Search

Regulatory protein access to the DNA duplex ‘interior’ depends on local DNA ‘breathing’ fluctuations, and the most fundamental of these are thermally-driven base stacking-unstacking interactions. The smallest DNA unit that can undergo such transitions is the dinucleotide, whose structural and dynamic properties are dominated by stacking, while the ion condensation, cooperative stacking and inter-base hydrogen-bonding present in duplex DNA are not involved. We use dApdA to study stacking-unstacking at the dinucleotide level because the fluctuations observed are likely to resemble those of larger DNA molecules, but in the absence of constraints introduced by cooperativity are likely to be more pronounced, and thus more accessible to measurement. We study these fluctuations with a combination of Molecular Dynamics simulations on the microsecond timescale and Markov State Model analyses, and validate our results by calculations of circular dichroism (CD) spectra, with results that agree well with the experimental spectra. Our analyses show that the CD spectrum of dApdA is defined by two distinct chiral conformations that correspond, respectively, to a Watson–Crick form and a hybrid form with one base in a Hoogsteen configuration. We find also that ionic structure and water orientation around dApdA play important roles in controlling its breathing fluctuations.

Macromolecular liquids display short-time anomalous behaviors in disagreement with conventional single-molecule mean-field theories. In this study, we analyze the behavior of the simplest but most realistic macromolecular system that displays anomalous dynamics, i.e., a melt of short homopolymer chains, starting from molecular dynamics simulation trajectories. Our study sheds some light on the microscopic molecular mechanisms responsible for the observed anomalous behavior. The relevance of the correlation hole, a unique property of polymer liquids, in relation to the observed subdiffusive dynamics, naturally emerges from the analysis of the van Hove distribution functions and other properties.

Coarse-graining (CG) approaches are becoming essential tools in the study of complex systems because they can considerably speed up computer simulations, with the promise of determining properties in a range of length scales and time scales never before possible. While much progress in this field has been achieved in recent years, application of CG methods is still inhibited by the limited understanding of a number of conceptual points that need to be resolved to open up the field of CG to a wide range of applications in material science and biology. In this paper, we present some of the key findings that emerged from the development of the integral equation theory of coarse-graining (IECG), which addresses some of the fundamental questions in coarse-graining. Although the IECG method pertains to the CG of polymer liquids, and specifically homopolymer melts are illustrated here, many of the results that emerge from the study of the IECG approach are general and apply to the CG of any molecular liquid. Through this method, we developed a formal relation between the statistical mechanics of CG and a number of predicted physical properties. On the basis of the theory of liquids, the IECG affords the analytical solution of the intermolecular potential for macromolecules represented by a Markov chain of CG sites, thus providing a transparent tool for analysis of the properties in coarse-graining. We identify three key requirements that render a CG model useful: accuracy, transferability, and computational efficiency. When these three requirements are fulfilled, the CG model becomes widely applicable and useful for studying regions in the phase space that are not covered by atomistic simulations. In the process, the IECG answers formally a number of relevant questions on how structural, thermodynamic, and dynamical properties are modified during coarse-graining. It sheds light upon how the level of CG affects the shape of the CG potential and how, in turn, the shape of the potential affects the physical properties. It tests the validity of selecting the potential-of-mean force as the effective pairwise CG potential and the role of higher-order many-body corrections to the pairwise potential to recover structural and thermodynamic consistency of the CG model. Because the IECG theory can be analytically formalized, it does not suffer from the problem of transferability and, in the canonical ensemble, leads to consistent pair distribution functions, pressure, isothermal compressibility, and excess free energy at variable levels of CG from the atomistic to the ultra-CG model, where macromolecules are represented as interpenetrable soft spheres.

Coarse-graining (CG) procedures provide computationally efficient methods for investigating the corresponding long time- and length-scale processes. In the bottom-up approaches, the effective interactions between the CG sites are obtained using the information from the atomistic simulations, but reliable CG procedures are required to preserve the structure and thermodynamics. In this regard, the integral equation coarse-graining (IECG) method is a promising approach that uses the first-principles Ornstein-Zernike equation in liquid state theory to determine the effective potential between CG sites. In this work, we present the details of the IECG method while treating the density as an intrinsic property and active variable of the CG system. Performing extensive simulations of polymer melts, we show that the IECG theory/simulation and atomistic simulation results are consistent in structural properties such as the pair-correlation functions and form factors, and also thermodynamic properties such as pressure. The atomistic simulations of the liquids show that the structure is largely sensitive to the repulsive part of the potential. Similarly, the IECG simulations of polymeric liquids show that the structure can be determined by the relatively short-range CG repulsive interactions, but the pressure is only accurately determined once the long-range, weak CG attractive interactions are included. This is in agreement with the seminal work by Widom on the influence of the potential on the phase diagram of the liquid [Widom, B. Science 1967 , 157 , 375 - 382 ]. Other aspects of the IECG theory/simulations are also discussed.

The Integral Equation Coarse-Grained method is an approach that simplifies the representation of a polymer melt into a liquid of coarse-grained chains, considerably speeding up the computation of the melt properties, while reproducing with accuracy structure and thermodynamics of the corresponding atomistic description. In a recent paper [Polymer 111 , 103 (2017)], it was stated that the structure-based Integral Equation Coarse-Grained approach does not give thermodynamic consistency. Here we present new calculations that confirm the validity of this method in predicting consistent pressure and radial distribution functions with atomistic simulations. Other details of the method are also discussed.

Local fluctuations are important for protein binding and molecular recognition because they provide conformational states that can be trapped through a selection mechanism of binding. Thus, an accurate characterization of local fluctuations may be important for modeling the kinetic mechanism that leads to the biological activity of a protein. In this paper, we study the fluctuation dynamics of the regulatory protein ubiquitin and propose a novel theoretical approach to model its fluctuations. A coarse-grained, diffusive, mode-dependent description of fluctuations is accomplished using the Langevin Equation for Protein Dynamics (LE4PD). This equation decomposes the dynamics of a protein, simulated by molecular dynamics, into dynamical pathways that explore mode-dependent free energy surfaces. We calculate the time scales of the slow, high-amplitude fluctuations by modeling the kinetics of barrier crossing in the two-dimensional free energy surfaces using Markov state modeling. We find that the LE4PD predicts slow fluctuations in three important binding regions in ubiquitin: the C-terminal tail, the Lys11 loop, and the 50 s loop. These results suggest that the LE4PD can provide useful information on the role of fluctuations in the process of molecular recognition regulating the biological activity of ubiquitin.

Proteins’ biological function and folding mechanisms are often guided by large-scale, slow motions, which involve crossing high energy barriers. In a simulation trajectory, these slow fluctuations are commonly identified using a principal component analysis (PCA). Despite the popularity of this method, a complete analysis of its predictions based on the physics of protein motion has been so far limited. This study formally connects the PCA to a Langevin model of protein dynamics and analyzes the contributions of energy barriers and hydrodynamic interactions to the slow PCA modes of motion. To do so, we introduce an anisotropic extension of the Langevin Equation for Protein Dynamics, called the LE4PD-XYZ, which formally connects to the PCA ‘essential dynamics’. The LE4PD-XYZ is an accurate coarse-grained diffusive method to model protein motion, which describes anisotropic fluctuations in the protein’s alpha-carbons. The LE4PD accounts for hydrodynamic effects and mode-dependent free-energy barriers. This study compares large-scale anisotropic fluctuations identified by the LE4PD-XYZ to the mode-dependent PCA’s predictions, starting from a microsecond-long alpha-carbon molecular dynamics atomistic trajectory of the protein ubiquitin. We observe that the inclusion of free-energy barriers and hydrodynamic interactions has important effects on the identification and timescales of ubiquitin’s slow modes.

The integral equation coarse-graining (IECG) approach is a promising high-level coarse-graining (CG) method for polymer melts, with variable resolution from soft spheres to multi CG sites, which preserves the structural and thermodynamical consistencies with the related atomistic simulations. When compared to the atomistic description, the procedure of coarse-graining results in smoother free energy surfaces, longer-ranged potentials, a decrease in the number of interaction sites for a given polymer, and more. Because these changes have competing effects on the computational efficiency of the CG model, care needs to be taken when studying the effect of coarse-graining on the computational speed-up in CG molecular dynamics simulations. For instance, treatment of long-range CG interactions requires the selection of cutoff distances that include the attractive part of the effective CG potential and force. In particular, we show how the complex nature of the range and curvature of the effective CG potential, the selection of a suitable CG timestep, the choice of the cutoff distance, the molecular dynamics algorithms, and the smoothness of the CG free energy surface affect the efficiency of IECG simulations. By direct comparison with the atomistic simulations of relatively short chain polymer melts, we find that the overall computational efficiency is highest for the highest level of CG (soft spheres), with an overall improvement of the computational efficiency being about 106–108 for various CG levels/resolutions. Therefore, the IECG method can have important applications in molecular dynamics simulations of polymeric systems. Finally, making use of the standard spatial decomposition algorithm, the parallel scalability of the IECG simulations for various levels of CG is presented. Optimal parallel scaling is observed for a reasonably large number of processors. Although this study is performed using the IECG approach, its results on the relation between the level of CG and the computational efficiency are general and apply to any properly-constructed CG model.

Adaptive resolution methods are becoming increasingly important in the study of complex systems by multi scale modeling. In this paper we present a brief overview of the method and highlight some questions that in our opinion are relevant for the future development of the method, and more in general of the field of multiscale modeling.

This paper presents a critical discussion of coarse-graining models of complex molecular liquids, starting from the Integral Equation Coarse-Graining method (IECG). For liquids of macro- molecules this method allows for the analytical solution of the coarse-graining formalism, including the effective pair potential, and providing in this way a convenient framework to study general issues concerning coarse-graining.

CUG repeat expansions in the 3′ UTR of dystrophia myotonica protein kinase (DMPK) cause myotonic dystrophy type 1 (DM1). As RNA, these repeats elicit toxicity by sequestering splicing proteins, such as MBNL1, into protein–RNA aggregates. Structural studies demonstrate that CUG repeats can form A-form helices, suggesting that repeat secondary structure could be important in pathogenicity. To evaluate this hypothesis, we utilized structure-stabilizing RNA modifications pseudouridine (Ψ) and 2′-O-methylation to determine if stabilization of CUG helical conformations affected toxicity. CUG repeats modified with Ψ or 2′-O-methyl groups exhibited enhanced structural stability and reduced affinity for MBNL1. Molecular dynamics and X-ray crystallography suggest a potential water-bridging mechanism for Ψ-mediated CUG repeat stabilization. Ψ modification of CUG repeats rescued mis-splicing in a DM1 cell model and prevented CUG repeat toxicity in zebrafish embryos. This study indicates that the structure of toxic RNAs has a significant role in controlling the onset of neuromuscular diseases.

Given that the physical properties of polymeric liquids extend on a wide range of length scales, it is computationally convenient to represent them by coarse-grained descriptions at various granularities to investigate local and global properties simultaneously. We use the Integral Equation Coarse-Graining (IECG) theory for a mixture of two species with various resolutions representing polyethylene polymeric liquids and derive interacting potentials that ensure consistencies of relevant thermodynamical and structural properties. These properties are in agreement with the corresponding atomistic resolution description. The composition, temperature, and density dependences of such mixed resolution potentials are investigated numerically and analytically. In the limit of long polymer chains, where Markovian statistics is obeyed, the potentials are analytically solved and decay with characteristic scaling exponents that depend on the mixture composition and CG resolution of the two components. The implications of the effective IECG potentials are also discussed for multiresolution simulation approaches.

Myotonic dystrophy type 2 is a genetic neuromuscular disease caused by the expression of expanded CCUG repeat RNAs from the non-coding region of the C CHC-type zinc finger n ucleic acid- b inding p rotein (CNBP) gene. These CCUG repeats bind and sequester a family of RNA-binding proteins known as Muscleblind-like 1, 2, and 3 (MBNL1, MBNL2, and MBNL3), and sequestration plays a significant role in pathogenicity. MBNL proteins are alternative splicing regulators that bind to the consensus RNA sequence YGCY (Y = pyrimidine). This consensus sequence is found in the toxic RNAs (CCUG repeats) and in cellular RNA substrates that MBNL proteins have been shown to bind. Replacing the uridine in CCUG repeats with pseudouridine (Ψ) resulted in a modest reduction of MBNL1 binding. Interestingly, Ψ modification of a minimally structured RNA containing YGCY motifs resulted in more robust inhibition of MBNL1 binding. The different levels of inhibition between CCUG repeat and minimally structured RNA binding appear to be due to the ability to modify both pyrimidines in the YGCY motif, which is not possible in the CCUG repeats. Molecular dynamic studies of unmodified and pseudouridylated minimally structured RNAs suggest that reducing the flexibility of the minimally structured RNA leads to reduced binding by MBNL1.

We investigate the universal scaling of protein fluctuation dynamics with a site-specific diffusive model of protein motion, which predicts an initial subdiffusive regime in the configurational relaxation. The long-time dynamics of proteins is controlled by an activated regime. We argue that the hierarchical free energy barriers set the time scales of biological processes and establish an upper limit to the size of single protein domains. We find it compelling that the scaling behavior for the protein dynamics is in close agreement with the Kardar-Parisi-Zhang scaling exponents.

We present the equation of state for a coarse-grained model of polymer melts where each chain is represented as a soft colloidal particle centered on its center-of-mass. The formalism is based on the solution of the Ornstein–Zernike equation and is analytical, allowing for the formal investigation of the elements that ensure thermodynamic consistency in coarse-grained models of polymer melts. By comparing predictions from our expressions with those from computer simulations of the coarse-grained system and with atomistic polymer integral equation theory, we demonstrate that both structural and thermodynamic consistency with the atomistic level description is maintained during our coarse-graining procedures.

A first-principle multiscale modeling approach is presented, which is derived from the solution of the Ornstein-Zernike equation for the coarse-grained representation of polymer liquids. The approach is analytical, and for this reason is transferable. It is here applied to determine the structure of several polymeric systems, which have different parameter values, such as molecular length, monomeric structure, local flexibility, and thermodynamic conditions. When the pair distribution function obtained from this procedure is compared with the results from a full atomistic simulation, it shows quantitative agreement. Moreover, the multiscale procedure accurately captures both large and local scale properties while remaining computationally advantageous.

We present a comparison between theoretical predictions of the generalized Langevin equation for cooperative dynamics (CDGLE) and neutron spin echo data of dynamic structure factors for polyethylene melts. Experiments cover an extended range of length and time scales, providing a compelling test for the theoretical approach. Samples investigated include chains with increasing molecular weights undergoing dynamics across the unentangled to entangled transition. Measured center-of-mass (com) mean-square displacements display a crossover from subdiffusive to diffusive dynamics. The generalized Langevin equation for cooperative dynamics relates this anomalous diffusion to the presence of the interpolymer potential, which correlates the dynamics of a group of slowly diffusing molecules in a dynamically heterogeneous liquid. Theoretical predictions of the subdiffusive behavior, of its crossover to free diffusion, and of the number of macromolecules undergoing cooperative motion are in quantitative agreement with experiments.

The dynamics of polymer liquids present a rich variety of phenomena with characteristic scaling exponents that change across the transition from unentangled to entangled dynamics as the degree of polymerization of the polymer increases beyond a specific value. Entanglements are the result of topological interactions that have their origin in hard-core repulsive interactions between chains, which prevent the chains from crossing themselves and other chains. Entanglements are present in liquids of polymers with any degree of polymerization, but they only affect the dynamics of long chains. Conventional theoretical approaches to describing entangled and unentangled dynamics (i.e. the Rouse theory and the reptation model) are formally incompatible and do not encompass the dynamics across the transition. In this paper, we extend our approach for the cooperative dynamics of a group of polymers across the transition from unentangled to entangled dynamics. We test the robustness of the approach by comparing theor...

Our analytically based technique for coarse-graining (CG) polymer simulations dramatically improves spatial and temporal scaling while preserving thermodynamic quantities and bulk properties. The purpose of CG codes is to run more efficient molecular dynamics simulations, yet the research field generally lacks thorough analysis of how such codes scale with respect to full-atom representations. This paper conducts an in-depth performance study of highly realistic polymer melts on modern supercomputing systems. We also present a workflow that integrates our analytical solution for calculating CG forces with new high-performance techniques for mapping back and forth between the atomistic and CG descriptions in LAMMPS. The workflow benefits from the performance of CG, while maintaining full-atom accuracy. Our results show speedups up to 12x faster than atomistic simulations.

The biological properties of proteins are uniquely determined by their structure and dynamics. A protein in solution populates a structural ensemble of metastable configurations around the global fold. From overall rotation to local fluctuations, the dynamics of proteins can cover several orders of magnitude in time scales. We propose a simulation-free coarse-grained approach which utilizes knowledge of the important metastable folded states of the protein to predict the protein dynamics. This approach is based upon the Langevin Equation for Protein Dynamics (LE4PD), a Langevin formalism in the coordinates of the protein backbone. The linear modes of this Langevin formalism organize the fluctuations of the protein, so that more extended dynamical cooperativity relates to increasing energy barriers to mode diffusion. The accuracy of the LE4PD is verified by analyzing the predicted dynamics across a set of seven different proteins for which both relaxation data and NMR solution structures are available. Using experimental NMR conformers as the input structural ensembles, LE4PD predicts quantitatively accurate results, with correlation coefficient \r{ho} = .93 to NMR backbone relaxation measurements for the seven proteins. The NMR solution structure derived ensemble and predicted dynamical relaxation is compared with molecular dy- namics simulation-derived structural ensembles and LE4PD predictions, and are consistent in the timescale of the simulations. The use of the experimental NMR conformers frees the approach from computationally demanding simulations.

The ability to noninvasively observe translational diffusion of proteins and protein complexes is important to many biophysical problems. We report high signal/noise (≥250) measurements of the translational diffusion in viscous solution of the fluorescent protein, DsRed. This is carried out using a new technique: molecular Fourier imaging correlation spectroscopy (M-FICS). M-FICS is an interferometric method that detects a collective Fourier component of the fluctuating density of a small population of fluorescent molecules, and provides information about the distribution of molecular diffusivities. A theoretical analysis is presented that expresses the detected signal fluctuations in terms of the relevant time-correlation functions for molecular translational diffusion. Furthermore, the role played by optical orientational degrees of freedom is established. We report Fickian self-diffusion of the DsRed tetramer at short timescales. The long-time deviation of our data from Fickian behavior is used to determine the variance of the distribution of the protein self-diffusion coefficient. We compare our results to the expected outcomes for 1), a bi-disperse distribution of protein species, and 2), dynamic disorder of the host solvent.

We present a generalized Langevin equation for the dynamics of semiflexible polymer chains of finite size in a dynamically heterogeneous fluid. Local and global dynamical properties, calculated in the framework of this approach, display anomalous behavior in agreement with experiments and computer simulations. The presence of heterogeneous dynamics induces non-Fickian center-of-mass diffusion and an anomalous slowdown of intramolecular modes of motion. Intermolecular interactions mostly perturb lowest-index modes, which correspond to polymer global dynamics. Internal polymer stiffness induces anomalies in the relaxation of highest-index modes, which characterize local dynamics and monomer diffusion.

We utilize a multi-scale approach where molecular dynamic simulations are performed to obtain quantitative structural averages used as input to a coarse-grained Langevin Equation for Protein Dynamics, which can be solved analytically. The approach describes proteins as fundamentally semiflexible objects collapsed into the free energy well representing the folded state. The normal mode analytical solution to this Langevin equation naturally separates into global modes describing the fully anisotropic tumbling of the macromolecule as a whole, and internal modes which describe local fluctuations about the folded structure. Complexity in the configurational free energy landscape around the folded state of the macromolecule leads to a renormalization of the internal modes, while the global modes provide a basis set in which the dipolar orientation and global anisotropy can be accounted for when comparing to experiments. Fundamental to this approach is the inclusion of internal dissipation which is absent in any rigid-body hydrodynamical modeling scheme. This simple approach predicts the dynamics of both global rotational diffusion and internal motion from the picosecond to the nanosecond regime, and is quantitative when compared to time correlation functions calculated from molecular dynamic simulations and in good agreement with Nuclear Magnetic Resonance relaxation experiments. Results for several well-characterized globular proteins are presented, suggesting our method describes the relevant dynamics around the global minimum well. Use of non-equilibrium simulation techniques such as metadynamics to sample the full free-energy landscape of the protein, and extension of the theoretical treatment to describe the dynamics into the biologically interesting microsecond to millisecond regime, will be discussed.

Structural and thermodynamic consistency of coarse-graining models across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. Our approach is a coarse-grained model based on integral equation theory, which can represent polymer chains at variable levels of chemical details. The model is analytical and depends on molecular and thermodynamic parameters of the system under study, as well as on the direct correlation function in the k --> 0 limit, c0. A numerical solution to the PRISM integral equations is used to determine c0, by adjusting the value of the effective hard sphere diameter, d, to agree with the predicted equation of state. This single quantity parameterizes the coarse-grained potential, which is used to perform mesoscale simulations that are directly compared with atomistic-level simulations of the same system. We test our coarse-graining formalism by comparing structural correlations, isothermal compressibility, equation of state, Helmholtz and Gibbs free energies, and potential energy and entropy using both united atom and coarse-grained descriptions. We find quantitative agreement between the analytical formalism for the thermodynamic properties, and the results of Molecular Dynamics simulations, independent of the chosen level of representation. In the mesoscale description, the potential energy of the soft-particle interaction becomes a free energy in the coarse-grained coordinates which preserves the excess free energy from an ideal gas across all levels of description. The structural consistency between the united-atom and mesoscale descriptions means the relative entropy between descriptions has been minimized without any variational optimization parameters. The approach is general and applicable to any polymeric system in different thermodynamic conditions.

The dynamics of polymer melts in both the unentangled and entangled regimes is described by a Langevin equation for the correlated motion of a group of chains, interacting through both intra- and inter-molecular potentials. Entanglements are represented by an intermolecular monomer-monomer confining potential that has no effect on short chains, while interpolymer interactions, responsible for correlated motion and subdiffusive center-of-mass dynamics, are represented by an intermolecular center-of-mass potential derived from the Ornstein-Zernike equation. This potential ensures that the liquid of phantom chains reproduces the compressibility and free energy of the real samples. For polyethylene melts the calculated dynamic structure factor is found to be in quantitative agreement with neutron spin echo experiments of polyethylene melts with chain lengths that span both the unentangled and the entangled regimes. The theory shows a progressive localization of the cooperative chain dynamics at the crossover from the unentangled to the entangled regime, in the spirit of the reptation model.

Starting from the formally exact Liouville equation, we derive a generalized Langevin equation for the simultaneous correlated motion of several molecules in dense melts. Our calculations are based upon phase space kinetic theory and Mori–Zwanzig projection operator techniques. In the overdamped regime, a set of nonlinear coupled equations is found containing cross-interaction contributions to the frequency matrix and to the memory functions. Specializing the problem to the correlated dynamics of polymer melts enables an analytical solution for the nonlinear cross contribution of the frequency matrix. The memory functions are calculated using a generalization of the Schweizer’s single molecule mode-coupling approach. A self-consistent procedure allows a numerical solution of the diffusive dynamics of the chains on the scale of the intermolecular interactions. At long time, depending on the strength of the intermolecular mean-force potential, two different scenarios take place. For weak intermolecular interactions the short-time correlated diffusive dynamics crosses over to the uncorrelated single chain dynamics. For stronger intermolecular interactions, when the time scale of relaxation of the many chain domains exceeds the time scales investigated, collective diffusion dominates the dynamical behavior.

A microscopic theory of self-diffusion in diblock copolymer melts and solutions has been developed based on polymeric mode-coupling methods formulated at the level of the time and space correlated interchain excluded volume and chi-parameter forces. Equilibrium structural correlations are determined via microscopic liquid state integral equation or coarse-grained field theoretic methods. The specific dynamical consequences of self-assembly are predicted to depend rather sensitively on temperature, degree of polymerization, copolymer composition and concentration, and local block friction coefficients. The dominant physical effect for entangled diblocks is the retardation of the relaxation time of the interchain excluded volume forces due to the thermodynamically-driven segregation of blocks into microdomains, resulting in suppression of translational motion. Analytic analysis in the long chain limit allows the derivation of new scaling laws relating the self-diffusion constant and chain degree of polymeri...

The predictions of polymer-mode-coupling theory for self-diffusion in entangled structurally and interaction symmetric diblock copolymer fluids are illustrated by explicit numerical calculations. We find that retardation of translational motion emerges near and somewhat below the order–disorder transition (ODT) in an approximately exponential and/or thermally activated manner. At fixed reduced temperature, suppression of diffusion is enhanced with increasing diblock molecular weight, compositional symmetry, and/or copolymer concentration. At very low temperatures, a new entropic-like regime of mobility suppression is predicted based on an isotropic supercooled liquid description of the copolymer structure. Preliminary generalization of the theory to treat diblock tracer diffusion is also presented. Quantitative applications to recent self and tracer diffusion measurements on compositionally symmetric polyolefin diblock materials have been carried out, and very good agreement between theory and experiment ...

We present a microscopic Langevin Equation that describes the dynamics of a group of interacting polymers in a melt, for samples with increasing chain length, covering the whole regime from the unentangled to the entangled dynamics. The confinement of the dynamics due to the presence of entanglements is accounted for by a potential acting between a pair of monomers belonging to different, but interpenetrating, chains. This potential is zero until the distance between those two monomers reaches a characteristic value, which in the conventional reptation model corresponds to the so-called "tube" diameter. At that distance, the pair of monomers experiences an effective constraint potential, which then decays following diffusive dynamics, as the two entangled chains inter-diffuse and their dynamics becomes progressively less correlated. The same potential acts on both unentangled and entangled polymer chains, but short chains are not affected as they relax faster than they experience the presence of the constraint potential. The approach shows good agreement with experimental data in both the unentangled and the entangled regimes. More recently, it has been extended to treat the dynamics of a short polymer chain diffusing inside a matrix of long, entangled polymers.

On the basis of the simplest Gaussian thread model for structurally symmetric copolymers, the polymer reference interaction site model (PRISM) theory is applied to study the equilibrium properties of diblock copolymer solutions under neutral solvent conditions. Analytic predictions are obtained for the influence of local and microdomain scale concentration fluctuations on the relationship between temperature, degree of polymerization, and polymer concentration at the order−disorder transition (ODT). In the semidilute regime, PRISM predictions agree with blob scaling and fluctuation-corrected field theoretic analyses. However, in the concentrated solution and melt regime strong disagreements occur, and the naive mean field dilution approximation is found to fail. Nevertheless, apparent scaling laws emerge under concentrated conditions with effective exponents which depend on solvent quality, melt screening length, and other nonuniversal structural features. The primary origin of the dilution approximation ...

The polymer-mode coupling (PMC) theory is applied to simultaneously treat diblock copolymer self-diffusion above and wel below the order-disorder transition (ODT). This requires combining the PRISM theory of diblock melts including recent extensions to estimate the location of the ODT and quantitatively describe scattering data, with the PMC approach. New dynamic scaling laws are derived and both model calculations and quantitative applications to experiments are presented

The analytic Polymer Reference Interaction Site Model (PRISM) theory of structurally and interaction symmetric Gaussian diblock copolymer fluids is reformulated, extended, and applied to make predictions for experimentally observable equilibrium properties of the disordered state. These include the temperature, degree of polymerization, copolymer composition, and polymer density or concentration dependences of the peak scattering intensity, effective chi-parameter, and heat capacity. The location of the order-disorder transition is empirically estimated based on the disordered, strongly fluctuating state scattering function. Detailed numerical applications of PRISM theory demonstrates it provides an excellent and consistent description of the data. An in depth comparison of the mathematical structure and predictions of PRISM theory with the highly coarse-grained, incompressible Brazovski–Leibler–Fredrickson–Helfand (BLFH) fluctuation corrected field theory is also carried out. Under some conditions (nearl...

An extended rotational isomeric states (RIS) model is used in conjunction with the matrix expansion method for describing the long time dynamics of flexible polymers in solution. The extended RIS model is derived directly from the potential functions that contain hindered torsional potentials, nonbonded interactions, etc. The matrix expansion method for describing the long time dynamics contains equilibrium conformational averages which are evaluated here from the extended RIS model. The theory effectively assumes that the torsional barriers provide the dominant mechanism for the decay of orientational correlations in the polymer chains. The theory is applied to united atom alkane chain dynamics where previous Brownian dynamics simulations with the same potentials are available for an unambiguous, no‐parameter test of the theory. The present computation of equilibrium averages with the extended RIS model represents a significant advancement over the prior treatments that evaluate the equilibrium averages using Brownian dynamics simulations. The comparison with the previous approach indicates the degree to which bond angle fluctuations affect the orientational time correlation functions.

Numerically optimized reduced descriptions of macromolecular liquids often present thermodynamic inconsistency with atomistic level descriptions even if the total correlation function, i.e. the structure, appears to be in agreement. An analytical expression for the effective potential between a pair of coarse-grained units is derived starting from the first-principles Ornstein-Zernike equation, for a polymer liquid where each chain is represented as a collection of interpenetrating blobs, with a variable number of blobs, ${n}_{b}$, of size ${N}_{b}$. The potential is characterized by a long tail, slowly decaying with characteristic scaling exponent of ${N}_{b}^{1/4}$. This general result applies to any coarse-grained model of polymer melts with units larger than the persistence length, highlighting the importance of the long, repulsive, potential tail for the model to correctly predict both structural and thermodynamic properties of the macromolecular liquid.

The theory to reconstruct the atomistic-level chain diffusion from the accelerated dynamics that is measured in mesoscale simulations of the coarse-grained system, is applied here to the dynamics of cis-1,4-Polybutadiene melts where each chain is described as a soft interacting colloidal particle. The rescaling formalism accounts for the corrections in the dynamics due to the change in entropy and the change in friction that are a consequence of the coarse-graining procedure. By including these two corrections the dynamics is rescaled to reproduce the realistic dynamics of the system described at the atomistic level. The rescaled diffusion coefficient obtained from mesoscale simulations of coarse-grained cis-1,4-Polybutadiene melts shows good agreement with data from united atom simulations performed by Tsolou et al. The derived monomer friction coefficient is used as an input to the theory for cooperative dynamics that describes the internal dynamics of a polymer moving in a transient regions of slow cooperative motion in a liquid of macromolecules. Theoretically predicted time correlation functions show good agreement with simulations in the whole range of length and time scales in which data are available. The theory provides, from data of mesoscale simulations of soft spheres, the correct atomistic-level dynamics, having as solo input static quantities., Comment: 15 pages, 12 figures, 3 tables. Submitted to J. Chem. Phys

A semi-empirical formula for orientational relaxation times of worm-like chains in dilute solutions is proposed : π ≅ (27/8)x 3 .[1 - (3/4)x + (3/4)x exp(-4/3x)] 3 π rod where τ rod = τ 0 N 3 is the relaxation time of a rigid rod composed of N segments, and x = 2 a/L is the chain rigidity, i. e. the ratio of the double persistence length to the chain contour length, L. The formula, which can be used in the entire range of molecular rigidities and chain lengths, has been tested against segment relaxation times for semi-rigid chains calculated from the optimized Rouse-Zimm model.

The optimized Rouse-Zimm approximation to the local dynamics (ORZLD theory) is extended to treat three-dimensional structures. Rigid model chains of different dimensionality are considered. The local dynamics of random peptides are compared to the rotational correlation times of rigid three-dimensional protein structures. The treatment of these rigid limits is a necessary step in a more advanced ORZLD theory of the dynamics of proteins including fluctuations relative to the three-dimensional structure. © 1995 John Wiley & Sons, Inc.

Static and dynamic properties of star polymers in theta solutions are derived for semiflexible and the partially stretched (PS) arm models. The extension of the Optimized Rouse-Zimm approach to describe the local dynamics (ORZLD) of star polymers is presented, together with some results for static and dynamic structure factors.

We present a theoretical approach to scale the artificially fast dynamics of simulated coarse-grained polymer liquids down to its realistic value. As coarse-graining affects entropy and dissipation, two factors enter the rescaling: inclusion of intramolecular vibrational degrees of freedom, and rescaling of the friction coefficient. Because our approach is analytical, it is general and transferable. Translational and rotational diffusion of unentangled and entangled polyethylene melts, predicted from mesoscale simulations of coarse-grained polymer melts using our rescaling procedure, are in quantitative agreement with united atom simulations and with experiments., Comment: 6 pages, 2 figures, 2 tables

The static and dynamic structure factors for star polymers in θ solutions are derived for semiflexible models and the partially stretched (PS) arm model. The PS model for the static structure factor is found to be in fairly good agreement with SANS experiments with exclusion of the high-a region, where only a qualitative agreement is obtained. The nonpreaveraged first cumulant for the PS model reproduces fairly well the peculiar effects found by neutron spin-echo experiments even though those experiments were carried out in good solvents. The effects of preaveraging and screening of the hydrodynamic interaction are considered. Results for the full dynamic structure factor are presented only in the preaveraging approximation

We present a detailed derivation and testing of our approach to rescale the dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y. Lyubimov et al. J. Chem. Phys. \textbf{132}, 11876, 2010). Starting from the first-principle Liouville equation and applying the Mori-Zwanzig projection operator technique, we derive the Generalized Langevin Equations (GLE) for the coarse-grained representations of the liquid. The chosen slow variables in the projection operators define the length scale of coarse graining. Each polymer is represented at two levels of coarse-graining: monomeric as a bead-and-spring model and molecular as a soft-colloid. In the long-time regime where the center-of-mass follows Brownian motion and the internal dynamics is completely relaxed, the two descriptions must be equivalent. By enforcing this formal relation we derive from the GLEs the analytical rescaling factors to be applied to dynamical data in the coarse-grained representation to recover the monomeric description. Change in entropy and change in friction are the two corrections to be accounted for to compensate the effects of coarse-graining on the polymer dynamics. The solution of the memory functions in the coarse-grained representations provides the dynamical rescaling of the friction coefficient. The calculation of the internal degrees of freedom provides the correction of the change in entropy due to coarse-graining. The resulting rescaling formalism is a function of the coarse-grained model and thermodynamic parameters of the system simulated. The rescaled dynamics obtained from mesoscale simulations of polyethylene, represented as soft colloidal particles, by applying our rescaling approach shows a good agreement with data of translational diffusion measured experimentally and from simulations. The proposed method is used to predict self-diffusion coefficients of new polyethylene samples., Comment: 21 pages, 6 figures, 6 tables. Submitted to Phys. Rev. E

Mesoscopic molecular dynamics simulations are used to determine the large scale structure of several binary polymer mixtures of various chemical architecture, concentration, and thermodynamic conditions. By implementing an analytical formalism, which is based on the solution to the Ornstein-Zernike equation, each polymer chain is mapped onto the level of a single soft colloid. From the appropriate closure relation, the effective, soft-core potential between coarse-grained units is obtained and used as input to our mesoscale simulations. The potential derived in this manner is analytical and explicitly parameter dependent, making it general and transferable to numerous systems of interest. From computer simulations performed under various thermodynamic conditions the structure of the polymer mixture, through pair correlation functions, is determined over the entire miscible region of the phase diagram. In the athermal regime mesoscale simulations exhibit quantitative agreement with united atom simulations. Furthermore, they also provide information at larger scales than can be attained by united atom simulations and in the thermal regime approaching the phase transition., 19 pages, 11 figures, 3 tables

A reduced description of the ORZLD local dynamic of homogeneous star polymers in θ solutions is presented. The reduced description directly uses bond variables whose dynamics are solved in terms of normal bond model. The bond modes enable us to take advantage of the symmetry of the star, thus drastically reducing the computer time required to diagonalize the involved matrices. The behavior of the reduced relaxation modes as a function of mode range, flexibility, and hydrodynamic interaction is obtained and discussed.

The optimized Rouse-Zimm approach to the local dynamics of polymer solutions (ORZLD) is extended to describe star polymers. A first-order model in the ORZLD hierarchy is defined for dilute θ solutions, based on a freely rotating chain (FRC) description of semiflexible stars. The partially stretched FRC star model is found in fairly good agreement with the available shrinking factor data on polystyrene stars as a function of molecular weight.