Combining Coarse-Grained Protein Models with Replica-Exchange All-Atom Molecular Dynamics

We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting from the extended chain conformation, demonstrated by the analysis of melting curves, the number of native-like conformations as a function of time and secondary structure propagation. The results strongly suggest that the proposed multiscale method could be an efficient and accurate tool for high-resolution studies of protein folding dynamics in larger systems.     

Refinement of protein cores and protein-peptide interfaces using a potential scaling approach

Refinement of side chain conformations in protein model structures and at the interface of predicted protein-protein or protein-peptide complexes is an important step during protein structural modelling and docking. A common approach for side chain prediction is to assume a rigid protein main chain for both docking partners and search for an optimal set of side chain rotamers to optimize the steric fit. However, depending on the target-template similarity in the case of comparative protein modelling and on the accuracy of an initially docked complex, the main chain template structure is only an approximation of a realistic target main chain. An inaccurate rigid main chain conformation can in turn interfere with the prediction of side chain conformations. In the present study, a potential scaling approach (PS-MD) during a molecular dynamics (MD) simulation that also allows the inclusion of explicit solvent has been used to predict side chain conformations on semi-flexible protein main chains. The PS-MD method converges much faster to realistic protein-peptide interface structures or protein core structures than standard MD simulations. Depending on the accuracy of the protein main chain, it also gives significantly better results compared with the standard rotamer search method.     

Protein dynamics determined by backbone conformation and atom packing

To study the factors determining the collective motions in thermal, conformational fluctuations of a globular protein, molecular dynamics simulations were performed with a backbone model and an atomic-level model. In the backbone model, only the C alpha atoms were explicitly treated with two types of pairwise interactions assigned between the C alpha atoms; atom-packing interactions to take into account the effect of tight atom packing in the protein interior and chain-restoring interactions to maintain the backbone around the native conformation. A quasi-harmonic method was used to decompose the overall fluctuations into independent, collective modes. The modes assigned to large conformational fluctuations showed a good correlation between the backbone and atomic-level models. From this study, it was suggested that the collective modes were motions in which a protein fluctuates, keeping the tertiary structure around the native one and avoiding backbone overlap and, hence, rough aspects of the collective modes can be derived without details of the atomic interactions. The backbone model is useful in obtaining the overall backbone motions of a protein without heavy simulations, even though the simulation starts from a poorly determined conformation of experiments and in sampling main chain conformations, from which the side chain conformations may be predicted.      

Molecular dynamics simulations of ovalbumin adsorption at squalene/water interface

The adsorption of protein molecules to oil/water (O/W) interface is of critical importance for the product design in a wide range of technologies and industries such as biotechnology, food industry and pharmaceutical industry. In this work, with ovalbumin (OVA) as the model protein, the adsorption conformations at the O/W interface and the adsorption stability have been systematically studied via multiple simulation methods, including all-atom molecular dynamic (AAMD) simulations, coarse-grained molecular dynamic (CGMD) simulations and enhanced sampling methods. The computational results of AAMD and CGMD show that the hydrophobic tail of OVA tends to be folded under long time relaxation in aqueous phase, and multiple adsorption conformations can exist at the interface due to heterogeneous interactions raising from oil and water respectively. To further study the adsorption sites of the protein, the adsorption kinetics of OVA at the O/W interface is simulated using metadynamics method combined with CGMD simulations, and the result suggests the existence of multiple adsorption conformations of OVA at interface with the head-on conformation as the most stable one. In all, this work focuses on the adsorption behaviors of OVA at squalene/water interface, and provides a theoretical basis for further functionalization of the proteins in emulsion-based products and engineering.     

Multi-scale models for cross-linked sulfonated poly (1, 3-cyclohexadiene) polymer

Atomistic and coarse-grained (CG) models of cross-linked sulfonated Poly (1, 3-cyclohexadiene) (xsPCHD) were developed and implemented in Molecular Dynamics (MD) simulations of PCHD chains with different architectures. In the atomistic model, PCHD chains are cross linked by a sulfur–sulfur bond. Sulfonic acid groups are evenly distributed along the chain. The architecture is specifically aimed for application as a proton exchange membrane used in fuel cells. An atomistic force field for this architecture was tested and applied in the atomistic MD simulation of xsPCHD for the first time. The atomistic simulations generate the density and cross-linker separation distribution. To further study the structural properties of longer chain systems, a CG model was proposed. The bonded structural probability distribution functions (PDFs) and non-bonded pair correlation function (PCF) of the CG beads were obtained from the atomistic simulation results. The bonded CG potentials are obtained by simple inversion of the corresponding PDFs. The CG non-bonded potential is parameterized to the PCF using the Iterative Boltzmann Inversion (IBI) method. The CGMD simulations of xsPCHD chains using potentials from above method satisfactorily reproduce the structural properties from atomistic MD simulation of the same system. The transferability of the CG potentials has been further tested through CGMD simulation of xsPCHD homopolymer with different architectures.     

Determinants of side chain conformational preferences in protein structures

A discriminatory function based on a statistical analysis of atomic contacts in protein structures is used for selecting side chain rotamers given a peptide main chain. The function allows us to rank different possible side chain conformations on the basis of contacts between side chain atoms and atoms in the environment. We compare the differences in constructing side chain conformations using contacts with only the local main chain, using the entire main chain, and by building pairs of side chains simultaneously with local main chain information. Using only the local main chain allows us to construct side chains with approximately 75% of the chi1 angles within 30 degrees of the experimental value, and an average side chain atom r.m.s.d. of 1.72 A in a set of 10 proteins. The results of constructing side chains for the 10 proteins are compared with the results of other side chain building methods previously published. The comparison shows similar accuracies. An advantage of the present method is that it can be used to select a small number of likely side chain conformations for each residue, thus permitting limited combinatorial searches for building multiple protein side chains simultaneously.      

A Monte Carlo simulation of coarse-grained poly(silylenemethylene) and poly(dimethylsilylenemethylene) melts

Dense melts of coarse-grained representations of poly(silylenemethylene) (PSM) and poly(dimethylsilylenemethylene) (PDMSM) have been simulated at 373 K. The PSM melt has very little structure, and the individual chains have conformations in good agreement with the prediction from the rotational isomeric state (RIS) model for the single chain. For PDMSM, however, the melt is much more strongly structured, and the individual chains have mean square dimensions 40% higher than the ones predicted by the RIS model for the single chain. Intermolecular packing interactions in the structured PDMSM melt are accompanied by expansion of individual chains.     

A systematic procedure to build a relaxed dense-phase atomistic representation of a complex amorphous polymer using a coarse-grained modeling approach

A systematic procedure has been developed to construct a relaxed dense-phase atomistic structure of a complex amorphous polymer. The numerical procedure consists of (1) coarse graining the atomistic model of the polymer into a mesoscopic model based on an iterative algorithm for potential inversion from distribution functions of the atomistic model, (2) relaxation of the coarse-grained chain using a molecular dynamics scheme, and (3) recovery of the atomistic structure by reverse mapping based on the superposition of atomistic counterparts on the corresponding coarse-grained coordinates. These methods are demonstrated by their application to construct a relaxed, dense-phase model of poly(DTB succinate), which is an amorphous tyrosine-derived biodegradable polymer that is being developed for biomedical applications. Both static and dynamic properties from the coarse-grained and atomistic simulations are analyzed and compared. The coarse-grained model, which contains the essential features of the DTB succinate structure, successfully described both local and global structural properties of the atomistic chain. The effective speedup compared to the corresponding atomistic simulation is substantially above 10², thus enabling simulation times to reach well into the characteristic experimental regime. The computational approach for reversibly bridging between coarse-grained and atomistic models provides an efficient method to produce relaxed dense-phase all-atom molecular models of complex amorphous polymers that can subsequently be used to study and predict the atomistic-level behavior of the polymer under different environmental conditions in order to optimally design polymers for targeted applications.     

Novel method to detect a motif of local structures in different protein conformations

In order to detect a motif of local structures in different protein conformations, the Delaunay tessellation is applied to protein structures represented by C(alpha) atoms only. By the Delaunay tessellation the interior space of the protein is uniquely divided up into Delaunay tetrahedra whose vertices are the C(alpha) atom positions. Some edges of the tetrahedra are virtual bonds connecting adjacent residues' C(alpha) atoms along the polypeptide chain and others indicate interactions between residues nearest neighbouring in space. The rules are proposed to assign a code, i.e., a string of digits, to each tetrahedron to characterize the local structure constructed by the vertex residues of one relevant tetrahedron and four surrounding it. Many sets comprised of the local structures with the same code are obtained from 293 proteins, each of which has relatively low sequence similarity with the others. The local structures in each set are similar enough to each other to represent a motif. Some of them are parts of secondary or supersecondary structures, and others are irregular, but definite structures. The method proposed here can find motifs of local structures in the Protein Data Bank much more easily and rapidly than other conventional methods, because they are represented by codes. The motifs detected in this method can provide more detailed information about specific interactions between residues in the local structures, because the edges of the Delaunay tetrahedra are regarded to express interactions between residues nearest neighbouring in space.      

Towards an understanding of stacked base interactions: non-equilibrium phase transitions as a probable model

Summary The distances of stacked bases of DNA in different conformations can-not be calculated by equilibrium potentials, since they exhibit not more than only one minimum. However, a double potential minimum is obtained by considering the most simple semiclassical model of excitons that are coupled adiabatically to lattice vibrations, hence forming polaritons. By use of Danilov's extended Hückel approximation of DNA excitons, stacked base distances can be calculated that agree fairly well with the experimental data. The errors of this approach are small as compared to the differences of the distances in various conformations. Consequently, this model may work as a first base of understanding molecular interactions in DNA.     

Viscoelastic phase separation in soft matter: Numerical-simulation study on its physical mechanism

Viscoelastic phase separation is a new type of phase separation, which may be universal to any dynamically asymmetric mixture composed of slow and fast components. Dynamic asymmetry can arise from (i) a large size disparity between the components and (ii) a large difference in glass-transition temperature. Origin (i) often exists in the so-called soft matter, while origin (ii) can exist in any material including oxide, metallic, and molecular glass formers. For case (i), phase separation generally leads to the formation of a long-lived “interaction network” (transient gel) of the slow components, if the concentration is high enough and attractive interactions between them are strong enough. This new type of phase separation allows us to form a network structure of the minority slow-component-rich phase, contrary to the conventional wisdom on phase separation. This has a significant technological impact on the morphological control of multi-phase materials. Here we review our numerical simulation studies on viscoelastic phase separation. Effects of transient gelation on phase-separation kinetics are studied by numerical simulations based on the coarse-grained two-fluid model. We find that the bulk mechanical stress originating from connectivity of the slow components of a mixture plays a crucial role in pattern evolution of viscoelastic phase separation. We also discuss how we can control the phase-separation morphology by controlling the viscoelastic properties of component materials. This coarse-grained model cannot describe how a transient gel itself is formed. Thus, to study the formation process of a transient gel in colloidal suspensions, we develop a new simulation method (“fluid particle dynamics (FPD) method”), which can properly treat interparticle hydrodynamic interactions. This new method can be applied to various fields of colloidal science, where hydrodynamic interactions play important roles. Our FPD simulations of colloidal aggregation clearly indicate that hydrodynamic interactions play crucial roles in the formation of a transient gel. We emphasize that the percolation threshold is crucially affected by hydrodynamic interactions. We point out that viscoelastic phase separation should be universally observed in not only polymer solutions and mixtures but also colloidal suspensions, emulsions, and protein solutions.     

On the molecular basis of adsorbed solution behaviour

A theoretical study, based on statistical thermodynamics, of the adsorbed solution behaviour of binary gas monolayers on a homogeneous solid surface is presented. The adsorbate—solid interactions are modelled via the summed 10-4 potential and the adsorbate—adsorbate interactions as those of a two-dimensional fluid mixture in which the molecules interact via Lennard-Jones 12-6 potentials. The thermodynamic properties of the two-dimensional mixture are obtained from the van der Waals one-fluid model. We present results from Monte Carlo computer simulations of two-dimensional fluid mixtures which support the accuracy of this procedure. The model can be used to study the relative importance of adsorbate—solid and adsorbate—adsorbate interactions in determining the adsorbed solution behaviour.Comparisons with experimental adsorption equilibria data for ethane—propane mixtures adsorbed on graphitized carbon black show that the theory gives excellent predictions of the adsorption equilibria, without adjustable parameters. For this system at 298 K and 700 Torr the adsorption selectivity is dominated by the difference in the Henry's law constants. However, it is shown that the adsorbate—adsorbate interactions and nonideal adsorbed solution behaviour become more or less important depending on the conditions in relation to the two-dimensional phase diagram.     

Residue-residue mean-force potentials for protein structure recognition

We present two new sets of energy functions for protein structure recognition, given the primary sequence of amino acids along the polypeptide chain. The first set of potentials is based on the positions of alpha- and the second on positions of beta- and alpha- carbon atoms of amino acid residues. The potentials are derived using a theory of Boltzmann-like statistics of protein structure. The energy terms incorporate both long-range interactions between residues remote along a chain and short-range interactions between near neighbors. Distance dependence is approximated by a piecewise constant function defined on intervals of equal size. The size of the interval is optimized to preserve as much detail as possible without introducing excessive error due to limited statistics. A database of 214 non- homologous proteins was used both for the derivation of the potentials, and for the 'threading' test originally suggested by Hendlich et al. (1990) J. Mol. Biol., 216, 167-180. Special care is taken to avoid systematic error in this test. For threading, we used 100 non- homologous protein chains of 60-205 residues. The energy of each of the native structures was compared with the energy of 43,000 to 19,000 alternative structures generated by threading. Of these 100 native structures, 92 have the lowest energy with alpha-carbon-based potentials and, even more, 98 of these 100 structures, have the lowest energy with the beta- and alpha-carbon based potentials.      

Molecular dynamics model structures for the molten globule state of {alpha}-lactalbumin: aromatic residue clusters I and II

To model the molten globule structure of -lactalbumin, moleculardynamics (MD) simulations were carried out for the protein inexplicit water at high temperature. In these simulations, long-rangeCoulomb interactions were evaluated explicitly with an originalmethod (particle–particle and particle–cell: PPPC)to avoid artifacts caused by the cut-off. The MD simulationswere started from two initial conditions to verify that similarresults would be obtained. From the last 150 ps trajectoriesof the two MD simulations, two partially unfolded average structureswere obtained. These structures had the following common structuralfeatures which are characteristic of the molten globule state.The radii of gyration for these conformations were 7.4 and 9.6%larger than that of the native state. These values were almostthe same as the experimental value (9.6%) observed recentlyby small-angle X-ray scattering (Kataoka,M., Kuwajima,K., Tokunaga,F.and Goto,Y., 1997, Protein Sci., 6, 422–430). Furthermore,aromatic residues of clusters I and II in these structures werefar apart from each other except for Try103–Trp104. Thisresult is in good agreement with NMR experimental results forthe acid-denatured molten globule state (Alexandrescu et al.,1992, 1993); that is, NOE signals between the aromatic residueswere not observed, except for that of Try103–Trp104 inthe molten globule state. Other structural features of thesemodels for the molten globule state are discussed with referenceto native state structures.     

Simulation of high-concentration self-interactions for monoclonal antibodies from well-behaved to poorly-behaved systems

Attractive self-interactions of therapeutic proteins are linked to problematic solution behaviors at high protein concentrations such as reversible or irreversible aggregation, high viscosity, opalescence, phase separation, and low solubility. Prediction of attractive self-interactions early in development can improve the processes of formulation development and candidate selection. To that end, a coarse-grained model with explicit representation of charged sites was used to accurately predict a broad range of protein self-interactions at high protein concentrations (up to 160 mg/ml) for multiple monoclonal antibodies and formulations, including strong electrostatic attractions, with static light scattering measurements at low protein concentrations as the only experimental input. In addition, Mayer-weighted electrostatic energies for charged residues from these simulations can contribute to understanding of electrostatic interactions and guide the development of protein variants.     

Do bending and torsional potentials affect the unraveling dynamics of flexible polymer chains in extensional or shear flows?

We compare the flow-induced unraveling of a bead-spring model chain in which each stiff spring corresponds to a single Kuhn step to that of an atomistic representation of the backbone of the same polymer chain with realistic bending and torsional potentials. In our earlier work [Jain, S. and Larson, R.G. 2008. Effect of bending and torsional potentials on high-frequency viscoelasticity of dilute polymer solutions. Macromolecules 41(10), 3692-3700], we showed that in the linear viscoelastic regime, bending and torsional potentials suppress fast local diffusive modes. Now, in strong shear and extensional flows, we observe that bending and torsional potentials have only a slight effect on unraveling dynamics. However, in shear flow, we find that for relatively short coarse-grained chains having less than 20 or so Kuhn steps—representing polymers with fewer than around 150 backbone bonds—coarse-graining introduces periodic peaks in the probability distribution of steady-state stretch. We believe this occurs at high shear because of the dominance of a discrete set of stretch values each of which corresponds to an integral number of bonds that are nearly fully aligned between back-folds that are created during the chain's tumbling orbit. Even this difference between coarse-grained and realistic fine-grained chains disappears for more typical long chain lengths.     

Recognition of protein structure on coarse lattices with residue- residue energy functions

We suggest and test potentials for the modeling of protein structure on coarse lattices. The coarser the lattice, the more complete and faster is the exploration of the conformational space of a molecule. However, there are inevitable energy errors in lattice modeling caused by distortions in distances between interacting residues; the coarser the lattice, the larger are the energy errors. It is generally believed that an improvement in the accuracy of lattice modelling can be achieved only by reducing the lattice spacing. We reduce the errors on coarse lattices with lattice-adapted potentials. Two methods are used: in the first approach, 'lattice-derived' potentials are obtained directly from a database of lattice models of protein structure; in the second approach, we derive 'lattice-adjusted' potentials using our previously developed method of statistical adjustment of the 'off- lattice' energy functions for lattices. The derivation of off-lattice Calpha atom-based distance-dependent pairwise potentials has been reported previously. The accuracy of 'lattice-derived', 'lattice- adjusted' and 'off-lattice' potentials is estimated in threading tests. It is shown that 'lattice-derived' and 'lattice-adjusted' potentials give virtually the same accuracy and ensure reasonable protein fold recognition on the coarsest considered lattice (spacing 3.8 A), however, the 'off-lattice' potentials, which efficiently recognize off- lattice folds, do not work on this lattice, mainly because of the errors in short-range interactions between neighboring residues.      

喷雾干燥颗粒表面形貌形成过程粗粒化模拟

喷雾干燥制粒有着广泛的应用。颗粒表面形貌的调控对提升颗粒品质起到至关重要的作用。本研究旨在建立分子尺度粗粒化模型，描述蒸发诱导下溶质的自组装行为，预测不同干燥条件下表面形貌的演变过程。文中建立的粗粒化网格Monte Carlo模型可以处理球形固体溶质，并充分考虑各物质之间相互作用及相变过程。开发的分析方法可以定量蒸发过程中液体残留率、颗粒分布与组装形貌。通过初步的二维系统模拟可以发现，溶剂不断蒸发过程中溶质逐渐移动，形成各种自组装结构。溶剂化学势越小，液体残留率越低。随着初始溶质浓度升高，最终溶质组装形貌从点状变为网状结构。不同的物质间相互作用也会导致紧密或松散的溶质分布。     

Relationship between the coefficient of friction of additive in the bulk and chain graft surface density through a diffusion process: Erucamide–stearyl erucamide mixtures in polypropylene films

A relationship between chain graft density calculated by coarse-grained simulation and the one obtained from experimental results is compared in the present work. Two slip additives for polypropylene films were studied, erucamide and stearyl erucamide. The diffusion equation (Fick's second law) was used to relate real-time experimental results with coarse-grained simulations and rendered slip additive surface density as a function of the coefficient of friction. The normalized surface density values obtained from the simulation showed a qualitative trend consistent with the experimentally observed results.     

Surface-Induced Interphases During Curing Processes Between Bi- and Pentafunctional Components: Reactive Coarse-Grained Molecular Dynamics Simulations

The present reactive molecular dynamics (RMD) simulations discuss the formation of interphase regions in cured polymer adhesives. The latter are obtained from the curing of reactive liquid mixtures composed of pentafunctional linkers and bifunctional monomers in contact with idealized surfaces. The present reactive scheme mimics the one of epoxies with amine linkers, i.e., processes investigated experimentally by Possart and co-workers. Generic RMD simulations are performed in a coarse-grained (CG) resolution to evaluate basic principles in curing characterized by preferential interactions. The creation of linker-rich domains is promoted by preferential surface-linker as well as linker-linker interactions in the reactive mixtures. The dimension of the interphase both in the starting mixture and the cured network depends on these preferential interactions which lead to a retardation of the curing velocity. This retardation behavior is mapped by conversion curves as a function of the number of reactive steps and by the spatially resolved profiles of the connected linkers. Although derived by generic potentials, the simulated reduction of the curing velocity is in agreement with experimental results in epoxies. The chosen interactions also imply a smaller number of linker bonds in the interphase than in the bulk region. The present RMD approach offers insight into key parameters of curing processes under the influence of preferential surface interactions coupled to selective attractions in the liquid starting mixture.