Assessing the quality of absolute hydration free energies among CHARMM‐compatible ligand parameterization schemes

Multipurpose atom‐typer for CHARMM (MATCH), an atom‐typing toolset for molecular mechanics force fields, was recently developed in our laboratory. Here, we assess the ability of MATCH‐generated parameters and partial atomic charges to reproduce experimental absolute hydration free energies for a series of 457 small neutral molecules in GBMV2, Generalized Born with a smooth SWitching (GBSW), and fast analytical continuum treatment of solvation (FACTS) implicit solvent models. The quality of hydration free energies associated with small molecule parameters obtained from ParamChem, SwissParam, and Antechamber are compared. Given optimized surface tension coefficients for scaling the surface area term in the nonpolar contribution, these automated parameterization schemes with GBMV2 and GBSW demonstrate reasonable agreement with experimental hydration free energies (average unsigned errors of 0.9–1.5 kcal/mol and R² of 0.63–0.87). GBMV2 and GBSW consistently provide slightly more accurate estimates than FACTS, whereas Antechamber parameters yield marginally more accurate estimates than the current generation of MATCH, ParamChem, and SwissParam parameterization strategies. Modeling with MATCH libraries that are derived from different CHARMM topology and parameter files highlights the importance of having sufficient coverage of chemical space within the underlying databases of these automated schemes and the benefit of targeting specific functional groups for parameterization efforts to maximize both the breadth and the depth of the parameterized space. © 2013 Wiley Periodicals, Inc.     

The SGB/NP hydration free energy model based on the surface generalized born solvent reaction field and novel nonpolar hydration free energy estimators

The development and parameterization of a solvent potential of mean force designed to reproduce the hydration thermodynamics of small molecules and macromolecules aimed toward applications in conformation prediction and ligand binding free energy prediction is presented. The model, named SGB/NP, is based on a parameterization of the Surface Generalized Born continuum dielectric electrostatic model using explicit solvent free energy perturbation calculations and a newly developed nonpolar hydration free energy estimator motivated by the results of explicit solvent simulations of the thermodynamics of hydration of hydrocarbons. The nonpolar model contains, in addition to the more commonly used solvent accessible surface area term, a component corresponding to the attractive solute-solvent interactions. This term is found to be important to improve the accuracy of the model, particularly for cyclic and hydrogen bonding compounds. The model is parameterized against the experimental hydration free energies of a set of small organic molecules. The model reproduces the experimental hydration free energies of small organic molecules with an accuracy comparable or superior to similar models employing more computationally demanding estimators and/or a more extensive set of parameters.     

Application of the multiensemble sampling to the hydration free energy

We demonstrate the feasibility of using multiensemble sampling method (MESM) to determine the free energy difference between two far states for which the configurational distributions do not overlap at all. The MESM is a recently developed non‐Boltzmann sampling technique. The free energy of charging a sodium ion in water is accurately calculated in a single simulation, introducing nine intermediate ionic states. This is due to the ability of the method to explore the relevant parts of configuration space equally for every state, and this ability comes from the universality of weighting function W and the simplicity in adjusting its parameters. Detailed procedures of adjusting the parameters are presented. The comparison with a free energy perturbation method (FEPM) shows that the MESM is more reliable and efficient. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1004–1009, 2001     

计算受体和配体结合自由能的新方法

利用ABEEMσπ浮动电荷力场与连续介质模型相结合的方法,计算了受体和配体的结合自由能.将结合自由能分解为真空中的力场作用项、溶剂化能量以及熵效应.由于ABEEMσπ/MM方法充分考虑了外界环境发生变化引起的体系中各个位点之间的电荷极化,因而极大地提高了结合自由能的计算精度.利用该方法计算的2个复合物的结合自由能与实验值的偏差均小于0.5kJ/mol.     

A highly efficient hybrid method for calculating the hydration free energy of a protein

We develop a new method for calculating the hydration free energy (HFE) of a protein with any net charge. The polar part of the energetic component in the HFE is expressed as a linear combination of four geometric measures (GMs) of the protein structure and the generalized Born (GB) energy plus a constant. The other constituents in the HFE are expressed as linear combinations of the four GMs. The coefficients (including the constant) in the linear combinations are determined using the three‐dimensional reference interaction site model (3D‐RISM) theory applied to sufficiently many protein structures. Once the coefficients are determined, the HFE and its constituents of any other protein structure are obtained simply by calculating the four GMs and GB energy. Our method and the 3D‐RISM theory give perfectly correlated results. Nevertheless, the computation time required in our method is over four orders of magnitude shorter.     

Rapid approximate calculation of water binding free energies in the whole hydration domain of (bio)macromolecules

The evaluation of water binding free energies around solute molecules is important for the thermodynamic characterization of hydration or association processes. Here, a rapid approximate method to estimate water binding free energies around (bio)macromolecules from a single molecular dynamics simulation is presented. The basic idea is that endpoint free‐energy calculation methods are applied and the endpoint quantities are monitored on a three‐dimensional grid around the solute. Thus, a gridded map of water binding free energies around the solute is obtained, that is, from a single short simulation, a map of favorable and unfavorable water binding sites can be constructed. Among the employed free‐energy calculation methods, approaches involving endpoint information pertaining to actual thermodynamic integration calculations or endpoint information as exploited in the linear interaction energy method were examined. The accuracy of the approximate approaches was evaluated on the hydration of a cage‐like molecule representing either a nonpolar, polar, or charged water binding site and on α‐ and β‐cyclodextrin molecules. Among the tested approaches, the linear interaction energy method is considered the most viable approach. Applying the linear interaction energy method on the grid around the solute, a semi‐quantitative thermodynamic characterization of hydration around the whole solute is obtained. Disadvantages are the approximate nature of the method and a limited flexibility of the solute. © 2016 Wiley Periodicals, Inc.     

Evaluating the relative free energy of hydration of new thrombin inhibitor candidates using the finite difference thermodynamic integration (FDTI) method

Thrombin is a serine protease involved in blood coagulation. Since thrombin inhibitors appear to be effective in the treatment and prevention of thrombotic and embolic disorders, considerable attention has been focused on the structure and interactions of the enzyme. In this work, we calculated the relative free energies of hydration of the new thrombin inhibitor candidates, p‐substituted derivatives of benzamidine, a well‐known noncovalent thrombin inhibitor. We used molecular dynamics and the finite difference thermodynamic integration (FDTI) algorithm within the Discover program of MSI. We have shown that the orthogonality problem that occurs in the calculation of intraperturbed‐group contributions to the free energy is treated adequately by the FDTI method. We have also shown that problems of singularity and convergence in free energy calculations can be properly solved using this method. To conclude, the calculated free energies of hydration gave the following order of solvation for the candidates: p‐(2‐oxo‐1‐propyl)benzamidine > p‐methylbenzamidine > p‐ethylbenzamidine > p‐(1‐propyl)benzamidine > benzamidine. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Accuracy of free energies of hydration using CM1 and CM3 atomic charges

Absolute free energies of hydration (DeltaGhyd) have been computed for 25 diverse organic molecules using partial atomic charges derived from AM1 and PM3 wave functions via the CM1 and CM3 procedures of Cramer, Truhlar, and coworkers. Comparisons are made with results using charges fit to the electrostatic potential surface (EPS) from ab initio 6-31G* wave functions and from the OPLS-AA force field. OPLS Lennard-Jones parameters for the organic molecules were used together with the TIP4P water model in Monte Carlo simulations with free energy perturbation theory. Absolute free energies of hydration were computed for OPLS united-atom and all-atom methane by annihilating the solutes in water and in the gas phase, and absolute DeltaGhyd values for all other molecules were computed via transformation to one of these references. Optimal charge scaling factors were determined by minimizing the unsigned average error between experimental and calculated hydration free energies. The PM3-based charge models do not lead to lower average errors than obtained with the EPS charges for the subset of 13 molecules in the original study. However, improvement is obtained by scaling the CM1A partial charges by 1.14 and the CM3A charges by 1.15, which leads to average errors of 1.0 and 1.1 kcal/mol for the full set of 25 molecules. The scaled CM1A charges also yield the best results for the hydration of amides including the E/Z free-energy difference for N-methylacetamide in water.     

A biomolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6

Successive parameterizations of the GROMOS force field have been used successfully to simulate biomolecular systems over a long period of time. The continuing expansion of computational power with time makes it possible to compute ever more properties for an increasing variety of molecular systems with greater precision. This has led to recurrent parameterizations of the GROMOS force field all aimed at achieving better agreement with experimental data. Here we report the results of the latest, extensive reparameterization of the GROMOS force field. In contrast to the parameterization of other biomolecular force fields, this parameterization of the GROMOS force field is based primarily on reproducing the free enthalpies of hydration and apolar solvation for a range of compounds. This approach was chosen because the relative free enthalpy of solvation between polar and apolar environments is a key property in many biomolecular processes of interest, such as protein folding, biomolecular association, membrane formation, and transport over membranes. The newest parameter sets, 53A5 and 53A6, were optimized by first fitting to reproduce the thermodynamic properties of pure liquids of a range of small polar molecules and the solvation free enthalpies of amino acid analogs in cyclohexane (53A5). The partial charges were then adjusted to reproduce the hydration free enthalpies in water (53A6). Both parameter sets are fully documented, and the differences between these and previous parameter sets are discussed.     

Calculation of hydration free energy for a solute with many atomic sites using the RISM theory: A robust and efficient algorithm

We have developed an algorithm for solving the reference interaction site model (RISM) equations for water near a solute molecule with many atomic sites (interaction sites). It is a hybrid of the Newton–Raphson and Picard methods and is judiciously constructed. Various considerations are given so that the computer time can be saved as much as possible. The robustness and high efficiency of the algorithm has been demonstrated for calculating hydration free energies of Met-enkephalin (a peptide with 75 sites) with different conformations. The Jacobian matrix is treated as part of the input data, and it has been found that the same matrix can be used for a considerably large set of different conformations of the solute molecule. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1320–1326, 1997     

Comparative assessment of computational methods for the determination of solvation free energies in alcohol‐based molecules

The determination of differences in solvation free energies between related drug molecules remains an important challenge in computational drug optimization, when fast and accurate calculation of differences in binding free energy are required. In this study, we have evaluated the performance of five commonly used polarized continuum model (PCM) methodologies in the determination of solvation free energies for 53 typical alcohol and alkane small molecules. In addition, the performance of these PCM methods, of a thermodynamic integration (TI) protocol and of the Poisson–Boltzmann (PB) and generalized Born (GB) methods, were tested in the determination of solvation free energies changes for 28 common alkane‐alcohol transformations, by the substitution of an hydrogen atom for a hydroxyl substituent. The results show that the solvation model D (SMD) performs better among the PCM‐based approaches in estimating solvation free energies for alcohol molecules, and solvation free energy changes for alkane‐alcohol transformations, with an average error below 1 kcal/mol for both quantities. However, for the determination of solvation free energy changes on alkane‐alcohol transformation, PB and TI yielded better results. TI was particularly accurate in the treatment of hydroxyl groups additions to aromatic rings (0.53 kcal/mol), a common transformation when optimizing drug‐binding in computer‐aided drug design. © 2013 Wiley Periodicals, Inc.     

Theoretical determination of absolute free energy of reduction of plastoquinone-9 in photosystem II and of plastoquinone-n in DMF

We employed static continuum electrostatics and multi-conformation continuum electrostatics (MCCE) methods to determine the reduction potential () of PQ-9 in a section of Photosystem II (PSII). Both methods relied on the finite difference Poisson–Boltzmann (FDPB) solution. The static method brings out a value (0.01 V) that is close to the experimental one (0.05 V), thereby demonstrating that the surrounding environment critically decides the net free energy change. The value obtained from MCCE (0.04 V) is even closer to the observed value, thereby indicating the importance of protein side-chain and proton motions in the electron transfer process. Furthermore, density functional theory-dielectric polarisable continuum model (DFT-DPCM) was employed to calculate the absolute free energy of reduction of plastoquinone-n (PQ-n, where n is the number of isoprenoid units) in N,N dimethyl formamide (DMF) solvent. The DFT-DPCM method produced reduction potential values of −0.59 and −0.65 V for PQ-1 and PQ-9, respectively. These are more or less in agreement with the experimentally reported values of −0.64 and −0.62 V, respectively.     

Improved precision and efficiency of free energy calculations for small systems using lambda-scaled atomic masses and separating conformational and transformational sampling

We present results showing the importance of appropriate treatment of atomic masses in molecular dynamics (MD)-based single topology free-energy perturbations (FEPs) on small molecule systems. The reversibility of gas phase simulations is significantly improved by scaling the atomic mass of mutated atoms with the lambda variable normally used for the scaling of energy terms. Because this effect is less pronounced for solvated systems, it will not cancel in estimates of the relative hydration free energy difference. The advantage of mass scaling is demonstrated by a null mutation of ethane to ethane and the calculation of the relative hydration free energy difference between ethane and n-propane. Furthermore, it is found that the simulation time necessary for converged MD/FEPs is prohibitively large for relative hydration free energy calculations on cyclic alkanes. Therefore, we explore an alternative free energy pathway including strongly constrained conformations to improve convergence in FEP simulations of flexible molecules.     

The generalized Born/volume integral implicit solvent model: estimation of the free energy of hydration using London dispersion instead of atomic surface area

A new generalized Born model for estimating the free energy of hydration is presented. The new generalized Born/volume integral (GB/VI) estimates the free energy of hydration as a classical electrostatic energy plus a cavitation energy that is not based upon atomic surface area (SA) used in GB/SA hydration models but on a VI London dispersion energy estimated from quantities already calculated in the classical electrostatic energy. The (relatively few) GB/VI model parameters are fitted to experimental data, and parameterizations for two different atomic partial charge models are presented. Comparison of the calculated and experimental free energies of hydration for 560 small molecules (both neutral and charged) shows good agreement (r(2) = 0.94).     

Electronegativity equalization method: parameterization and validation for organic molecules using the Merz-Kollman-Singh charge distribution scheme

The electronegativity equalization method (EEM) was developed by Mortier et al. as a semiempirical method based on the density-functional theory. After parameterization, in which EEM parameters A(i), B(i), and adjusting factor kappa are obtained, this approach can be used for calculation of average electronegativity and charge distribution in a molecule. The aim of this work is to perform the EEM parameterization using the Merz-Kollman-Singh (MK) charge distribution scheme obtained from B3LYP/6-31G* and HF/6-31G* calculations. To achieve this goal, we selected a set of 380 organic molecules from the Cambridge Structural Database (CSD) and used the methodology, which was recently successfully applied to EEM parameterization to calculate the HF/STO-3G Mulliken charges on large sets of molecules. In the case of B3LYP/6-31G* MK charges, we have improved the EEM parameters for already parameterized elements, specifically C, H, N, O, and F. Moreover, EEM parameters for S, Br, Cl, and Zn, which have not as yet been parameterized for this level of theory and basis set, we also developed. In the case of HF/6-31G* MK charges, we have developed the EEM parameters for C, H, N, O, S, Br, Cl, F, and Zn that have not been parameterized for this level of theory and basis set so far. The obtained EEM parameters were verified by a previously developed validation procedure and used for the charge calculation on a different set of 116 organic molecules from the CSD. The calculated EEM charges are in a very good agreement with the quantum mechanically obtained ab initio charges.     

A new set of atomic radii for accurate estimation of solvation free energy by Poisson–Boltzmann solvent model

The Poisson–Boltzmann implicit solvent (PB) is widely used to estimate the solvation free energies of biomolecules in molecular simulations. An optimized set of atomic radii (PB radii) is an important parameter for PB calculations, which determines the distribution of dielectric constants around the solute. We here present new PB radii for the AMBER protein force field to accurately reproduce the solvation free energies obtained from explicit solvent simulations. The presented PB radii were optimized using results from explicit solvent simulations of the large systems. In addition, we discriminated PB radii for N‐ and C‐terminal residues from those for nonterminal residues. The performances using our PB radii showed high accuracy for the estimation of solvation free energies at the level of the molecular fragment. The obtained PB radii are effective for the detailed analysis of the solvation effects of biomolecules. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Electrostatic solvation free energy of amino acid side chain analogs: implications for the validity of electrostatic linear response in water

Electrostatic free energies of solvation for 15 neutral amino acid side chain analogs are computed. We compare three methods of varying computational complexity and accuracy for three force fields: free energy simulations, Poisson-Boltzmann (PB), and linear response approximation (LRA) using AMBER, CHARMM, and OPLS-AA force fields. We find that deviations from simulation start at low charges for solutes. The approximate PB and LRA produce an overestimation of electrostatic solvation free energies for most of molecules studied here. These deviations are remarkably systematic. The variations among force fields are almost as large as the variations found among methods. Our study confirms that success of the approximate methods for electrostatic solvation free energies comes from their ability to evaluate free energy differences accurately.     

Incorporating the excluded solvent volume and surface charges for computing solvation free energy

Gauss's law or Poisson's equation is conventionally used to calculate solvation free energy. However, the near‐solute dielectric polarization from Gauss's law or Poisson's equation differs from that obtained from molecular dynamics (MD) simulations. To mimic the near‐solute dielectric polarization from MD simulations, the first‐shell water was treated as two layers of surface charges, the densities of which are proportional to the electric field at the solvent molecule that is modeled as a hard sphere. The intermediate water was treated as a bulk solvent. An equation describing the solvation free energy of ions using this solvent scheme was derived using the TIP3P water model. © 2013 Wiley Periodicals, Inc.     

Application of the frozen atom approximation to the GB/SA continuum model for solvation free energy

The generalized Born/surface area (GB/SA) continuum model for solvation free energy is a fast and accurate alternative to using discrete water molecules in molecular simulations of solvated systems. However, computational studies of large solvated molecular systems such as enzyme-ligand complexes can still be computationally expensive even with continuum solvation methods simply because of the large number of atoms in the solute molecules. Because in such systems often only a relatively small portion of the system such as the ligand binding site is under study, it becomes less attractive to calculate energies and derivatives for all atoms in the system. To curtail computation while still maintaining high energetic accuracy, atoms distant from the site of interest are often frozen; that is, their coordinates are made invariant. Such frozen atoms do not require energetic and derivative updates during the course of a simulation. Herein we describe methodology and results for applying the frozen atom approach to both the generalized Born (GB) and the solvent accessible surface area (SASA) parts of the GB/SA continuum model for solvation free energy. For strictly pairwise energetic terms, such as the Coulombic and van-der-Waals energies, contributions from pairs of frozen atoms can be ignored. This leaves energetic differences unaffected for conformations that vary only in the positions of nonfrozen atoms. Due to the nonlocal nature of the GB analytical form, however, excluding such pairs from a GB calculation leads to unacceptable inaccuracies. To apply a frozen-atom scheme to GB calculations, a buffer region within the frozen-atom zone is generated based on a user-definable cutoff distance from the nonfrozen atoms. Certain pairwise interactions between frozen atoms in the buffer region are retained in the GB computation. This allows high accuracy in conformational GB comparisons to be maintained while achieving significant savings in computational time compared to the full (nonfrozen) calculation. A similar approach for using a buffer region of frozen atoms is taken for the SASA calculation. The SASA calculation is local in nature, and thus exact SASA energies are maintained. With a buffer region of 8 A for the frozen-atom cases, excellent agreement in differences in energies for three different conformations of cytochrome P450 with a bound camphor ligand are obtained with respect to the nonfrozen cases. For various minimization protocols, simulations run 2 to 10.5 times faster and memory usage is reduced by a factor of 1.5 to 5. Application of the frozen atom method for GB/SA calculations thus can render computationally tractable biologically and medically important simulations such as those used to study ligand-receptor binding conformations and energies in a solvated environment.     

Evaluation of solvation free energies for small molecules with the AMOEBA polarizable force field

The effects of electronic polarization in biomolecular interactions will differ depending on the local dielectric constant of the environment, such as in solvent, DNA, proteins, and membranes. Here the performance of the AMOEBA polarizable force field is evaluated under nonaqueous conditions by calculating the solvation free energies of small molecules in four common organic solvents. Results are compared with experimental data and equivalent simulations performed with the GAFF pairwise‐additive force field. Although AMOEBA results give mean errors close to “chemical accuracy,” GAFF performs surprisingly well, with statistically significantly more accurate results than AMOEBA in some solvents. However, for both models, free energies calculated in chloroform show worst agreement to experiment and individual solutes are consistently poor performers, suggesting non‐potential‐specific errors also contribute to inaccuracy. Scope for the improvement of both potentials remains limited by the lack of high quality experimental data across multiple solvents, particularly those of high dielectric constant. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.