David S. Cerutti

OPLS3: A Force Field Providing Broad Coverage of Drug-like Small Molecules and Proteins

The parametrization and validation of the OPLS3 force field for small molecules and proteins are reported. Enhancements with respect to the previous version (OPLS2.1) include the addition of off-atom charge sites to represent halogen bonding and aryl nitrogen lone pairs as well as a complete refit of peptide dihedral parameters to better model the native structure of proteins. To adequately cover medicinal chemical space, OPLS3 employs over an order of magnitude more reference data and associated parameter types relative to other commonly used small molecule force fields (e.g., MMFF and OPLS_2005). As a consequence, OPLS3 achieves a high level of accuracy across performance benchmarks that assess small molecule conformational propensities and solvation. The newly fitted peptide dihedrals lead to significant improvements in the representation of secondary structure elements in simulated peptides and native structure stability over a number of proteins. Together, the improvements made to both the small molecule and protein force field lead to a high level of accuracy in predicting protein-ligand binding measured over a wide range of targets and ligands (less than 1 kcal/mol RMS error) representing a 30% improvement over earlier variants of the OPLS force field.

Simulations of a Protein Crystal with a High Resolution X-ray Structure: Evaluation of Force Fields and Water Models

We use classical molecular dynamics and 16 combinations of force fields and water models to simulate a protein crystal observed by room-temperature X-ray diffraction. The high resolution of the diffraction data (0.96 Å) and the simplicity of the crystallization solution (nearly pure water) make it possible to attribute any inconsistencies between the crystal structure and our simulations to artifacts of the models rather than inadequate representation of the crystal environment or uncertainty in the experiment. All simulations were extended for 100 ns of production dynamics, permitting some long-time scale artifacts of each model to emerge. The most noticeable effect of these artifacts is a model-dependent drift in the unit cell dimensions, which can become as large as 5% in certain force fields; the underlying cause is the replacement of native crystallographic contacts with non-native ones, which can occur with heterogeneity (loss of crystallographic symmetry) in simulations with some force fields. We find that the AMBER FF99SB force field maintains a lattice structure nearest that seen in the X-ray data, and produces the most realistic atomic fluctuations (by comparison to crystallographic B-factors) of all the models tested. We find that the choice of water model has a minor effect in comparison to the choice of protein model. We also identify a number of artifacts that occur throughout all of the simulations: excessive formation of hydrogen bonds or salt bridges between polar groups and loss of hydrophobic interactions. This study is intended as a foundation for future work that will identify individual parameters in each molecular model that can be modified to improve their representations of protein structure and thermodynamics.

Derivation of fixed partial charges for amino acids accommodating a specific water model and implicit polarization.

We have developed the IPolQ method for fitting nonpolarizable point charges to implicitly represent the energy of polarization for systems in pure water. The method involves iterative cycles of molecular dynamics simulations to estimate the water charge density around the solute of interest, followed by quantum mechanical calculations at the MP2/cc-pV(T+d)Z level to determine updated solute charges. Lennard-Jones parameters are updated starting from the Amber FF99SB nonbonded parameter set to accommodate the new charge model, guided by the comparisons to experimental hydration free energies (HFEs) of neutral amino acid side chain analogs and assumptions about the computed HFEs for charged side chains. These Lennard-Jones parameter adjustments for side-chain analogs are assumed to be transferable to amino acids generally, and new charges for all standard amino acids are then derived in the presence of water modeled by TIP4P-Ew. Overall, the new charges depict substantially more polarized amino acids, particularly in the backbone moieties, than previous Amber charge sets. Efforts to complete a new force field with appropriate torsion parameters for this charge model are underway. The IPolQ method is general and applicable to arbitrary solutes.

Solvent reaction field potential inside an uncharged globular protein: A bridge between implicit and explicit solvent models?

The solvent reaction field potential of an uncharged protein immersed in simple point charge/extended explicit solvent was computed over a series of molecular dynamics trajectories, in total 1560 ns of simulation time. A finite, positive potential of 13-24 kbTec(-1) (where T=300 K), dependent on the geometry of the solvent-accessible surface, was observed inside the biomolecule. The primary contribution to this potential arose from a layer of positive charge density 1.0 A from the solute surface, on average 0.008 ec/A3, which we found to be the product of a highly ordered first solvation shell. Significant second solvation shell effects, including additional layers of charge density and a slight decrease in the short-range solvent-solvent interaction strength, were also observed. The impact of these findings on implicit solvent models was assessed by running similar explicit solvent simulations on the fully charged protein system. When the energy due to the solvent reaction field in the uncharged system is accounted for, correlation between per-atom electrostatic energies for the explicit solvent model and a simple implicit (Poisson) calculation is 0.97, and correlation between per-atom energies for the explicit solvent model and a previously published, optimized Poisson model is 0.99.

ff14ipq: A Self-Consistent Force Field for Condensed-Phase Simulations of Proteins.

We present the ff14ipq force field, implementing the previously published IPolQ charge set for simulations of complete proteins. Minor modifications to the charge derivation scheme and van der Waals interactions between polar atoms are introduced. Torsion parameters are developed through a generational learning approach, based on gas-phase MP2/cc-pVTZ single-point energies computed of structures optimized by the force field itself rather than the quantum benchmark. In this manner, we sacrifice information about the true quantum minima in order to ensure that the force field maintains optimal agreement with the MP2/cc-pVTZ benchmark for the ensembles it will actually produce in simulations. A means of making the gas-phase torsion parameters compatible with solution-phase IPolQ charges is presented. The ff14ipq model is an alternative to ff99SB and other Amber force fields for protein simulations in programs that accommodate pair-specific Lennard–Jones combining rules. The force field gives strong performance on α-helical and β-sheet oligopeptides as well as globular proteins over microsecond time scale simulations, although it has not yet been tested in conjunction with lipid and nucleic acid models. We show how our choices in parameter development influence the resulting force field and how other choices that may have appeared reasonable would actually have led to poorer results. The tools we developed may also aid in the development of future fixed-charge and even polarizable biomolecular force fields.

Configurational-bias sampling technique for predicting side-chain conformations in proteins

Prediction of side‐chain conformations is an important component of several biological modeling applications. In this work, we have developed and tested an advanced Monte Carlo sampling strategy for predicting side‐chain conformations. Our method is based on a cooperative rearrangement of atoms that belong to a group of neighboring side‐chains. This rearrangement is accomplished by deleting groups of atoms from the side‐chains in a particular region, and regrowing them with the generation of trial positions that depends on both a rotamer library and a molecular mechanics potential function. This method allows us to incorporate flexibility about the rotamers in the library and explore phase space in a continuous fashion about the primary rotamers. We have tested our algorithm on a set of 76 proteins using the all‐atom AMBER99 force field and electrostatics that are governed by a distance‐dependent dielectric function. When the tolerance for correct prediction of the dihedral angles is a <20° deviation from the native state, our prediction accuracies for χ1 are 83.3% and for χ1 and χ2 are 65.4%. The accuracies of our predictions are comparable to the best results in the literature that often used Hamiltonians that have been specifically optimized for side‐chain packing. We believe that the continuous exploration of phase space enables our method to overcome limitations inherent with using discrete rotamers as trials.

Dynamics of the streptavidin-biotin complex in solution and in its crystal lattice: distinct behavior revealed by molecular simulations.

We present a 250 ns simulation of the wild-type, biotin-liganded streptavidin tetramer in the solution phase and compare the trajectory to two previously published simulations of the protein in its crystal lattice. By performing both types of simulations, we are able to interpret the proteins behavior in solution in the context of its X-ray structure. We find that the rate of conformational sampling is increased in solution over the lattice environment, although the relevant conformational space in solution is also much larger, as indicated by overall fluctuations in the positions of backbone atoms. We also compare the distributions of chi1 angles sampled by side chains exposed to solvent in the lattice and in the solution phase, obtaining overall good agreement between the distributions obtained in our most rigorous lattice simulation and the crystallographic chi1 angles. We observe changes in the chi1 distributions in the solution phase, and note an apparent progression of the distributions as the environment changes from a tightly packed lattice filled with crystallization media to a bath of pure water. Finally, we examine the interaction of biotin and streptavidin in each simulation, uncovering a possible alternate conformation of the biotin carboxylate tail. We also note that a hydrogen bond observed to break transiently in previous solution-phase simulations is predominantly broken in this much longer solution-phase trajectory; in the lattice simulations, the lattice environment appears to help maintain the hydrogen bond, but more sampling will be needed to confirm whether the simulation model truly gives good agreement with the X-ray data in the lattice simulations. We expect that pairing solution-phase biomolecular simulations with crystal lattice simulations will help to validate simulation models and improve the interpretation of experimentally determined structures.

Peptide crystal simulations reveal hidden dynamics.

Molecular dynamics simulations of biomolecular crystals at atomic resolution have the potential to recover information on dynamics and heterogeneity hidden in X-ray diffraction data. We present here 9.6 μs of dynamics in a small helical peptide crystal with 36 independent copies of the unit cell. The average simulation structure agrees with experiment to within 0.28 Å backbone and 0.42 Å all-atom RMSD; a model refined against the average simulation density agrees with the experimental structure to within 0.20 Å backbone and 0.33 Å all-atom RMSD. The R-factor between the experimental structure factors and those derived from this unrestrained simulation is 23% to 1.0 Å resolution. The B-factors for most heavy atoms agree well with experiment (Pearson correlation of 0.90), but B-factors obtained by refinement against the average simulation density underestimate the coordinate fluctuations in the underlying simulation where the simulation samples alternate conformations. A dynamic flow of water molecules through channels within the crystal lattice is observed, yet the average water density is in remarkable agreement with experiment. A minor population of unit cells is characterized by reduced water content, 310 helical propensity and a gauche(-) side-chain rotamer for one of the valine residues. Careful examination of the experimental data suggests that transitions of the helices are a simulation artifact, although there is indeed evidence for alternate valine conformers and variable water content. This study highlights the potential for crystal simulations to detect dynamics and heterogeneity in experimental diffraction data as well as to validate computational chemistry methods.

Simulations of a protein crystal: explicit treatment of crystallization conditions links theory and experiment in the streptavidin-biotin complex.

A 250 ns molecular dynamics simulation of the biotin-liganded streptavidin crystal lattice, including cryoprotectant molecules and crystallization salts, is compared to a 250 ns simulation of the lattice solvated with pure water. The simulation using detailed crystallization conditions preserves the initial X-ray structure better than the simulation using pure water, even though the protein molecules display comparable mobility in either simulation. Atomic fluctuations computed from the simulation with crystallization conditions closely reproduce fluctuations derived from experimental temperature factors (correlation coefficient of 0.88, omitting two N-terminal residues with very high experimental B-factors). In contrast, fluctuations calculated from the simulation with pure water were less accurate, particularly for two of the streptavidin loops exposed to solvent in the crystal lattice. Finally, we obtain good agreement between the water and cryoprotectant densities obtained from the simulated crystallization conditions and the electron density due to solvent molecules in the X-ray structure. Our results suggest that detailed lattice simulations with realistic crystallization conditions can be used to assess potential function parameters, validate simulation protocols, and obtain valuable insights that solution-phase simulations do not easily provide. We anticipate that this will prove to be a powerful strategy for molecular dynamics simulations of biomolecules.

Further along the Road Less Traveled: AMBER ff15ipq, an Original Protein Force Field Built on a Self-Consistent Physical Model.

We present the AMBER ff15ipq force field for proteins, the second-generation force field developed using the Implicitly Polarized Q (IPolQ) scheme for deriving implicitly polarized atomic charges in the presence of explicit solvent. The ff15ipq force field is a complete rederivation including more than 300 unique atomic charges, 900 unique torsion terms, 60 new angle parameters, and new atomic radii for polar hydrogens. The atomic charges were derived in the context of the SPC/Eb water model, which yields more-accurate rotational diffusion of proteins and enables direct calculation of nuclear magnetic resonance (NMR) relaxation parameters from molecular dynamics simulations. The atomic radii improve the accuracy of modeling salt bridge interactions relative to contemporary fixed-charge force fields, rectifying a limitation of ff14ipq that resulted from its use of pair-specific Lennard-Jones radii. In addition, ff15ipq reproduces penta-alanine J-coupling constants exceptionally well, gives reasonable agreement with NMR relaxation rates, and maintains the expected conformational propensities of structured proteins/peptides, as well as disordered peptides—all on the microsecond (μs) time scale, which is a critical regime for drug design applications. These encouraging results demonstrate the power and robustness of our automated methods for deriving new force fields. All parameters described here and the mdgx program used to fit them are included in the AmberTools16 distribution.