A Polarizable Force Field and Continuum Solvation Methodology for Modeling of Protein−Ligand Interactions (original) (raw)
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Journal of Computational Chemistry, 2004
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 -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 Å (with a range of 1.0 to 2.5 Å). 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 Å (both helix and -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.
Protein–Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation
Journal of Chemical Theory and Computation, 2015
Accurate yet efficient computational models of solvent environment are central for most calculations that rely on atomistic modeling, such as prediction of protein-ligand binding affinities. In this study, we evaluate the accuracy of a recently developed generalized Born implicit solvent model, GBNSR6 (Aguilar et al. J. Chem. Theory Comput. 2010, 6, 3613-3639), in estimating the electrostatic solvation free energies (ΔG pol) and binding free energies (ΔΔG pol) for small proteinligand complexes. We also compare estimates based on three different explicit solvent models (TIP3P, TIP4PEw and OPC). The two main findings are as follows. First, the deviation (RMSD=7.04 kcal/mol) of GBNSR6 binding affinities from commonly used TIP3P reference values is comparable to the deviations between explicit models themselves, e.g. TIP4PEw vs. TIP3P (RMSD=5.30 kcal/mol). A simple uniform adjustment of the atomic radii by a single scaling factor reduces the RMS deviation of GBNSR6 from TIP3P to within the above "error margin"-differences between ΔΔG pol estimated by different common explicit solvent models. The simple radii scaling virtually eliminates the systematic deviation (ΔΔG pol) between GBNSR6 and two out of the three explicit water models, and significantly reduces the deviation from the third explicit model. Second, the differences between electrostatic binding energy estimates from different explicit models is disturbingly large; for example, the deviation between TIP4PEw and TIP3P estimates of ΔΔG pol values can be up to ~50% in relative error, or ~9 kcal/mol in absolute error, which is significantly larger than "chemical accuracy" goal of ~1 kcal/mol. The absolute ΔG pol calculated with different explicit models could differ by tens of kcal/mol. These discrepancies point to unacceptably high sensitivity of binding affinity estimates to the choice of common explicit water models. The absence of a clear "gold standard" among these models strengthens the case for the use of accurate implicit solvation models for binding energetics, which may be orders of magnitude faster.
Journal of Computational Chemistry, 2002
We present results of developing a methodology suitable for producing molecular mechanics force fields with explicit treatment of electrostatic polarization for proteins and other molecular system of biological interest. The technique allows simulation of realistic-size systems. Employing high-level ab initio data as a target for fitting allows us to avoid the problem of the lack of detailed experimental data. Using the fast and reliable quantum mechanical methods supplies robust fitting data for the resulting parameter sets. As a result, gas-phase many-body effects for dipeptides are captured within the average RMSD of 0.22 kcal/mol from their ab initio values, and conformational energies for the di-and tetrapeptides are reproduced within the average RMSD of 0.43 kcal/mol from their quantum mechanical counterparts. The latter is achieved in part because of application of a novel torsional fitting technique recently developed in our group, which has already been used to greatly improve accuracy of the peptide conformational equilibrium prediction with the OPLS-AA force field. 1 Finally, we have employed the newly developed first-generation model in computing gas-phase conformations of real proteins, as well as in molecular dynamics studies of the systems. The results show that, although the overall accuracy is no better than what can be achieved with a fixed-charges model, the methodology produces robust results, permits reasonably low computational cost, and avoids other computational problems typical for polarizable force fields. It can be considered as a solid basis for building a more accurate and complete second-generation model.
Biomolecular electrostatics and solvation: a computational perspective
Quarterly reviews of biophysics, 2012
An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of t...
Solvent effects play a crucial role in mediating the interactions between proteins and their ligands. Implicit solvent models offer some advantages for modeling these interactions, but they have not been parameterized on such complex problems, and therefore, it is not clear how reliable they are. We have studied the binding of an octapeptide ligand to the murine MHC class I protein using both explicit solvent and implicit solvent models. The solvation free energy calculations are more than 10 3 faster using the Surface Generalized Born implicit solvent model compared to FEP simulations with explicit solvent. For some of the electrostatic calculations needed to estimate the binding free energy, there is near quantitative agreement between the explicit and implicit solvent model results; overall, the qualitative trends in the binding predicted by the explicit solvent FEP simulations are reproduced by the implicit solvent model. With an appropriate choice of reference system based on the binding of the discharged ligand, electrostatic interactions are found to enhance the binding affinity because the favorable Coulomb interaction energy between the ligand and protein more than compensates for the unfavorable free energy cost of partially desolvating the ligand upon binding. Some of the effects of Correspondence to: R. M. Levy;
Charge Transfer and Polarization in Solvated Proteins from Ab Initio Molecular Dynamics
The Journal of Physical Chemistry Letters, 2011
b S Supporting Information I t has been long recognized that water plays an important role in protein structure and dynamics. Water on the protein surface, often referred to as biological water, 1 is an essential element of protein interactions 2 and enzyme function. 3 Some water molecules reside in the same location near the protein surface for a long time 1 compared with the typical relaxation time under bulk conditions. These water molecules form strong hydrogen bonds 4 and can be directly observed in accurate model-free crystallographic experiments. 5 Classical force fields have made tremendous progress in describing interactions at proteinÀwater interfaces and can accurately predict such important energetic properties as solvation free energies of amino acids. 6,7 However, most of these theoretical models use a simplified "charged ball-and-spring" representation that is incapable of describing quantum mechanical phenomena like charge transfer (CT) and electronic polarization. Recently, it was demonstrated that CT effects account for approximately one-third of the binding energy in a neutral water dimer, 8 and for stronger H-bonds, one can anticipate this contribution to be even larger. Although CT and polarization effects are typically parametrized in classical force fields implicitly as a part of the electrostatic and Lennard-Jones two-body interactions, it remains an open question as to how accurately such approximations can describe biological water. Another recent study has stressed the importance of CT interactions in proteins and suggested this missing term should be explicitly included in future classical force field parametrizations. Although the effect of explicit solvent on protein structure and function has been studied for more than two decades, 4 solvated proteins have almost exclusively been treated using nonpolarizable classical force fields. Only a few attempts have been made to study proteinÀwater systems at higher levels of theory, such as semiempirical 10À12,35 or fragment molecular orbital 13 approaches. However, even these efforts have still relied on molecular dynamics (MD) simulations with classical force fields to provide atomic coordinates for higher level calculations. More rigorous treatment of solvated proteins by means of HartreeÀFock (HF) or density functional theory (DFT) methods is clearly needed. Ideally, one would use ab initio rather than classical MD trajectories in such calculations because classical and ab initio dynamics could potentially sample configurational space quite differently. In fact, DFT MD has been applied to study model systems such as solvated glycine dipeptide, 14 and substantial CT was observed in these simulations. However, to the best of our knowledge, ab initio (HF or DFT) MD has never been used to treat entire proteins. The major obstacle to the use of ab initio methods in this context is their high computational cost. Recent single-point energy calculations of solvated rubredoxin represent an illustrative example. 15 Calculation of the energy for the resulting 2825 atoms required over 1 h on 8196 processor cores. Dynamical simulations requiring hundreds or thousands of such calculations would appear to be completely out of reach. Fortunately, graphical processing units (GPUs) (essentially consumer videogame graphics cards) have emerged as a powerful alternative to traditional processors. We have redesigned algorithms for electronic structure theory and ab initio MD to leverage the strengths of GPUs, with promising results. 16À18 In this Letter, we ABSTRACT: Charge transfer at the Bovine pancreatic trypsin inhibitor (BPTI) proteinÀwater interface was analyzed by means of ab initio BornÀOppenheimer molecular dynamics simulation of the entire protein running on graphical processing units (GPUs). The efficiency of the GPU-based quantum chemistry algorithms implemented in our TeraChem program enables us to perform these calculations on a desktop computer. Mulliken and Voronoi deformation density (VDD) population analysis reveals that between 2.0 and 3.5 electrons are transferred from surrounding water molecules to the protein over the course of the 8.8 ps simulation. Solving for the electronic structure of BPTI in the absence of surrounding water molecules (i.e., in the gas phase) leads to large intraprotein charge transfer, where approximately one electron in total is transferred from neutral to polar residues. Solvation relieves this polarization stress, leading to a neutralization of the excess positive charge of the neutral residues.
Journal of Computational Chemistry, 2009
We have calculated the binding free energies of a series of benzamidine-like inhibitors to trypsin with a polarizable force field using both explicit and implicit solvent approaches. Free energy perturbation has been performed for the ligands in bulk water and in protein complex with molecular dynamics simulations. The binding free energies calculated from explicit solvent simulations are well within the accuracy of experimental measurement and the direction of change is predicted correctly in all cases. We analyzed the molecular dipole moments of the ligands in gas, water and protein environments. Neither binding affinity nor ligand solvation free energy in bulk water shows much dependence on the molecular dipole moments of the ligands. Substitution of the aromatic or the charged group in the ligand results in considerable change in the solvation energy in bulk water and protein whereas the binding affinity varies insignificantly due to cancellation. The effect of chemical modification on ligand charge distribution is mostly local. Replacing benzene with diazine has minimal impact on the atomic multipoles at the amidinium group. We have also utilized an implicit solvent based end-state approach to evaluate the binding free energies of these inhibitors. In this approach, the polarizable multipole model combined with Poisson-Boltzmann/surface area (PMPB/ SA) provides the electrostatic interaction energy and the polar solvation free energy. Overall the relative binding free energies obtained from the MM-PMPB/SA model are in good agreement with the experimental data. q
PMFF: Development of a Physics-Based Molecular Force Field for Protein Simulation and Ligand Docking
The Journal of Physical Chemistry B, 2020
The physics-based molecular force field (PMFF) was developed by integrating a set of potential energy functions in which each term in an intermolecular potential energy function is derived based on experimental values, such as the dipole moments, lattice energy, proton transfer energy, and X-ray crystal structures. The term "physics-based" is used to emphasize the idea that the experimental observables that are considered to be the most relevant to each term are used for the parameterization rather than parameterizing all observables together against the target value. PMFF uses MM3 intramolecular potential energy terms to describe intramolecular interactions and includes an implicit solvation model specifically developed for the PMFF. We evaluated the PMFF in three ways. We concluded that the PMFF provides reliable information based on the structure in a biological system and interprets the biological phenomena accurately by providing more accurate evidence of the biological phenomena.
Journal of Chemical Theory and Computation, 2007
We present an overview of the SIBFA polarizable molecular mechanics procedure, which is formulated and calibrated on the basis of quantum chemistry (QC). It embodies nonclassical effects such as electrostatic penetration, exchange-polarization, and charge transfer. We address the issues of anisotropy, nonadditivity, and transferability by performing parallel QC computations on multimolecular complexes. These encompass multiply H-bonded complexes and polycoordinated complexes of divalent cations. Recent applications to the docking of inhibitors to Zn-metalloproteins are presented next, namely metallo-lactamase, phosphomannoisomerase, and the nucleocapsid of the HIV-1 retrovirus. Finally, toward third-generation intermolecular potentials based on density fitting, we present the development of a novel methodology, the Gaussian electrostatic model (GEM), which relies on ab initio-derived fragment electron densities to compute the components of the total interaction energy. As GEM offers the possibility of a continuous electrostatic model going from distributed multipoles to densities, it allows an inclusion of short-range quantum effects in the molecular mechanics energies. The perspectives of an integrated SIBFA/GEM/QM procedure are discussed.
Scientific reports, 2016
Interfacial waters are increasingly appreciated as playing a key role in protein-protein interactions. We report on a study of the prediction of interfacial water positions by both Molecular Dynamics and explicit solvent-continuum electrostatics based on the Dipolar Poisson-Boltzmann Langevin (DPBL) model, for three test cases: (i) the barnase/barstar complex (ii) the complex between the DNase domain of colicin E2 and its cognate Im2 immunity protein and (iii) the highly unusual anti-freeze protein Maxi which contains a large number of waters in its interior. We characterize the waters at the interface and in the core of the Maxi protein by the statistics of correctly predicted positions with respect to crystallographic water positions in the PDB files as well as the dynamic measures of diffusion constants and position lifetimes. Our approach provides a methodology for the evaluation of predicted interfacial water positions through an investigation of water-mediated inter-chain cont...