Combining Force Fields and Neural Networks for an Accurate Representation of Bonded Interactions.

We present a formalism of a neural network encoding bonded interactions in molecules. This intramolecular encoding is consistent with the models of intermolecular interactions previously designed by this group. Variants of the encoding fed into a corresponding neural network may be used to economically improve the representation of torsional degrees of freedom in any force field. We test the accuracy of the reproduction of the ab initio potential energy surface on a set of conformations of two dipeptides, methyl-capped ALA and ASP, in several scenarios. The encoding, either alone or in conjunction with an analytical potential, improves agreement with ab initio energies that are on par with those of other neural network-based potentials. Using the encoding and neural nets in tandem with an analytical model places the agreements firmly within "chemical accuracy" of ±0.5 kcal/mol.

Combining Force Fields and Neural Networks for an Accurate Representation of Chemically Diverse Molecular Interactions.

A key goal of molecular modeling is the accurate reproduction of the true quantum mechanical potential energy of arbitrary molecular ensembles with a tractable classical approximation. The challenges are that analytical expressions found in general purpose force fields struggle to faithfully represent the intermolecular quantum potential energy surface at close distances and in strong interaction regimes; that the more accurate neural network approximations do not capture crucial physics concepts, e.g., nonadditive inductive contributions and application of electric fields; and that the ultra-accurate narrowly targeted models have difficulty generalizing to the entire chemical space. We therefore designed a hybrid wide-coverage intermolecular interaction model consisting of an analytically polarizable force field combined with a short-range neural network correction for the total intermolecular interaction energy. Here, we describe the methodology and apply the model to accurately determine the properties of water, the free energy of solvation of neutral and charged molecules, and the binding free energy of ligands to proteins. The correction is subtyped for distinct chemical species to match the underlying force field, to segment and reduce the amount of quantum training data, and to increase accuracy and computational speed. For the systems considered, the hybrid ab initio parametrized Hamiltonian reproduces the two-body dimer quantum mechanics (QM) energies to within 0.03 kcal/mol and the nonadditive many-molecule contributions to within 2%. Simulations of molecular systems using this interaction model run at speeds of several nanoseconds per day.

On the importance of accounting for nuclear quantum effects in ab initio calibrated force fields in biological simulations.

In many important processes in chemistry, physics, and biology the nuclear degrees of freedom cannot be described using the laws of classical mechanics. At the same time, the vast majority of molecular simulations that employ wide-coverage force fields treat atomic motion classically. In light of the increasing desire for and accelerated development of quantum mechanics (QM)-parameterized interaction models, we reexamine whether the classical treatment is sufficient for a simple but crucial chemical species: alkanes. We show that when using an interaction model or force field in excellent agreement with the "gold standard" QM data, even very basic simulated properties of liquid alkanes, such as densities and heats of vaporization, deviate significantly from experimental values. Inclusion of nuclear quantum effects via techniques that treat nuclear degrees of freedom using the laws of classical mechanics brings the simulated properties much closer to reality.

FoldNucleus: web server for the prediction of RNA and protein folding nuclei from their 3D structures.

MOTIVATION: To gain insight into how biopolymers fold as quickly as they do, it is useful to determine which structural elements limit the rate of RNA/protein folding. SUMMARY: We have created a new web server, FoldNucleus. Using this server, it is possible to calculate the folding nucleus for RNA molecules with known 3D structures-including pseudoknots, tRNAs, hairpins and ribozymes-and for protein molecules with known 3D structures, as long as they are smaller than 200 amino acid residues. Researchers can determine and understand which elements of the structure limit the folding process for various types of RNAs and protein molecules. Experimental Ф values for 21 proteins can be found and compared with those determined by our method: http://bioinfo.protres.ru/resources/phi_values.htm. AVAILABILITY AND IMPLEMENTATION: http://bioinfo.protres.ru/foldnucleus/. CONTACT: ogalzit@vega.protres.ru.

What handedness and angles between helices has the studied three-helical protein domain?

We have created a new server FoldHandedness. Using this server it is possible: (i) to define the regions of helices from two issues (from the PDB file and using the last version of the DSSP program), (ii) to determine the handedness for any chosen three helices and (iii) to calculate the angle and sign between the chosen pairs of the helices for large proteins and complexes of proteins with DNA or RNA.

Prediction of cyclohexane-water distribution coefficient for SAMPL5 drug-like compounds with the QMPFF3 and ARROW polarizable force fields.

We present the performance of blind predictions of water-cyclohexane distribution coefficients for 53 drug-like compounds in the SAMPL5 challenge by three methods currently in use within our group. Two of them utilize QMPFF3 and ARROW, polarizable force-fields of varying complexity, and the third uses the General Amber Force-Field (GAFF). The polarizable FF's are implemented in an in-house MD package, Arbalest. We find that when we had time to parametrize the functional groups with care (batch 0), the polarizable force-fields outperformed the non-polarizable one. Conversely, on the full set of 53 compounds, GAFF performed better than both QMPFF3 and ARROW. We also describe the torsion-restrain method we used to improve sampling of molecular conformational space and thus the overall accuracy of prediction. The SAMPL5 challenge highlighted several drawbacks of our force-fields, such as our significant systematic over-estimation of hydrophobic interactions, specifically for alkanes and aromatic rings.

The Determination of Free Energy of Hydration of Water Ions from First Principles.

We model the autoionization of water by determining the free energy of hydration of the major intermediate species of water ions. We represent the smallest ions─the hydroxide ion OH-, the hydronium ion H3O+, and the Zundel ion H5O2+─by bonded models and the more extended ionic structures by strong nonbonded interactions (e.g., the Eigen H9O4+ = H3O+ + 3(H2O) and the Stoyanov H13O6+ = H5O2+ + 4(H2O)). Our models are faithful to the precise QM energies and their components to within 1% or less. Using the calculated free energies and atomization energies, we compute the pKa of pure water from first principles as a consistency check and arrive at a value within 1.3 log units of the experimental one. From these calculations, we conclude that the hydronium ion, and its hydrated state, the Eigen cation, are the dominant species in the water autoionization process.

Neural Network Corrections to Intermolecular Interaction Terms of a Molecular Force Field Capture Nuclear Quantum Effects in Calculations of Liquid Thermodynamic Properties.

We incorporate nuclear quantum effects (NQE) in condensed matter simulations by introducing short-range neural network (NN) corrections to the ab initio fitted molecular force field ARROW. Force field NN corrections are fitted to average interaction energies and forces of molecular dimers, which are simulated using the Path Integral Molecular Dynamics (PIMD) technique with restrained centroid positions. The NN-corrected force field allows reproduction of the NQE for computed liquid water and methane properties such as density, radial distribution function (RDF), heat of evaporation (HVAP), and solvation free energy. Accounting for NQE through molecular force field corrections circumvents the need for explicit computationally expensive PIMD simulations in accurate calculations of the properties of chemical and biological systems. The accuracy and locality of pairwise NN NQE corrections indicate that this approach could be applicable to complex heterogeneous systems, such as proteins.

Right- and left-handed three-helix proteins. I. Experimental and simulation analysis of differences in folding and structure.

Despite the large number of publications on three-helix protein folding, there is no study devoted to the influence of handedness on the rate of three-helix protein folding. From the experimental studies, we make a conclusion that the left-handed three-helix proteins fold faster than the right-handed ones. What may explain this difference? An important question arising in this paper is whether the modeling of protein folding can catch the difference between the protein folding rates of proteins with similar structures but with different folding mechanisms. To answer this question, the folding of eight three-helix proteins (four right-handed and four left-handed), which are similar in size, was modeled using the Monte Carlo and dynamic programming methods. The studies allowed us to determine the orders of folding of the secondary-structure elements in these domains and amino acid residues which are important for the folding. The obtained data are in good correlation with each other and with the experimental data. Structural analysis of these proteins demonstrated that the left-handed domains have a lesser number of contacts per residue and a smaller radius of cross section than the right-handed domains. This may be one of the explanations of the observed fact. The same tendency is observed for the large dataset consisting of 332 three-helix proteins (238 right- and 94 left-handed). From our analysis, we found that the left-handed three-helix proteins have some less-dense packing that should result in faster folding for some proteins as compared to the case of right-handed proteins.

Protein-Ligand Binding Free-Energy Calculations with ARROW─A Purely First-Principles Parameterized Polarizable Force Field.

Protein-ligand binding free-energy calculations using molecular dynamics (MD) simulations have emerged as a powerful tool for in silico drug design. Here, we present results obtained with the ARROW force field (FF)─a multipolar polarizable and physics-based model with all parameters fitted entirely to high-level ab initio quantum mechanical (QM) calculations. ARROW has already proven its ability to determine solvation free energy of arbitrary neutral compounds with unprecedented accuracy. The ARROW FF parameterization is now extended to include coverage of all amino acids including charged groups, allowing molecular simulations of a series of protein-ligand systems and prediction of their relative binding free energies. We ensure adequate sampling by applying a novel technique that is based on coupling the Hamiltonian Replica exchange (HREX) with a conformation reservoir generated via potential softening and nonequilibrium MD. ARROW provides predictions with near chemical accuracy (mean absolute error of ∼0.5 kcal/mol) for two of the three protein systems studied here (MCL1 and Thrombin). The third protein system (CDK2) reveals the difficulty in accurately describing dimer interaction energies involving polar and charged species. Overall, for all of the three protein systems studied here, ARROW FF predicts relative binding free energies of ligands with a similar accuracy level as leading nonpolarizable force fields.

Accurate determination of solvation free energies of neutral organic compounds from first principles.

The main goal of molecular simulation is to accurately predict experimental observables of molecular systems. Another long-standing goal is to devise models for arbitrary neutral organic molecules with little or no reliance on experimental data. While separately these goals have been met to various degrees, for an arbitrary system of molecules they have not been achieved simultaneously. For biophysical ensembles that exist at room temperature and pressure, and where the entropic contributions are on par with interaction strengths, it is the free energies that are both most important and most difficult to predict. We compute the free energies of solvation for a diverse set of neutral organic compounds using a polarizable force field fitted entirely to ab initio calculations. The mean absolute errors (MAE) of hydration, cyclohexane solvation, and corresponding partition coefficients are 0.2 kcal/mol, 0.3 kcal/mol and 0.22 log units, i.e. within chemical accuracy. The model (ARROW FF) is multipolar, polarizable, and its accompanying simulation stack includes nuclear quantum effects (NQE). The simulation tools' computational efficiency is on a par with current state-of-the-art packages. The construction of a wide-coverage molecular modelling toolset from first principles, together with its excellent predictive ability in the liquid phase is a major advance in biomolecular simulation.

Is there an advantageous arrangement of aromatic residues in proteins? Statistical analysis of aromatic interactions in globular proteins.

The aim of this study was to evaluate the favorability of different conformations of aromatic residues in proteins by analysing the occurrence of particular conformations. The clustering of protein structures from the Protein Data Bank (PDB) was performed. Conformations of interacting aromatic residues were analyzed for 511 282 pairs in 35 493 protein structures sharing less than 50% identity. Pairs with a parallel arrangement of aromatic residues made up 6.2% of all possible ones, which was twice as much as expected. Pairs with a perpendicular arrangement of aromatic residues made up 25%. We demonstrate that the most favorable arrangement was at an angle of 60° between the interacting aromatic residues. Among all possible aromatic pairs, the His-His pair was twice as frequent as expected, and the His-Phe pair was less frequent than expected. A server (CARP - Contacts of Aromatic Residues in Proteins) has been created for calculating essential structural features of interacting aromatic residues in proteins: http://bioproteom.protres.ru/arom_q_prog/.

Assessment of performance of the general purpose polarizable force field QMPFF3 in condensed phase.

The recently introduced force field (FF) QMPFF3 is thoroughly validated in gas, liquid, and solid phases. For the first time, it is demonstrated that a physically well-grounded general purpose FF fitted exclusively to a comprehensive set of high level vacuum quantum mechanical data applied as it is to simulation of condensed phase provides high transferability for a wide range of chemical compounds. QMPFF3 demonstrates accuracy comparable with that of the FFs explicitly fitted to condensed phase data, but due to high transferability it is expected to be successful in simulating large molecular complexes.

On the universe of protein folds.

In the fifty years since the first atomic structure of a protein was revealed, tens of thousands of additional structures have been solved. Like all objects in biology, proteins structures show common patterns that seem to define family relationships. Classification of proteins structures, which started in the 1970s with about a dozen structures, has continued with increasing enthusiasm, leading to two main fold classifications, SCOP and CATH, as well as many additional databases. Classification is complicated by deciding what constitutes a domain, the fundamental unit of structure. Also difficult is deciding when two given structures are similar. Like all of biology, fold classification is beset by exceptions to all rules. Thus, the perspectives of protein fold space that the fold classifications offer differ from each other. In spite of these ambiguities, fold classifications are useful for prediction of structure and function. Studying the characteristics of fold space can shed light on protein evolution and the physical laws that govern protein behavior.

Development and testing of PFFSol1.1, a new polarizable atomic force field for calculation of molecular interactions in implicit water environment.

A detailed calculation of protein interactions with explicitly considered water molecules takes enormous time. If water is considered implicitly (as media rather than as molecules), calculations become faster. These calculations are less precise, unless one uses voluminous computations of solvent-accessible areas. Our goal is to obtain parameters for nonbonded atom-atom interactions in implicitly considered water without computation of solvent-accessible areas. Because the "in-vacuum" interactions of atoms are obtained from experimental structures of crystals and enthalpies of their sublimation, the "in-water" interactions must be corrected using solvation free energies obtained from Henry's constants. Thus, we obtained parameters for the in-water van der Waals, electrostatic, and polarized interactions for atoms typical of protein structures. Parameters of covalent interactions were taken from the ENCAD force field and partial charges of atoms from quantum-mechanical calculations. The sought parameters of the in-water nonbonded interactions were optimized to achieve the best description of crystal structures and their sublimation and solvation at the room temperature. With the optimized parameters, the correlation between the calculated and experimental cohesion of molecules in crystals is 98.3% in the in-vacuum case (the supplementary force field PFFSubl1.1) and 95.4% the in-water case (the sought force field PFFSol1.1).