Conformational Statistics Research Articles

The conformational statistics of amphiphilic polymers with distinct topological structures at the interface between two phases

The conformational statistics of amphiphilic polymers with distinct topological structures at the interface between two phases

Linear and Nonlinear Dielectric Response of Intrinsically Disordered Proteins.

Linear and nonlinear dielectric responses of solutions of intrinsically disordered proteins (IDPs) were analyzed by combining molecular dynamics simulations with formal theories. A large increment of the linear dielectric function over that of the solvent is found and related to large dipole moments of IDPs. The nonlinear dielectric effect (NDE) of the IDP far exceeds that of the bulk electrolyte, offering a route to interrogate protein conformational and rotational statistics and dynamics. Conformational flexibility of the IDP makes the dipole moment statistics consistent with the gamma/log-normal distributions and contributes to the NDE through the dipole moment's non-Gaussian parameter. The intrinsic non-Gaussian parameter of the dipole moment combines with the protein osmotic compressibility in the nonlinear dielectric susceptibility when dipolar correlations are screened by the electrolyte. The NDE is dominated by dipolar correlations when electrolyte screening is reduced.

Illuminating protein space with a programmable generative model

Three billion years of evolution has produced a tremendous diversity of protein molecules1, but the full potential of proteins is likely to be much greater. Accessing this potential has been challenging for both computation and experiments because the space of possible protein molecules is much larger than the space of those likely to have functions. Here we introduce Chroma, a generative model for proteins and protein complexes that can directly sample novel protein structures and sequences, and that can be conditioned to steer the generative process towards desired properties and functions. To enable this, we introduce a diffusion process that respects the conformational statistics of polymer ensembles, an efficient neural architecture for molecular systems that enables long-range reasoning with sub-quadratic scaling, layers for efficiently synthesizing three-dimensional structures of proteins from predicted inter-residue geometries and a general low-temperature sampling algorithm for diffusion models. Chroma achieves protein design as Bayesian inference under external constraints, which can involve symmetries, substructure, shape, semantics and even natural-language prompts. The experimental characterization of 310 proteins shows that sampling from Chroma results in proteins that are highly expressed, fold and have favourable biophysical properties. The crystal structures of two designed proteins exhibit atomistic agreement with Chroma samples (a backbone root-mean-square deviation of around 1.0 Å). With this unified approach to protein design, we hope to accelerate the programming of protein matter to benefit human health, materials science and synthetic biology.

Conformational Statistics of Ribbon-like Chains

Conformational Statistics of Ribbon-like Chains

Effect of flexibility of arms on the nematic ordering of V-shaped molecules

The nematic ordering of a melt of V-shaped molecules composed of two semiflexible arms connected by one end at an external angle α is inspected within the Landau theory of phase transitions. The conformational statistics of arms is described by a discrete worm-like chain model. It is found that for a sufficiently high stiffness of the arms the phase diagram contains the regions of stability of isotropic (I), prolate (NU+) and oblate (NU−) uniaxial, and biaxial (NB) nematic phases. The isotropic–uniaxial nematic and uniaxial nematic – biaxial nematic phase transitions are of the first and second order, respectively. At lowering the stiffness of arms the stability area of NB phase decreases; the re-entrant NB phase becomes possible in the certain range of angles α and the sequence of phase transitions I−NU−−NB−NU+−NB occurs. At a sufficiently low stiffness, the stability region of the nematic biaxial phase disappears completely, and phase diagrams display only the first order transitions between I−NU+, I−NU−, and NU+−NU− phases. A further decrease in the stiffness of arms leaves only the first order I−NU+ transition in the phase diagrams. The tricritical points appear at the curves of NU−−NB transition in the phase diagrams in certain intervals of values of the stiffness parameter.

Multiscale equilibration of highly entangled isotropic model polymer melts.

We present a computationally efficient multiscale method for preparing equilibrated, isotropic long-chain model polymer melts. As an application, we generate Kremer-Grest melts of 1000 chains with 200 entanglements and 25 000-2000 beads/chain, which cover the experimentally relevant bending rigidities up to and beyond the limit of the isotropic-nematic transition. In the first step, we employ Monte Carlo simulations of a lattice model to equilibrate the large-scale chain structure above the tube scale while ensuring a spatially homogeneous density distribution. We then use theoretical insight from a constrained mode tube model to introduce the bead degrees of freedom together with random walk conformational statistics all the way down to the Kuhn scale of the chains. This is followed by a sequence of simulations with carefully parameterized force-capped bead-spring models, which slowly introduce the local bead packing while reproducing the larger-scale chain statistics of the target Kremer-Grest system at all levels of force-capping. Finally, we can switch to the full Kremer-Grest model without perturbing the structure. The resulting chain statistics is in excellent agreement with literature results on all length scales accessible in brute-force simulations of shorter chains.

Quantifying structure and dynamics of bound and bulk polymer in tailor-made rubber-silica nanocomposites

The dynamics of long polymer chains in the presence of nanoparticles have been investigated. The nanocomposites of interest were inspired by tire industry-like rubber materials and consisted of entangled polyisoprene linear chains mixed with chemically pre-treated silica nanoparticles. Combining rheology, dielectric spectroscopy, and neutron spin echo measurements, we measured the modification of the polymer chain dynamics from bulk state to high filler concentration over a broad range of time and length scales. We show that the end-to-end relaxation does not seem to be impacted, whereas the polymer dynamics is significantly slowed down at a very local scale in the presence of nano-fillers. In addition to this length scale dependent different dynamics, additional Neutron Spin Echo spectroscopy experiments and Small Angle Scattering on labelled polymer chains, irreversibly bound to the filler surface and re-dispersed in a fully deuterated matrix, revealed a negligible dynamical behavior of this particular population of localized chains in the rubber layer. The conformational statistics of these chains is that of self-avoiding walk train within a shell that is thinner than the size of the chain. To the best of our knowledge, this work is the first of its kind which measures the single chain form factor in the bound layer of chemically multi-linked chains to the filler surface.

Thermodynamics and Conformations of Single Polyalanine, Polyserine, and Polyglutamine Chains within the PRIME20 Model.

Understanding the conformational behavior of proteins has been a long-standing challenge to which computer simulations could contribute significantly. This concerns the folding behavior of proteins as well as the conformational statistics of intrinsically disordered proteins. A well-converged sampling of the conformational statistics over a broad range of control parameters is computationally extremely challenging and best addressed by coarse-grained modeling, for example, with an intermediate resolution model like the PRIME20 model. A comprehensive understanding of the thermodynamics and conformational statistics of individual protein chains is, however, not only a goal in itself but also a prerequisite for a better understanding of their aggregation tendency into oligomers and further into amyloid fibrils. We present here an extensive comparison of the ability of the PRIME20 model (in its documented variants in the literature) to faithfully reproduce the thermodynamics and statistics of three homopeptides having very different folding temperatures and different typical secondary structures.

Stretching of a Fractal Polymer around a Disc Reveals Kardar-Parisi-Zhang Scaling.

While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting open question. We use scaling analysis and computer simulations to examine stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius R. We reveal that the typical excursions of the polymer away from the surface and curvature-induced correlation length scale as Δ∼R^{β} and S^{*}∼R^{1/z}, respectively, with the Kardar-Parisi-Zhang (KPZ) growth β=1/3 and dynamic exponents z=3/2. Although probability distribution of excursions does not belong to KPZ universality class, the KPZ scaling is independent of the fractal dimension of the polymer and, thus, is universal across classical polymer models, e.g., SAW, randomly branching polymers, crumpled unknotted rings. Additionally, our Letter establishes a mapping between stretched polymers in curved geometry and the Balagurov-Vaks model of random walks among traps.

Multistage transitions in viscoelastic turbulent flow: Vortex structures and self-sustaining mechanisms

Viscoelastic dilute polymer solutions are known to display drag reduction in turbulent flows. At constant Re and as the fluid becomes more elastic (increasing Wi), the flow undergoes transitions between several stages of different behaviors. The first is the onset of drag reduction, before which the turbulent friction factor remains indistinguishable from its Newtonian limit. The second is the transition from low-extent (LDR) to high-extent drag reduction (HDR), which increasing evidences have shown to be a qualitative transition between different types of turbulent dynamics. The third is the convergence to the maximum drag reduction (MDR) asymptote, after which the friction factor becomes constant. Although increasing drag reduction with increasing Wi is intuitively expected, transitions between these stages are accompanied by drastic changes in flow statistics and structural patterns, indicating fundamental differences in the underlying turbulent dynamics. Mechanistic understanding into these transitions is far from complete. Our latest work has offered fresh insights into both the LDR-HDR and HDR-MDR transitions. For the former, we developed a new vortex analysis method, called VATIP, and applied it to analyze the differences between the conformation statistics in LDR and HDR regimes. The result links the occurrence of HDR to the dominance of a new turbulence self-sustaining mechanism. For the latter, although a full answer to the MDR problem remains elusive, our analysis of the so-called elastoinertial turbulence (EIT) challenges the long-held presumption of MDR being an ultimate flow state that is no longer affected by polymers. The finding calls for a new direction of thought in constructing a theoretical explanation for MDR.

Molecular dynamics simulation of demulsification of O/W emulsion containing soil in direct current electric field

The collision under direct current (DC) electric field and non-electric field coalescence behavior of heavy oil droplets in complex oil-in-water (O/W) emulsion system were studied by molecular dynamics (MD). By changing the simulation parameters of electric field intensity, the movement of various molecules of emulsified oil droplets, such as Sodium dodecyl sulfate (SDS) molecules, silica nanoparticles (SiO2 NPs), asphaltene and resin molecules under six electric field intensities, and the aggregation process of colliding oil droplets after electric field excitation are discussed. At the same time, the radial distribution function and conformational statistics are used to analyze the charge distribution of oil droplets and the change of interaction force of different molecules from the microscopic point of view, and further explore the demulsification mechanism of oil droplets under the electric field. The simulation results show that when the electric field intensity is lower than 1.5 V/nm, the oily components of emulsified oil droplets cannot contact because of the blocking effect of SDS molecules. When the electric field intensity is greater than or equal to 1.5 V/nm, SDS molecules separate from the oil phase and enter the water phase, and emulsified oil droplets contact. The interface is a bridge structure formed by the face-to-face accumulation of asphaltene and resin. The existence of this structure is the key to further coalesce oil droplets into a whole. The local oil droplets will spontaneously coalesce without electric field, and the bridge structure formed by asphaltene will gradually disappear. SiO2 nanoparticles will promote the coalescence of oil droplets.

A multiscale simulation of amorphous poly(vinyl alcohol)

A recently developed method to generate and equilibrate the amorphous structure of polymers at bulk density was applied for polyvinyl alcohol (PVA). PVA chains were coarse-grained by grouping each monomer unit into one bead and then placed onto the high coordination lattice with intra- and inter-molecular interactions. Amorphous PVA bulks were generated and readily equilibrated using on-lattice Monte Carlo (MC) simulation. The fully atomistic models of amorphous PVA bulks could be obtained by the reverse-mapping step to restore the missing atoms followed by energy minimization. To validate these atomistic models, some molecular and material properties of amorphous PVA structures were determined and compared with experimental data including conformational statistics, solubility parameter and x-ray scattering structure factor.

Mobility gradients yield rubbery surfaces on top of polymer glasses.

Many emerging materials, such as ultrastable glasses1,2 of interest for phone displays and OLED television screens, owe their properties to a gradient of enhanced mobility at the surface of glass-forming liquids. The discovery of this surface mobility enhancement3-5 has reshaped our understanding of the behaviour of glass formers and of how to fashion them into improved materials. In polymeric glasses, these interfacial modifications are complicated by the existence of a second length scale-the size of the polymer chain-as well as the length scale of the interfacial mobility gradient6-9. Here we present simulations, theory and time-resolved surface nano-creep experiments to reveal that this two-scale nature of glassy polymer surfaces drives the emergence of a transient rubbery, entangled-like surface behaviour even in polymers comprised of short, subentangled chains. We find that this effect emerges from superposed gradients in segmental dynamics and chain conformational statistics. The lifetime of this rubbery behaviour, which will have broad implications in constraining surface relaxations central to applications including tribology, adhesion, and surface healing of polymeric glasses, extends as the material is cooled. The surface layers suffer a general breakdown in time-temperature superposition (TTS), a fundamental tenet of polymer physics and rheology.This findingmay require a reevaluation of strategies for the prediction of long-time properties in polymeric glasseswith high interfacial areas. We expect that this interfacial transient elastomer effect and TTS breakdown should normally occur in macromolecular systems ranging from nanocomposites to thin films, where interfaces dominate material properties5,10.

Conformations and diffusion of flexibly linked colloidal chains

For biologically relevant macromolecules such as intrinsically disordered proteins, internal degrees of freedom that allow for shape changes have a large influence on both the motion and function of the compound. A detailed understanding of the effect of flexibility is needed in order to explain their behavior. Here, we study a model system of freely-jointed chains of three to six colloidal spheres, using both simulations and experiments. We find that in spite of their short lengths, their conformational statistics are well described by two-dimensional Flory theory, while their average translational and rotational diffusivity follow the Kirkwood–Riseman scaling. Their maximum flexibility does not depend on the length of the chain, but is determined by the near-wall in-plane translational diffusion coefficient of an individual sphere. Furthermore, we uncover shape-dependent effects in the short-time diffusivity of colloidal tetramer chains, as well as non-zero couplings between the different diffusive modes. Our findings may have implications for understanding both the diffusive behavior and the most likely conformations of macromolecular systems in biology and industry, such as proteins, polymers, single-stranded DNA and other chain-like molecules.

Conformational statistics of non-equilibrium polymer loops in Rouse model with active loop extrusion

Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper, we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in the statistics of the extruded loop, regardless of the specific time dependence of the extrusion velocity. In addition, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits.

A multiscale simulation of amorphous polystyrene

A multiscale simulation method to investigate amorphous polymeric materials for vinyl polymer was applied for glassy polystyrene (PS) with different tacticity. PS chains were coarse-grained and then mapped onto the second nearest neighbor diamond (2nnd) lattice incorporating short- and long-range interactions from the modified rotational isomeric state (RIS) model and the discretized Lennard-Jones (LJ) potential function, respectively. Bulk PS structures composed of 14 chains with 42 monomer units was generated and equilibrated on lattice Monte Carlo (MC) simulation. The on-lattice properties including molecular size, conformational statistics and chain dynamics were compared. The chain mobility of neat PS melts with different stereochemistry are qualitatively ordered as: iPS < aPS << sPS. There is no clear correlation for these relative diffusions with molecular size and chain stiffness but can possibly be related to the intermolecular contribution i.e. chain packing among neighboring chains. Next, fully atomistic amorphous PS models at the bulk density were obtained by the reverse-mapping procedure to convert the coarse-grained chains to recover the missing atoms. After energy minimization, molecular and material properties including torsional angle distribution, solubility parameter, radial distribution function and neutron scattering intensity are determined and compared for amorphous PS structures.

Fractal Dimension Meets Topology: Statistical and Topological Properties of Globular Macromolecules with Volume Interactions

In the paper we investigate statistical and topological properties of fractional Brownian polymer chains, equipped with the short-range volume interactions. The attention is paid to statistical properties of collapsed conformations with the fractal dimension $D_f\ge 2$ in the three-dimensional space, which are analyzed both numerically and \textit{via} the mean-field Flory approach. Our study is motivated by an attempt to mimic the conformational statistics of collapsed unknotted polymer rings, which are known to form compact hierarchical crumpled globules (CG) with $D_f=3$ at large scales. Replacing the topologically-stabilized CG state by a self-avoiding fractal path adjusted to the fractal dimension $D_f=3$ we tremendously simplify the problem of generating compact self-avoiding conformations since we wash out the topological constraints from the consideration. We make use of the Monte-Carlo simulations to prepare the equilibrium ensemble of swollen chains with various fractal dimensions. A combination of the Flory arguments with statistical analysis of the conformations from simulations allows one to infer the dependence of the critical exponent of the swollen chains on the fractal dimension of the seed chain. We show that with the increase of $D_f$, typical conformations become more territorial and less knotted. Distributions of the knot complexity, $P(\chi)$ for various fractal dimensions of the swollen chains suggest a close relationship between statistical and topological properties of fractal paths with volume interactions.

Quantitative bridging between full-atomistic and bead-spring models for polybutadiene and poly(butadiene-styrene) copolymers.

Despite lots of attempts on the bridging between full-atomistic and coarse-grained models for polymers, a practical methodology has not been established yet. One of the problems is computation costs for the determination of spatial and temporal conversion parameters, which are ideally obtained for the long chain limit. In this study, we propose a practical, yet quantitative, bridging method utilizing the simulation results for rather short chains. We performed full-atomistic simulations for polybutadiene and some poly(butadiene-styrene) copolymers in the melt state by varying the number of repeating units as 20, 30, and 40. We attempted to construct corresponding coarse-grained models for such systems. We employed the Kremer-Grest type bead-spring chains with bending rigidity. The stiffness parameter of coarse-grained models and the spatial conversion factor between the full-atomistic and coarse-grained models were obtained according to the conformational statistics of polymer chains. Although such a bridging strategy is similar to the earlier studies, we incorporated the molecular weight dependence of the conformational statistics for the first time. By introducing several empirical functions of the conformational statistics for the molecular weight dependence, we attained a rigorous bridging for the conformational statistics. We confirmed that the structural distribution functions of the coarse-grained systems are entirely consistent with the target full-atomistic ones. Owing to the structural conversion parameters thus obtained, we constructed the coarse-grained models that corresponded to the polymers consisting of 200 repeating units and traced the segmental diffusion. The full-atomistic simulations were also performed from the initial configurations created from the equilibrated coarse-grained models via the back-mapping scheme. From the comparison of the mean-square-displacement of the segments positioned at the middle of the chain, we obtained the temporal conversion factors.

Aggregation of a macromolecule in a nano cube

We model a macromolecule as an infinitely long Gaussian semi-flexible polymer chain and the conformations of the chain were realized in the nano cube using a cubic lattice. A modified version of the recursion relations is used to calculate the grand canonical partition function of the chain to investigate distinct thermo-dynamical properties of the nano polymer aggregate than corresponding bulk behaviour of the macromolecule. Our analytical estimates on the thermo-dynamical properties of the macromolecule clearly show that the nano aggregate of the polymer chain has interesting and distinct conformational statistics than its corresponding bulk state, and the method described in the present report can be easily extend to investigate the thermodynamics of the self-avoiding polymer chain in the nano dimensions.

Chain Conformation of Hyperbranched Polymers with Uniform Branching Subchains in Dilute Solution near the θ Point

Conformation statistics of macromolecules in dilute solution is one of the fundamental issues in polymer physics. Herein, we experimentally explore the average conformation of model randomly hyperb...