Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections

Molecular Density Functional Theory (MDFT) offers an efficient implicit- solvent method to estimate molecule solvation free-energies whereas conserving a fully molecular representation of the solvent. Even within a second order ap- proximation for the free-energy functional, the so-called homogeneous reference uid approximation, we show that the hydration free-energies computed for a dataset of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by two to three orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canoni- cal to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justifcation to empirical partial molar volume corrections that have been proposed recently.Comment: Version with correct equation numbers is here: http://compchemmpi.wikispaces.com/file/view/sergiievskyi_et_al.pdf/513575848/sergiievskyi_et_al.pdf Supporting information available online at: http://compchemmpi.wikispaces.com/file/view/SuppInf_sergiievskyi_et_al_07-04-2014.pdf/513576008/SuppInf_sergiievskyi_et_al_07-04-2014.pd

Prediction of the n‑octanol/water partition coefficients in the SAMPL6 blind challenge from MST continuum solvation calculations

The IEFPCM/MST continuum solvation model is used for the blind prediction of n-octanol/water partition of a set of 11 fragment-like small molecules within the SAMPL6 Part II Partition Coefficient Challenge. The partition coefficient of the neutral species (log P) was determined using an extended parametrization of the B3LYP/6-31G(d) version of the Miertus-Scrocco-Tomasi continuum solvation model in n-octanol. Comparison with the experimental data provided for partition coefficients yielded a root-mean square error (rmse) of 0.78 (log P units), which agrees with the accuracy reported for our method (rmse = 0.80) for nitrogen-containing heterocyclic compounds. Out of the 91 sets of log P values submitted by the participants, our submission is within those with an rmse < 1 and among the four best ranked physical methods. The largest errors involve three compounds: two with the largest positive deviations (SM13 and SM08), and one with the largest negative deviations (SM15). Here we report the potentiometric determination of the log P for SM13, leading to a value of 3.62 ± 0.02, which is in better agreement with most empirical predictions than the experimental value reported in SAMPL6. In addition, further inclusion of several conformations for SM08 significantly improved our results. Inclusion of these refinements led to an overall error of 0.51 (log P units), which supports the reliability of the IEFPCM/MST model for predicting the partitioning of neutral compounds

Accuracy comparison of several common implicit solvent models and their implementations in the context of protein-ligand binding.

In this study several commonly used implicit solvent models are compared with respect to their accuracy of estimating solvation energies of small molecules and proteins, as well as desolvation penalty in protein-ligand binding. The test set consists of 19 small proteins, 104 small molecules, and 15 protein-ligand complexes. We compared predicted hydration energies of small molecules with their experimental values; the results of the solvation and desolvation energy calculations for small molecules, proteins and protein-ligand complexes in water were also compared with Thermodynamic Integration calculations based on TIP3P water model and Amber12 force field. The following implicit solvent (water) models considered here are: PCM (Polarized Continuum Model implemented in DISOLV and MCBHSOLV programs), GB (Generalized Born method implemented in DISOLV program, S-GB, and GBNSR6 stand-alone version), COSMO (COnductor-like Screening Model implemented in the DISOLV program and the MOPAC package) and the Poisson-Boltzmann model (implemented in the APBS program). Different parameterizations of the molecules were examined: we compared MMFF94 force field, Amber12 force field and the quantum-chemical semi-empirical PM7 method implemented in the MOPAC package. For small molecules, all of the implicit solvent models tested here yield high correlation coefficients (0.87-0.93) between the calculated solvation energies and the experimental values of hydration energies. For small molecules high correlation (0.82-0.97) with the explicit solvent energies is seen as well. On the other hand, estimated protein solvation energies and protein-ligand binding desolvation energies show substantial discrepancy (up to 10kcal/mol) with the explicit solvent reference. The correlation of polar protein solvation energies and protein-ligand desolvation energies with the corresponding explicit solvent results is 0.65-0.99 and 0.76-0.96 respectively, though this difference in correlations is caused more by different parameterization and less by methods and indicates the need for further improvement of implicit solvent models parameterization. Within the same parameterization, various implicit methods give practically the same correlation with results obtained in explicit solvent model for ligands and proteins: e.g. correlation values of polar ligand solvation energies and the corresponding energies in the frame of explicit solvent were 0.953-0.966 for the APBS program, the GBNSR6 program and all models used in the DISOLV program. The DISOLV program proved to be on a par with the other used programs in the case of proteins and ligands solvation energy calculation. However, the solution of the Poisson-Boltzmann equation (APBS program) and Generalized Born method (implemented in the GBNSR6 program) proved to be the most accurate in calculating the desolvation energies of complexes

Evaluation of log P, pKa, and log D predictions from the SAMPL7 blind challenge

The Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) challenges focuses the computational modeling community on areas in need of improvement for rational drug design. The SAMPL7 physical property challenge dealt with prediction of octanol-water partition coefficients and pKa for 22 compounds. The dataset was composed of a series of N-acylsulfonamides and related bioisosteres. 17 research groups participated in the log P challenge, submitting 33 blind submissions total. For the pKa challenge, 7 different groups participated, submitting 9 blind submissions in total. Overall, the accuracy of octanol-water log P predictions in the SAMPL7 challenge was lower than octanol-water log P predictions in SAMPL6, likely due to a more diverse dataset. Compared to the SAMPL6 pKa challenge, accuracy remains unchanged in SAMPL7. Interestingly, here, though macroscopic pKa values were often predicted with reasonable accuracy, there was dramatically more disagreement among participants as to which microscopic transitions produced these values (with methods often disagreeing even as to the sign of the free energy change associated with certain transitions), indicating far more work needs to be done on pKa prediction methods

Energy-entropy prediction of octanol–water logP of SAMPL7 N-acyl sulfonamide bioisosters

From Springer Nature via Jisc Publications RouterHistory: received 2021-03-04, accepted 2021-06-17, registration 2021-06-18, pub-print 2021-07, pub-electronic 2021-07-10, online 2021-07-10Publication status: PublishedFunder: Engineering and Physical Sciences Research Council; doi: http://dx.doi.org/10.13039/501100000266; Grant(s): EP/L015218/1, EP/N025105/1Abstract: Partition coefficients quantify a molecule’s distribution between two immiscible liquid phases. While there are many methods to compute them, there is not yet a method based on the free energy of each system in terms of energy and entropy, where entropy depends on the probability distribution of all quantum states of the system. Here we test a method in this class called Energy Entropy Multiscale Cell Correlation (EE-MCC) for the calculation of octanol–water logP values for 22 N-acyl sulfonamides in the SAMPL7 Physical Properties Challenge (Statistical Assessment of the Modelling of Proteins and Ligands). EE-MCC logP values have a mean error of 1.8 logP units versus experiment and a standard error of the mean of 1.0 logP units for three separate calculations. These errors are primarily due to getting sufficiently converged energies to give accurate differences of large numbers, particularly for the large-molecule solvent octanol. However, this is also an issue for entropy, and approximations in the force field and MCC theory also contribute to the error. Unique to MCC is that it explains the entropy contributions over all the degrees of freedom of all molecules in the system. A gain in orientational entropy of water is the main favourable entropic contribution, supported by small gains in solute vibrational and orientational entropy but offset by unfavourable changes in the orientational entropy of octanol, the vibrational entropy of both solvents, and the positional and conformational entropy of the solute

Atomic radius and charge parameter uncertainty in biomolecular solvation energy calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parameterization problems, including those beyond continuum solvation calculations.The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters

Can approximate integral equation theories accurately predict solvation thermodynamics?

The thesis focuses on the prediction of solvation thermodynamics using integral equation theories. Our main goal is to improve the approach using a rational correction. We achieve it by extending recently introduced pressure correction, and rationalizing it in the context of solvation entropy. The improved model (to which we refer as advanced pressure correction) is rather universal. It can accurately predict solvation free energies in water at both ambient and non-ambient temperatures, is capable of addressing ionic solutes and salt solutions, and can be extended to non-aqueous systems. The developed approach can be used to model processes in biological systems, as well as to extend related theoretical models further.Comment: Author's Ph.D. thesis (University of Strathclyde, 2016). Supervisors: Maxim V. Fedorov and David S. Palme

Prédiction des propriétés d'équilibre dans les milieux biologiques et alimentaires par le modèle COSMO-RS

Food and biological systems are generally multicomponent mixtures (including water, organic solvents, dissolved solids, dissolved gases, ionic species, macromolecules). The prediction of the equilibrium properties of such environments requires the use of a fully predictive thermodynamic model. This model must be able to ensure the consistency between experimental data and to ensure the robustness of the simultaneous representation of physical equilibria (liquid-vapour, solubility, etc.) and chemical equilibria (dissociation, redox, complexation, etc.). The chemical potential is an essential property for modelling such equilibria. Its determination depends on two variables: the Gibbs free energy of formation in a chosen reference state, and the prediction of the activity coefficient which also depends on the chosen reference state. The COSMO-RS model is an excellent model for predicting activity coefficients that is widely used in chemical engineering where the studied molecules are generally neutral. This PhD study enabled to extend the performance of the COSMO-RS model toward the treatment of food and biological systems where there are systematically electrolytes in solution (in addition to neutral molecules). A new tool based on the recent advances of quantum mechanics has been developed in order to predict gas phase formation properties. By combining concepts of thermodynamics, quantum physics, electrostatics and statistical physics, it has been demonstrated that it is possible to use the COSMO-RS model to ensure the transition between the gas phase and the condensed phase. In this context, this work demonstrates that it is possible to treat simultaneously physical and chemical equilibria and thus to predict physico-chemical properties (aW, pH, Eh) in food and biological systems using the COSMO-RS model.Les milieux biologiques et alimentaires sont généralement des mélanges contenant un nombre élevé de constituants (eau, solvants organiques, solides dissous, gaz dissous, espèces ioniques, macromolécules). La prédiction des propriétés d’équilibre de tels milieux requiert l’utilisation d’un modèle thermodynamique entièrement prédictif. Ce modèle doit également permettre d’assurer la cohérence entre des données expérimentales et garantir la robustesse de la représentation simultanée des équilibres physiques (liquide-vapeur, solubilité, etc.) et chimiques (dissociation, oxydo-réduction, complexation, etc.). Le potentiel chimique est une donnée indispensable pour modéliser ces équilibres. Sa connaissance dépend de la prédiction de deux variables : l’enthalpie libre de formation dans un état de référence choisi, et le coefficient d’activité qui dépend aussi de l’état de référence choisi. Le modèle COSMO-RS est un excellent modèle de prédiction des coefficients d’activité très largement utilisé dans le domaine du génie chimique où on s’intéresse essentiellement à des molécules neutres. Ce travail de thèse a permis d’étendre les performances du modèle COSMO-RS au traitement des milieux biologiques et alimentaires dans lesquels on trouve systématiquement des électrolytes en solution (en plus des molécules neutres). Un nouvel outil utilisant les récentes avancées de la mécanique quantique a été développé pour prédire les propriétés de formation à l’état gaz. En combinant des concepts de la thermodynamique, de la mécanique quantique, de l’électrostatique, et de la physique statistique, il a été démontré qu’il est possible d’utiliser le modèle COSMO-RS pour faire la transition entre l’état gaz et la phase condensée. Partant de là, ce travail démontre qu’il est maintenant possible de traiter simultanément les équilibres physiques et chimiques et donc de prédire les propriétés physico-chimiques (aW, pH, Eh) dans les milieux biologiques et alimentaires par le modèle COSMO-RS