Using PC clusters to evaluate the transferability of molecular mechanics force fields for proteins

The transferability of molecular mechanics parameters derived for small model systems to larger biopolymers such as proteins can be difficult to assess. Even for small peptides, molecular dynamics simulations are typically too short to sample structures significantly different than initial conformations, making comparison to experimental data questionable. We employed a PC cluster to generate large numbers of native and non-native conformations for peptides with experimentally measured structural data, one predominantly helical and the other forming a beta-hairpin. These atomic-detail sets do not suffer from slow convergence, and can be used to rapidly evaluate important force field properties. In this case a suspected bias toward alpha-helical conformations in the ff94 and ff99 force fields distributed with the AMBER package was verified. The sets provide critical feedback not only on force field transferability, but may also predict modifications for improvement. Such predictions were used to modify the ff99 parameter set, and the resulting force field was used to test stability and folding of model peptides. Structural behavior during molecular dynamics with the modified force field is found to be very similar to expectations, suggesting that these basis sets of conformations may themselves have significant transferability among force fields. We continue to improve and expand this data set and plan to make it publicly accessible. The calculations involved in this process are trivially parallel and can be performed using inexpensive personal computers with commodity components.     

Recent applications and developments of charge equilibration force fields for modeling dynamical charges in classical molecular dynamics simulations

With the continuing advances in computational hardware and novel force fields constructed using quantum mechanics, the outlook for non-additive force fields is promising. Our work in the past several years has demonstrated the utility of polarizable force fields, in our hands those based on the charge equilibration formalism, for a broad range of physical and biophysical systems. We have constructed and applied polarizable force fields for small molecules, proteins, lipids, and lipid bilayers and recently have begun work on carbohydrate force fields. The latter area has been relatively untouched by force field developers with particular focus on polarizable, non-additive interaction potential models. In this review of our recent work, we discuss the formalism we have adopted for implementing the charge equilibration method for phase-dependent polarizable force fields, lipid molecules, and small-molecule carbohydrates. We discuss the methodology, related issues, and briefly discuss results from recent applications of such force fields.     

On the use of electrostatic potential derived charges in molecular mechanics force fields. The relative solvation free energy of cis- and trans-N-methyl-acetamide

We have carried out free energy perturbation calculations on the relative solvation free energy of cis- and trans-N-methyl-acetamide (NMA). Experimentally, the solvation free energy difference has been found to be near zero. Using 6-31G* ab initio electrostatic potential derived charges for both the cis and trans conformations, we calculate a solvation free energy difference of 0.1 ± 0.1 kcal/mol. Using the 6-31G* charges derived for the trans conformation for both the cis and trans models leads to a solvation free energy difference of 0.9 ± 0.1 kcal/mol, compared to the value of 2.2 kcal/mol determined for the OPLS model for trans-NMA.     

Tailor-made force fields for crystal-structure prediction

A general procedure is presented to derive a complete set of force-field parameters for flexible molecules in the crystalline state on a case-by-case basis. The force-field parameters are fitted to the electrostatic potential as well as to accurate energies and forces generated by means of a hybrid method that combines solid-state density functional theory (DFT) calculations with an empirical van der Waals correction. All DFT calculations are carried out with the VASP program. The mathematical structure of the force field, the generation of reference data, the choice of the figure of merit, the optimization algorithm, and the parameter-refinement strategy are discussed in detail. The approach is applied to cyclohexane-1,4-dione, a small flexible ring. The tailor-made force field obtained for cyclohexane-1,4-dione is used to search for low-energy crystal packings in all 230 space groups with one molecule per asymmetric unit, and the most stable crystal structures are reoptimized in a second step with the hybrid method. The experimental crystal structure is found as the most stable predicted crystal structure both with the tailor-made force field and the hybrid method. The same methodology has also been applied successfully to the four compounds of the fourth CCDC blind test on crystal-structure prediction. For the five aforementioned compounds, the root-mean-square deviations between lattice energies calculated with the tailor-made force fields and the hybrid method range from 0.024 to 0.053 kcal/mol per atom around an average value of 0.034 kcal/mol per atom.     

Accounting for electronic polarization in non-polarizable force fields

The issues of electronic polarizability in molecular dynamics simulations are discussed. We argue that the charges of ionized groups in proteins, and charges of ions in conventional non-polarizable force fields such as CHARMM, AMBER, GROMOS, etc should be scaled by a factor about 0.7. Our model explains why a neglect of electronic solvation energy, which typically amounts to about a half of total solvation energy, in non-polarizable simulations with un-scaled charges can produce a correct result; however, the correct solvation energy of ions does not guarantee the correctness of ion-ion pair interactions in many non-polarizable simulations. The inclusion of electronic screening for charged moieties is shown to result in significant changes in protein dynamics and can give rise to new qualitative results compared with the traditional non-polarizable force field simulations. The model also explains the striking difference between the value of water dipole μ～ 3D reported in recent ab initio and experimental studies with the value μ(eff)～ 2.3D typically used in the empirical potentials, such as TIP3P or SPC/E. It is shown that the effective dipole of water can be understood as a scaled value μ(eff) = μ/√ε(el), where ε(el) = 1.78 is the electronic (high-frequency) dielectric constant of water. This simple theoretical framework provides important insights into the nature of the effective parameters, which is crucial when the computational models of liquid water are used for simulations in different environments, such as proteins, or for interaction with solutes.     

Reactive force fields for proton transfer dynamics

A force field-inspired method based on fitted, high-quality multidimensional potential energy surfaces to follow proton transfer (PT) reactions in molecular dynamics simulations is presented. In molecular mechanics with proton transfer (MMPT) a system is partitioned into a region where proton transfer takes place and the remaining degrees of freedom which are treated with a conventional force field. The implementation of the method and applications to specific chemically and biologically relevant scenarios are presented. MMPT is developed in view of two primary areas in mind: to follow the molecular dynamics of proton transfer in the condensed phase on realistic time scales and to adapt the shape (morphing) of the potential energy surface for specific applications. MMPT is applied to PT in protonated ammonia dimer, double proton transfer in 2-pyridone-2-hydroxypyridine, and the first step of PT from a protein side-chain towards a buried [3Fe4S] cluster in ferredoxin I. Specific findings of the work include the fundamental role of the N-N vibration as the gating mode for PT in NH4+...NH3 and the qualitative understanding of PT from the protein to a metastable active-site water molecule in Ferredoxin I.     

Automated site-directed drug design: An assessment of the transferability of atomic residual charges (CNDO) for molecular fragments

Summary In this paper a database of atomic residual charges has been constructed for all the molecular fragments defined previously in a combinatorial search of the Cambridge Structural Database. The charges generated for the atoms in each fragment are compared with charges calculated for whole molecules containing those fragments. The fragment atomic charges lie within 1 S.D. of the mean for 68%, and within 2 S.D. for 91%, of the atoms whose charges were computed for whole molecules. The actual charges on any atom are strongly influenced by the adjacent connected atoms. There is a large spread of atomic residual charge within the fragments database.     

The use of ultraviolet resonance Raman intensities to test proposed molecular force fields for nucleic acid bases

The harmonic molecular force fields for the nucleic acid bases, cytosine, and guanine, that have been previously published by several investigators are tested by the calculation of the relative intensities of the in-plane modes in the ultraviolet resonance Raman (UVRR) effect from the two lowest lying absorption bands using a theoretical approach devised previously.^1–3 Since only a fraction of the 2N – 3 in-plane vibrations of a molecule are active in the UVRR, the two criteria that are taken for the adjustment of the force constant are: (1) the closest possible agreement between the observed and calculated frequencies of the 2N – 3 in-plane vibrations, and (2) the closest possible agreement between the calculated and observed intensities of those few vibrations that are strongly active in the ultraviolet resonance Raman effect. In particular it is necessary that the force constants be adjusted to avoid the calculation of intense Raman lines with frequencies that are not observed in the UVRR spectrum. Using this criteria, a new force field has been developed that appears to give better agreement with the observed UVRR intensities than previously published ones. It is suggested that this calculation of the UVRR intensities can be used to refine molecular force fields in combination with other methods such as isotopic replacement currently in use to refine force constants.     

Polarizable and nonpolarizable force fields for alkyl nitrates

Quantum-chemistry-based many-body polarizable and two-body nonpolarizable atomic force fields were developed for alkyl nitrate liquids and pentaerythritol tetranitrate (PETN) crystal. Bonding, bending, and torsional parameters, partial charges, and atomic polarizabilities for the polarizable force field were determined from gas-phase quantum chemistry calculations for alkyl nitrate oligomers and PETN performed at the MP2/aug-cc-pvDz level of theory. Partial charges for the nonpolarizable force field were determined by fitting the dipole moments and electrostatic potential to values for PETN molecules in the crystal phase obtained from molecular dynamics simulations using the polarizable force field. Molecular dynamics simulations of alkyl nitrate liquids and two polymorphs of PETN crystal demonstrate the ability of the quantum-chemistry-based force fields to accurately predict thermophysical and mechanical properties of these materials.     

Scaling of quantum-mechanical molecular force fields

Comparative analysis of various methods of empirical scaling of quantum-mechanical harmonic molecular force fields has been performed. The efficiency of using each particular scaling technique was shown to depend on the theoretical level of the quantum-mechanical calculation. The Pulay method of scaling (congruent transformation of the force constant matrix) is applicable in the case where the relative accuracies of determination of diagonal and off-diagonal quantum-mechanical force constants are approximately equal. This requirement is satisfied for a quantum-mechanical force field determined close to the HartreeFock limit. This makes it possible to carry out its correction with maximum retention of the peculiarities inherent in the molecule under investigation.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 840–807, April, 1996.     

A transferable active-learning strategy for reactive molecular force fields

Predictive molecular simulations require fast, accurate and reactive interatomic potentials. Machine learning offers a promising approach to construct such potentials by fitting energies and forces to high-level quantum-mechanical data, but doing so typically requires considerable human intervention and data volume. Here we show that, by leveraging hierarchical and active learning, accurate Gaussian Approximation Potential (GAP) models can be developed for diverse chemical systems in an autonomous manner, requiring only hundreds to a few thousand energy and gradient evaluations on a reference potential-energy surface. The approach uses separate intra- and inter-molecular fits and employs a prospective error metric to assess the accuracy of the potentials. We demonstrate applications to a range of molecular systems with relevance to computational organic chemistry: ranging from bulk solvents, a solvated metal ion and a metallocage onwards to chemical reactivity, including a bifurcating Diels–Alder reaction in the gas phase and non-equilibrium dynamics (a model S_N2 reaction) in explicit solvent. The method provides a route to routinely generating machine-learned force fields for reactive molecular systems.

An efficient strategy for training Gaussian Approximation Potential (GAP) models to study chemical reactions using hierarchical and active learning.     

Empirical force fields for complex hydrated calcio-silicate layered materials

The use of empirical force fields is now a standard approach in predicting the properties of hydrated oxides which are omnipresent in both natural and engineering applications. Transferability of force fields to analogous hydrated oxides without rigorous investigations may result in misleading property predictions. Herein, we focus on two common empirical force fields, the simple point charge ClayFF potential and the core-shell potential to study tobermorite minerals, the most prominent family of Calcium-Silicate-Hydrates that are complex hydrated oxides. We benchmark the predictive capabilities of these force fields against first principles results. While the structural information seem to be in close agreement with DFT results, we find that for higher order properties such as elastic constants, the core-shell potential quantitatively improves upon the simple point charge model, and shows a larger degree of transferability to complex materials. In return, to remedy the deficiencies of the simple point charge potential for hydrated calcio-silicates, we suggest using both structural data and elasticity data for potential calibration, a new force field potential, CSH-FF. This re-parameterized version of ClayFF is then applied to simulating an atomistic model of cement (Pellenq et al., PNAS, 2009). We demonstrate that this force field improves the predictive capabilities of ClayFF, being considerably less computational intensive than the core-shell model.     

On the representation of force fields for chemically reacting systems

“Relaxed” force constants are uniquely defined for systems involving redundant coordinates, in contradistinction to the usual “rigid” force constants, and thus their use allows meaningful correlations to be made between force fields calculated for reactants, transition state, and product of a chemical reaction, for example formaldehyde hydration.     

Empirical force fields for biologically active divalent metal cations in water

We have presented a strategy for deriving ion-water van der Waals (vdW) parameters that implicitly include the microscopic solvent molecular effects around the ion. The strategy can be used to obtain vdW parameters for metal cations of the same formal charge and known experimental hydration free energies. In this work, it was applied to derive the vdW parameters for 24 divalent metal ions with measured hydration free energies ranging from -300 to -572 kcal/mol, coordination numbers (CNs) from 4 to 15, and ion-O (water) distances from 1.67 to 2.90 angstroms. The strategy used to derive the vdW parameters employs (1) a numerical procedure that links the coupling parameter used in free energy simulations with the experimental hydration free energies and (2) the first-shell CNs and structure for the entire series of divalent cations. One of the parameter sets obtained (referred to as MWc) simultaneously reproduces the observed (i) relative hydration free energies, (ii) first-shell CNs, and (iii) average ion-water distances of all the dications studied. In particular, the MWc parameters reproduce the observed (i) decrease in the CN from 6 for Cu2+ to 4 for Be2+, (ii) no change in the CN of 6 for dications with hydration free energies between those of Cu2+ and Cd2+, and (iii) an expansion of the CN from 6 for Cd2+ to 9.5 for Ba2+. The ion-water parameters derived herein represent a first step in the simulations of metalloproteins, which will also require potential energy functions incorporating polarizability, charge transfer, and other electronic effects to accurately model the protein-metal interactions in aqueous solution.     

Automatic parameterization of force fields for liquids by simplex optimization

In this study we demonstrate an automatic method of force field development for molecular simulations. Parameter tuning is taken as an optimization problem in many dimensions. The parameters are automatically adapted to reproduce known experimental data such as the density and the heat of vaporization. Our method is more systematic than guessing parameters and, at the same time, saves human labor in parameterization. It was applied successfully to several molecular liquids. As a test, force fields for 2-methylpentane, tetrahydrofurane, cyclohexene, and cyclohexane were developed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1009–1017, 1999     

Modification of Morse potential in conventional force fields for applying FPDP parameters

Although the Morse potential function is widely used in molecular modeling software, newer potential functions that possess more parameters provide greater accuracy. Against this backdrop, the Four-Parameter-Diatomic-Potential (FPDP) was selected for converting its parameter into those of the Morse potential due to the former’s resemblance to the latter. A pair of modified Morse indices was extracted by imposing equal force constant for infinitesimal bond stretching and equal energy integral for complete interatomic separation. Results reveal very good agreement for both bond compression and bond stretching. The developed parameter conversion would enable all FPDP parameters to be converted into the modified Morse parameters. Only minor algorithm alterations are required for incorporating the modified Morse function into molecular modeling packages that adopt the conventional Morse potential for describing 2-body bonded interaction.