In situ data analytics and indexing of protein trajectories

The transition toward exascale computing will be accompanied by a performance dichotomy. Computational peak performance will rapidly increase; I/O performance will either grow slowly or be completely stagnant. Essentially, the rate at which data are generated will grow much faster than the rate at which data can be read from and written to the disk. MD simulations will soon face the I/O problem of efficiently writing to and reading from disk on the next generation of supercomputers. This article targets MD simulations at the exascale and proposes a novel technique for in situ data analysis and indexing of MD trajectories. Our technique maps individual trajectories' substructures (i.e., α-helices, β-strands) to metadata frame by frame. The metadata captures the conformational properties of the substructures. The ensemble of metadata can be used for automatic, strategic analysis within a trajectory or across trajectories, without manually identify those portions of trajectories in which critical changes take place. We demonstrate our technique's effectiveness by applying it to 26.3k helices and 31.2k strands from 9917 PDB proteins and by providing three empirical case studies. © 2017 Wiley Periodicals, Inc.

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino Acid Side Chains in Water. VII. Charged-Hydrophobic/Polar and Polar-Hydrophobic/Polar Side Chains

The physics-based potentials of side-chain-side-chain interactions corresponding to pairs composed of charged and polar, polar and polar, charged and hydrophobic, and hydrophobic and hydrophobic side chains have been determined. A total of 144 four-dimensional potentials of mean force (PMFs) of all possible pairs of molecules modeling these pairs were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation, and the analytical expressions were then fitted to the PMFs. Depending on the type of interacting sites, the analytical approximation to the PMF is a sum of terms corresponding to van der Waals interactions and cavity-creation involving the nonpolar sections of the side chains and van der Waals, cavity-creation, and electrostatic (charge-dipole or dipole-dipole) interaction energies and polarization energies involving the charged or polar sections of the side chains. The model used in this work reproduces all features of the interacting pairs. The UNited RESidue force field with the new side-chain-side-chain interaction potentials was preliminarily tested with the N-terminal part of the B-domain of staphylococcal protein A (PDBL 1BDD ; a three-α-helix bundle) and UPF0291 protein YnzC from Bacillus subtilis (PDB: 2HEP ; an α-helical hairpin).

Role of the sulfur to α-carbon thioether bridges in thurincin H

Thurincin H is a small protein produced by Bacillus thuringiensis SF361 with gram-positive antimicrobial properties. The toxins produced by B. thuringiensis are widely used in the agriculture as, e.g. natural preservatives in dairy products. The structure of thurincin H possesses four covalent sulfur to [Formula: see text]-carbon bonds that involve the cysteine side-chains; these bonds are probably responsible for the shape and stability of the protein and, thereby, for its antimicrobial properties. To examine the influence of the formation of the sulfur-carbon bonds on the folding pathways and stability of the protein, a series of canonical and multiplexed replica-exchange simulations with the coarse-grained UNRES force field was carried out without and with distance restraints imposed on selected S-C[Formula: see text] atom pairs. It was found that the order of the formation and breaking of the S-C[Formula: see text] thioether bonds significantly impacts on the foldability and stability of the thurincin H. It was also observed that thioether bridges play a major role in stabilizing the global fold of the protein, although it significantly diminishes the entropy of the system. The maximum foldability of thurincin H was observed in the presence of the optimal set of three out of four thioether bridges. Thus, the results suggest that the presence of ThnB enzyme and other agents that catalyze the formation of thioether bridges can be essential for correct folding of thurincin H and that the formation of the fourth bridge does not seem to facilitate folding; instead, it seems to rigidify the loop and prevent proteolysis.

Optimization of a Nucleic Acids united-RESidue 2-Point model (NARES-2P) with a maximum-likelihood approach

Coarse-grained models are useful tools to investigate the structural and thermodynamic properties of biomolecules. They are obtained by merging several atoms into one interaction site. Such simplified models try to capture as much as possible information of the original biomolecular system in all-atom representation but the resulting parameters of these coarse-grained force fields still need further optimization. In this paper, a force field optimization method, which is based on maximum-likelihood fitting of the simulated to the experimental conformational ensembles and least-squares fitting of the simulated to the experimental heat-capacity curves, is applied to optimize the Nucleic Acid united-RESidue 2-point (NARES-2P) model for coarse-grained simulations of nucleic acids recently developed in our laboratory. The optimized NARES-2P force field reproduces the structural and thermodynamic data of small DNA molecules much better than the original force field.

Physics-Based Potentials for Coarse-Grained Modeling of Protein-DNA Interactions

Physics-based potentials have been developed for the interactions between proteins and DNA for simulations with the UNRES + NARES-2P force field. The mean-field interactions between a protein and a DNA molecule can be divided into eight categories: (1) nonpolar side chain–DNA base, (2) polar uncharged side chain–DNA base, (3) charged side chain–DNA base, (4) peptide group–phosphate group, (5) peptide group–DNA base, (6) nonpolar side chain–phosphate group, (7) polar uncharged side chain–phosphate group, and (8) charged side chain–phosphate group. Umbrella-sampling molecular dynamics simulations in explicit TIP3P water using the AMBER force field were carried out to determine the potentials of mean force (PMF) for all 105 pairs of interacting components. Approximate analytical expressions for the mean-field interaction energy of each pair of the different kinds of interacting molecules were then fitted to the PMFs to obtain the parameters of the analytical expressions. These analytical expressions can reproduce satisfactorily the PMF curves corresponding to different orientations of the interacting molecules. The results suggest that the physics-based mean-field potentials of amino acid–nucleotide interactions presented here can be used in coarse-grained simulation of protein–DNA interactions.

Performance of protein-structure predictions with the physics-based UNRES force field in CASP11

Participating as the Cornell-Gdansk group, we have used our physics-based coarse-grained UNited RESidue (UNRES) force field to predict protein structure in the 11th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP11). Our methodology involved extensive multiplexed replica exchange simulations of the target proteins with a recently improved UNRES force field to provide better reproductions of the local structures of polypeptide chains. All simulations were started from fully extended polypeptide chains, and no external information was included in the simulation process except for weak restraints on secondary structure to enable us to finish each prediction within the allowed 3-week time window. Because of simplified UNRES representation of polypeptide chains, use of enhanced sampling methods, code optimization and parallelization and sufficient computational resources, we were able to treat, for the first time, all 55 human prediction targets with sizes from 44 to 595 amino acid residues, the average size being 251 residues. Complete structures of six single-domain proteins were predicted accurately, with the highest accuracy being attained for the T0769, for which the CαRMSD was 3.8 Å for 97 residues of the experimental structure. Correct structures were also predicted for 13 domains of multi-domain proteins with accuracy comparable to that of the best template-based modeling methods. With further improvements of the UNRES force field that are now underway, our physics-based coarse-grained approach to protein-structure prediction will eventually reach global prediction capacity and, consequently, reliability in simulating protein structure and dynamics that are important in biochemical processes.

AVAILABILITY AND IMPLEMENTATION

Freely available on the web at http://www.unres.pl/ CONTACT: has5@cornell.edu.

Molecular dynamics of protein A and a WW domain with a united-residue model including hydrodynamic interaction

The folding of the N-terminal part of the B-domain of staphylococcal protein A (PDB ID: 1BDD, a 46-residue three-α-helix bundle) and the formin-binding protein 28 WW domain (PDB ID: 1E0L, a 37-residue three-stranded anti-parallel β protein) was studied by means of Langevin dynamics with the coarse-grained UNRES force field to assess the influence of hydrodynamic interactions on protein-folding pathways and kinetics. The unfolded, intermediate, and native-like structures were identified by cluster analysis, and multi-exponential functions were fitted to the time dependence of the fractions of native and intermediate structures, respectively, to determine bulk kinetics. It was found that introducing hydrodynamic interactions slows down both the formation of an intermediate state and the transition from the collapsed structures to the final native-like structures by creating multiple kinetic traps. Therefore, introducing hydrodynamic interactions considerably slows the folding, as opposed to the results obtained from earlier studies with the use of Gō-like models.

Dynamic Formation and Breaking of Disulfide Bonds in Molecular Dynamics Simulations with the UNRES Force Field

Many proteins contain disulfide bonds that are usually essential for maintaining function and a stable structure. Several algorithms attempt to predict the arrangement of disulfide bonds in the context of protein structure prediction, but none can simulate the entire process of oxidative folding, including dynamic formation and breaking of disulfide bonds. In this work, a potential function developed to model disulfide bonds is coupled with the united-residue (UNRES) force field, and used in both canonical and replica exchange molecular dynamics simulations to produce complete oxidative folding pathways. The potential function is obtained by introducing a transition barrier that separates the bonded and nonbonded states of the half-cystine residues. Tests on several helical proteins show that improved predictions are obtained when dynamic disulfide-bond formation and breaking are considered. The effect of the disulfide bonds on the folding kinetics is also investigated, particularly their role in stabilizing folding intermediates, resulting in slower folding.

Theoretical Studies of Interactions between O-Phosphorylated and Standard Amino-Acid Side-Chain Models in Water

Phosphorylation is a common post-translational modification of the amino-acid side chains (serine, tyrosine, and threonine) that contain hydroxyl groups. The transfer of the negatively charged phosphate group from an ATP molecule to such amino-acid side chains leads to changes in the local conformations of proteins and the pattern of interactions with other amino-acid side-chains. A convenient characteristic of the side chain-side chain interactions in the context of an aqueous environment is the potential of mean force (PMF) in water. A series of umbrella-sampling molecular dynamic (MD) simulations with the AMBER force field were carried out for pairs of O-phosphorylated serine (pSer), threonine (pThr), and tyrosine, (pTyr) with natural amino acids in a TIP3P water model as a solvent at 298 K. The weighted-histogram analysis method was used to calculate the four-dimensional potentials of mean force. The results demonstrate that the positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the relative orientation depend on the character of the interacting pairs. More distinct minima are observed for oppositely charged pairs such as, e.g., O-phosphorylated side-chains and positively charged ones, such as the side-chains of lysine and arginine.

Molecular modeling of the binding modes of the iron-sulfur protein to the Jac1 co-chaperone from Saccharomyces cerevisiae by all-atom and coarse-grained approaches

The iron-sulfur protein 1 (Isu1) and the J-type co-chaperone Jac1 from yeast are part of a huge ATP-dependent system, and both interact with Hsp70 chaperones. Interaction of Isu1 and Jac1 is a part of the iron-sulfur cluster biogenesis system in mitochondria. In this study, the structure and dynamics of the yeast Isu1-Jac1 complex has been modeled. First, the complete structure of Isu1 was obtained by homology modeling using the I-TASSER server and YASARA software and thereafter tested for stability in the all-atom force field AMBER. Then, the known experimental structure of Jac1 was adopted to obtain initial models of the Isu1-Jac1 complex by using the ZDOCK server for global and local docking and the AutoDock software for local docking. Three most probable models were subsequently subjected to the coarse-grained molecular dynamics simulations with the UNRES force field to obtain the final structures of the complex. In the most probable model, Isu1 binds to the left face of the Γ-shaped Jac1 molecule by the β-sheet section of Isu1. Residues L105 , L109 , and Y163 of Jac1 have been assessed by mutation studies to be essential for binding (Ciesielski et al., J Mol Biol 2012; 417:1-12). These residues were also found, by UNRES/molecular dynamics simulations, to be involved in strong interactions between Isu1 and Jac1 in the complex. Moreover, N(95), T(98), P(102), H(112), V(159), L(167), and A(170) of Jac1, not yet tested experimentally, were also found to be important in binding.

Physics-based potentials for the coupling between backbone- and side-chain-local conformational states in the UNited RESidue (UNRES) force field for protein simulations

The UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained model in which each amino-acid residue is reduced to two interaction sites, namely, a united peptide group (p) located halfway between the two neighboring α-carbon atoms (Cαs), which serve only as geometrical points, and a united side chain (SC) attached to the respective Cα. Owing to this simplification, millisecond molecular dynamics simulations of large systems can be performed. While UNRES predicts overall folds well, it reproduces the details of local chain conformation with lower accuracy. Recently, we implemented new knowledge-based torsional potentials (Krupa et al. J. Chem. Theory Comput. 2013, 9, 4620–4632) that depend on the virtual-bond dihedral angles involving side chains: Cα···Cα···Cα···SC (τ(1)), SC···Cα···Cα···Cα (τ(2)), and SC···Cα···Cα···SC (τ(3)) in the UNRES force field. These potentials resulted in significant improvement of the simulated structures, especially in the loop regions. In this work, we introduce the physics-based counterparts of these potentials, which we derived from the all-atom energy surfaces of terminally blocked amino-acid residues by Boltzmann integration over the angles λ(1) and λ(2) for rotation about the Cα···Cα virtual-bond angles and over the side-chain angles χ. The energy surfaces were, in turn, calculated by using the semiempirical AM1 method of molecular quantum mechanics. Entropy contribution was evaluated with use of the harmonic approximation from Hessian matrices. One-dimensional Fourier series in the respective virtual-bond-dihedral angles were fitted to the calculated potentials, and these expressions have been implemented in the UNRES force field. Basic calibration of the UNRES force field with the new potentials was carried out with eight training proteins, by selecting the optimal weight of the new energy terms and reducing the weight of the regular torsional terms. The force field was subsequently benchmarked with a set of 22 proteins not used in the calibration. The new potentials result in a decrease of the root-mean-square deviation of the average conformation from the respective experimental structure by 0.86 Å on average; however, improvement of up to 5 Å was observed for some proteins.

Common functionally important motions of the nucleotide-binding domain of Hsp70

The 70 kDa heat shock proteins (Hsp70) are a family of molecular chaperones involved in protein folding, aggregate prevention, and protein disaggregation. They consist of the substrate-binding domain (SBD) that binds client substrates, and the nucleotide-binding domain (NBD), whose cycles of nucleotide hydrolysis and exchange underpin the activity of the chaperone. To characterize the structure-function relationships that link the binding state of the NBD to its conformational behavior, we analyzed the dynamics of the NBD of the Hsp70 chaperone from Bos taurus (PDB 3C7N:B) by all-atom canonical molecular dynamics simulations. It was found that essential motions within the NBD fall into three major classes: the mutual class, reflecting tendencies common to all binding states, and the ADP- and ATP-unique classes, which reflect conformational trends that are unique to either the ADP- or ATP-bound states, respectively. "Mutual" class motions generally describe "in-plane" and/or "out-of-plane" (scissor-like) rotation of the subdomains within the NBD. This result is consistent with experimental nuclear magnetic resonance data on the NBD. The "unique" class motions target specific regions on the NBD, usually surface loops or sites involved in nucleotide binding and are, therefore, expected to be involved in allostery and signal transmission. For all classes, and especially for those of the "unique" type, regions of enhanced mobility can be identified; these are termed "hot spots," and their locations generally parallel those found by NMR spectroscopy. The presence of magnesium and potassium cations in the nucleotide-binding pocket was also found to influence the dynamics of the NBD significantly.

DNA Duplex Formation with a Coarse-Grained Model

A middle-resolution coarse-grained model of DNA is proposed. The DNA chain is built of spherical and planar rigid bodies connected by elastic virtual bonds. The bonded part of the potential energy function is fit to potentials of mean force of model systems. The rigid bodies are sets of neutral, charged, and dipolar beads. Electrostatic and van der Waals interactions are parametrized by our recently developed procedure [Maciejczyk, M.; Spasic, A.; Liwo, A.; Scheraga, H.A. J. Comp. Chem.2010, 31, 1644]. Interactions with the solvent and an ionic cloud are approximated by a multipole-multipole Debye-Hückel model. A very efficient R-RATTLE algorithm, for integrating the movement of rigid bodies, is implemented. It is the first coarse-grained model, in which both bonded and nonbonded interactions were parametrized ab initio and which folds stable double helices from separated complementary strands, with the final conformation close to the geometry of experimentally determined structures.

WeFold: a coopetition for protein structure prediction

The protein structure prediction problem continues to elude scientists. Despite the introduction of many methods, only modest gains were made over the last decade for certain classes of prediction targets. To address this challenge, a social-media based worldwide collaborative effort, named WeFold, was undertaken by 13 labs. During the collaboration, the laboratories were simultaneously competing with each other. Here, we present the first attempt at "coopetition" in scientific research applied to the protein structure prediction and refinement problems. The coopetition was possible by allowing the participating labs to contribute different components of their protein structure prediction pipelines and create new hybrid pipelines that they tested during CASP10. This manuscript describes both successes and areas needing improvement as identified throughout the first WeFold experiment and discusses the efforts that are underway to advance this initiative. A footprint of all contributions and structures are publicly accessible at http://www.wefold.org.

A unified coarse-grained model of biological macromolecules based on mean-field multipole-multipole interactions

A unified coarse-grained model of three major classes of biological molecules—proteins, nucleic acids, and polysaccharides—has been developed. It is based on the observations that the repeated units of biopolymers (peptide groups, nucleic acid bases, sugar rings) are highly polar and their charge distributions can be represented crudely as point multipoles. The model is an extension of the united residue (UNRES) coarse-grained model of proteins developed previously in our laboratory. The respective force fields are defined as the potentials of mean force of biomacromolecules immersed in water, where all degrees of freedom not considered in the model have been averaged out. Reducing the representation to one center per polar interaction site leads to the representation of average site–site interactions as mean-field dipole–dipole interactions. Further expansion of the potentials of mean force of biopolymer chains into Kubo’s cluster-cumulant series leads to the appearance of mean-field dipole–dipole interactions, averaged in the context of local interactions within a biopolymer unit. These mean-field interactions account for the formation of regular structures encountered in biomacromolecules, e.g., α-helices and β-sheets in proteins, double helices in nucleic acids, and helicoidally packed structures in polysaccharides, which enables us to use a greatly reduced number of interacting sites without sacrificing the ability to reproduce the correct architecture. This reduction results in an extension of the simulation timescale by more than four orders of magnitude compared to the all-atom representation. Examples of the performance of the model are presented.

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Notizen: A CNDO/2 Study of the Homoconjugation Energies of 4-Substituted Pyridine N-Oxides

Homoconjugation energies in vacuo have been calculated for pyridine N-oxide (PyO) and its 4-methyl- (4 PicO) and 4-nitro- (4-NO2PyO) derivatives with the use of the CNDO/2 method. Comparison with the experimental homoconjugation constants in some aprotic solvents reveals the opposite order of the stability of homocomplexes than could be expected based on the calculated homoconjugation energies. This formal inconsistency can be explained in terms of the solvation effect.

Revised Backbone-Virtual-Bond-Angle Potentials to Treat the l- and d-Amino Acid Residues in the Coarse-Grained United Residue (UNRES) Force Field

Continuing our effort to introduce d-amino-acid residues in the united residue (UNRES) force field developed in our laboratory, in this work the Cα ··· Cα ··· Cα backbone-virtual-bond-valence-angle (θ) potentials for systems containing d-amino-acid residues have been developed. The potentials were determined by integrating the combined energy surfaces of all possible triplets of terminally blocked glycine, alanine, and proline obtained with ab initio molecular quantum mechanics at the MP2/6-31G(d,p) level to calculate the corresponding potentials of mean force (PMFs). Subsequently, analytical expressions were fitted to the PMFs to give the virtual-bond-valence potentials to be used in UNRES. Alanine represented all types of amino-acid residues except glycine and proline. The blocking groups were either the N-acetyl and N',N'-dimethyl or N-acetyl and pyrrolidyl group, depending on whether the residue next in sequence was an alanine-type or a proline residue. A total of 126 potentials (63 symmetry-unrelated potentials for each set of terminally blocking groups) were determined. Together with the torsional, double-torsional, and side-chain-rotamer potentials for polypeptide chains containing d-amino-acid residues determined in our earlier work (Sieradzan et al. J. Chem. Theory Comput., 2012, 8, 4746), the new virtual-bond-angle (θ) potentials now constitute the complete set of physics-based potentials with which to run coarse-grained simulations of systems containing d-amino-acid residues. The ability of the extended UNRES force field to reproduce thermodynamics of polypeptide systems with d-amino-acid residues was tested by comparing the experimentally measured and the calculated free energies of helix formation of model KLALKLALxxLKLALKLA peptides, where x denotes any d- or l- amino-acid residue. The obtained results demonstrate that the UNRES force field with the new potentials reproduce the changes of free energies of helix formation upon d-substitution but overestimate the free energies of helix formation. To test the ability of UNRES with the new potentials to reproduce the structures of polypeptides with d-amino-acid residues, an ab initio replica-exchange folding simulation of thurincin H from Bacillus thuringiensis, which has d-amino-acid residues in the sequence, was carried out. UNRES was able to locate the native α-helical hairpin structure as the dominant structure even though no native sulfide-carbon bonds were present in the simulation.

Kinks, loops, and protein folding, with protein A as an example

The dynamics and energetics of formation of loops in the 46-residue N-terminal fragment of the B-domain of staphylococcal protein A has been studied. Numerical simulations have been performed using coarse-grained molecular dynamics with the united-residue (UNRES) force field. The results have been analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger (DNLS) equation. In the case of proteins, the DNLS equation arises from a C(α)-trace-based energy function. Three individual kink profiles were identified in the experimental three-α-helix structure of protein A, in the range of the Glu16-Asn29, Leu20-Asn29, and Gln33-Asn44 residues, respectively; these correspond to two loops in the native structure. UNRES simulations were started from the full right-handed α-helix to obtain a clear picture of kink formation, which would otherwise be blurred by helix formation. All three kinks emerged during coarse-grained simulations. It was found that the formation of each is accompanied by a local free energy increase; this is expressed as the change of UNRES energy which has the physical sense of the potential of mean force of a polypeptide chain. The increase is about 7 kcal/mol. This value can thus be considered as the free energy barrier to kink formation in full α-helical segments of polypeptide chains. During the simulations, the kinks emerge, disappear, propagate, and annihilate each other many times. It was found that the formation of a kink is initiated by an abrupt change in the orientation of a pair of consecutive side chains in the loop region. This resembles the formation of a Bloch wall along a spin chain, where the C(α) backbone corresponds to the chain, and the amino acid side chains are interpreted as the spin variables. This observation suggests that nearest-neighbor side chain-side chain interactions are responsible for initiation of loop formation. It was also found that the individual kinks are reflected as clear peaks in the principal modes of the analyzed trajectory of protein A, the shapes of which resemble the directional derivatives of the kinks along the chain. These observations suggest that the kinks of the DNLS equation determine the functionally important motions of proteins.