Modern protein force fields behave comparably in molecular dynamics simulations

Several molecular dynamics simulations were performed on three proteins--bovine apo-calbindin D9K, human interleukin-4 R88Q mutant, and domain IIA of bacillus subtilis glucose permease--with each of the AMBER94, CHARMM22, and OPLS-AA force fields as implemented in CHARMM. Structural and dynamic properties such as solvent-accessible surface area, radius of gyration, deviation from their respective experimental structures, secondary structure, and backbone order parameters are obtained from each of the 2-ns simulations for the purpose of comparing the protein portions of these force fields. For one of the proteins, the interleukin-4 mutant, two independent simulations were performed using the CHARMM22 force field to gauge the sensitivity of some of these properties to the specific trajectory. In general, the force fields tested performed remarkably similarly with differences on the order of those found for the two independent trajectories of interleukin-4 with CHARMM22. When all three proteins are considered together, no force field showed any consistent trend in variations for most of the properties monitored in the study.     

Paramfit: Automated optimization of force field parameters for molecular dynamics simulations

The generation of bond, angle, and torsion parameters for classical molecular dynamics force fields typically requires fitting parameters such that classical properties such as energies and gradients match precalculated quantum data for structures that scan the value of interest. We present a program, Paramfit, distributed as part of the AmberTools software package that automates and extends this fitting process, allowing for simplified parameter generation for applications ranging from single molecules to entire force fields. Paramfit implements a novel combination of a genetic and simplex algorithm to find the optimal set of parameters that replicate either quantum energy or force data. The program allows for the derivation of multiple parameters simultaneously using significantly fewer quantum calculations than previous methods, and can also fit parameters across multiple molecules with applications to force field development. Paramfit has been applied successfully to systems with a sparse number of structures, and has already proven crucial in the development of the Assisted Model Building with Energy Refinement Lipid14 force field. © 2014 Wiley Periodicals, Inc.     

CHARMM force field and molecular dynamics simulations of protonated polyethylenimine

As a gene delivery vector, polyethylenimine (PEI) shows one of the highest transfection efficiencies, while effectively protecting DNA from enzyme degradation. The distinctive charge pattern of protonated PEI is widely considered responsible for fundamental process such as DNA condensation into PEI/DNA polyplexes (which are able to enter cells via endocytosis), proton sponge effect (which triggers the release of polyplexes from endosome), and release of DNA from polyplexes (to be further processed inside the nucleus). Our investigations are largely motivated by the crucial need for a realistic molecular mechanics force field (FF) for PEI, and, accordingly, we focus on two major issues: (1) development of a new atomistic (CHARMM) FF for PEI in different protonation states, rigorously derived from high‐quality ab initio calculations performed on model polymers, and (2) molecular dynamics investigations of solvated PEI, providing a detailed picture of the dynamic structuring thereof in dependence on their size and protonation state. The modeled PEI chains are essentially described in terms of gyration radius, end‐to‐end distance, persistence length, radial distribution functions, coordination numbers, and diffusion coefficients. They turn out to be more rigid than in other computational studies and we find diffusion coefficients in fair agreement with experimental data. The developed atomistic FF proves adequate for the realistic modeling of the size and protonation behavior of linear PEI, either as individual chains or composing polyplexes. © 2017 Wiley Periodicals, Inc.     

CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model

A fluctuating charge (FQ) force field is applied to molecular dynamics simulations for six small proteins in explicit polarizable solvent represented by the TIP4P-FQ potential. The proteins include 1FSV, 1ENH, 1PGB, 1VII, 1H8K, and 1CRN, representing both helical and beta-sheet secondary structural elements. Constant pressure and temperature (NPT) molecular dynamics simulations are performed on time scales of several nanoseconds, the longest simulations yet reported using explicitly polarizable all-atom empirical potentials (for both solvent and protein) in the condensed phase. In terms of structure, the FQ force field allows deviations from native structure up to 2.5 A (with a range of 1.0 to 2.5 A). This is commensurate to the performance of the CHARMM22 nonpolarizable model and other currently existing polarizable models. Importantly, secondary structural elements maintain native structure in general to within 1 A (both helix and beta-strands), again in good agreement with the nonpolarizable case. In qualitative agreement with QM/MM ab initio dynamics on crambin (Liu et al. Proteins 2001, 44, 484), there is a sequence dependence of average condensed phase atomic charge for all proteins, a dependence one would anticipate considering the differing chemical environments around individual atoms; this is a subtle quantum mechanical feature captured in the FQ model but absent in current state-of-the-art nonpolarizable models. Furthermore, there is a mutual polarization of solvent and protein in the condensed phase. Solvent dipole moment distributions within the first and second solvation shells around the protein display a shift towards higher dipole moments (increases on the order of 0.2-0.3 Debye) relative to the bulk; protein polarization is manifested via the enhanced condensed phase charges of typical polar atoms such as backbone carbonyl oxygens, amide nitrogens, and amide hydrogens. Finally, to enlarge the sample set of proteins, gas-phase minimizations and 1 ps constant temperature simulations are performed on various-sized proteins to compare to earlier work by Kaminsky et al. (J Comp Chem 2002, 23, 1515). The present work establishes the feasibility of applying a fully polarizable force field for protein simulations and demonstrates the approach employed in extending the CHARMM force field to include these effects.     

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.     

Systematic comparison of force fields for microscopic simulations of NaCl in aqueous solutions: diffusion, free energy of hydration, and structural properties

In this article we compare different force fields that are widely used (Gromacs, Charmm-22/x-Plor, Charmm-27, Amber-1999, OPLS-AA) in biophysical simulations containing aqueous NaCl. We show that the uncertainties of the microscopic parameters of, in particular, sodium, and, to a lesser extent, chloride, translate into large differences in the computed radial-distribution functions. This uncertainty reflect the incomplete experimental knowledge of the structural properties of ionic aqueous solutions at finite molarity. We discuss possible implications on the computation of potential of mean force and effective potentials.     

Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations

Computational studies of proteins based on empirical force fields represent a powerful tool to obtain structure-function relationships at an atomic level, and are central in current efforts to solve the protein folding problem. The results from studies applying these tools are, however, dependent on the quality of the force fields used. In particular, accurate treatment of the peptide backbone is crucial to achieve representative conformational distributions in simulation studies. To improve the treatment of the peptide backbone, quantum mechanical (QM) and molecular mechanical (MM) calculations were undertaken on the alanine, glycine, and proline dipeptides, and the results from these calculations were combined with molecular dynamics (MD) simulations of proteins in crystal and aqueous environments. QM potential energy maps of the alanine and glycine dipeptides at the LMP2/cc-pVxZ//MP2/6-31G* levels, where x = D, T, and Q, were determined, and are compared to available QM studies on these molecules. The LMP2/cc-pVQZ//MP2/6-31G* energy surfaces for all three dipeptides were then used to improve the MM treatment of the dipeptides. These improvements included additional parameter optimization via Monte Carlo simulated annealing and extension of the potential energy function to contain peptide backbone phi, psi dihedral crossterms or a phi, psi grid-based energy correction term. Simultaneously, MD simulations of up to seven proteins in their crystalline environments were used to validate the force field enhancements. Comparison with QM and crystallographic data showed that an additional optimization of the phi, psi dihedral parameters along with the grid-based energy correction were required to yield significant improvements over the CHARMM22 force field. However, systematic deviations in the treatment of phi and psi in the helical and sheet regions were evident. Accordingly, empirical adjustments were made to the grid-based energy correction for alanine and glycine to account for these systematic differences. These adjustments lead to greater deviations from QM data for the two dipeptides but also yielded improved agreement with experimental crystallographic data. These improvements enhance the quality of the CHARMM force field in treating proteins. This extension of the potential energy function is anticipated to facilitate improved treatment of biological macromolecules via MM approaches in general.     

The distributed diagonal force decomposition method for parallelizing molecular dynamics simulations

Parallelization is an effective way to reduce the computational time needed for molecular dynamics simulations. We describe a new parallelization method, the distributed-diagonal force decomposition method, with which we extend and improve the existing force decomposition methods. Our new method requires less data communication during molecular dynamics simulations than replicated data and current force decomposition methods, increasing the parallel efficiency. It also dynamically load-balances the processors' computational load throughout the simulation. The method is readily implemented in existing molecular dynamics codes and it has been incorporated into the CHARMM program, allowing its immediate use in conjunction with the many molecular dynamics simulation techniques that are already present in the program. We also present the design of the Force Decomposition Machine, a cluster of personal computers and networks that is tailored to running molecular dynamics simulations using the distributed diagonal force decomposition method. The design is expandable and provides various degrees of fault resilience. This approach is easily adaptable to computers with Graphics Processing Units because it is independent of the processor type being used.     

Force-field modeling through quantum mechanical calculations: molecular dynamics simulations of a nematogenic molecule in its condensed phases

Interaction energy of the 4-n-pentyloxy-4'-cyanobiphenyl (5OCB) dimer is computed at MP2 level, for many geometrical arrangements using the Fragmentation Reconstruction Method (FRM). DFT calculations are performed for a number of geometries of the monomer. The resulting database is used to parameterize an atomistic intra- and inter-molecular force-field suitable for classical bulk simulations. Several structural and dynamical properties in 5OCB isotropic and liquid crystalline phases are computed from molecular dynamics simulation mainly in the NPT ensemble. Lengthy runs (more than 70 ns) and large sample sizes (up to 806 molecules) were used to determine the nematic to isotropic transition temperature up to a precision of few K. Good agreement was found in most of the investigated properties, thus validating the accuracy of the proposed model potential, only derived by quantum mechanical calculations.     

Accelerated molecular dynamics simulations of protein folding

Folding of four fast‐folding proteins, including chignolin, Trp‐cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred‐of‐microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2–2.1 Å of the native NMR or X‐ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second‐order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein‐folding studies. © 2015 Wiley Periodicals, Inc.     

Fluctuating charge normal modes: An algorithm for implementing molecular dynamics simulations with polarizable potentials

A new method for performing molecular dynamics simulations with fluctuating charge polarizable potentials is introduced. In fluctuating charge models, polarizability is treated by allowing the partial charges to be variables, with values that are coupled to charges on the same molecule as well as those on other molecules. The charges can be efficiently propagated in a molecular dynamics simulation using extended Lagrangian dynamics. By making a coordinate change from the charge variables to a set of normal mode charge coordinates for each molecule, a new method is constructed in which the normal mode charge variables uncouple from those on the same molecule. The method is applied to the TIP4P-FQ model of water and compared to other methods for implementing the dynamics. The methods are compared using different molecular dynamics time steps.     

Liquid properties of dimethyl ether from molecular dynamics simulations using Ab Initio force fields

We have used molecular dynamic simulations to study the structural and dynamical properties of liquid dimethyl ether (DME) with a newly constructed ab initio force field in this article. The ab initio potential energy data were calculated at the second order Møller‐Plesset (MP2) perturbation theory with Dunning's correlation consistent basis sets (up to aug‐cc‐pVQZ). We considered 17 configurations of the DME dime for the orientation sampling. The calculated MP2 potential data were used to construct a 3‐site united atom force field model. The simulation results are compared with those using the empirical force field of Jorgensen and Ibrahim (Jorgensen and Ibrahim, J Am Chem Soc 1981, 103, 3976) and with available experimental measurements. We obtain quantitative agreements for the atom‐wise radial distribution functions, the self‐diffusion coefficients, and the shear viscosities over a wide range of experimental conditions. This force field thus provides a suitable starting point to predict liquid properties of DME from first principles intermolecular interactions with no empirical data input a priori. © 2012 Wiley Periodicals, Inc.     

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     

Comparative analysis of nucleotide translocation through protein nanopores using steered molecular dynamics and an adaptive biasing force

The translocation of nucleotide molecules across biological and synthetic nanopores has attracted attention as a next generation technique for sequencing DNA. Computer simulations have the ability to provide atomistic‐level insight into important states and processes, delivering a means to develop a fundamental understanding of the translocation event, for example, by extracting the free energy of the process. Even with current supercomputing facilities, the simulation of many‐atom systems in fine detail is limited to shorter timescales than the real events they attempt to recreate. This imposes the need for enhanced simulation techniques that expand the scope of investigation in a given timeframe. There are numerous free energy calculation and translocation methodologies available, and it is by no means clear which method is best applied to a particular problem. This article explores the use of two popular free energy calculation methodologies in a nucleotide‐nanopore translocation system, using the α‐hemolysin nanopore. The first uses constant velocity‐steered molecular dynamics (cv‐SMD) in conjunction with Jarzynski's equality. The second applies an adaptive biasing force (ABF), which has not previously been applied to the nucleotide‐nanpore system. The purpose of this study is to provide a comprehensive comparison of these methodologies, allowing for a detailed comparative assessment of the scientific merits, the computational cost, and the statistical quality of the data obtained from each technique. We find that the ABF method produces results that are closer to experimental measurements than those from cv‐SMD, whereas the net errors are smaller for the same computational cost. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Toward force fields for atomistic simulations of iridium‐containing complexes

The structural and energetic characterization of metal complexes is important in catalysis and photochemical applications. Unraveling their modes‐of‐action can be greatly assisted by computation, which typically is restricted to computationally demanding methods including electronic structure calculations with density functional theory. Here, we present an empirical force field based on valence bond theory applicable to a range of octahedral Ir(III) complexes with different coordinating ligands, including iridium complexes with a chiral P,N ligand. Using an approach applicable to metal‐containing complexes in general, it is shown that with one common parametrization 85% of the 116 diastereomers—all within 21 kcal/mol of the lowest energy conformation of each series—can be correctly ranked. For neutral complexes, all diastereomers are ranked correctly. This helps to identify the most relevant diastereomers which, if necessary, can be further investigated by more demanding computational methods. Furthermore, if one specific complex is considered, the root mean square deviation between reference data from electronic structure calculations and the force field is . This, together with the possibility to carry out explicit simulations in solution paves the way for an atomistic understanding of iridium‐containing complexes in catalysis. © 2013 Wiley Periodicals, Inc.     

MATCH: an atom-typing toolset for molecular mechanics force fields

We introduce a toolset of program libraries collectively titled multipurpose atom-typer for CHARMM (MATCH) for the automated assignment of atom types and force field parameters for molecular mechanics simulation of organic molecules. The toolset includes utilities for the conversion of multiple chemical structure file formats into a molecular graph. A general chemical pattern-matching engine using this graph has been implemented whereby assignment of molecular mechanics atom types, charges, and force field parameters are achieved by comparison against a customizable list of chemical fragments. While initially designed to complement the CHARMM simulation package and force fields by generating the necessary input topology and atom-type data files, MATCH can be expanded to any force field and program, and has core functionality that makes it extendable to other applications such as fragment-based property prediction. In this work, we demonstrate the accurate construction of atomic parameters of molecules within each force field included in CHARMM36 through exhaustive cross validation studies illustrating that bond charge increment rules derived from one force field can be transferred to another. In addition, using leave-one-out substitution it is shown that it is also possible to substitute missing intra and intermolecular parameters with ones included in a force field to complete the parameterization of novel molecules. Finally, to demonstrate the robustness of MATCH and the coverage of chemical space offered by the recent CHARMM general force field (Vanommeslaeghe, et al., J Comput Chem 2010, 31, 671), one million molecules from the PubChem database of small molecules are typed, parameterized, and minimized.     

New energy terms for reduced protein models implemented in an off‐lattice force field

Parameterization and test calculations of a reduced protein model with new energy terms are presented. The new energy terms retain the steric properties and the most significant degrees of freedom of protein side chains in an efficient way using only one to three virtual atoms per amino acid residue. The energy terms are implemented in a force field containing predefined secondary structure elements as constraints, electrostatic interaction terms, and a solvent‐accessible surface area term to include the effect of solvation. In the force field the main‐chain peptide units are modeled as electric dipoles, which have constant directions in α‐helices and β‐sheets and variable conformation‐dependent directions in loops. Protein secondary structures can be readily modeled using these dipole terms. Parameters of the force field were derived using a large set of experimental protein structures and refined by minimizing RMS errors between the experimental structures and structures generated using molecular dynamics simulations. The final average RMS error was 3.7 Å for the main‐chain virtual atoms (C_α atoms) and 4.2 Å for all virtual atoms for a test set of 10 proteins with 58–294 amino acid residues. The force field was further tested with a substantially larger test set of 608 proteins yielding somewhat lower accuracy. The fold recognition capabilities of the force field were also evaluated using a set of 27,814 misfolded decoy structures. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1229–1242, 2001     

A method for predicting protein conformational pathways by using molecular dynamics simulations guided by difference distance matrices

Here, an efficient method that predicts natural transition pathways between two endpoint states of an allosteric protein has been proposed. This method helps create structures that bridge these endpoints through multiple iterative and unbiased molecular dynamics simulations with explicit water. Difference distance matrices provide an approach for identifying states involving concerted slow motion. A series of structures are readily generated along the transition pathways of adenylate kinase. Predicted structures may be useful for an initial pathway to evaluate free energy landscapes via umbrella sampling and chain‐of‐states methods. © 2016 Wiley Periodicals, Inc.     

Refinement of the primary hydration shell model for molecular dynamics simulations of large proteins

A realistic representation of water molecules is important in molecular dynamics simulation of proteins. However, the standard method of solvating biomolecules, that is, immersing them in a box of water with periodic boundary conditions, is computationally expensive. The primary hydration shell (PHS) method, developed more than a decade ago and implemented in CHARMM, uses only a thin shell of water around the system of interest, and so greatly reduces the computational cost of simulations. Applying the PHS method, especially to larger proteins, revealed that further optimization and a partial reworking was required and here we present several improvements to its performance. The model is applied to systems with different sizes, and both water and protein behaviors are compared with those observed in standard simulations with periodic boundary conditions and, in some cases, with experimental data. The advantages of the modified PHS method over its original implementation are clearly apparent when it is applied to simulating the 82 kDa protein Malate Synthase G. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

Comparison of the accuracy of periodic reaction field methods in molecular dynamics simulations of a model liquid crystal system

A periodic reaction field (PRF) method is a technique to estimate long‐range interactions. The method has the potential to effectively reduce the computational cost while maintaining adequate accuracy. We performed molecular dynamics (MD) simulations of a model liquid‐crystal system to assess the accuracy of some variations of the PRF method in low‐charge‐density systems. All the methods had adequate accuracy compared with the results of the particle mesh Ewald (PME) method, except for a few simulation conditions. Furthermore, in all of the simulation conditions, one of the PRF methods had the same accuracy as the PME method. © 2015 Wiley Periodicals, Inc.