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.

Molecular conformations of dumbbell-shaped polymers in good solvent.

We study conformational properties of diluted dumbbell polymers composed of two rings attached to both ends of a linear spacer segment. Our investigation involves analytical methods of field theory and bead-spring coarse-grained molecular dynamics simulations. We focus on the influence of the relative length of the spacer segment to the length of side rings on the shape and the relative size of dumbbells as compared to linear polymers of equal mass. We find that dumbbells with short spacers exhibit a significantly more compact structure than linear polymers. Conversely, as the spacer length increases, the influence of the side rings on the size of the dumbbells becomes negligible. Consequently, dumbbell molecules with long spacers attain a size comparable to corresponding linear chains. Our analytical theory accurately predicts a quantitative conformational crossover between the behaviors of short-spacer and long-spacer dumbbells, which is further confirmed by our numerical simulations.

Self-Assembled Nanostructures in Aprotic Ionic Liquids Facilitate Charge Transport at Elevated Pressure.

Ionic liquids (ILs), revealing a tendency to form self-assembled nanostructures, have emerged as promising materials in various applications, especially in energy storage and conversion. Despite multiple reports discussing the effect of structural factors and external thermodynamic variables on ion organization in a liquid state, little is known about the charge-transport mechanism through the self-assembled nanostructures and how it changes at elevated pressure. To address these issues, we chose three amphiphilic ionic liquids containing the same tetra(alkyl)phosphonium cation and anions differing in size and shape, i.e., thiocyanate [SCN]-, dicyanamide [DCA]-, and tricyanomethanide [TCM]-. From ambient pressure dielectric and mechanical experiments, we found that charge transport of all three examined ILs is viscosity-controlled at high temperatures. On the other hand, ion diffusion is much faster than structural dynamics in a nanostructured supercooled liquid (at T < 210 ± 3 K), which constitutes the first example of conductivity independent from viscosity in neat aprotic ILs. High-pressure measurements and MD simulations reveal that the created nanostructures depend on the anion size and can be modified by compression. For small anions, increasing pressure shapes immobile alkyl chains into lamellar-type phases, leading to increased anisotropic diffusivity of anions through channels. Bulky anions drive the formation of interconnected phases with continuous 3D curvature, which render ion transport independent of pressure. This work offers insight into the design of high-density electrolytes with percolating conductive phases providing efficient ion flow.

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.

Supramolecular structures of self-assembled oligomers under confinement.

We study the molecular origin of a prepeak (PP) observed at low q values in the structure factors of three oligomers in a bulk (poly(mercaptopropyl)methylsiloxane, PMMS, poly(methylmercaptopropyl)-grafted-hexylmethacrylate, PMMS-g-HMA, and poly(methylphenyl)siloxane, PMPS) in order to understand the lowering of the PP intensity detected for oligomers confined in cylindrical pores with low diameter. For this purpose, we use a combination of X-ray diffraction measurements and coarse-grained bead-spring molecular dynamics simulations. Our molecular modelling demonstrated that the planarity of the pendant groups triggers the self-association of oligomers into nanoaggregates. However, the formation of oligomeric nanodomains is not sufficient for building-up the PP. The latter requires spatial disturbance in the arrangement of the side groups of oligomers within clusters. Importantly, our numerical analysis revealed that the increasing degree of the confinement of oligomers limits their aggregation and consequently lowers the amplitude of the PP observed in the experimental data.

Conformational properties of hybrid star-shaped polymers comprised of linear and ring arms.

We study the influence of arm architecture on the conformational properties of hybrid star-shaped macromolecules called rosette polymers containing linear and ring grafts connected to a central branching point in a good solvent regime. We utilize analytical methods and molecular dynamics simulations to determine the estimates for the relative size ratios of these polymers with respect to linear chains and starlike polymers composed of the same number of solely linear arms and equal molecular weights. The results of numerical simulations corroborate our theoretical prediction that rosette polymers undergo conformational compactification with increasing functionality of grafted rings. Our results quantitatively describe the impact of the complex architecture of the molecules with excluded volume on their effective size measures.

Universal size ratios of Gaussian polymers with complex architecture: radius of gyration vs hydrodynamic radius.

We study the impact of arm architecture of polymers with a single branch point on their structure in solvents. Many physical properties of polymer liquids strongly dependent on the size and shape measures of individual macromolecules, which in turn are determined by their topology. Here, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing [Formula: see text] linear branches and [Formula: see text] closed loops grafted to the central core. We determine size measures such as the gyration radius [Formula: see text] and the hydrodynamic radii [Formula: see text], and obtain the estimates for the size ratio [Formula: see text] with its dependence on the functionality [Formula: see text] of grafted polymers. In particular, we obtain the quantitative estimate of the degree of compactification of these polymers with increasing number of closed loops [Formula: see text] as compared to linear or star-shape molecules of the same total molecular weight. Numerical simulations corroborate theoretical prediction that [Formula: see text] decreases towards unity with increasing f. These findings provide qualitative description of polymers with complex architecture in [Formula: see text] solvents.

Nanoparticle assembly under block copolymer confinement: The effect of nanoparticle size and confinement strength.

We investigate the self-assembly of cylinder-forming polystyrene-block-poly(4-vinylpyridine) (PS-b-P4VP) block copolymers (BCP) mixed with metal nanoparticles (NP) coated with short-chain polystyrene (PS) ligands. The NP formed hierarchical superstructures under confinement of cylindrical PS domains of PS-b-P4VP BCP. The complexity of NP superstructures was found to depend on the ratio between PS cylindrical domain size and NP size (DC/DNP). As the DC/DNP ratio increased, the number of NP layers normal to the cylinder axis also increased. However, the packing density of the NP decreased at higher DC/DNP. Furthermore, the morphology of the structures obtained during different solvent casting conditions revealed that the initial clustering of NP and micellization around these clusters act as a precursor for the subsequent formation of closely packed structures of NP in cylinders. The experimental results were further supported by modeling results obtained from molecular dynamics (MD) simulation. Based on MD simulations, we constructed structural phase diagram of nanoparticle assemblies in the presence of asymmetric diblock copolymers comprising short NP-attractive blocks. The MD simulation results indicate that NP undergo transition from spherical to cylindrical assemblies depending on the NP size, the overall concentration of components and the degree of affinity of the minor block to NP.

Universal Equation of State for Flexible Polymers Beyond the Semidilute Regime.

We reconsider the isothermal equation of state (EOS) for linear homopolymers in good solvents, p=p(c,T), which relates the osmotic pressure p of polymers with the bulk concentration c and the temperature T. The classical scaling theory predicts the EOS in dilute and semidilute regimes. We suggest a generalized EOS that extends the universal behavior of polymer solutions up to the highly concentrated state and confirm it by molecular dynamics simulations and available experimental data. Our conjecture implies that properties of polymer chains dominate the EOS in the presence of many-body interactions. Our theoretical approach is based on a viral expansion in terms of concentration blobs leading to a superposition of two power laws in the regime of concentrated solutions.

Hierarchical excluded volume screening in solutions of bottlebrush polymers.

Polymer bottlebrushes provide intriguing features being relevant both in nature and in synthetic systems. While their presence in the articular cartilage optimizes synovial joint lubrication, bottlebrushes offer pathways for fascinating applications, such as within super-soft elastomers or for drug delivery. However, the current theoretical understanding lacks completeness, primarily due to the complicated interplay of many length scales. Herein, we develop an analytical model that demonstrates how structural properties of bottlebrushes depend on the concentration, ranging from dilute solutions to highly concentrated melts. The validity of our model is supported by data from extensive molecular dynamics simulations. We demonstrate that the hierarchical structure of bottlebrushes dictates a sequence of conformational changes as the solution concentration increases. The effect is mediated by screening of excluded volume interactions at subsequent structural parts of the bottlebrushes. Our findings provide important insights that should enable improved customization of novel materials based on the architectural design of polymer bottlebrushes.

Molecular structure of bottlebrush polymers in melts.

Bottlebrushes are fascinating macromolecules that display an intriguing combination of molecular and particulate features having vital implications in both living and synthetic systems, such as cartilage and ultrasoft elastomers. However, the progress in practical applications is impeded by the lack of knowledge about the hierarchic organization of both individual bottlebrushes and their assemblies. We delineate fundamental correlations between molecular architecture, mesoscopic conformation, and macroscopic properties of polymer melts. Numerical simulations corroborate theoretical predictions for the effect of grafting density and side-chain length on the dimensions and rigidity of bottlebrushes, which effectively behave as a melt of flexible filaments. These findings provide quantitative guidelines for the design of novel materials that allow architectural tuning of their properties in a broad range without changing chemical composition.

Solvent-free, supersoft and superelastic bottlebrush melts and networks.

Polymer gels are the only viable class of synthetic materials with a Young's modulus below 100 kPa conforming to biological applications, yet those gel properties require a solvent fraction. The presence of a solvent can lead to phase separation, evaporation and leakage on deformation, diminishing gel elasticity and eliciting inflammatory responses in any surrounding tissues. Here, we report solvent-free, supersoft and superelastic polymer melts and networks prepared from bottlebrush macromolecules. The brush-like architecture expands the diameter of the polymer chains, diluting their entanglements without markedly increasing stiffness. This adjustable interplay between chain diameter and stiffness makes it possible to tailor the network's elastic modulus and extensibility without the complications associated with a swollen gel. The bottlebrush melts and elastomers exhibit an unprecedented combination of low modulus (∼100 Pa), high strain at break (∼1,000%), and extraordinary elasticity, properties that are on par with those of designer gels.

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.

Force spectroscopy of polymer desorption: theory and molecular dynamics simulations.

Forced detachment of a single polymer chain, strongly adsorbed on a solid substrate, is investigated by two complementary methods: a coarse-grained analytical dynamical model, based on the Onsager stochastic equation, and Molecular Dynamics (MD) simulations with a Langevin thermostat. The suggested approach makes it possible to go beyond the limitations of the conventional Bell-Evans model. We observe a series of characteristic force spikes when the pulling force is measured against the cantilever displacement during detachment at constant velocity vc (displacement control mode) and find that the average magnitude of this force increases as vc increases. The probability distributions of the pulling force and the end-monomer distance from the surface at the moment of the final detachment are investigated for different adsorption energies ε and pulling velocities vc. Our extensive MD simulations validate and support the main theoretical findings. Moreover, the simulations reveal a novel behavior: for a strong-friction and massive cantilever the force spike pattern is smeared out at large vc. As a challenging task for experimental bio-polymer sequencing in future we suggest the fabrication of a stiff, super-light, nanometer-sized AFM probe.

Unexpected crossover dynamics of single polymer in a corrugated tube.

We present molecular dynamics study of a generic (coarse-grained) model for single-polymer diffusion confined in a corrugated cylinder. For a narrow tube, i.e., diameter of the cylinder δ < 2.3, the axial diffusion coefficient D(∣∣) scales as D(∣∣) ∝ N(-3∕2), with chain length N, up to N ≈ 100 and then crosses over to Rouse scaling for the larger N values. The N(-3∕2) scaling is due to the large fluctuation of the polymer chain along its fully stretched equilibrium conformation. The stronger scaling, namely N(-3∕2), is not observed for an atomistically smooth tube and/or for a cylinder with larger diameter.

Path-integral approach to the dynamics of a random chain with rigid constraints.

In this work the dynamics of a chain consisting of a set of beads attached to the ends of segments of fixed lengths is investigated. The chain fluctuates at constant temperature in a viscous medium. For simplicity, all interactions among the beads have been switched off and the number of spatial dimensions has been limited to two. In the limit in which the chain becomes a continuous system, its behavior may be described by a path integral, in which the rigid constraints coming from the infinitesimally small segments are imposed by means of a functional delta function. In this way a model of the dynamics of the chain is obtained, which closely resembles a two-dimensional nonlinear sigma model. The partition function of this generalized nonlinear sigma model is computed explicitly for a ring-shaped chain in the semiclassical approximation. The behavior of the chain at both long and short scales of time and distances is investigated. The connection between the generalized nonlinear sigma model presented here and the Rouse model is discussed.