustered pattern as compared to uniform pattern can be up to fifty percent for identical amounts of acetylation. Given that acetylated MTs affect several cellular functions as well as diseases such as cancer, our study indicates that spatial patterns of acetylation need to be focused on, apart from the overall amount of acetylation.

Coupling of replisome movement with nucleosome dynamics can contribute to the parent-daughter information transfer.

Positioning of nucleosomes along the genomic DNA is crucial for many cellular processes that include gene regulation and higher order packaging of chromatin. The question of how nucleosome-positioning information from a parent chromatin gets transferred to the daughter chromatin is highly intriguing. Accounting for experimentally known coupling between replisome movement and nucleosome dynamics, we propose a model that can obtain de novo nucleosome assembly similar to what is observed in recent experiments. Simulating nucleosome dynamics during replication, we argue that short pausing of the replication fork, associated with nucleosome disassembly, can be a event crucial for communicating nucleosome positioning information from parent to daughter. We show that the interplay of timescales between nucleosome disassembly (τp) at the replication fork and nucleosome sliding behind the fork (τs) can give rise to a rich 'phase diagram' having different inherited patterns of nucleosome organization. Our model predicts that only when τp ≥ τs the daughter chromatin can inherit nucleosome positioning of the parent.

Universality of the collapse transition of sticky polymers.

The universality of the swelling of the radius of gyration of a homopolymer relative to its value in the θ state, independent of polymer-solvent chemistry, in the crossover regime between θ and athermal solvent conditions, is well known. Here we study, by Brownian dynamics, a polymer model where a subset of monomers is labelled as "stickers". The mutual interaction of the stickers is more attractive than those of the other ("backbone") monomers, and has an additional important characteristic of "functionality" φ, i.e., the maximum number of stickers that can locally bind to a given sticker. A saturated bond formed in this manner remains bound until it breaks due to thermal fluctuations, a requirement which can be viewed as an additional Boolean degree of freedom that describes the bonding. This, in turn, makes the question of the order of the collapse transition a non-trivial one. Nevertheless, for the parameters that we have studied (in particular, φ = 1), we find a standard second-order θ collapse, using a renormalised solvent quality parameter that takes into account the increased average attraction due to the presence of stickers. We examine the swelling of the radius of gyration of such a sticky polymer relative to its value in the altered θ state, using a novel potential to model the various excluded volume interactions that occur between the monomers on the chain. We find that the swelling of such sticky polymers is identical to the universal swelling of homopolymers in the thermal crossover regime. Additionally, for our model, the Kuhn segment length under θ conditions is found to be the same for chains with and without stickers.

Complexation of NAC-Derived Peptide Ligands with the C-Terminus of α-Synuclein Accelerates Its Aggregation.

Aggregation of α-synuclein (α-Syn) into neurotoxic oligomers and amyloid fibrils is suggested to be the pathogenic mechanism for Parkinson's disease (PD). Recent studies have indicated that oligomeric species of α-Syn are more cytotoxic than their mature fibrillar counterparts, which are responsible for dopaminergic neuronal cell death in PD. Therefore, the effective therapeutic strategies for tackling aggregation-associated diseases would be either to prevent aggregation or to modulate the aggregation process to minimize the formation of toxic oligomers during aggregation. In this work, we showed that arginine-substituted α-Syn ligands, based on the most aggregation-prone sequence of α-Syn, accelerate the protein aggregation in a concentration-dependent manner. To elucidate the mechanism by which Arg-substituted peptides could modulate α-Syn aggregation kinetics, we performed surface plasmon resonance (SPR) spectroscopy, nuclear magnetic resonance (NMR) studies, and all-atom molecular dynamics (MD) simulation. The SPR analysis showed a high binding potency of these peptides with α-Syn but one that was nonspecific in nature. The two-dimensional NMR studies suggest that a large stretch within the C-terminus of α-Syn displays a chemical shift perturbation upon interacting with Arg-substituted peptides, indicating C-terminal residues of α-Syn might be responsible for this class of peptide binding. This is further supported by MD simulation studies in which the Arg-substituted peptide showed the strongest interaction with the C-terminus of α-Syn. Overall, our results suggest that the binding of Arg-substituted ligands to the highly acidic C-terminus of α-Syn leads to reduced charge density and flexibility, resulting in accelerated aggregation kinetics. This may be a potentially useful strategy while designing peptides, which act as α-Syn aggregation modulators.

Binding of DNA-bending non-histone proteins destabilizes regular 30-nm chromatin structure.

Why most of the in vivo experiments do not find the 30-nm chromatin fiber, well studied in vitro, is a puzzle. Two basic physical inputs that are crucial for understanding the structure of the 30-nm fiber are the stiffness of the linker DNA and the relative orientations of the DNA entering/exiting nucleosomes. Based on these inputs we simulate chromatin structure and show that the presence of non-histone proteins, which bind and locally bend linker DNA, destroys any regular higher order structures (e.g., zig-zag). Accounting for the bending geometry of proteins like nhp6 and HMG-B, our theory predicts phase-diagram for the chromatin structure as a function of DNA-bending non-histone protein density and mean linker DNA length. For a wide range of linker lengths, we show that as we vary one parameter, that is, the fraction of bent linker region due to non-histone proteins, the steady-state structure will show a transition from zig-zag to an irregular structure-a structure that is reminiscent of what is observed in experiments recently. Our theory can explain the recent in vivo observation of irregular chromatin having co-existence of finite fraction of the next-neighbor (i + 2) and neighbor (i + 1) nucleosome interactions.

Theoretical estimates of exposure timescales of protein binding sites on DNA regulated by nucleosome kinetics.

It is being increasingly realized that nucleosome organization on DNA crucially regulates DNA-protein interactions and the resulting gene expression. While the spatial character of the nucleosome positioning on DNA has been experimentally and theoretically studied extensively, the temporal character is poorly understood. Accounting for ATPase activity and DNA-sequence effects on nucleosome kinetics, we develop a theoretical method to estimate the time of continuous exposure of binding sites of non-histone proteins (e.g. transcription factors and TATA binding proteins) along any genome. Applying the method to Saccharomyces cerevisiae, we show that the exposure timescales are determined by cooperative dynamics of multiple nucleosomes, and their behavior is often different from expectations based on static nucleosome occupancy. Examining exposure times in the promoters of GAL1 and PHO5, we show that our theoretical predictions are consistent with known experiments. We apply our method genome-wide and discover huge gene-to-gene variability of mean exposure times of TATA boxes and patches adjacent to TSS (+1 nucleosome region); the resulting timescale distributions have non-exponential tails.

Defining a Physical Basis for Diversity in Protein Self-Assemblies Using a Minimal Model.

Self-assembly of proteins into ordered, fibrillar structures is a commonly observed theme in biology. It has been observed that diverse set of proteins (e.g., alpha-synuclein, insulin, TATA-box binding protein, Sup35, p53), independent of their sequence, native structure, or function could self-assemble into highly ordered structures known as amyloids. What are the crucial features underlying amyloidogenesis that make it so generic? Using coarse-grained simulations of peptide self-assembly, we argue that variation in two physical parameters-bending stiffness of the polypeptide and strength of intermolecular interactions-can give rise to many of the structural features typically associated with amyloid self-assembly. We show that the interplay between these two factors gives rise to a rich phase diagram displaying high diversity in aggregated states. For certain parameters, we find a bimodal distribution for the order parameter implying the coexistence of ordered and disordered aggregates. Our findings may explain the experimentally observed variability including the "off-pathway" aggregated structures. Further, we demonstrate that sequence-dependence and protein-specific signatures could be mapped to our coarse-grained framework to study self-assembly behavior of realistic systems such as the STVIIE peptide and Aß42. The work also provides certain guiding principles that could be used to design novel peptides with desired self-assembly properties, by tuning a few physical parameters.

Statistical mechanics provides novel insights into microtubule stability and mechanism of shrinkage.

Microtubules are nano-machines that grow and shrink stochastically, making use of the coupling between chemical kinetics and mechanics of its constituent protofilaments (PFs). We investigate the stability and shrinkage of microtubules taking into account inter-protofilament interactions and bending interactions of intrinsically curved PFs. Computing the free energy as a function of PF tip position, we show that the competition between curvature energy, inter-PF interaction energy and entropy leads to a rich landscape with a series of minima that repeat over a length-scale determined by the intrinsic curvature. Computing Langevin dynamics of the tip through the landscape and accounting for depolymerization, we calculate the average unzippering and shrinkage velocities of GDP protofilaments and compare them with the experimentally known results. Our analysis predicts that the strength of the inter-PF interaction (E(s)(m)) has to be comparable to the strength of the curvature energy (E(b)(m)) such that E(s)(m) - E(b)(m) ≈ 1kBT, and questions the prevalent notion that unzippering results from the domination of bending energy of curved GDP PFs. Our work demonstrates how the shape of the free energy landscape is crucial in explaining the mechanism of MT shrinkage where the unzippered PFs will fluctuate in a set of partially peeled off states and subunit dissociation will reduce the length.