Molecular force fields have been approaching a generational transition over the past several years, moving away from well-established and well-tuned, but intrinsically limited, fixed point charge models toward more intricate and expensive polarizable models that should allow more accurate description of molecular properties. The recently introduced AMOEBA force field is a leading publicly available example of this next generation of theoretical model, but to date, it has only received relatively limited validation, which we address here. We show that the AMOEBA force field is in fact a significant improvement over fixed charge models for small molecule structural and thermodynamic observables in particular, although further fine-tuning is necessary to describe solvation free energies of drug-like small molecules, dynamical properties away from ambient conditions, and possible improvements in aromatic interactions. State of the art electronic structure calculations reveal generally very good agreement with...

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Current Status of the AMOEBA Polarizable Force Field

Molecular dynamics (MD) and related methods are close to becoming routine computational tools for drug discovery. Their main advantage is in explicitly treating structural flexibility and entropic effects. This allows a more accurate estimate of the thermodynamics and kinetics associated with drug-target recognition and binding, as better algorithms and hardware architectures increase their use. Here, we review the theoretical background of MD and enhanced sampling methods, focusing on free-energy perturbation, metadynamics, steered MD, and other methods most consistently used to study drug-target binding. We discuss unbiased MD simulations that nowadays allow the observation of unsupervised ligand-target binding, assessing how these approaches help optimizing target affinity and drug residence time toward improved drug efficacy. Further issues discussed include allosteric modulation and the role of water molecules in ligand binding and optimization. We conclude by calling for more prospective studies to attest to these methods' utility in discovering novel drug candidates.

Role of Molecular Dynamics and Related Methods in Drug Discovery.

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...

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Polarizable Atomic Multipole-Based AMOEBA Force Field for Proteins

Binding of Small-Molecule Ligands to Proteins: “What You See” Is Not Always “What You Get”

An increasing number of studies have reported computations of the standard (absolute) binding free energy of small ligands to proteins using molecular dynamics (MD) simulations and explicit solvent molecules that are in good agreement with experiments. This encouraging progress suggests that physics-based approaches hold the promise of making important contributions to the process of drug discovery and optimization in the near future. Two types of approaches are principally used to compute binding free energies with MD simulations. The most widely known is the alchemical double decoupling method, in which the interaction of the ligand with its surroundings are progressively switched off. It is also possible to use a potential of mean force (PMF) method, in which the ligand is physically separated from the protein receptor. For both of these computational approaches, restraining potentials may be activated and released during the simulation for sampling efficiently the changes in translational, rotational, and conformational freedom of the ligand and protein upon binding. Because such restraining potentials add bias to the simulations, it is important that their effects be rigorously removed to yield a binding free energy that is properly unbiased with respect to the standard state. A review of recent results is presented, and differences in computational methods are discussed. Examples of computations with T4-lysozyme mutants, FKBP12, SH2 domain, and cytochrome P450 are discussed and compared. Remaining difficulties and challenges are highlighted.

Computations of standard binding free energies with molecular dynamics simulations.

The binding of charged ligands benzamidine and diazamidine to trypsin was investigated by using a polarizable potential energy function and explicit-water molecular dynamics simulations. The binding free energies were computed from the difference between the free energies of decoupling the ligand from water and protein environments. Both the absolute and the relative free energies from the perturbation simulations agree with experimental measurements to within 0.5 kcal.mol(-1). Comparison of free-energy components sampled from different thermodynamic paths indicates that electrostatics is the main driving force behind benzamidine recognition of trypsin. The contribution of electronic polarization to binding appears to be crucial. By computing the free-energy contribution caused by the polarization between the ligand and its surroundings, we found that polarization has the opposite effect in dissimilar environments. Although polarization favors ligand solvation in water, it weakens the protein-ligand attraction by screening the electrostatic interaction between trypsin and benzamidine. We also examined the relative binding free energies of a benzamidine analog diazamidine to trypsin. The changes in free energy on benzamidine-diazamidine substitution were tens of kilocalories in both water and trypsin environments; however, the change in the total binding free energy is <2 kcal.mol(-1) because of cancellation, consistent with the experimental results. Overall, our results suggest that the use of a polarizable force field, given adequate sampling, is capable of achieving chemical accuracy in molecular simulations of protein-ligand recognition.

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Calculation of protein–ligand binding free energy by using a polarizable potential

This paper presents a general coarse-grained molecular mechanics model based on electric point multipole expansion and Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] potential. Coarse graining of van der Waals potential is achieved by treating molecules as soft uniaxial ellipsoids interacting via a generalized anisotropic Gay-Berne function. The charge distribution is represented by point multipole expansion, including point charge, dipole, and quadrupole moments placed at the center of mass. The Gay-Berne and point multipole potentials are combined in the local reference frame defined by the inertial frame of the all-atom counterpart. The coarse-grained model has been applied to rigid-body molecular dynamics simulations of molecular liquids including benzene and methanol. The computational efficiency is improved by several orders of magnitude, while the results are in reasonable agreement with all-atom models and experimental data. We also discuss the implications of using point multipole for polar molecules capable of hydrogen bonding and the applicability of this model to a broad range of molecular systems including highly charged biopolymers.

Generalized coarse-grained model based on point multipole and Gay-Berne potentials.

We present here a recent development of a generalized coarse-grained model for use in molecular simulations. In this model, interactions between coarse-grained particles consist of both van der Waals and explicit electrostatic components. As a result, the coarse-grained model offers the transferability that is lacked by most current effective-potential based approaches. The previous center-of-mass framework (P. A. Golubkov and P. Ren, J. Chem. Phys., 2006, 125, 64103) is generalized here to include arbitrary off-center interaction sites for both Gay-Berne and multipoles. The new model has been applied to molecular dynamic simulations of neat methanol liquid. By placing a single point multipole at the oxygen atom rather than at the center of mass of methanol, there is a significant improvement in the ability to capture hydrogen-bonding. The critical issue of transferability of the coarse-grained model is verified on methanol-water mixtures, using parameters derived from neat liquids without any modification. The mixture density and internal energy from coarse-grained molecular dynamics simulations show good agreement with experimental measurements, on a par with what has been obtained from more detailed atomic models. By mapping the dynamics trajectory from the coarse-grained simulation into the all-atom counterpart, we are able to investigate atomic-level structure and interaction. Atomic radial distribution functions of neat methanol, neat water and mixtures compare favorably to experimental measurements. Furthermore, hydrogen-bonded 6- and 7-molecule chains of water and methanol observed in the mixture are in agreement with previous atomic simulations.

A transferable coarse-grained model for hydrogen-bonding liquids

The human tissue kallikrein (KLK) family contains 15 secreted serine proteases that are expressed in a wide range of tissues and have been implicated in different physiological functions and disease states. Of these, KLK1 has been shown to be involved in the regulation of multiple physiological processes such as blood pressure, smooth muscle contraction, and vascular cell growth. KLK6 is overexpressed in breast and ovarian cancer tissues and has been shown to cleave peptide derived from human myelin protein and Aβ amyloid peptide in vitro. Here we analyzed the substrate specificity of KLK1 and KLK6, by substrate phage display using a random octapeptide library. Consistent with earlier biochemical data, KLK1 was shown to exhibit both trypsin- and chymotrypsin-like selectivities with Tyr/Arg preferred at site P1, Ser/Arg strongly preferred at P1′, and Phe/Leu at P2. KLK6 displayed trypsin-like activity, with the P1 position occupied only by Arg and a strong preference for Ser in P1′. Docking simulations of consensus peptide provide information on the identity of the enzyme residues that are responsible for substrate binding. Bioinformatic analysis suggested several putative KLK6 protein substrates, such as ionotropic glutamate receptor (GluR) and synphilin.

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Pavel A. Golubkov

Papers

Calculation of protein–ligand binding free energy by using a polarizable potential

Generalized coarse-grained model based on point multipole and Gay-Berne potentials.

A transferable coarse-grained model for hydrogen-bonding liquids

Substrate specificity of human kallikreins 1 and 6 determined by phage display

Inactivation of the phenylpyruvate tautomerase activity of macrophage migration inhibitory factor by 2-oxo-4-phenyl-3-butynoate.