Simple models for nonpolar solvation: Parameterization and testing

Implicit solvent models are important for many biomolecular simulations. The polarity of aqueous solvent is essential and qualitatively captured by continuum electrostatics methods like Generalized Born (GB). However, GB does not account for the solvent‐induced interactions between exposed hydrophobic sidechains or solute‐solvent dispersion interactions. These “nonpolar” effects are often modeled through surface area (SA) energy terms, which lack realism, create mathematical singularities, and have a many‐body character. We have explored an alternate, Lazaridis–Karplus (LK) gaussian energy density for nonpolar effects and a dispersion (DI) energy term proposed earlier, associated with GB electrostatics. We parameterized several combinations of GB, SA, LK, and DI energy terms, to reproduce 62 small molecule solvation free energies, 387 protein stability changes due to point mutations, and the structures of 8 protein loops. With optimized parameters, the models all gave similar results, with GBLK and GBDILK giving no performance loss compared to GBSA, and mean errors of 1.7 kcal/mol for the stability changes and 2 Å deviations for the loop conformations. The optimized GBLK model gave poor results in MD of the Trpcage mini‐protein, but parameters optimized specifically for MD performed well for Trpcage and three other small proteins. Overall, the LK and DI nonpolar terms are valid alternatives to SA treatments for a range of applications. © 2017 Wiley Periodicals, Inc.     

Theory for the solvation of nonpolar solutes in water

We recently developed an angle-dependent Wertheim integral equation theory (IET) of the Mercedes-Benz (MB) model of pure water [Silverstein et al., J. Am. Chem. Soc. 120, 3166 (1998)]. Our approach treats explicitly the coupled orientational constraints within water molecules. The analytical theory offers the advantage of being less computationally expensive than Monte Carlo simulations by two orders of magnitude. Here we apply the angle-dependent IET to studying the hydrophobic effect, the transfer of a nonpolar solute into MB water. We find that the theory reproduces the Monte Carlo results qualitatively for cold water and quantitatively for hot water.     

Extended hydrodynamic approach to quantum-classical nonequilibrium evolution. II. Application to nonpolar solvation

The mixed quantum-classical formulation derived in our companion paper [D. Bousquet, K. H. Hughes, D. Micha, and I. Burghardt, J. Chem. Phys. 134, 064116 (2011)], which is based upon a hydrodynamic representation of the classical sector, is applied to nonequilibrium nonpolar solvation dynamics as exemplified by the solvation of the electronically excited NO molecule in a rare gas environment. Derived from a partition of the Hamiltonian into a primary (quantum) part and a secondary (classical) part the hydrodynamic equations are formulated for multi-quantum states and result in explicit equations of motion for populations and coherences. The hierarchy of hydrodynamic equations is truncated by the following approximate closure schemes: Gauss-Hermite closure, dynamical density functional theory approximation, and a generalized Maxwellian closure. A comparison of the dynamics using these three closure methods showed that the suitability of a particular closure scheme was dependent on the initial conditions and the nonequilibrium character of the dynamics.     

Local structure of solvation of nonpolar chains in nonpolar solvents at infinite dilution

The SSOZ (site-site Ornstein-Zernike) equation is used to study the local structure of solvation of linear nonpolar molecules in nonpolar solvents. The atom-atomic interaction potentials are described by the Lennard-Jones potential. The chain-solvent atom-atomic pair correlation functions are calculated in relation to the chain length (number of atoms), solvent density, and the ratio of the geometrical parameters of solvent and chain atoms. Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 4, pp. 742–749, July–August, 1996. Translated by L. Smolina     

Role of water structure in thermodynamics of nonpolar solvation

The SSOZ (site-site Ornstein-Zernike) equation with an original closure condition for liquid molecular systems is used to calculate thermodynamic functions of noble gas solvation in water. Water is modeled by two close sets of atom-atomic potential functions. The calculations indicate that the chemical solvation potential is strongly sensitive to water structure. A comparison with experiment is given. Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 4, pp. 736–741, July–August, 1996. Translated by L. Smolina     

A novel approach to solvation time scale in nonpolar solvents via instability of solvent density modes

We perform linear stability analysis of solvent density modes in the presence of nonpolar solute-solvent interaction in a nonpolar solvent. The dominant instability given by the maximum positive eigenvalue of the stability matrix provides the time scale of the solvent rearrangement around a solute. Our theory predicts two long time scales for both in normal nonpolar and supercritical fluids. We discuss the existing experimental results on nonpolar solvation dynamics in light of our prediction.     

Breaking the polar‐nonpolar division in solvation free energy prediction

Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature‐function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson–Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave‐one‐out test gives an optimal root‐mean‐square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94 molecules and its associated training set, the present approach was carefully compared with a classic solvation model based on weighted solvent accessible surface area. © 2017 Wiley Periodicals, Inc.     

Application of the level-set method to the implicit solvation of nonpolar molecules

A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model [Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. 104, 527 (2006); J. Chem. Phys. 124, 084905 (2006)]. In the level-set method, a possible solute-solvent interface is represented by the zero level set (i.e., the zero level surface) of a level-set function and is eventually evolved into the equilibrium solute-solvent interface. The evolution law is determined by minimization of a solvation free energy functional that couples both the interfacial energy and the van der Waals type solute-solvent interaction energy. The surface evolution is thus an energy minimizing process, and the equilibrium solute-solvent interface is an output of this process. The method is implemented and applied to the solvation of nonpolar molecules such as two xenon atoms, two parallel paraffin plates, helical alkane chains, and a single fullerence C(60). The level-set solutions show good agreement for the solvation energies when compared to available molecular dynamics simulations. In particular, the method captures solvent dewetting (nanobubble formation) and quantitatively describes the interaction in the strongly hydrophobic plate system.     

Accurate predictions of nonpolar solvation free energies require explicit consideration of binding-site hydration

Continuum solvation methods are frequently used to increase the efficiency of computational methods to estimate free energies. In this paper, we have evaluated how well such methods estimate the nonpolar solvation free-energy change when a ligand binds to a protein. Three different continuum methods at various levels of approximation were considered, viz., the polarized continuum model (PCM), a method based on cavity and dispersion terms (CD), and a method based on a linear relation to the solvent-accessible surface area (SASA). Formally rigorous double-decoupling thermodynamic integration was used as a benchmark for the continuum methods. We have studied four protein-ligand complexes with binding sites of varying solvent exposure, namely the binding of phenol to ferritin, a biotin analogue to avidin, 2-aminobenzimidazole to trypsin, and a substituted galactoside to galectin-3. For ferritin and avidin, which have relatively hidden binding sites, rather accurate nonpolar solvation free energies could be obtained with the continuum methods if the binding site is prohibited to be filled by continuum water in the unbound state, even though the simulations and experiments show that the ligand replaces several water molecules upon binding. For the more solvent exposed binding sites of trypsin and galectin-3, no accurate continuum estimates could be obtained, even if the binding site was allowed or prohibited to be filled by continuum water. This shows that continuum methods fail to give accurate free energies on a wide range of systems with varying solvent exposure because they lack a microscopic picture of binding-site hydration as well as information about the entropy of water molecules that are in the binding site before the ligand binds. Consequently, binding affinity estimates based upon continuum solvation methods will give absolute binding energies that may differ by up to 200 kJ/mol depending on the method used. Moreover, even relative energies between ligands with the same scaffold may differ by up to 75 kJ/mol. We have tried to improve the continuum solvation methods by adding information about the solvent exposure of the binding site or the hydration of the binding site, and the results are promising at least for this small set of complexes.     

Effect of nonpolar solvents on the solute rotation and solvation dynamics in an imidazolium ionic liquid

Recognizing the potential of the mixed solvent systems comprising ionic liquid as one of the constituents in real applications, the steady-state and time-resolved fluorescence behavior of C153 has been studied in neat 1-butyl-3-methylimidazolium hexafluorophosphate and its mixtures with nonpolar solvents, namely, toluene and 1,4-dioxane. No significant effect of the cosolvent on the steady-state absorption or fluorescence spectra of C153 in ionic liquid has been observed. Time-resolved fluorescence anisotropy measurements show a decrease of the rotational correlation time of C153 with gradual addition of the cosolvent. Solvation dynamics in ionic liquid-cosolvent mixtures is found to be biphasic, and a decrease of the average solvation time is observed with increasing amount of the cosolvent in solution. The time-zero spectrum of C153 is found to shift toward higher energy with gradual addition of the nonpolar solvent, suggesting that the probe molecule experiences a more nonpolar environment at the early stage of the dynamics in mixed solvents. The blue shift of the time-zero spectrum caused by the addition of the nonpolar solvent results in a larger Stokes shift of the time-dependent spectra due to solvent relaxation in mixed solvents. A comparison of the time-dependent spectral data of the ionic liquid-toluene and ionic liquid-dioxane systems shows that, while a small amount of toluene can significantly affect the dynamics, comparatively, a larger amount of dioxane is required to bring about the same effect. This is explained in terms of favorable interactions between toluene and the imidazolium ring system leading to a more effective solubilization of toluene in the cybotactic region of the probe.     

A morphometric approach for the accurate solvation thermodynamics of proteins and ligands

We have developed a versatile method for calculating solvation thermodynamic quantities for molecules, starting from their atomic coordinates. The contribution of each atom to the thermodynamic quantities is estimated as a linear combination of four fundamental geometric measures of the atomic species, which are defined by Hadwiger's theorem, and the coefficients reflecting their solvation properties. This treatment enables us to calculate the solvation free energy with high accuracy despite of the limited computational load. The method can readily be applied to macromolecules in an all‐atom molecular model, allowing the stability of these molecules' structures in solution to be evaluated. © 2013 Wiley Periodicals, Inc.     

Application of nonpolar matrices for the analysis of low molecular weight nonpolar synthetic polymers by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

The application of nonpolar matrices for the analysis of low molecular weight nonpolar synthetic polymers using matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) is demonstrated. Anthracene, pyrene, and acenaphthene were utilized as nonpolar matrices for the analysis of polybutadiene, polyisoprene, and polystyrene samples of various average molecular weights ranging from about 700 to 5000. The standard MALDI-MS approach for the analysis of these types of polymers involves the use of conventional acidic matrices, such asall-trans-retinoic acid, with an additional cationization reagent. The nonpolar matrices used in this study are shown to be as equally effective as the conventional matrices. The uniform mixing of the nonpolar matrices and the nonpolar analytes enhances the MALDI-MS spectral reproducibility. Silver salts were found to be the best cationization reagents for all of the cases studied. Copper salts worked well for polystyrene, poorly for polyisoprene, and not at all for polybutadiene samples. These matrices should be useful for the characterization of hydrocarbon polymers and other analytes, such as modified polymers, which may potentially be sensitive to acidic matrices.     

Multipole moments and polarizabilities of nonpolar diatomic molecules through quantum solvation in solid parahydrogen: the quadrupole moment of N2

It is shown in this paper that from the study of the induced infrared absorption spectra of homonuclear diatomic molecules solvated as impurities in a molecular quantum solid, it is possible to extract information about the rovibrational matrix elements of the multipole moments and polarizability of the embedded molecule. Theoretical expressions are derived for the integrated absorption coefficients of various multipole-field-induced double transitions involving guest-host pairs in a solid para-H(2) matrix. The intensities of some of the quadrupole moment induced transitions involving the N(2)-para-H(2) pair have been measured. From a comparison of the experimental and theoretical intensities, rovibrational matrix elements of the quadrupole moment of N(2) are determined in its ground vibrational state.     

Confusing cause and effect: energy-entropy compensation in the preferential solvation of a nonpolar solute in dimethyl sulfoxide/water mixtures

We performed molecular simulations to analyze the thermodynamics of methane solvation in dimethyl sulfoxide (DMSO)/water mixtures (298 K, 1 atm). Two contributions to the interaction thermodynamics are studied separately: (i) the introduction of solute-solvent interactions (primary contribution) and (ii) the solute-induced disruption of cohesive solvent-solvent interactions (secondary contribution). The energy and entropy changes of the secondary contribution always exactly cancel in the free energy (energy-entropy compensation), hence only the primary contribution is important for understanding changes of the free energy. We analyze the physical significance of the solute-solvent energy and solute-solvent entropy associated with the primary contribution and discuss how to obtain these quantities from experiments combining solvation thermodynamic and solvent equation of state data. We show that the secondary contribution dominates changes in the methane solvation entropy and enthalpy: below 30 mol % DMSO in the mixture, methane, because of more favorable dispersion interactions with DMSO molecules, preferentially attracts DMSO molecules, which, in response, release water molecules into the bulk, causing an increase in the entropy. This large energy-entropy compensating process easily causes a confusion in the cause for and the effect of preferred methane-DMSO interactions. Methane-DMSO dispersion interactions are the cause, and the entropy change is the effect. Procedures that infer thermodynamic driving forces from analyses of the solvation entropies and enthalpies should therefore be used with caution.