Volodymyr P. Sergiievskyi

An accurate prediction of hydration free energies by combination of molecular integral equations theory with structural descriptors.

In this work, we report a novel method for the estimation of the hydration free energy of organic molecules, the structural descriptors correction (SDC) model. The method is based on a combination of the reference interaction site model (RISM) with several empirical corrections. The model requires only a small number of chemical descriptors associated with the main features of the chemical structure of solutes: excluded volume, branch, double bond, benzene ring, hydroxyl group, halogen atom, aldehyde group, ketone group, ether group, and phenol fragment. The optimum model was selected after testing of different RISM free energy expressions on a training set of 65 molecules. We show that the correction parameters of the SDC model are transferable between different chemical classes, which allows one to cover a wide range of organic solutes. The new model substantially increases the accuracy of calculated HFEs by RISM giving the standard deviation of the error for a test set of 120 organic molecules around 1.2 kcal/mol.

Accurate calculations of the hydration free energies of druglike molecules using the reference interaction site model.

We report on the results of testing the reference interaction site model (RISM) for the estimation of the hydration free energy of druglike molecules. The optimum model was selected after testing of different RISM free energy expressions combined with different quantum mechanics and empirical force-field methods of structure optimization and atomic partial charge calculation. The final model gave a systematic error with a standard deviation of 2.6 kcal/mol for a test set of 31 molecules selected from the SAMPL1 blind challenge set [J. P. Guthrie, J. Phys. Chem. B 113, 4501 (2009)]. After parametrization of this model to include terms for the excluded volume and the number of atoms of different types in the molecule, the root mean squared error for a test set of 19 molecules was less than 1.2 kcal/mol.

3DRISM Multigrid Algorithm for Fast Solvation Free Energy Calculations

In this paper we present a fast and accurate method for modeling solvation properties of organic molecules in water with a main focus on predicting solvation (hydration) free energies of small organic compounds. The method is based on a combination of (i) a molecular theory, three-dimensional reference interaction sites model (3DRISM); (ii) a fast multigrid algorithm for solving the high-dimensional 3DRISM integral equations; and (iii) a recently introduced universal correction (UC) for the 3DRISM solvation free energies by properly scaled molecular partial volume (3DRISM-UC, Palmer et al., J. Phys.: Condens. Matter2010, 22, 492101). A fast multigrid algorithm is the core of the method because it helps to reduce the high computational costs associated with solving the 3DRISM equations. To facilitate future applications of the method, we performed benchmarking of the algorithm on a set of several model solutes in order to find optimal grid parameters and to test the performance and accuracy of the algorithm. We have shown that the proposed new multigrid algorithm is on average 24 times faster than the simple Picard method and at least 3.5 times faster than the MDIIS method which is currently actively used by the 3DRISM community (e.g., the MDIIS method has been recently implemented in a new 3DRISM implicit solvent routine in the recent release of the AmberTools 1.4 molecular modeling package (Luchko et al. J. Chem. Theory Comput. 2010, 6, 607-624). Then we have benchmarked the multigrid algorithm with chosen optimal parameters on a set of 99 organic compounds. We show that average computational time required for one 3DRISM calculation is 3.5 min per a small organic molecule (10-20 atoms) on a standard personal computer. We also benchmarked predicted solvation free energy values for all of the compounds in the set against the corresponding experimental data. We show that by using the proposed multigrid algorithm and the 3DRISM-UC model, it is possible to obtain good correlation between calculated and experimental results for solvation free energies of aqueous solutions of small organic compounds (correlation coefficient 0.97, root-mean-square deviation <1 kcal/mol).

Multigrid solver for the reference interaction site model of molecular liquids theory

In this article, we propose a new multigrid‐based algorithm for solving integral equations of the reference interactions site model (RISM). We also investigate the relationship between the parameters of the algorithm and the numerical accuracy of the hydration free energy calculations by RISM. For this purpose, we analyzed the performance of the method for several numerical tests with polar and nonpolar compounds. The results of this analysis provide some guidelines for choosing an optimal set of parameters to minimize computational expenses. We compared the performance of the proposed multigrid‐based method with the one‐grid Picard iteration and nested Picard iteration methods. We show that the proposed method is over 30 times faster than the one‐grid iteration method, and in the high accuracy regime, it is almost seven times faster than the nested Picard iteration method.

Molecular density functional theory for water with liquid-gas coexistence and correct pressure

The solvation of hydrophobic solutes in water is special because liquid and gas are almost at coexistence. In the common hypernetted chain approximation to integral equations, or equivalently in the homogenous reference fluid of molecular density functional theory, coexistence is not taken into account. Hydration structures and energies of nanometer-scale hydrophobic solutes are thus incorrect. In this article, we propose a bridge functional that corrects this thermodynamic inconsistency by introducing a metastable gas phase for the homogeneous solvent. We show how this can be done by a third order expansion of the functional around the bulk liquid density that imposes the right pressure and the correct second order derivatives. Although this theory is not limited to water, we apply it to study hydrophobic solvation in water at room temperature and pressure and compare the results to all-atom simulations. The solvation free energy of small molecular solutes like n-alkanes and hard sphere solutes whose radii range from angstroms to nanometers is now in quantitative agreement with reference all atom simulations. The macroscopic liquid-gas surface tension predicted by the theory is comparable to experiments. This theory gives an alternative to the empirical hard sphere bridge correction used so far by several authors.

Model for calculating the free energy of hydration of bioactive compounds based on integral equation theory of liquids

The applicability of the reference interaction site model (RISM) to calculating the free energy of hydration of a set of 63 bioactive compounds presented in the work of J.P. Guthrie (Phys. Chem. B. 2009. V. 443. P. 4504) is tested. The performance of four different formulas for calculating the hydration free energy within the framework of the RISM, KH, HNCB, GF, and PW, is compared. Based on a training set of 32 compounds, the results are parameterized with corrections for the excluded volume and the number of atoms of each type in the molecule. It is shown that, for CHELPG charges, the parameterization predicts the results with a root-mean-square deviation from the experimental data of RMSD = 1.9 kcal/mol, a prediction almost 1.5-fold better than the results of parameterization without the use of the RISM.

A universal bridge functional for infinitely diluted solutions: A case study for Lennard-Jones spheres of different diameters

We propose a universal bridge functional for closure of the Ornstein-Zernike (OZ) equation for infinitely diluted solutions of Lennard-Jones spheres of different sizes in a Lennard-Jones fluid. The bridge functional is parameterized using data from molecular dynamics (MD) simulations. We show that for all of the investigated systems, the bridge functional can be efficiently parameterized with an exponential function that depends only on the ratio of the sizes of solute and solvent atoms. To check the parameterization, we solve the OZ equation with a closure that includes the parametrized functional, and with a closure without the bridge functional (a hypernetted chain closure). We show that introducing the bridge functional allows us to obtain radial distribution functions (RDFs) close to the MD results, and to improve substantially predictions of the location and height of the first peak of an RDF.