Polymer physics view of peripheral chromatin: de Gennes' self-similar carpet.

Using scaling arguments to model peripheral chromatin localized near the inner surface of the nuclear envelope (NE) as a flexible polymer chain, we discuss the structural properties of the peripheral chromatin composed of alternating lamin-associated domains (LADs) and inter-LADs. Modeling the attraction of LADs to NE by de Gennes' self-similar carpet, which treats the chromatin layer as a polymer fractal, explains two major experimental observations. (i) The high density of chromatin close to the nuclear periphery decays to a constant density as the distance to the periphery increases. (ii) Due to the decreasing mesh size towards the nuclear periphery, the chromatin carpet inside NE excludes molecules (via nonspecific interactions) above a threshold size that depends on the distance from the nuclear periphery.

Chromatin phase separation and nuclear shape fluctuations are correlated in a polymer model of the nucleus.

Abnormal cell nuclear shapes are hallmarks of diseases, including progeria, muscular dystrophy, and many cancers. Experiments have shown that disruption of heterochromatin and increases in euchromatin lead to nuclear deformations, such as blebs and ruptures. However, the physical mechanisms through which chromatin governs nuclear shape are poorly understood. To investigate how heterochromatin and euchromatin might govern nuclear morphology, we studied chromatin microphase separation in a composite coarse-grained polymer and elastic shell simulation model. By varying chromatin density, heterochromatin composition, and heterochromatin-lamina interactions, we show how the chromatin phase organization may perturb nuclear shape. Increasing chromatin density stabilizes the lamina against large fluctuations. However, increasing heterochromatin levels or heterochromatin-lamina interactions enhances nuclear shape fluctuations by a "wetting"-like interaction. In contrast, fluctuations are insensitive to heterochromatin's internal structure. Our simulations suggest that peripheral heterochromatin accumulation could perturb nuclear morphology, while nuclear shape stabilization likely occurs through mechanisms other than chromatin microphase organization.

Chromatin phase separation and nuclear shape fluctuations are correlated in a polymer model of the nucleus.

Abnormalities in the shapes of mammalian cell nuclei are hallmarks of a variety of diseases, including progeria, muscular dystrophy, and various cancers. Experiments have shown that there is a causal relationship between chromatin organization and nuclear morphology. Decreases in heterochromatin levels, perturbations to heterochromatin organization, and increases in euchromatin levels all lead to misshapen nuclei, which exhibit deformations, such as nuclear blebs and nuclear ruptures. However, the polymer physical mechanisms of how chromatin governs nuclear shape and integrity are poorly understood. To investigate how heterochromatin and euchromatin, which are thought to microphase separate in vivo , govern nuclear morphology, we implemented a composite coarse-grained polymer and elastic shell model. By varying chromatin volume fraction (density), heterochromatin levels and structure, and heterochromatin-lamina interactions, we show how the spatial organization of chromatin polymer phases within the nucleus could perturb nuclear shape in some scenarios. Increasing the volume fraction of chromatin in the cell nucleus stabilizes the nuclear lamina against large fluctuations. However, surprisingly, we find that increasing heterochromatin levels or heterochromatin-lamina interactions enhances nuclear shape fluctuations in our simulations by a "wetting"-like interaction. In contrast, shape fluctuations are largely insensitive to the internal structure of the heterochromatin, such as the presence or absence of chromatin-chromatin crosslinks. Therefore, our simulations suggest that heterochromatin accumulation at the nuclear periphery could perturb nuclear morphology in a nucleus or nuclear region that is sufficiently soft, while stabilization of the nucleus via heterochromatin likely occurs through mechanisms other than chromatin microphase organization.

Mechanical deformation affects the counterion condensation in highly-swollen polyelectrolyte hydrogels.

Polyelectrolyte gels can generate electric potentials under mechanical deformation. While the underlying mechanism of such a response is often attributed to changes in counterion-condensation levels or alterations in the ionic conditions in the pervaded volume of the hydrogel, the exact molecular origins are largely unknown. By using all-atom molecular dynamics simulations of a polyacrylic acid hydrogel in explicit water as a model system, we simulate the uniaxial compression and uniaxial stretching of weakly to highly swollen (i.e., between 60-90% solvent content) hydrogel networks and calculate the microscopic condensation levels of counterions around the hydrogel chains. The counterion condensation under deformation is highly non-monotonic. Ionic condensation around the constituting chains of the deformed hydrogel tends to increase as the chains are stretched. This increase reaches a maximum and decreases as the chains are strongly stretched. The condensation around the collapsed chains of the hydrogel is weakly affected by the deformation. As a result, both compressing and stretching the model hydrogel lead to an overall increase in the counterion condensation. The effect vanishes for weakly swollen hydrogels, for which most ions are already condensed. The simulations with single, stretched polyelectrolyte chains show a qualitatively similar response, suggesting the effect of chain elongation on the ionic distribution throughout the hydrogel. Notably, this deformation-induced counterion condensation phenomenon does not occur in a polyelectrolyte solution at its critical concentration, indicating the role of hydrogel topology constraining the chain ends. Our results indicate that counterion condensation in a deforming polyelectrolyte hydrogel can be highly heterogeneous and exhibit a rich behaviour of electrostatic responses.

Cyclic-polymer grafted colloids in spherical confinement: insights for interphase chromosome organization.

Interphase chromosomes are known to organize non-randomly in the micron-sized eukaryotic cell nucleus and occupy certain fraction of nuclear volume, often without mixing. Using extensive coarse-grained simulations, we model such chromosome structures as colloidal particles whose surfaces are grafted by cyclic polymers. This model system is known as Rosetta. The cyclic polymers, with varying polymerization degrees, mimic chromatin loops present in interphase chromosomes, while the rigid core models the chromocenter section of the chromosome. Our simulations show that the colloidal chromosome model provides a well-separated particle distribution without specific attraction between the chain monomers. As the polymerization degree of the grafted cyclic chains decreases while maintaining the total chromosomal length (e.g. the more potent activity of condensin-family proteins), the average chromosomal volume becomes smaller, inter-chromosomal contacts decrease, and chromocenters organize in a quasi-crystalline order reminiscent of a glassy state. This order weakens for polymer chains with a characteristic size on the order of the confinement radius. Notably, linear-polymer grafted particles also provide the same chromocenter organization scheme. However, unlike linear chains, cyclic chains result in less contact between the polymer layers of neighboring chromosome particles, demonstrating the effect of DNA breaks in altering genome-wide contacts. Our simulations show that polymer-grafted colloidal systems could help decipher 3D genome architecture along with the fractal globular and loop-extrusion models.

Effect of Charge State on the Equilibrium and Kinetic Properties of Mechanically Interlocked [5]Rotaxane: A Molecular Dynamics Study.

Rotaxanes can exhibit stimuli-responsive behavior by allowing positional fluctuations of their rota groups in response to physiochemical conditions such as the changes in solution pH. However, ionic strength of the solution also affects the molecular conformation by altering the charge state of the entire molecule, coupling the stimuli-responsiveness of rotaxanes with their conformation. A molecular-scale investigation on a model system can allow the decoupling and identification of various effects and can greatly benefit applications of such molecular switches. By using atomistic molecular dynamics simulations, we study equilibrium and kinetics properties of various charge states of the [5]rotaxane, which is a supramolecular moiety with four rotaxanes bonded to a porphyrin core. We model various physiochemical charge states, each of which can be realized at various solution pH levels as well as several exotic charge distributions. By analyzing molecular configurations, hydrogen bonding, and energetics of single molecules in salt-free water and its polyrotaxanated network at the interface of water and chloroform, we demonstrate that charge-neutral and negatively charged molecules often tend to collapse in a way that they can expose their porphyrin core. Contrarily, positively charged moieties tend to take more extended molecular configurations blocking the core. Further, sudden changes in the charge states emulating the pH alterations in solution conditions lead to rapid, sub-10 ns level, changes in the molecular conformation of [5]rotaxane via shuttling motion of CB6 rings along axles. Finally, simulations of 2D [5]rotaxane network structures support our previous findings on a few nanometer-thick film formation at oil-water interfaces. Overall, our results suggest that rotaxane-based structures can exhibit a rich spectrum of molecular configurations and kinetics depending on the ionic strength of the solution.

Facilitated dissociation of nucleoid-associated proteins from DNA in the bacterial confinement.

Transcription machinery depends on the temporal formation of protein-DNA complexes. Recent experiments demonstrated that not only the formation but also the lifetime of such complexes can affect the transcriptional machinery. In parallel, in vitro single-molecule studies showed that nucleoid-associated proteins (NAPs) leave the DNA rapidly as the bulk concentration of the protein increases via facilitated dissociation (FD). Nevertheless, whether such a concentration-dependent mechanism is functional in a bacterial cell, in which NAP levels and the 3d chromosomal structure are often coupled, is not clear a priori. Here, by using extensive coarse-grained molecular simulations, we model the unbinding of specific and nonspecific dimeric NAPs from a high-molecular-weight circular DNA molecule in a cylindrical structure mimicking the cellular confinement of a bacterial chromosome. Our simulations confirm that physiologically relevant peak protein levels (tens of micromolar) lead to highly compact chromosomal structures. This compaction results in rapid off rates (shorter DNA residence times) for specifically DNA-binding NAPs, such as the factor for inversion stimulation, which mostly dissociate via a segmental jump mechanism. Contrarily, for nonspecific NAPs, which are more prone to leave their binding sites via 1d sliding, the off rates decrease as the protein levels increase. The simulations with restrained chromosome models reveal that chromosome compaction is in favor of faster dissociation but only for specific proteins, and nonspecific proteins are not affected by the chromosome compaction. Overall, our results suggest that the cellular concentration level of a structural DNA-binding protein can be highly intermingled with its DNA residence time.

The Role of Ligand Rebinding and Facilitated Dissociation on the Characterization of Dissociation Rates by Surface Plasmon Resonance (SPR) and Benchmarking Performance Metrics.

Surface plasmon resonance (SPR) is a real-time kinetic measurement principle that can probe the kinetic interactions between ligands and their binding sites, and lies at the backbone of pharmaceutical, biosensing, and biomolecular research. The extraction of dissociation rates from SPR-response signals often relies on several commonly adopted assumptions, one of which is the exponential decay of the dissociation part of the response signal. However, certain conditions, such as high density of binding sites or high concentration fluctuations near the surface as compared to the bulk, can lead to non-exponential decays via ligand rebinding or facilitated dissociation. Consequently, fitting the data with an exponential function can underestimate or overestimate the measured dissociation rates. Here, we describe a set of alternative fit functions that can take such effects into consideration along with plasmonic sensor design principles with key performance metrics, thereby suggesting methods for error-free high-precision extraction of the dissociation rates.

How do DNA-bound proteins leave their binding sites? The role of facilitated dissociation.

Dissociation of a protein from DNA is often assumed to be described by an off rate that is independent of other molecules in solution. Recent experiments and computational analyses have challenged this view by showing that unbinding rates (residence times) of DNA-bound proteins can depend on concentrations of nearby molecules that are competing for binding. This 'facilitated dissociation' (FD) process can occur at the single-binding site level via formation of a ternary complex, and can dominate over 'spontaneous dissociation' at low (submicromolar) concentrations. In the crowded intracellular environment FD introduces new regulatory possibilities at the level of individual biomolecule interactions.

Receptor-Ligand Rebinding Kinetics in Confinement.

Rebinding kinetics of molecular ligands plays a key role in the operation of biomachinery, from regulatory networks to protein transcription, and is also a key factor in design of drugs and high-precision biosensors. In this study, we investigate initial release and rebinding of ligands to their binding sites grafted on a planar surface, a situation commonly observed in single-molecule experiments and that occurs in vivo, e.g., during exocytosis. Via scaling arguments and molecular dynamic simulations, we analyze the dependence of nonequilibrium rebinding kinetics on two intrinsic length scales: the average separation distance between the binding sites and the total diffusible volume (i.e., height of the experimental reservoir in which diffusion takes place or average distance between receptor-bearing surfaces). We obtain time-dependent scaling laws for on rates and for the cumulative number of rebinding events. For diffusion-limited binding, the (rebinding) on rate decreases with time via multiple power-law regimes before the terminal steady-state (constant on-rate) regime. At intermediate times, when particle density has not yet become uniform throughout the diffusible volume, the cumulative number of rebindings exhibits a novel, to our knowledge, plateau behavior because of the three-dimensional escape process of ligands from binding sites. The duration of the plateau regime depends on the average separation distance between binding sites. After the three-dimensional diffusive escape process, a one-dimensional diffusive regime describes on rates. In the reaction-limited scenario, ligands with higher affinity to their binding sites (e.g., longer residence times) delay entry to the power-law regimes. Our results will be useful for extracting hidden timescales in experiments such as kinetic rate measurements for ligand-receptor interactions in microchannels, as well as for cell signaling via diffusing molecules.

Effects of electrostatic interactions on ligand dissociation kinetics.

We study unbinding of multivalent cationic ligands from oppositely charged polymeric binding sites sparsely grafted on a flat neutral substrate. Our molecular dynamics simulations are suggested by single-molecule studies of protein-DNA interactions. We consider univalent salt concentrations spanning roughly a 1000-fold range, together with various concentrations of excess ligands in solution. To reveal the ionic effects on unbinding kinetics of spontaneous and facilitated dissociation mechanisms, we treat electrostatic interactions both at a Debye-Hückel (DH) (or implicit ions, i.e., use of an electrostatic potential with a prescribed decay length) level and by the more precise approach of considering all ionic species explicitly in the simulations. We find that the DH approach systematically overestimates unbinding rates, relative to the calculations where all ion pairs are present explicitly in solution, although many aspects of the two types of calculation are qualitatively similar. For facilitated dissociation (FD) (acceleration of unbinding by free ligands in solution) explicit-ion simulations lead to unbinding at lower free-ligand concentrations. Our simulations predict a variety of FD regimes as a function of free-ligand and ion concentrations; a particularly interesting regime is at intermediate concentrations of ligands where nonelectrostatic binding strength controls FD. We conclude that explicit-ion electrostatic modeling is an essential component to quantitatively tackle problems in molecular ligand dissociation, including nucleic-acid-binding proteins.

Co-assembly of Peptide Amphiphiles and Lipids into Supramolecular Nanostructures Driven by Anion-π Interactions.

Co-assembly of binary systems driven by specific non-covalent interactions can greatly expand the structural and functional space of supramolecular nanostructures. We report here on the self-assembly of peptide amphiphiles and fatty acids driven primarily by anion-π interactions. The peptide sequences investigated were functionalized with a perfluorinated phenylalanine residue to promote anion-π interactions with carboxylate headgroups in fatty acids. These interactions were verified here by NMR and circular dichroism experiments as well as investigated using atomistic simulations. Positioning the aromatic units close to the N-terminus of the peptide backbone near the hydrophobic core of cylindrical nanofibers leads to strong anion-π interactions between both components. With a low content of dodecanoic acid in this position, the cylindrical morphology is preserved. However, as the aromatic units are moved along the peptide backbone away from the hydrophobic core, the interactions with dodecanoic acid transform the cylindrical supramolecular morphology into ribbon-like structures. Increasing the ratio of dodecanoic acid to PA leads to either the formation of large vesicles in the binary systems where the anion-π interactions are strong, or a heterogeneous mixture of assemblies when the peptide amphiphiles associate weakly with dodecanoic acid. Our findings reveal how co-assembly involving designed specific interactions can drastically change supramolecular morphology and even cross from nano to micro scales.

Facilitated dissociation of transcription factors from single DNA binding sites.

The binding of transcription factors (TFs) to DNA controls most aspects of cellular function, making the understanding of their binding kinetics imperative. The standard description of bimolecular interactions posits that TF off rates are independent of TF concentration in solution. However, recent observations have revealed that proteins in solution can accelerate the dissociation of DNA-bound proteins. To study the molecular basis of facilitated dissociation (FD), we have used single-molecule imaging to measure dissociation kinetics of Fis, a key Escherichia coli TF and major bacterial nucleoid protein, from single dsDNA binding sites. We observe a strong FD effect characterized by an exchange rate [Formula: see text], establishing that FD of Fis occurs at the single-binding site level, and we find that the off rate saturates at large Fis concentrations in solution. Although spontaneous (i.e., competitor-free) dissociation shows a strong salt dependence, we find that FD depends only weakly on salt. These results are quantitatively explained by a model in which partially dissociated bound proteins are susceptible to invasion by competitor proteins in solution. We also report FD of NHP6A, a yeast TF with structure that differs significantly from Fis. We further perform molecular dynamics simulations, which indicate that FD can occur for molecules that interact far more weakly than those that we have studied. Taken together, our results indicate that FD is a general mechanism assisting in the local removal of TFs from their binding sites and does not necessarily require cooperativity, clustering, or binding site overlap.

Morphology-enhanced conductivity in dry ionic liquids.

Ionic liquids exhibit fascinating nanoscale morphological phases and are promising materials for energy storage applications. Liquid crystalline order emerges in ionic liquids with specific chemical structures. Here, we investigate the phase behaviour and related ionic conductivities of dry ionic liquids, using extensive molecular dynamics simulations. Temperature dependence, properties of polymeric tail and excluded volume symmetry of the amphiphilic ionic liquid molecules are investigated in large scale systems with both short and long-range Coulomb interactions. Our results suggest that by adjusting stiffness and steric interactions of the amphiphilic molecules, lamellar or 3D continuous phases result in these molecular salts. The resulting phases are composed of ion rich and ion pure domains. In 3D phases, ion rich clusters form ionic channels and have significant effects on the conductive properties of the observed nano-phases. If there is no excluded-volume asymmetry along the molecules, mostly lamellar phases with anisotropic conductivities emerge. If the steric interactions become asymmetric, lamellar phases are replaced by complex 3D continuous phases. Within the temperature ranges for which morphological phases are observed, conductivities exhibit low-temperature maxima in accord with experiments on ionic liquid crystals. Stiffer molecules increase the high-conductivity interval and strengthen temperature-resistance of morphological phases. Increasing the steric interactions of cation leads to higher conductivities. Moreover, at low monomeric volume fractions and at low temperatures, cavities are observed in the nano-phases of flexible ionic liquids. We also demonstrate that, in the absence of electrostatic interactions, the morphology is distorted. Our findings inspire new design principles for room temperature ionic liquids and help explain previously-reported experimental data.

Friction between ring polymer brushes.

Friction between ring polymer brush bilayers sliding past each other at melt densities is studied using extensive coarse-grained molecular dynamics simulations and scaling arguments, and the results are compared to the friction between bilayers of linear polymer brushes. We show that for a velocity range spanning over three decades, the frictional forces measured for ring polymer brushes are half of the corresponding friction in the case of linear brushes. In the linear-force regime, the weak inter-digitation between ring brush layers as compared to linear brushes leads also to a lower number of binary collisions between the monomers from opposing brushes. At high velocities, where the thickness of the inter-digitation between bilayers is on the order of monomer size regardless of brush topology, stretched segments of ring polymers adopt the double-stranded conformation. As a result, monomers of the double-stranded segments collide on average less with the monomers of the opposing ring brush even though a similar number of monomers occupies the inter-digitation layer for ring and linear brush bilayers. The numerical data obtained from our simulations are consistent with the proposed scaling analysis. Conformation-dependent friction reduction observed in ring brushes can have important consequences in non-equilibrium bulk systems.

Energy Conversion in Polyelectrolyte Hydrogels.

Using extensive molecular dynamics simulations of polyelectrolyte hydrogels we demonstrate that, on deformation, these hydrogels adjust their deformed state predominantly by altering electrostatic interactions between their charged groups rather than excluded-volume and bond energies. On deformation, due to the hydrogel's inherent tendency to preserve electroneutrality in its interior, the translational entropy of counterions decreases and the total electrostatic energy becomes more attractive. This result is valid for a wide range of compression ratios and Bjerrum lengths. The change in the electrostatic energy is more marked in highly swollen gels at low ionic strengths. At high Bjerrum lengths, where most of the counterions are condensed on hydrogel chains and the gel resembles a neutral system, the electrostatic-energy change with deformation is weaker.

Confinement-dependent friction in peptide bundles.

Friction within globular proteins or between adhering macromolecules crucially determines the kinetics of protein folding, the formation, and the relaxation of self-assembled molecular systems. One fundamental question is how these friction effects depend on the local environment and in particular on the presence of water. In this model study, we use fully atomistic MD simulations with explicit water to obtain friction forces as a single polyglycine peptide chain is pulled out of a bundle of k adhering parallel polyglycine peptide chains. The whole system is periodically replicated along the peptide axes, so a stationary state at prescribed mean sliding velocity V is achieved. The aggregation number is varied between k = 2 (two peptide chains adhering to each other with plenty of water present at the adhesion sites) and k = 7 (one peptide chain pulled out from a close-packed cylindrical array of six neighboring peptide chains with no water inside the bundle). The friction coefficient per hydrogen bond, extrapolated to the viscous limit of vanishing pulling velocity V → 0, exhibits an increase by five orders of magnitude when going from k = 2 to k = 7. This dramatic confinement-induced friction enhancement we argue to be due to a combination of water depletion and increased hydrogen-bond cooperativity.

Viscous friction of hydrogen-bonded matter.

Amontons' law successfully describes friction between macroscopic solid bodies for a wide range of velocities and normal forces. For the diffusion and forced sliding of adhering or entangled macromolecules, proteins, and biological complexes, temperature effects are invariably important, and a similarly successful friction law at biological length and velocity scales is missing. Hydrogen bonds (HBs) are key to the specific binding of biomatter. Here we show that friction between hydrogen-bonded matter obeys in the biologically relevant low-velocity viscous regime a simple law: the friction force is proportional to the number of HBs, the sliding velocity, and a friction coefficient γ(HB). This law is deduced from atomistic molecular dynamics simulations for short peptide chains that are laterally pulled over planar hydroxylated substrates in the presence of water and holds for widely different peptides, surface polarities, and applied normal forces. The value of γ(HB) is extrapolated from simulations at sliding velocities in the range from V = 10(-2) to 100 m/s by mapping on a simple stochastic model and turns out to be of the order of γ(HB) ≃ 10(-8) kg/s. The friction of a single HB thus amounts to the Stokes friction of a sphere with an equivalent radius of roughly 1 µm moving in water. Cooperativity is pronounced: roughly three HBs act collectively.

Phase diagrams and crossover in spatially anisotropic d = 3 Ising, XY magnetic, and percolation systems: exact renormalization-group solutions of hierarchical models.

Hierarchical lattices that constitute spatially anisotropic systems are introduced. These lattices provide exact solutions for hierarchical models and, simultaneously, approximate solutions for uniaxially or fully anisotropic d = 3 physical models. The global phase diagrams, with d = 2 and d = 1 to d = 3 crossovers, are obtained for Ising and XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.