Molecular modeling and dynamics studies with explicit inclusion of electronic polarizability. Theory and applications

Constant pH Molecular Dynamics in Explicit Solvent with Enveloping Distribution Sampling and Hamiltonian Exchange

We present a new computational approach for constant pH simulations in explicit solvent based on the combination of the enveloping distribution sampling (EDS) and Hamiltonian replica exchange (HREX) methods. Unlike constant pH methods based on variable and continuous charge models, our method is based on discrete protonation states. EDS generates a hybrid Hamiltonian of different protonation states. A smoothness parameter s is used to control the heights of energy barriers of the hybrid-state energy landscape. A small s value facilitates state transitions by lowering energy barriers. Replica exchange between EDS potentials with different s values allows us to readily obtain a thermodynamically accurate ensemble of multiple protonation states with frequent state transitions. The analysis is performed with an ensemble obtained from an EDS Hamiltonian without smoothing, s = ∞, which strictly follows the minimum energy surface of the end states. The accuracy and efficiency of this method is tested on aspartic acid, lysine, and glutamic acid, which have two protonation states, a histidine with three states, a four-residue peptide with four states, and snake cardiotoxin with eight states. The pKa values estimated with the EDS-HREX method agree well with the experimental pKa values. The mean absolute errors of small benchmark systems range from 0.03 to 0.17 pKa units, and those of three titratable groups of snake cardiotoxin range from 0.2 to 1.6 pKa units. This study demonstrates that EDS-HREX is a potent theoretical framework, which gives the correct description of multiple protonation states and good calculated pKa values.

Modeling ion channels: past, present, and future

Ion channels are membrane-bound enzymes whose catalytic sites are ion-conducting pores that open and close (gate) in response to specific environmental stimuli. Ion channels are important contributors to cell signaling and homeostasis. Our current understanding of gating is the product of 60 plus years of voltage-clamp recording augmented by intervention in the form of environmental, chemical, and mutational perturbations. The need for good phenomenological models of gating has evolved in parallel with the sophistication of experimental technique. The goal of modeling is to develop realistic schemes that not only describe data, but also accurately reflect mechanisms of action. This review covers three areas that have contributed to the understanding of ion channels: traditional Eyring kinetic theory, molecular dynamics analysis, and statistical thermodynamics. Although the primary emphasis is on voltage-dependent channels, the methods discussed here are easily generalized to other stimuli and could be applied to any ion channel and indeed any macromolecule.

All-atom polarizable force field for DNA based on the classical Drude oscillator model

Presented is a first generation atomistic force field (FF) for DNA in which electronic polarization is modeled based on the classical Drude oscillator formalism. The DNA model is based on parameters for small molecules representative of nucleic acids, including alkanes, ethers, dimethylphosphate, and the nucleic acid bases and empirical adjustment of key dihedral parameters associated with the phosphodiester backbone, glycosidic linkages, and sugar moiety of DNA. Our optimization strategy is based on achieving a compromise between satisfying the properties of the underlying model compounds in the gas phase targeting quantum mechanical (QM) data and reproducing a number of experimental properties of DNA duplexes in the condensed phase. The resulting Drude FF yields stable DNA duplexes on the 100-ns time scale and satisfactorily reproduce (1) the equilibrium between A and B forms of DNA and (2) transitions between the BI and BII substates of B form DNA. Consistency with the gas phase QM data for the model compounds is significantly better for the Drude model as compared to the CHARMM36 additive FF, which is suggested to be due to the improved response of the model to changes in the environment associated with the explicit inclusion of polarizability. Analysis of dipole moments associated with the nucleic acid bases shows the Drude model to have significantly larger values than those present in CHARMM36, with the dipoles of individual bases undergoing significant variations during the MD simulations. Additionally, the dipole moment of water was observed to be perturbed in the grooves of DNA.

A theoretical view of protein dynamics

Proteins are fascinating supramolecular structures, which are able to recognize ligands transforming binding information into chemical signals. They can transfer information across the cell, can catalyse complex chemical reactions, and are able to transform energy into work with much more efficiency than any human engine. The unique abilities of proteins are tightly coupled with their dynamic properties, which are coded in a complex way in the sequence and carefully refined by evolution. Despite its importance, our experimental knowledge of protein dynamics is still rather limited, and mostly derived from theoretical calculations. I will review here, in a systematic way, the current state-of-the-art theoretical approaches to the study of protein dynamics, emphasizing the most recent advances, examples of use and the expected lines of development in the near future.

A Comparative Study of Transferable Aspherical Pseudoatom Databank and Classical Force Fields for Predicting Electrostatic Interactions in Molecular Dimers

Accurate and fast evaluation of electrostatic interactions in molecular systems is one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry and drug design. Electrostatic interactions are of crucial importance in biological systems. They are well represented by quantum mechanical methods; however, such calculations are computationally expensive. In this study, we have evaluated the University of Buffalo Pseudoatom Databank (UBDB)1,2 approach for approximation of electrostatic properties of macromolecules and their complexes. We selected the S663 and JSCH-20054 data sets (208 molecular complexes in total) for this study. These complexes represent a wide range of chemical and biological systems for which hydrogen bonding, electrostatic, and van der Waals interactions play important roles. Reference electrostatic energies were obtained directly from wave functions at the B3LYP/aug-cc-pVTZ level of theory using the SAPT (Symmetry-Adapted Perturbation Theory) scheme for calculation of electrostatic contributions to total intermolecular interaction energies. Electrostatic energies calculated on the basis of the UBDB were compared with corresponding reference results. Results were also compared with energies computed using a point charge model from popular force fields (AM1-BCC and RESP used in AMBER and CGenFF from CHARMM family). The energy trends are quite consistent (R2 ≈ 0.98) for the UBDB method as compared to the AMBER5 and CHARMM force field methods6(R2 ≈ 0.93 on average). The RSMEs do not exceed 3.2 kcal mol-1 for the UBDB and are in the range of 3.7-7.6 kcal mol-1 for the point charge models. We also investigated the discrepancies in electrostatic potentials and magnitudes of dipole moments among the tested methods. This study shows that estimation of electrostatic interaction energies using the UBDB databank is accurate and reasonably fast when compared to other known methods, which opens potential new applications to macromolecules.

Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II.Towards Massively Parallel Computations using Smooth Particle Mesh Ewald

In this paper, we present a scalable and efficient implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The Smooth Particle-Mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the Direct Inversion in the Iterative Subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy-force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package which is the first implementation for a polarizable model making large scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of spme and a noticeable improvement of the memory management giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations.

Current and emerging opportunities for molecular simulations in structure-based drug design

An overview of the current capabilities and limitations of molecular simulation of biomolecular complexes in the context of computer-aided drug design is provided. Steady improvements in computer hardware coupled with more refined representations of energetics are leading to a new appreciation of the driving forces of molecular recognition. Molecular simulations are poised to more frequently guide the interpretation of biophysical measurements of biomolecular complexes. Ligand design strategies emerge from detailed analyses of computed structural ensembles. The feasibility of routine applications to ligand optimization problems hinges upon successful extensive large scale validation studies and the development of protocols to intelligently automate computations.

Polarizable empirical force field for hexopyranose monosaccharides based on the classical Drude oscillator

A polarizable empirical force field based on the classical Drude oscillator is presented for the hexopyranose form of selected monosaccharides. Parameter optimization targeted quantum mechanical (QM) dipole moments, solute-water interaction energies, vibrational frequencies, and conformational energies. Validation of the model was based on experimental data on crystals, densities of aqueous-sugar solutions, diffusion constants of glucose, and rotational preferences of the exocylic hydroxymethyl of d-glucose and d-galactose in aqueous solution as well as additional QM data. Notably, the final model involves a single electrostatic model for all sixteen diastereomers of the monosaccharides, indicating the transferability of the polarizable model. The presented parameters are anticipated to lay the foundation for a comprehensive polarizable force field for saccharides that will be compatible with the polarizable Drude parameters for lipids and proteins, allowing for simulations of glycolipids and glycoproteins.

Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations

Hybrid molecular dynamics (MD) simulations, in which the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10(3)-10(5) molecules, pose a challenge. A corresponding computational approach should guarantee energy conservation, exclude artificial distortions of the electron density at the interface between the DFT and PMM fragments, and should treat the long-range electrostatic interactions within the hybrid simulation system in a linearly scaling fashion. Here we describe a corresponding Hamiltonian DFT/(P)MM implementation, which accounts for inducible atomic dipoles of a PMM environment in a joint DFT/PMM self-consistency iteration. The long-range parts of the electrostatics are treated by hierarchically nested fast multipole expansions up to a maximum distance dictated by the minimum image convention of toroidal boundary conditions and, beyond that distance, by a reaction field approach such that the computation scales linearly with the number of PMM atoms. Short-range over-polarization artifacts are excluded by using Gaussian inducible dipoles throughout the system and Gaussian partial charges in the PMM region close to the DFT fragment. The Hamiltonian character, the stability, and efficiency of the implementation are investigated by hybrid DFT/PMM-MD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM.

Polarizable six-point water models from computational and empirical optimization

Tröster et al. (J. Phys. Chem B 2013, 117, 9486-9500) recently suggested a mixed computational and empirical approach to the optimization of polarizable molecular mechanics (PMM) water models. In the empirical part the parameters of Buckingham potentials are optimized by PMM molecular dynamics (MD) simulations. The computational part applies hybrid calculations, which combine the quantum mechanical description of a H2O molecule by density functional theory (DFT) with a PMM model of its liquid phase environment generated by MD. While the static dipole moments and polarizabilities of the PMM water models are fixed at the experimental gas phase values, the DFT/PMM calculations are employed to optimize the remaining electrostatic properties. These properties cover the width of a Gaussian inducible dipole positioned at the oxygen and the locations of massless negative charge points within the molecule (the positive charges are attached to the hydrogens). The authors considered the cases of one and two negative charges rendering the PMM four- and five-point models TL4P and TL5P. Here we extend their approach to three negative charges, thus suggesting the PMM six-point model TL6P. As compared to the predecessors and to other PMM models, which also exhibit partial charges at fixed positions, TL6P turned out to predict all studied properties of liquid water at p0 = 1 bar and T0 = 300 K with a remarkable accuracy. These properties cover, for instance, the diffusion constant, viscosity, isobaric heat capacity, isothermal compressibility, dielectric constant, density, and the isobaric thermal expansion coefficient. This success concurrently provides a microscopic physical explanation of corresponding shortcomings of previous models. It uniquely assigns the failures of previous models to substantial inaccuracies in the description of the higher electrostatic multipole moments of liquid phase water molecules. Resulting favorable properties concerning the transferability to other temperatures and conditions like the melting of ice are also discussed.

Molecular dynamics study of response of liquid N,N-dimethylformamide to externally applied electric field using a polarizable force field

The behavior of Liquid N,N-dimethylformamide subjected to a wide range of externally applied electric fields (from 0.001 V/nm to 1 V/nm) has been investigated through molecular dynamics simulation. To approach the objective the AMOEBA polarizable force field was extended to include the interaction of the external electric field with atomic partial charges and the contribution to the atomic polarization. The simulation results were evaluated with quantum mechanical calculations. The results from the present force field for the liquid at normal conditions were compared with the experimental and molecular dynamics results with non-polarizable and other polarizable force fields. The uniform external electric fields of higher than 0.01 V/nm have a significant effect on the structure of the liquid, which exhibits a variation in numerous properties, including molecular polarization, local cluster structure, rotation, alignment, energetics, and bulk thermodynamic and structural properties.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Molecular mechanics

Molecular Mechanics (MM) force fields are the methods of choice for protein simulations, which are essential in the study of conformational flexibility. Given the importance of protein flexibility in drug binding, MM is involved in most if not all Computational Structure-Based Drug Discovery (CSBDD) projects. This paper introduces the reader to the fundamentals of MM, with a special emphasis on how the target data used in the parametrization of force fields determine their strengths and weaknesses. Variations and recent developments such as polarizable force fields are discussed. The paper ends with a brief overview of common force fields in CSBDD.

Force Field for Peptides and Proteins based on the Classical Drude Oscillator

Presented is a polarizable force field based on a classical Drude oscillator framework, currently implemented in the programs CHARMM and NAMD, for modeling and molecular dynamics (MD) simulation studies of peptides and proteins. Building upon parameters for model compounds representative of the functional groups in proteins, the development of the force field focused on the optimization of the parameters for the polypeptide backbone and the connectivity between the backbone and side chains. Optimization of the backbone electrostatic parameters targeted quantum mechanical conformational energies, interactions with water, molecular dipole moments and polarizabilities and experimental condensed phase data for short polypeptides such as (Ala)₅. Additional optimization of the backbone φ, ψ conformational preferences included adjustments of the tabulated two-dimensional spline function through the CMAP term. Validation of the model included simulations of a collection of peptides and proteins. This 1^st generation polarizable model is shown to maintain the folded state of the studied systems on the 100 ns timescale in explicit solvent MD simulations. The Drude model typically yields larger RMS differences as compared to the additive CHARMM36 force field (C36) and shows additional flexibility as compared to the additive model. Comparison with NMR chemical shift data shows a small degradation of the polarizable model with respect to the additive, though the level of agreement may be considered satisfactory, while for residues shown to have significantly underestimated S² order parameters in the additive model, improvements are calculated with the polarizable model. Analysis of dipole moments associated with the peptide backbone and tryptophan side chains show the Drude model to have significantly larger values than those present in C36, with the dipole moments of the peptide backbone enhanced to a greater extent in sheets versus helices and the dipoles of individual moieties observed to undergo significant variations during the MD simulations. Although there are still some limitations, the presented model, termed Drude-2013, is anticipated to yield a molecular picture of peptide and protein structure and function that will be of increased physical validity and internal consistency in a computationally accessible fashion.

Three-Dimensional RISM Integral Equation Theory for Polarizable Solute Models

Modeling solute polarizability is a key ingredient for improving the description of solvation phenomena. In recent years, polarizable molecular mechanics force fields have emerged that circumvent the limitations of classical fixed charge force fields by the ability to adapt their electrostatic potential distribution to a polarizing environment. Solvation phenomena are characterized by the solute's excess chemical potential, which can be computed by expensive fully atomistic free energy simulations. The alternative is to employ an implicit solvent model, which poses a challenge to the formulation of the solute-solvent interaction term within a polarizable framework. Here, we adapt the three-dimensional reference interaction site model (3D RISM) integral equation theory as a solvent model, which analytically yields the chemical potential, to the polarizable AMOEBA force field using an embedding cluster (EC-RISM) strategy. The methodology is analogous to our earlier approach to the coupling of a quantum-chemical solute description with a classical 3D RISM solvent. We describe the conceptual physical and algorithmic basis as well as the performance for several benchmark cases as a proof of principle. The results consistently show reasonable agreement between AMOEBA and quantum-chemical free energies in solution in general and allow for separate assessment of energetic and solvation-related contributions. We find that, depending on the parametrization, AMOEBA reproduces the chemical potential in better agreement with reference quantum-chemical calculations than the intramolecular energies, which suggests possible routes toward systematic improvement of polarizable force fields.

Polarizable empirical force field for acyclic polyalcohols based on the classical Drude oscillator

A polarizable empirical force field for acyclic polyalcohols based on the classical Drude oscillator is presented. The model is optimized with an emphasis on the transferability of the developed parameters among molecules of different sizes in this series and on the condensed-phase properties validated against experimental data. The importance of the explicit treatment of electronic polarizability in empirical force fields is demonstrated in the cases of this series of molecules with vicinal hydroxyl groups that can form cooperative intra- and intermolecular hydrogen bonds. Compared to the CHARMM additive force field, improved treatment of the electrostatic interactions avoids overestimation of the gas-phase dipole moments resulting in significant improvement in the treatment of the conformational energies and leads to the correct balance of intra- and intermolecular hydrogen bonding of glycerol as evidenced by calculated heat of vaporization being in excellent agreement with experiment. Computed condensed phase data, including crystal lattice parameters and volumes and densities of aqueous solutions are in better agreement with experimental data as compared to the corresponding additive model. Such improvements are anticipated to significantly improve the treatment of polymers in general, including biological macromolecules.

A comparative Kirkwood-Buff study of aqueous methanol solutions modeled by the CHARMM additive and Drude polarizable force fields

A comparative study on aqueous methanol solutions modeled by the CHARMM additive and Drude polarizable force fields was carried out by employing Kirkwood-Buff analysis. It was shown that both models reproduced the experimental Kirkwood-Buff integrals and excess coordination numbers adequately well over the entire concentration range. The Drude model showed significant improvement over the additive model in solution densities, partial molar volumes, excess molar volumes, concentration-dependent diffusion constants, and dielectric constants. However, the additive model performed somewhat better than the Drude model in reproducing the activity derivative, excess molar Gibbs energy, and excess molar enthalpy of mixing. This is due to the additive achieving a better balance among solute-solute, solute-solvent, and solvent-solvent interactions, indicating the potential for improvements in the Drude polarizable alcohol model.

Kirkwood-Buff analysis of aqueous N-methylacetamide and acetamide solutions modeled by the CHARMM additive and Drude polarizable force fields

Kirkwood-Buff analysis was performed on aqueous solutions of N-methylacetamide and acetamide using the Chemistry at HARvard Molecular Mechanics additive and Drude polarizable all-atom force fields. Comparison of a range of properties with experimental results, including Kirkwood-Buff integrals, excess coordination numbers, solution densities, partial molar values, molar enthalpy of mixing, showed both models to be well behaved at higher solute concentrations with the Drude model showing systematic improvement at lower solution concentrations. However, both models showed difficulties reproducing experimental activity derivatives and the excess Gibbs energy, with the Drude model performing slightly better. At the molecular level, the improved agreement of the Drude model at low solute concentrations is due to increased structure in the solute-solute and solute-solvent interactions. The present results indicate that the explicit inclusion of electronic polarization leads to improved modeling of dilute solutions even when those properties are not included as target data during force field optimization.

Insights into the Binding of Intrinsically Disordered Proteins from Molecular Dynamics Simulation

Intrinsically disordered proteins (IDPs) are a class of protein that, in the native state, possess no well-defined secondary or tertiary structure, existing instead as dynamic ensembles of conformations. They are biologically important, with approximately 20% of all eukaryotic proteins disordered, and found at the heart of many biochemical networks. To fulfil their biological roles, many IDPs need to bind to proteins and/or nucleic acids. And while unstructured in solution, IDPs typically fold into a well-defined three-dimensional structure upon interaction with a binding partner. The flexibility and structural diversity inherent to IDPs makes this coupled folding and binding difficult to study at atomic resolution by experiment alone, and computer simulation currently offers perhaps the best opportunity to understand this process. But simulation of coupled folding and binding is itself extremely challenging; these molecules are large and highly flexible, and their binding partners, such as DNA or cyclins, are also often large. Therefore, their study requires either or both simplified representations and advanced enhanced sampling schemes. It is not always clear that existing simulation techniques, optimized for studying folded proteins, are well-suited to IDPs. In this article, we examine the progress that has been made in the study of coupled folding and binding using molecular dynamics simulation. We summarise what has been learnt, and examine the state of the art in terms of both methodologies and models. We also consider the lessons to be learnt from advances in other areas of simulation and highlight the issues that remain of be addressed.

The Polarizable Atomic Multipole-based AMOEBA Force Field for Proteins

Development of the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Simulation) force field for proteins is presented. The current version (AMOEBA-2013) utilizes permanent electrostatic multipole moments through the quadrupole at each atom, and explicitly treats polarization effects in various chemical and physical environments. The atomic multipole electrostatic parameters for each amino acid residue type are derived from high-level gas phase quantum mechanical calculations via a consistent and extensible protocol. Molecular polarizability is modeled via a Thole-style damped interactive induction model based upon distributed atomic polarizabilities. Inter- and intramolecular polarization is treated in a consistent fashion via the Thole model. The intramolecular polarization model ensures transferability of electrostatic parameters among different conformations, as demonstrated by the agreement between QM and AMOEBA electrostatic potentials, and dipole moments of dipeptides. The backbone and side chain torsional parameters were determined by comparing to gas-phase QM (RI-TRIM MP2/CBS) conformational energies of dipeptides and to statistical distributions from the Protein Data Bank. Molecular dynamics simulations are reported for short peptides in explicit water to examine their conformational properties in solution. Overall the calculated conformational free energies and J-coupling constants are consistent with PDB statistics and experimental NMR results, respectively. In addition, the experimental crystal structures of a number of proteins are well maintained during molecular dynamics (MD) simulation. While further calculations are necessary to fully validate the force field, initial results suggest the AMOEBA polarizable multipole force field is able to describe the structure and energetics of peptides and proteins, in both gas-phase and solution environments.

Polarizable water models from mixed computational and empirical optimization

Here we suggest a mixed computational and empirical approach serving to optimize the parameters of complex and polarizable molecular mechanics (PMM) models for complicated liquids. The computational part of the parameter optimization relies on hybrid calculations combining density functional theory (DFT) for a solute molecule with a PMM treatment of its solvent environment at well-defined thermodynamic conditions. As an application we have developed PMM models for water featuring ν = 3, 4, and 5 points of force action, a Gaussian inducible dipole and a Buckingham potential at the oxygen, the experimental liquid phase geometry, the experimental gas phase polarizability α(exp)(g) = 1.47 ų, and, for ν = 4 and 5, the gas phase value μ(exp)(g) = 1.855 D for the static dipole moment. The widths of the Gaussian dipoles and, for ν = 4 and 5, also the electrostatic geometries of these so-called TLνP models are derived from self-consistent DFT/PMM calculations, and the parameters of the Buckingham potentials (and the static TL3P dipole moment) are estimated from molecular dynamics (MD) simulations. The high quality of the resulting models is demonstrated for the observables targeted during optimization (potential energy per molecule, pressure, radial distribution functions) and a series of predicted properties (quadrupole moments, density at constant pressure, dielectric constant, diffusivity, viscosity, compressibility, heat capacity) at certain standard conditions. Remaining deficiencies and possible ways for their removal are discussed.

AUTOMATED FORCE FIELD PARAMETERIZATION FOR NON-POLARIZABLE AND POLARIZABLE ATOMIC MODELS BASED ON AB INITIO TARGET DATA

Classical molecular dynamics (MD) simulations based on atomistic models are increasingly used to study a wide range of biological systems. A prerequisite for meaningful results from such simulations is an accurate molecular mechanical force field. Most biomolecular simulations are currently based on the widely used AMBER and CHARMM force fields, which were parameterized and optimized to cover a small set of basic compounds corresponding to the natural amino acids and nucleic acid bases. Atomic models of additional compounds are commonly generated by analogy to the parameter set of a given force field. While this procedure yields models that are internally consistent, the accuracy of the resulting models can be limited. In this work, we propose a method, General Automated Atomic Model Parameterization (GAAMP), for generating automatically the parameters of atomic models of small molecules using the results from ab initio quantum mechanical (QM) calculations as target data. Force fields that were previously developed for a wide range of model compounds serve as initial guess, although any of the final parameter can be optimized. The electrostatic parameters (partial charges, polarizabilities and shielding) are optimized on the basis of QM electrostatic potential (ESP) and, if applicable, the interaction energies between the compound and water molecules. The soft dihedrals are automatically identified and parameterized by targeting QM dihedral scans as well as the energies of stable conformers. To validate the approach, the solvation free energy is calculated for more than 200 small molecules and MD simulations of 3 different proteins are carried out.

Matching of additive and polarizable force fields for multiscale condensed phase simulations

Inclusion of electronic polarization effects is one of the key aspects in which the accuracy of current biomolecular force fields may be improved. The principal drawback of such approaches is the computational cost, which typically ranges from 3 - 10 times that of the equivalent additive model, and may be greater for more sophisticated treatments of polarization or other many-body effects. Here, we present a multiscale approach which may be used to enhance the sampling in simulations with polarizable models, by using the additive model as a tool to explore configuration space. We use a method based on information theory to determine the charges for an additive model that has optimal overlap with the polarizable one, and we demonstrate the feasibility of enhancing sampling via a hybrid replica exchange scheme for several model systems. An additional advantage is that, in the process, we obtain a systematic method for deriving charges for an additive model that will be the natural complement to its polarizable parent. The additive charges are found by an effective coarse-graining of the polarizable force field, rather than by ad hoc procedures.

Investigation of polarization effects in the gramicidin A channel from ab initio molecular dynamics simulations

Polarization is an important component of molecular interactions and is expected to play a particularly significant role in inhomogeneous environments such as pores and interfaces. Here we investigate the effects of polarization in the gramicidin A ion channel by performing quantum mechanics/molecular mechanics molecular dynamics (MD) simulations and comparing the results with those obtained from classical MD simulations with non-polarizable force fields. We consider the dipole moments of backbone carbonyl groups and channel water molecules as well as a number of structural quantities of interest. The ab initio results show that the dipole moments of the carbonyl groups and water molecules are highly sensitive to the hydrogen bonds (H-bonds) they participate in. In the absence of a K(+) ion, water molecules in the channel are quite mobile, making the H-bond network highly dynamic. A central K(+) ion acts as an anchor for the channel waters, stabilizing the H-bond network and thereby increasing their average dipole moments. In contrast, the K(+) ion has little effect on the dipole moments of the neighboring carbonyl groups. The weakness of the ion-peptide interactions helps to explain the near diffusion-rate conductance of K(+) ions through the channel. We also address the sampling issue in relatively short ab initio MD simulations. Results obtained from a continuous 20 ps ab initio MD simulation are compared with those generated by sampling ten windows from a much longer classical MD simulation and running each window for 2 ps with ab initio MD. Both methods yield similar results for a number of quantities of interest, indicating that fluctuations are fast enough to justify the short ab initio MD simulations.

Visualizing functional motions of membrane transporters with molecular dynamics simulations

Computational modeling and molecular simulation techniques have become an integral part of modern molecular research. Various areas of molecular sciences continue to benefit from, indeed rely on, the unparalleled spatial and temporal resolutions offered by these technologies, to provide a more complete picture of the molecular problems at hand. Because of the continuous development of more efficient algorithms harvesting ever-expanding computational resources, and the emergence of more advanced and novel theories and methodologies, the scope of computational studies has expanded significantly over the past decade, now including much larger molecular systems and far more complex molecular phenomena. Among the various computer modeling techniques, the application of molecular dynamics (MD) simulation and related techniques has particularly drawn attention in biomolecular research, because of the ability of the method to describe the dynamical nature of the molecular systems and thereby to provide a more realistic representation, which is often needed for understanding fundamental molecular properties. The method has proven to be remarkably successful in capturing molecular events and structural transitions highly relevant to the function and/or physicochemical properties of biomolecular systems. Herein, after a brief introduction to the method of MD, we use a number of membrane transport proteins studied in our laboratory as examples to showcase the scope and applicability of the method and its power in characterizing molecular motions of various magnitudes and time scales that are involved in the function of this important class of membrane proteins.

A Critical Assessment of Two-Body and Three-Body Interactions in Water

The microscopic behavior of water under different conditions and in different environments remains the subject of intense debate. A great number of the controversies arise due to the contradictory predictions obtained within different theoretical models. Relative to conclusions derived from force fields or density functional theory, there is comparably less room to dispute highly correlated electronic structure calculations. Unfortunately, such ab initio calculations are severely limited by system size. In this study, a detailed analysis of the two- and three-body water interactions evaluated at the CCSD(T) level is carried out to quantitatively assess the accuracy of several force fields, DFT models, and ab initio based interaction potentials that are commonly used in molecular simulations. On the basis of this analysis, a new model, HBB2-pol, is introduced which is capable of accurately mapping CCSD(T) results for water dimers and trimers into an efficient analytical function. The accuracy of HBB2-pol is further established through comparison with the experimentally determined second and third virial coefficients.

Polarizable force fields

This chapter provides an overview of the most common methods for including an explicit description of electronic polarization in molecular mechanics force fields: the induced point dipole, shell, and fluctuating charge models. The importance of including polarization effects in biomolecular simulations is discussed, and some of the most important achievements in the development of polarizable biomolecular force fields to date are highlighted.