Automated Parameterization of Quantum Mechanically Derived Force Fields for Soft Materials and Complex Fluids: Development and Validation.

Development of accurate force field parameters for molecular ions in the context of a polarizable energy function based on the classical Drude oscillator is a crucial step toward an accurate polarizable model for modeling and simulations of biological macromolecules. Toward this goal we have undertaken a hierarchical approach in which force field parameter optimization is initially performed for small molecules for which experimental data exists that serve as building blocks of macromolecular systems. Small molecules representative of the ionic moieties of biological macromolecules include the cationic ammonium and methyl substituted ammonium derivatives, imidazolium, guanidinium and methylguanidinium, and the anionic acetate, phenolate, and alkanethiolates. In the present work, parameters for molecular ions in the context of the Drude polarizable force field are optimized and compared to results from the nonpolarizable additive CHARMM general force field (CGenFF). Electrostatic and Lennard-Jones parameters for the model compounds are developed in the context of the polarizable SWM4-NDP water model, with emphasis on assuring that the hydration free energies are consistent with previously reported parameters for atomic ions. The final parameters are shown to be in good agreement with the selected quantum mechanical (QM) and experimental target data. Analysis of the structure of water around the ions reveals substantial differences between the Drude and additive force fields indicating the important role of polarization in dictating the molecular details of aqueous solvation. The presented parameters represent the foundation for the charged functionalities in future generations of the Drude polarizable force field for biological macromolecules as well as for drug-like molecules.

The structural flexibility of DNA plays a key role in many biological processes of DNA, such as protein-DNA interactions, DNA packaging in viruses and nucleosome positioning on genomic DNA. Some experimental techniques have been employed to investigate the structural flexibility of DNA with the combination of elastic models, but these experiments could only provide the macroscopic properties of DNA, and thus, it is still difficult to understand the corresponding microscopic mechanisms. Recently, all-atom molecular dynamics (MD) simulation has emerged as a useful tool to investigate not only the macroscopic properties of DNA, but also the microscopic description of the flexibility of DNA at an atomic level. The most important issue in all-atom MD simulations of DNA is to choose an appropriate force field for simulating DNA. Very recently, a new force field for DNA has been developed based on the last generation force field of Amber bsc0, which was named Amber bsc1. In this work, all-atom MD simulations are employed to study the flexibility of a 30-bp DNA with the force fields of Amber bsc1 and Amber bsc0 in a comparative way. Our aim of the research is to examine the improvement of the new development of force field (Amber bsc1) in the macroscopic and microscopic properties of DNA, in comparison with the corresponding experimental measurements. All the MD simulations are performed with Gromacs 4.6 and lasted with a simulation time of 600 ns. The MD trajectories are analyzed with Curves+ for the last 500 ns, since the system reaches equilibrium approximately after ~100 ns. Our results show that the new force field (Amber bsc1) can lead to the improvements in the macroscopic parameters of DNA flexibility, i.e., stretch modulus S and twist-stretch coupling D become closer to experimental measurements, while bending persistence lengths lp and torsional persistence lengths C from the two force fields (bsc1 and bsc0) are both in good agreement with experimental data. Our microscopic analyses show that the microscopic structure parameters of DNA from the MD simulation with the Amber bsc1 force field are closer to the experimental values than those with the Amber bsc0 force field, except for slide, and the obvious improvements are observed in some microscopic parameters such as twist and inclination. Our further analyses show that the improvements in macroscopic flexibility from the Amber bsc1 force field are tightly related to the microscopic parameters and their fluctuations. This study would be helpful in understanding the performances of Amber bsc1 and bsc0 force fields in the description of DNA flexibility at both macroscopic and microscopic level.

Polyunsaturated lipids are an essential component of biological membranes, influencing order and dynamics of lipids, protein-lipid interaction, and membrane transport properties. To gain an atomic level picture of the impact of polyunsaturation on membrane properties, quantum mechanical (QM) and empirical force field based calculations have been undertaken. The QM calculations of the torsional energy surface for rotation about vinyl-methylene bonds reveal low barriers to rotation, indicating an intrinsic propensity toward flexibility. Based on QM and experimental data, empirical force field parameters were developed for polyunsaturated lipids and applied in a 16 ns molecular dynamics (MD) simulation of a 1-stearoyl-2-docosahexaenoyl-sn-glyerco-3-phosphocholine (SDPC) lipid bilayer. The simulation results are in good agreement with experimental data, suggesting an unusually high degree of conformational flexibility of polyunsaturated hydrocarbon chains in membranes. The detailed analysis of chain conformation and dynamics by simulations is aiding the interpretation of experimental data and is useful for understanding the unique role of polyunsaturated lipids in biological membranes. The complete force field is included as Supporting Information and is available from http://www.pharmacy.umaryland.edu/faculty/amackere/research.html.

Structure and dynamics are both critical to RNA’s vital functions in biology. Numerous techniques can elucidate the structural dynamics of RNA, but computational approaches based on experimental data arguably hold the promise of providing the most detail. In this Account, we highlight areas wherein molecular dynamics (MD) and quantum mechanical (QM) techniques are applied to RNA, particularly in relation to complementary experimental studies.We have expanded on atomic-resolution crystal structures of RNAs in functionally relevant states by applying explicit solvent MD simulations to explore their dynamics and conformational changes on the submicrosecond time scale. MD relies on simplified atomistic, pairwise additive interaction potentials (force fields). Because of limited sampling, due to the finite accessible simulation time scale and the approximated force field, high-quality starting structures are required.Despite their imperfection, we find that currently available force fields empower MD to provide meaningful and predictive information on RNA dynamics around a crystallographically defined energy minimum. The performance of force fields can be estimated by precise QM calculations on small model systems. Such calculations agree reasonably well with the Cornell et al. AMBER force field, particularly for stacking and hydrogen-bonding interactions. A final verification of any force field is accomplished by simulations of complex nucleic acid structures.The performance of the Cornell et al. AMBER force field generally corresponds well with and augments experimental data, but one notable exception could be the capping loops of double-helical stems. In addition, the performance of pairwise additive force fields is obviously unsatisfactory for inclusion of divalent cations, because their interactions lead to major polarization and charge-transfer effects neglected by the force field. Neglect of polarization also limits, albeit to a lesser extent, the description accuracy of other contributions, such as interactions with monovalent ions, conformational flexibility of the anionic sugar−phosphate backbone, hydrogen bonding, and solute polarization by solvent. Still, despite limitations, MD simulations are a valid tool for analyzing the structural dynamics of existing experimental structures. Careful analysis of MD simulations can identify problematic aspects of an experimental RNA structure, unveil structural characteristics masked by experimental constraints, reveal functionally significant stochastic fluctuations, evaluate the structural role of base ionization, and predict structurally and potentially functionally important details of the solvent behavior, including the presence of tightly bound water molecules. Moreover, combining classical MD simulations with QM calculations in hybrid QM/MM approaches helps in the assessment of the plausibility of chemical mechanisms of catalytic RNAs (ribozymes).In contrast, the reliable prediction of structure from sequence information is beyond the applicability of MD tools. The ultimate utility of computational studies in understanding RNA function thus requires that the results are neither blindly accepted nor flatly rejected, but rather considered in the context of all available experimental data, with great care given to assessing limitations through the available starting structures, force field approximations, and sampling limitations. The examples given in this Account showcase how the judicious use of basic MD simulations has already served as a powerful tool to help evaluate the role of structural dynamics in biological function of RNA.

Understanding the interaction of ligands with biomolecules is an integral component of drug discovery and development. Challenges for computing thermodynamic and kinetic quantities for pharmaceutically relevant receptor-ligand complexes include the size and flexibility of the ligands, large-scale conformational rearrangements of the receptor, accurate force field parameters, simulation efficiency, and sufficient sampling associated with rare events. Our recently developed multiscale milestoning simulation approach, SEEKR2 (Simulation Enabled Estimation of Kinetic Rates v.2), has demonstrated success in predicting unbinding (koff) kinetics by employing molecular dynamics (MD) simulations in regions closer to the binding site. The MD region is further subdivided into smaller Voronoi tessellations to improve the simulation efficiency and parallelization. To date, all MD simulations are run using general molecular mechanics (MM) force fields. The accuracy of calculations can be further improved by incorporating quantum mechanical (QM) methods into generating system-specific force fields through reparameterizing ligand partial charges in the bound state. The force field reparameterization process modifies the potential energy landscape of the bimolecular complex, enabling a more accurate representation of the intermolecular interactions and polarization effects at the bound state. We present QMrebind (Quantum Mechanical force field reparameterization at the receptor-ligand binding site), an ORCA-based software that facilitates reparameterizing the potential energy function within the phase space representing the bound state in a receptor-ligand complex. With SEEKR2 koff estimates and experimentally determined kinetic rates, we compare and interpret the receptor-ligand unbinding kinetics obtained using the newly reparameterized force fields for model host-guest systems and HSP90-inhibitor complexes. This method provides an opportunity to achieve higher accuracy in predicting receptor-ligand koff rate constants.

A previously introduced polarizable simulations with second-order interaction model (POSSIM) force field has been extended to include parameters for small molecules serving as models for peptide and protein side-chains. Parameters have been fitted to permit reproducing many-body energies, gas-phase dimerization energies, and geometries and liquid-phase heats of vaporization and densities. Quantum mechanical and experimental data have been used as the target for the fitting. The POSSIM framework combines accuracy of a polarizable force field and computational efficiency of the second-order approximation of the full-scale induced point dipole polarization formalism. The resulting parameters can be used for simulations of the parameterized molecules themselves or their analogues. In addition to this, these force field parameters are currently being used in further development of the POSSIM fast polarizable force field for proteins.

The role of ribonucleic acid (RNA) in biology continues to grow, but insight into important aspects of RNA behavior is lacking, such as dynamic structural ensembles in different environments, how flexibility is coupled to function, and how function might be modulated by small molecule binding. In the case of proteins, much progress in these areas has been made by complementing experiments with atomistic simulations, but RNA simulation methods and force fields are less mature. It remains challenging to generate stable RNA simulations, even for small systems where well-defined, thermostable structures have been established by experiments. Many different aspects of RNA energetics have been adjusted in force fields, seeking improvements that are transferable across a variety of RNA structural motifs. In this work, the role of weak CH···O interactions is explored, which are ubiquitous in RNA structure but have received less attention in RNA force field development. By comparing data extracted from high-resolution RNA crystal structures to energy profiles from quantum mechanics and force field calculations, it is shown that CH···O interactions are overly repulsive in the widely used Amber RNA force fields. A simple, targeted adjustment of CH···O repulsion that leaves the remainder of the force field unchanged was developed. Then, the standard and modified force fields were tested using molecular dynamics (MD) simulations with explicit water and salt, amassing over 300 μs of data for multiple RNA systems containing important features such as the presence of loops, base stacking interactions as well as canonical and noncanonical base pairing. In this work and others, standard force fields lead to reproducible unfolding of the NMR-based structures. Including a targeted CH···O adjustment in an otherwise identical protocol dramatically improves the outcome, leading to stable simulations for all RNA systems tested.

Molecular dynamic (MD) simulations using the BMS nucleic acid force field produce environment and sequence dependent DNA conformations that closely mimic experimentally derived structures. The parameters were initially developed to reproduce the potential energy surface, as defined by quantum mechanics, for a set of small molecules that can be used as the building blocks for nucleic acid macromolecules (dimethyl phosphate, cyclopentane, tetrahydrofuran, etc.). Then the dihedral parameters were fine tuned using a series of condensed phase MD simulations of DNA and RNA (in zero added salt, 4M NaCl, and 75% ethanol solutions). In the tuning process the free energy surface for each dihedral was derived from the MD ensemble and fitted to the conformational distributions and populations observed in 87 A- and B-DNA x-ray and 17 B-DNA NMR structures. Over 41 nanoseconds of MD simulations are presented which demonstrate that the force field is capable of producing stable trajectories, in the correct environments, of A-DNA, double stranded Aform RNA, B-DNA, Z-DNA, and a netropsin-DNA complex that closely reproduce the experimentally determined and/or canonical DNA conformations. Frequently the MD averaged structure is closer to the experimentally determined structure than to the canonical DNA conformation. MD simulations of A- to B- and B- to A-DNA transitions are also shown. A-DNA simulations in a low salt environment cleanly convert into the B-DNA conformation and converge into the RMS space sampled by a low salt simulation of the same sequence starting from B-DNA. In MD simulations using the BMS force field the B-form of d(GGGCCC)2 in a 75% ethanol solution converts into the A-form. Using the same methodology, parameters, and conditions the A-form of d(AAATTT)2 correctly converts into the B- DNA conformation. These studies demonstrate that the force field is capable of reproducing both environment and sequence dependent DNA structures. The 41 nanoseconds (nsec) of MD simulations presented in this paper paint a global picture which suggests that the DNA structures observed in low salt solutions are largely due to the favorable internal energy brought about by the nearly uniform screening of the DNA electrostatics. While the conformations sampled in high salt or mixed solvent environments occur from selective and asymmetric screening of the phosphate groups and DNA grooves, respectively, brought about by sequence induced ion and solvent packing.

The induced dipole and the classical Drude oscillator represent two major approaches for the explicit inclusion of electronic polarizability into force field-based molecular modeling and simulations. In this work, we explore the equivalency of these two models by comparing condensed phase properties computed using the Drude force field and a multipole and induced dipole (MPID) model. Presented is an approach to map the electrostatic model optimized in the context of the Drude force field onto the MPID model. Condensed phase simulations on water and 15 small model compounds show that without any reparametrization, the MPID model yields properties similar to the Drude force field with both models yielding satisfactory reproduction of a range of experimental values and quantum mechanical data. Our results illustrate that the Drude oscillator model and the point induced dipole model are different representations of essentially the same physical model. However, results indicate the presence of small differences between the use of atomic multipoles and off-center charge sites. Additionally, results on the use of dispersion particle mesh Ewald further support its utility for treating long-range Lennard Jones dispersion contributions in the context of polarizable force fields. The main motivation in demonstrating the transferability of parameters between the Drude and MPID models is that the more than 15 years of development of the Drude polarizable force field can now be used with MPID formalism without the need for dual-thermostat integrators nor self-consistent iterations. This opens up a wide range of new methodological opportunities for polarizable models.

Machine learning, trained on quantum mechanics (QM) calculations, is a powerful tool for modeling potential energy surfaces. A critical factor is the quality and diversity of the training dataset. Here we present a highly automated approach to dataset construction and demonstrate the method by building a potential for elemental aluminum (ANI-Al). In our active learning scheme, the ML potential under development is used to drive non-equilibrium molecular dynamics simulations with time-varying applied temperatures. Whenever a configuration is reached for which the ML uncertainty is large, new QM data is collected. The ML model is periodically retrained on all available QM data. The final ANI-Al potential makes very accurate predictions of radial distribution function in melt, liquid-solid coexistence curve, and crystal properties such as defect energies and barriers. We perform a 1.3M atom shock simulation and show that ANI-Al force predictions shine in their agreement with new reference DFT calculations.

A force field as accurate as quantum mechanics (QMs) and as fast as molecular mechanics (MMs), with which one can simulate a biomolecular system efficiently enough and meaningfully enough to get quantitative insights, is among the most ardent dreams of biophysicists—a dream, nevertheless, not to be fulfilled any time soon. Machine learning force fields (MLFFs) represent a meaningful endeavor in this direction, where differentiable neural functions are parametrized to fit ab initio energies and forces through automatic differentiation. We argue that, as of now, the utility of the MLFF models is no longer bottlenecked by accuracy but primarily by their speed, as well as stability and generalizability—many recent variants, on limited chemical spaces, have long surpassed the chemical accuracy of 1 kcal/mol—the empirical threshold beyond which realistic chemical predictions are possible—though still magnitudes slower than MM. Hoping to kindle exploration and design of faster, albeit perhaps slightly less accurate MLFFs, in this review, we focus our attention on the technical design space (the speed-accuracy trade-off) between MM and ML force fields. After a brief review of the building blocks (from a machine learning-centric point of view) of force fields of either kind, we discuss the desired properties and challenges now faced by the force field development community, survey the efforts to make MM force fields more accurate and ML force fields faster, and envision what the next generation of MLFF might look like.

Molecular dynamics (MD) simulations of six upgraded empirical force fields were compared and evaluated with short peptides, intrinsically disordered proteins, and folded proteins using trajectories of 1, 1.5, 5, or 10 μs (five replicates of 200 ns, 300 ns, 1 μs, or 2 μs) for each system. Previous studies have shown that different force fields, water models, simulation methods, and parameters can affect simulation outcomes. Here, the MD simulations were done in an explicit solvent with RS-peptide, HEWL19, HIV-rev, β amyloid (Aβ)-40, Aβ-42, phosphodiesterase-γ, CspTm, and ubiquitin using ff99IDPs, ff14IDPs, ff14IDPSFF, ff03w, CHARMM36m, and CHARMM22* force fields. The IDP ensembles generated by six all-atom empirical force fields were compared against NMR data. Despite using identical starting structures and simulation parameters, ensembles obtained with different force fields exhibit significant differences in NMR RMDs, secondary structure contents, and global properties such as the radius of gyration. The intrinsically disordered protein (IDP)-specific force fields could substantially reproduce the experimental observables in force field comparison: they have the lowest error in chemical shifts and J-couplings for short peptides/proteins, reasonably well for large IDPs and reasonably well with the radius of gyration. A high population of disorderness was observed in the IDP-specific force field for the IDP ensemble with a fraction of β sheets for β-amyloids. CHARMM22* performs better for many observables; however, it still has a preference toward the helicity for short peptides. The results of β-amyloid 42 starting from two different initial structures (Aβ421Z0Q and Aβ42model) were also compared with DSSP and NMR data. The results obtained with IDP-specific force fields within 2 μs simulation time are similar, even though starting from different structures. The current force fields perform equally well for folded proteins. The results of currently developed or modified force fields for IDPs are capable of enlightening the overall performance of the force field for disordered as well as folded proteins, thereby contributing to force field development.

The accuracy of force fields is of utmost importance in molecular modeling of proteins. Despite successful applications of force fields for about the past 30 years, some inherent flaws lying in force fields, such as biased secondary propensities and fixed atomic charges, have been observed in different aspects of biomolecular research; hence, a correction to current force fields is desirable. Because of the simplified functional form and the limited number of parameters for main chain torsion (MCT) in traditional force fields, it is not easy to propose an exquisite force field that is well-balanced among various conformations. Recently, AMBER-compatible force fields with coupled MCT term have been proposed, which show some improvement over AMBER03 and AMBER99SB force fields. In this work, further calibration of the torsional parameters has been conducted by changing the solvation model in quantum mechanical calculation and minimizing the deviation from the nuclear magnetic resonance experiments for some benchmark model systems and a folded protein. The results show that the revised force fields give excellent agreement with experiments in J coupling, chemical shifts, and secondary structure populations. In addition, the polarization effect is found to be crucial for the systems with ordered secondary structures.

Accurate force fields are one of the major pillars on which successful molecular dynamics simulations of complex biomolecular processes rest. They have been optimized for ambient conditions, whereas high-pressure simulations become increasingly important in pressure perturbation studies, using pressure as an independent thermodynamic variable. Here, we explore the design of non-polarizable force fields tailored to work well in the realm of kilobar pressures--while avoiding complete reparameterization. Our key is to first compute the pressure-induced electronic and structural response of a solute by combining an integral equation approach to include pressure effects on solvent structure with a quantum-chemical treatment of the solute within the embedded cluster reference interaction site model (EC-RISM) framework. Next, the solute's response to compression is taken into account by introducing pressure-dependence into selected parameters of a well-established force field. In our proof-of-principle study, the full machinery is applied to N,N,N-trimethylamine-N-oxide (TMAO) in water being a potent osmolyte that counteracts pressure denaturation. EC-RISM theory is shown to describe well the charge redistribution upon compression of TMAO(aq) to 10 kbar, which is then embodied in force field molecular dynamics by pressure-dependent partial charges. The performance of the high pressure force field is assessed by comparing to experimental and ab initio molecular dynamics data. Beyond its broad usefulness for designing non-polarizable force fields for extreme thermodynamic conditions, a good description of the pressure-response of solutions is highly recommended when constructing and validating polarizable force fields.

Condensed-phase computational studies of molecules using molecular mechanics approaches require the use of force fields to describe the energetics of the systems as a function of structure. The advantage of polarizable force fields over nonpolarizable (or additive) models lies in their ability to vary their electronic distribution as a function of the environment. Toward development of a polarizable force field for biological molecules, parameters for a series of sulfur-containing molecules are presented. Parameter optimization was performed to reproduce quantum mechanical and experimental data for gas phase properties including geometries, conformational energies, vibrational spectra, and dipole moments as well as for condensed phase properties such as heats of vaporization, molecular volumes, and free energies of hydration. Compounds in the training set include methanethiol, ethanethiol, propanethiol, ethyl methyl sulfide, and dimethyl disulfide. The molecular volumes and heats of vaporization are in good accordance with experimental values, with the polarizable model performing better than the CHARMM22 nonpolarizable force field. Improvements with the polarizable model were also obtained for molecular dipole moments and in the treatment of intermolecular interactions as a function of orientation, in part due to the presence of lone pairs and anisotropic atomic polarizability on the sulfur atoms. Significant advantage of the polarizable model was reflected in calculation of the dielectric constants, a property that CHARMM22 systematically underestimates. The ability of this polarizable model to accurately describe a range of gas and condensed phase properties paves the way for more accurate simulation studies of sulfur-containing molecules including cysteine and methionine residues in proteins.