Computational prediction of organic crystal thermodynamics using molecular dynamics

The solubility of organic molecules is of critical importance to the pharmaceutical industry; however, robust computational methods to predict this quantity from first-principles are lacking. Solubility can be computed from a thermodynamic cycle that decomposes standard state solubility into the sum of solid–vapor sublimation and vapor–liquid solvation free energies ΔGsolubility° = ΔGsub° + ΔGsolv°. Over the past few decades, alchemical simulation methods to compute solvation free energy using classical force fields have become widely used. However, analogous methods for determining the free energy of the sublimation/deposition phase transition are currently limited by the necessity of a priori knowledge of the atomic coordinates of the crystal. Here, we describe progress toward an alternative scheme based on growth of the asymmetric unit into a crystal via alchemy (GAUCHE). GAUCHE computes deposition free energy ΔGdep° = −ΔGsub° = −kBT ln(Vc/Vg) + ΔGAU + ΔGAU→UC as the sum of an entropic term to account for compressing a vapor at 1 M standard state (Vg) into the molar volume of the crystal (Vc), where kB is Boltzmann's constant and T is temperature in degrees Kelvin, plus two simulation steps. In the first simulation step, the deposition free energy ΔGAU for a system composed of only NAU asymmetric unit (AU) molecule(s) is computed beginning from an arbitrary conformation in vacuum. In the second simulation step, the change in free energy ΔGAU→UC to expand the asymmetric unit degrees of freedom into a unit cell (UC) composed of NUC independent molecules is computed. This latter step accounts for the favorable free energy of removing the constraint that every symmetry mate of the asymmetric unit has an identical conformation and intermolecular interactions. The current work is based on NVT simulations, which requires knowledge of the crystal space group and unit cell parameters from experiment, but not a priori knowledge of crystalline atomic coordinates. GAUCHE was applied to 5 organic molecules whose sublimation free energy has been measured experimentally, based on the polarizable AMOEBA force field and more than a microsecond of sampling per compound in the program Force Field X. The mean unsigned and RMS errors were only 1.6 and 1.7 kcal/mol, respectively, which indicates that GAUCHE is capable of accurate prediction of absolute sublimation thermodynamics.

The solid-fluid coexistence properties of the n - 6 Lennard-Jones system, n from 7 to 12, are reported. The procedure relies on determining Helmholtz free energy curves as a function of volume for each phase independently, from several NVT simulations, and then connecting it to points of known absolute free energy. For n = 12 this requires connecting the simulated points to states of very low densities on the liquid phase, and to a harmonic crystal for the solid phase, which involves many extra simulations for each temperature. For the reference points of the remaining systems, however, the free energy at a given density and temperature can be calculated relative to the n = 12 system. The method presented here involves a generalization of the multiple histogram method to combine simulations performed with different potentials, provided they visit overlapping regions of the phase space, and allows for a precise calculation of relative free energies. The densities, free energies, average potential energies, pressure, and chemical potential at coexistence are presented for up to T∗ = 5.0 and new estimations of the triple points are given for the n - 6 Lennard-Jones system.

Energetics was analyzed for cytochrome c in pure-water solvent and in a urea-water mixed solvent to elucidate the solvation effect in the structural variation of the protein. The solvation free energy was computed through all-atom molecular dynamics simulation combined with the solution theory in the energy representation, and its correlations were examined over sets of protein structures against the electrostatic and van der Waals components in the average interaction energy of the protein with the solvent and the excluded-volume component in the solvation free energy. It was observed in pure-water solvent that the solvation free energy varies in parallel to the electrostatic component with minor roles played by the van der Waals and excluded-volume components. The effect of urea on protein structure was then investigated in terms of the free-energy change upon transfer of the protein solute from pure-water solvent to the urea-water mixed solvent. The decomposition of the transfer free energy into the contributions from urea and water showed that the urea contribution is partially canceled by the water contribution and governs the total free energy of transfer. When correlated against the change in the solute-solvent interaction energy upon transfer and the corresponding changes in the electrostatic, van der Waals, and excluded-volume components, the transfer free energy exhibited strong correlations with the total change in the solute-solvent energy and its van der Waals component. The solute-solvent energy was decomposed into the contributions from the protein backbone and side chain, furthermore, and neither of the contributions was seen to be decisive in the correlation to the transfer free energy.

VX-478 belongs to a novel class of HIV-1 protease inhibitors that are based on N,N-disubstituted benzene sulfonamides. Force field parameters for the N,N-dialkyl benzene sulfonamide moiety have been assembled from the literature and from our own ab initio calculations. These parameters were employed to calculate solvation and binding free energy differences between VX-478 and two analogs. The free energy perturbation method has been used to determine these differences using two approaches. In the first approach, intergroup interaction terms only were included in the calculation of free energies (as in most reports of free energy calculations using AMBER). In the second approach, both the inter- and intragroup interaction terms were included. The results obtained with the two approaches are in excellent agreement with each other and are also in close agreement with the experimental results. The solvation free energies of N,N-dimethyl benzene sulfonamide derivatives (truncated models of the inhibitors), calculated using continuum solvation (AMSOL) methods, are found to be in qualitative agreement with the experimental and free energy perturbation results. The binding and solvation free energy results are discussed in the context of structure-based drug design to show how physicochemical properties (for example aqueous solubilities and bioavailabilities) of these HIV-I protease inhibitors were improved, while maintaining their inhibitory potency.

Grid Inhomogeneous Solvation Theory (GIST) maps out solvation thermodynamic properties on a fine meshed grid and provides a statistical mechanical formalism for thermodynamic end-state calculations. However, differences in how long-range nonbonded interactions are calculated in molecular dynamics engines and in the current implementation of GIST have prevented precise comparisons between free energies estimated using GIST and those from other free energy methods such as thermodynamic integration (TI). Here, we address this by presenting PME-GIST, a formalism by which particle mesh Ewald (PME)-based electrostatic energies and long-range Lennard-Jones (LJ) energies are decomposed and assigned to individual atoms and the corresponding voxels they occupy in a manner consistent with the GIST approach. PME-GIST yields potential energy calculations that are precisely consistent with modern simulation engines and performs these calculations at a dramatically faster speed than prior implementations. Here, we apply PME-GIST end-state analyses to 32 small molecules whose solvation free energies are close to evenly distributed from 2 kcal/mol to -17 kcal/mol and obtain solvation energies consistent with TI calculations (R2 = 0.99, mean unsigned difference 0.8 kcal/mol). We also estimate the entropy contribution from the second and higher order entropy terms that are truncated in GIST by the differences between entropies calculated in TI and GIST. With a simple correction for the high order entropy terms, PME-GIST obtains solvation free energies that are highly consistent with TI calculations (R2 = 0.99, mean unsigned difference = 0.4 kcal/mol) and experimental results (R2 = 0.88, mean unsigned difference = 1.4 kcal/mol). The precision of PME-GIST also enables us to show that the solvation free energy of small hydrophobic and hydrophilic molecules can be largely understood based on perturbations of the solvent in a region extending a few solvation shells from the solute. We have integrated PME-GIST into the open-source molecular dynamics analysis software CPPTRAJ.

The reduction potentials (E°(Red) versus SHE) of hypercloso boron hydrides B(n)H(n) (n = 6-13) and B(12)X(12) (X = F, Cl, OH, and CH(3)) in water have been computed using the Conductor-like Polarizable Continuum Model (CPCM) and the Solvation Model Density (SMD) method for solvation modeling. The B3LYP/aug-cc-pvtz and M06-2X/aug-cc-pvtz as well as G4 level of theory were applied to determine the free energies of the first and second electron attachment (ΔG(E.A.)) to boron clusters. The solvation free energies (ΔG(solv)) greatly depend on the choice of the cavity set (UAKS, Pauling, or SMD) while the dependence on the choice of exchange/correlation functional is modest. The SMD cavity set gives the largest ΔΔG(solv) for B(n)H(n)(0/-) and B(n)H(n)(-/2-) while the UAKS cavity set gives the smallest ΔΔG(solv) value. The E°(Red) of B(n)H(n)(-/2-) (n = 6-12) with the G4/M06-2X(Pauling) (energy/solvation(cavity)) combination agrees within 0.2 V of experimental values. The experimental oxidative stability (E(1/2)) of B(n)X(n)(2-) (X = F, Cl, OH, and CH(3)) is usually located between the values predicted using the B3LYP and M06-2X functionals. The disproportionation free energies (ΔG(dpro)) of 2B(n)H(n)(-) → B(n)H(n) + B(n)H(n)(2-) reveal that the stabilities of B(n)H(n)(-) (n = 6-13) to disproportionation decrease in the order B(8)H(8)(-) > B(9)H(9)(-) > B(11)H(11)(-) > B(10)H(10)(-). The spin densities in B(12)X(12)(-) (X = F, Cl, OH, and CH(3)) tend to delocalize on the boron atoms rather than on the exterior functional groups. The partitioning of ΔG(solv)(B(n)H(n)(2-)) over spheres allows a rationalization of the nonlinear correlation between ΔG(E.A.) and E°(Red) for B(6)H(6)(-/2-), B(11)H(11)(-/2-), and B(13)H(13)(-/2-).

Relative free energy calculations are fast becoming a critical part of early stage pharmaceu- tical design, making it important to know how to obtain the best performance with these calculations in applications which could span hundreds of calculations and molecules. In this work, we compared two different treatments of long-range electrostatics, Particle Mesh Ewald (PME) and Reaction Field (RF), in relative binding free energy calculations using a non-equilibrium switching protocol. We found simulations using RF achieve comparable re- sults as those using PME but gain more efficiency when using CPU and similar performance using GPU. The results from this work encourage more use of RF in molecular simulations.

The solvation free energy (SFE) plays a key role in thermodynamics. One well-established method for computing the SFE is through an alchemical transformation. However, experimental SFEs are generally determined according to the Ben-Naim equations relying on vapor pressure or density ratios. It is important to establish whether, or to what extent, typical alchemical-based free energy computations provide results comparable to experimental SFEs. In this work, we mimic experimental measurements by simulating the liquid-vapor coexistence of water without alchemical operations. The SFEs measured through vapor pressure and density ratios are used to validate the SFEs obtained through alchemical transformations. It is shown that proper consideration of the nonideal behavior of the vapor is important to ensure that the alchemical SFEs are consistent with the Ben-Naim SFEs. Alchemical transformations in the vapor phase should be performed in addition to solution phase transformations for strongly interacting solutes, such as those with low boiling temperatures and large second virial coefficients. A formula based on the virial expansion of pressure is proposed to provide a better estimate of the true SFE from the simulated vapor pressures. The proposed formula is also applicable to experimental determinations of SFE when the pressure-based route is used.

Free energies of supercritical solvation from molecular dynamics simulation and integral equation studies

Protein–protein interactions (PPIs) play a critical role in all biological processes. Menin is tumor suppressor protein, mutated in multiple endocrine neoplasia type 1 syndrome and has been shown to interact with multiple transcription factors including (RPA2) subunit of replication protein A (RPA). RPA2, heterotrimeric protein required for DNA repair, recombination and replication. However, it’s still remains unclear the specific amino acid residues that have been involved in Menin-RPA2 interaction. Thus, accurately predicting the specific amino acid involved in interaction and effects of MEN1 mutations on biological systems is of great interests. The experimental approaches for identifying amino acids in menin-RPA2 interactions are expensive, time-consuming, and challenging. This study leverages computational tools, free energy decomposition and configurational entropy scheme to annotate the menin-RPA2 interaction and effect on menin point mutation, thereby proposing a viable model of menin-RPA2 interaction. The menin–RPA2 interaction pattern was calculated on the basis of different 3D structures of menin and RPA2 complexes, constructed using homology modeling and docking strategy, generating three best-fit models: Model 8 (− 74.89 kJ/mol), Model 28 (− 92.04 kJ/mol) and Model 9 (− 100.4 kJ/mol). The molecular dynamic (MD) was performed for 200 ns and binding free energies and energy decomposition analysis were calculated using Molecular Mechanics Poisson–Boltzmann Surface Area (MM/PBSA) in GROMACS. From binding free energy change, model 8 of Menin-RPA2 exhibited most negative binding energy of − 205.624 kJ/mol, followed by model 28 of Menin-RPA2 with − 177.382 kJ/mol. After S606F point mutation in Menin, increase of BFE (ΔGbind) by − 34.09 kJ/mol in Model 8 of mutant Menin-RPA2 occurs. Interestingly, we found a significant reduction of BFE (ΔGbind) and configurational entropy by − 97.54 kJ/mol and − 2618 kJ/mol in mutant model 28 as compared the o wild type. Collectively, this is the first study to highlight the configurational entropy of protein–protein interactions thereby strengthening the prediction of two significant important interaction sites in menin for the binding of RPA2. These predicted sites could be vulnerable for structural alternation in terms of binding free energy and configurational entropy after missense mutation in menin.

The combination of quantum mechanics (QM) with molecular mechanics (MM) offers a route to improved accuracy in the study of biological systems, and there is now significant research effort being spent to develop QM/MM methods that can be applied to the calculation of relative free energies. Currently, the computational expense of the QM part of the calculation means that there is no single method that achieves both efficiency and rigor; either the QM/MM free energy method is rigorous and computationally expensive, or the method introduces efficiency-led assumptions that can lead to errors in the result, or a lack of generality of application. In this paper we demonstrate a combined approach to form a single, efficient, and, in principle, exact QM/MM free energy method. We demonstrate the application of this method by using it to explore the difference in hydration of water and methane. We demonstrate that it is possible to calculate highly converged QM/MM relative free energies at the MP2/aug-cc-pVDZ/OPLS level within just two days of computation, using commodity processors, and show how the method allows consistent, high-quality sampling of complex solvent configurational change, both when perturbing hydrophilic water into hydrophobic methane, and also when moving from a MM Hamiltonian to a QM/MM Hamiltonian. The results demonstrate the validity and power of this methodology, and raise important questions regarding the compatibility of MM and QM/MM forcefields, and offer a potential route to improved compatibility.

This review focuses on recent progress in two areas in which computer simulations with explicit solvent are being applied: the thermodynamic decomposition of free energies, and modeling electrostatic effects. The computationally intensive nature of these simulations has been an obstacle to the systematic study of many problems in solvation thermodynamics, such as the decomposition of solvation and ligand binding free energies into component enthalpies and entropies. With the revolution in computer power continuing, these problems are ripe for study but require the judicious choice of algorithms and approximations. We provide a critical evaluation of several numerical approaches to the thermodynamic decomposition of free energies and summarize applications in the current literature. Progress in computer simulations with explicit solvent of charge perturbations in biomolecules was slow in the early 1990s because of the widespread use of truncated Coulomb potentials in these simulations, among other factors. Development of the sophisticated technology described in this review to handle the long-range electrostatic interactions has increased the predictive power of these simulations to the point where comparisons between explicit and continuum solvent models can reveal differences that have their true physical origin in the inherent molecularity of the surrounding medium.

The binding free energies of the inhibitor-heme model complexes are calculated using the density functional methods and the implicit solvation models in water, where the 16 structurally diverse compounds with a spectrum of IC(50) values from 0.05 (clotrimazole) to 1000 (piroxicam) μM are chosen as inhibitors for Cytochrome P450 3A4 (CYP3A4). CYP3A4 is the most predominant constituent of the human hepatic CYP enzymes that play a role in metabolizing structurally diverse xenobiotics. The observed free energy change for each inhibitory binding, ΔG inh0, is obtained from its IC(50) value. The total binding free energy (ΔG b0) of each inhibitor-heme model complex is calculated by the sum of its relative free energy (ΔG(0) ) in the gas phase and solvation free energy to the water-heme model complex. The UB3LYP/LanL2DZ level of theory provides the correct relative stabilities of the high- and low-spin states for the penta- and hexa-coordinated ferric complexes, respectively. The optimized distances of the inhibitor nitrogen (or water oxygen) and the methyl mercaptide S to the ferric iron of the inhibitor-heme model complexes at the same level of theory are consistent with the values of the corresponding X-ray structures, except for the econazole complex. The correlation coefficient r(2) values of 0.91 and 0.75 are obtained from the ΔG b0-ΔG inh0 and ΔG(0) -ΔG inh0 plots, respectively, at the UM06/LanL2DZ:CPCM_UB3LYP/LanL2DZ//UB3LYP/LanL2DZ level of theory in water. This indicates that the total binding free energies calculated for the inhibitor-heme model complexes can be a good descriptor in interpreting the inhibitor binding to CYP3A4 and the relative free energies in the gas phase are mainly responsible for the total binding free energies in water, although the desolvation can be a factor to affect the binding affinity of the inhibitors to CYP3A4. From the theozyme analysis of the X-ray structures for ketoconazole- and metyrapone-CYP3A4 complexes, the interaction free energy of the neighboring residues with each inhibitor in the active site is calculated to be about -3 kcal mol(-1) in water, whose the interaction energy and the desolvation free energy change are about -5 and 2 kcal mol(-1) , respectively.

Multisite λ‐dynamics (MSλD) is a novel method for the calculation of relative free energies of binding for ligands to their targeted receptors. It can be readily used to examine a large number of molecules with multiple functional groups at multiple sites around a common core. This makes MSλD a powerful tool in structure‐based drug design. In the present study, MSλD is applied to calculate the relative binding free energies of 1296 inhibitors to the testis specific serine kinase 1B (TSSK1B), a validated target for male contraception. For this system, MSλD requires significantly fewer computational resources compared to traditional free energy methods like free energy perturbation or thermodynamic integration. From MSλD simulations, we examined whether modifications of a ligand at two different sites are coupled or not. Based on our calculations, we established a quantitative structure–activity relationship (QSAR) for this set of molecules and identified a site in the ligand where further modification, such as adding more polar groups, may lead to increased binding affinity.

Monte Carlo statistical mechanics simulations were used to compute absolute free energies of solvation in chloroform for 16 organic molecules. The intermolecular interactions were described by classical potential functions consisting of Coulomb and Lennard–Jones interactions. The partial charges for the solutes were derived from fitting to the electrostatic potential surfaces of ab initio 6–31G* wavefunctions. First, free energy perturbation (FEP) calculations yielded relative free energies of solvation. These were converted to absolute quantities through perturbations to the reference molecule, methane, which was annihilated. The average error in the FEP-computed free energies of solvation is 0·8 kcal mol−1. Then, a linear response equation, which contains terms proportional to the Lennard–Jones (van der Waals) and Coulombic components of the solute–solvent energy and to the solvent-accessible surface area of the solute, was optimized and reproduced both the FEP-calculated and experimental free energies of solvation with average errors of ca 0·5 kcal mol−1. In addition, an existing solute dataset for water, which had previously been fitted to the same equation, was expanded from 16 to 35 molecules. The fit of the Monte Carlo results for this set of molecules in TIP4P water to the experimental free energies of hydration yielded an average error of 0·8 kcal mol−1. Combination of the predictions of free energies of solvation in water and chloroform yields partition coefficients, log P, with an average error of 0·3–0·4 log unit. © 1997 John Wiley & Sons, Ltd.