Redox entropy of plastocyanin: developing a microscopic view of mesoscopic polar solvation

We report applications of analytical formalisms and molecular dynamics (MD) simulations to the calculation of redox entropy of plastocyanin metalloprotein in aqueous solution. The goal of our analysis is to establish critical components of the theory required to describe polar solvation at the mesoscopic scale. The analytical techniques include a microscopic formalism based on structure factors of the solvent dipolar orientations and density and continuum dielectric theories. The microscopic theory employs the atomistic structure of the protein with force-field atomic charges and solvent structure factors obtained from separate MD simulations of the homogeneous solvent. The MD simulations provide linear response solvation free energies and reorganization energies of electron transfer in the temperature range of 280-310 K. We found that continuum models universally underestimate solvation entropies, and a more favorable agreement is reported between the microscopic calculations and MD simulations. The analysis of simulations also suggests that difficulties of extending standard formalisms to protein solvation are related to the inhomogeneous structure of the solvation shell at the protein-water interface combining islands of highly structured water around ionized residues along with partial dewetting of hydrophobic patches. Quantitative theories of electrostatic protein hydration need to incorporate realistic density profile of water at the protein-water interface.     

Theoretical studies of UO2(H2O)n(2+), NpO2(H2O)n(+), and PuO2(H2O)n(2+) complexes (n=4-6) in aqueous solution and gas phase

Extensive ab initio calculations both in gas phase and solution have been carried out to study the equilibrium structure, vibrational frequencies, and bonding characteristics of various actinyl (UO2(2+), NpO2(+), and PuO2(2+)) and their hydrated forms, AnO2(H2O)n(z+) (n=4, 5, and 6). Bulk solvent effects were studied using a continuum method. The geometries were fully optimized at the coupled-cluster singles + doubles (CCSD), density-functional theory (DFT), and M?ller-Plesset (MP2) level of theories. In addition vibrational frequencies have been obtained at the CCSD as well as MP2/DFT levels. The results show that both the short-range and long-range solvent effects are important. The combined discrete-continuum model, in which the ionic solute and the solvent molecules in the first and second solvation shells are treated quantum mechanically while the solvent is simulated by a continuum model, can predict accurately the bonding characteristics. Moreover, our values of solvation free energies suggest that five- and six-coordinations are equally preferred for UO2(2+), and five-coordinated species are preferred for NpO2(+) and PuO2(2+). On the basis of combined quantum-chemical and continuum treatments of the hydrated complexes, we are able to determine the optimal cavity radii for the solvation models. The coupled-cluster computations with large basis sets were employed for the vibrational spectra and equilibrium geometries both of which compare quite favorably with experiment. Our most accurate computations reveal that both five- and six-coordination complexes are important for these species.     

Thermodynamics for nonequilibrium solvation and numerical evaluation of solvent reorganization energy

This work presents a thermodynamic method for treating nonequilibrium solvation. By imposing an extra electric field onto the nonequilibrium solvation system, a virtual constrained equilibrium state is prepared. In this way, the free energy difference between the real nonequilibrium state and the con-strained equilibrium one is simply the potential energy of the nonequilibrium polarization in the extra electronic field, according to thermodynamics. Further, new expressions of nonequilibrium solvation energy and solvent reorganization energy have been formulated. Analysis shows that the present formulations will give a value of reorganization energy about one half of the traditional Marcus theory in polar solvents, thus the explanation on why the traditional theory tends to overestimate this quantity has been found out. For the purpose of numerical determination of solvent reorganization energy, we have modified Gamess program on the basis of dielectric polarizable continuum model. Applying the procedure to the well-investigated intramolecular electron transfer in biphenyl-androstane-naphthyl and biphenyl-androstane-phenanthryl systems, the numerical results of solvent reorganization energy have been found to be in good agreement with the experimental fittings.     

COSMO-RS: A novel view to physiological solvation and partition questions

Both, dielectric continuum solvation models as well as surface or group based methods using polarity and lipophilicity parameters have been proven to be useful tools for the analysis of solvation and partition questions. For the first time, COSMO-RS provides an integrated theory, which combines the aspects of continuum solvation and surface interactions, and which ends up with chemical potentials of molecules in almost arbitrary solvents and mixtures. Due to its sound theoretical basis, COSMO-RS does not only provide a new quantitative access to solvation and partition properties in well defined solvents, but it also opens a novel view and gives a better understanding of the general problem of solvation. Finally, this allows for a generalisation of COSMO-RS to sophisticatedphysiological partition problems involving as complex phases as blood, brain, or cell membranes. The use of COSMO-RS for drug discovery and design is demonstrated by applications to blood-brain partition coefficients, and water solubility.     

A fast and Space-efficient boundary element method for computing electrostatic and hydration effects in large molecules

At present, there are two widely used approaches for computing molecular hydration and electrostatic effects within the continuum approximation: the finite difference method, in which the electric potential is directly computed on a cubic grid, and the induced polarization charge or boundary element method, in which an induced charge distribution is first computed on the molecular surface and in which solvation effects are then calculated by reference to the reaction field arising from this induced surface charge. While the induced surface charge approach has a number of advantages over finite differences, especially in the computation of hydration forces and solvent stabilization, the applications of this technique have been largely restricted to small molecules. This is primarily due to the very large system of equations that results when the surface of a macromolecule is discretized into elements small enough to ensure an acceptable level of numerical accuracy within the continuum model. This article describes a new algorithm for implementing boundary element calculations within the continuum model. The essence of our approach is only to compute explicitly those interactions between surface elements that are relatively close together and to approximate long-range interactions by grid-based multipole expansion. The resulting system of equations has a relatively sparse coefficient matrix and requires disk storage that increases linearly with molecular surface area. The technique has numerous applications in the analysis of solvation effects in large molecules, especially in the area of conformational analysis, where it is critical to accurately estimate the global hydration energy for the entire structure. © 1996 by John Wiley & Sons, Inc.     

Hybrid supermolecule-polarizable continuum approach to solvation: Application to the mechanism of the Stevens rearrangement

Semiempirical molecular orbital theory has been used to study the effects of solvation by acetonitrile on the Stevens rearrangement of methylammonium formylmethylide to 2-aminopropanal. Three methods of solvation have been used to investigate both the electrostatic and specific solvent–solute effects of solvation: a supermolecule calculation involving the complete geometry optimization of up to six solvent molecules about the solute, the conductor-like screening model (COSMO) polarizable continuum method which allows for geometry optimization of the solute in a solvent defined by its dielectric constant, and a hybrid method in which up to five solvent molecules are incorporated inside the solute cavity and complete geometry optimization of the complex is carried out within the polarizable continuum. A comparison of the calculated geometries, rearrangement activation energies, and enthalpies of solvation from these approaches is presented, and the explicit versus bulk solvation effects are discussed. The overall effect of all methods for incorporating solvation effects is that the radical pair pathway is perferred over the concerted mechanism. © 1996 by John Wiley & Sons, Inc.     

A density functional theory study of the conformational properties of 1,2-ethanediamine: protonation and solvent effects

 The structures and the conformational energies of nonprotonated, monoprotonated and diprotonated 1,2-ethanediamine have been investigated through density functional theory. The relative performance of local and gradient-corrected functionals is discussed. The existence of hydrogen-bond formation has been determined with electron localisation function calculations. Proton affinities for nonprotonated and monoprotonated 1,2-ethanediamine have been calculated and are in agreement with experimental data. The influence of solvation has been accounted for through the self-consistent isodensity polarisable continuum model. The results for the nonprotonated conformers show that solvation stabilises those conformers which have the lone pair in an antiperiplanar conformation. Solvation of the monoprotonated conformer stabilises significantly the “anti” conformation, which is unstable in the gas phase. For the di-protonated species, solvation stabilises slightly the gauche conformer, which is unstable in the gas phase. Received: 28 September 1999 / Accepted: 2 May 2000 / Published online: 27 September 2000     

Optimized parameters for continuum solvation calculations with carbohydrates

Continuum solvent models have been shown to be an efficient method for the calculation of the energetics of biomolecules in solution. However, for these methods to produce accurate results, an appropriate set of atomic radii or volumes is needed. While these have been developed for proteins and nucleic acids, the same is not true of carbohydrates. Here, a set of optimized parameters for continuum solvation calculations of carbohydrates in conjunction with the Carbohydrate Solution Force Field are presented. Explicit solvent free-energy perturbation simulations were performed on a set of hexapyranose sugars and used to fit atomic radii for Poisson-Boltzmann and generalized-Born calculations, and to fit atomic volumes for use with the analytical continuum electrostatics model. The solvation energetics computed with the optimized radii and a Poisson-Boltzmann model show remarkable agreement with explicit solvent simulation, with a root-mean-square error of 1.19 kcal/mol over a large test set of sugars in many conformations. The generalized-Born model gives slightly poorer agreement, but still correlates very strongly, with an error of 1.69 kcal/mol. The analytical continuum electrostatics model correlates well with the explicit solvent results, but gives a larger error of 4.71 kcal/mol. The remarkable agreement between the solvation free energies computed in explicit and implicit solvent provides strong motivation for the use of implicit solvent models in the simulation of carbohydrate-containing systems.     

Atomic decomposition of the protein solvation free energy and its application to amyloid-beta protein in water

We report the development of an atomic decomposition method of the protein solvation free energy in water, which ascribes global change in the solvation free energy to local changes in protein conformation as well as in hydration structure. So far, empirical decomposition analyses based on simple continuum solvation models have prevailed in the study of protein-protein interactions, protein-ligand interactions, as well as in developing scoring functions for computer-aided drug design. However, the use of continuum solvation model suffers serious drawbacks since it yields the protein free energy landscape which is quite different from that of the explicit solvent model and since it does not properly account for the non-polar hydrophobic effects which play a crucial role in biological processes in water. Herein, we develop an exact and general decomposition method of the solvation free energy that overcomes these hindrances. We then apply this method to elucidate the molecular origin for the solvation free energy change upon the conformational transitions of 42-residue amyloid-beta protein (Aβ42) in water, whose aggregation has been implicated as a primary cause of Alzheimer's disease. We address why Aβ42 protein exhibits a great propensity to aggregate when transferred from organic phase to aqueous phase.     

Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation

The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostatic free energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, CCl4, and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.     

Microsolvated transition state models for improved insight into chemical properties and reaction mechanisms

Over the years, several methods have been developed to effectively represent the chemical behavior of solutes in solvents. The environmental effects arising due to solvation can generally be achieved either through inclusion of discrete solvent molecules or by inscribing into a cavity in a homogeneous and continuum dielectric medium. In both these approaches of computational origin, the perturbations on the solute induced by the surrounding solvent are at the focus of the problem. While the rigor and method of inclusion of solvent effects vary, such solvation models have found widespread applications, as evident from modern chemical literature. A hybrid method, commonly referred to as cluster-continuum model (CCM), brings together the key advantages of discrete and continuum models. In this perspective, we intend to highlight the latent potential of CCM toward obtaining accurate estimates on a number of properties as well as reactions of contemporary significance. The objective has generally been achieved by choosing illustrative examples from the literature, besides expending efforts to bring out the complementary advantages of CCM as compared to continuum or discrete solvation models. The majority of examples emanate from the prevalent applications of CCM to organic reactions, although a handful of interesting organometallic reactions have also been discussed. In addition, increasingly accurate computations of properties like pK(a) and solvation of ions obtained using the CCM protocol are also presented.     

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.     

Solvation enthalpies of neutral solutes in water and octanol

The balance between electrostatic and non-electrostatic enthalpic contributions to the free energy of solvation of a series of neutral solutes in water and n-octanol is examined by means of continuum solvation calculations based on the Miertus–Scrocco–Tomasi (MST) method. The experimental data indicate that the solvation enthalpy of hydrocarbons is very similar in water and n-octanol, and that the enthalpic contribution measured for polar compounds is larger in water than in n-octanol. According to MST calculations, the different magnitude of the solvation enthalpy found for polar compounds in the two solvents can be largely attributed to the electrostatic contribution. Moreover, the results point out that there is close resemblance between the non-electrostatic components for both hydrocarbons and polar compounds in the two solvents. Finally, the results show the power of current continuum models like MST to dissect the total free energy of solvation in entropic and enthalpic contributions and suggest that new refinements of continuum solvation models should include not only the fitting to solvation free energies, but also their enthalpic components.     

An Accurate Approach for Computational pKa Determination of Phenolic Compounds

Computational chemistry is a valuable tool, as it allows for in silico prediction of key parameters of novel compounds, such as pKa. In the framework of computational pKa determination, the literature offers several approaches based on different level of theories, functionals and continuum solvation models. However, correction factors are often used to provide reliable models that adequately predict pKa. In this work, an accurate protocol based on a direct approach is proposed for computing phenols pKa. Importantly, this methodology does not require the use of correction factors or mathematical fitting, making it highly practical, easy to use and fast. Above all, DFT calculations performed in the presence two explicit water molecules using CAM-B3LYP functional with 6-311G+dp basis set and a solvation model based on density (SMD) led to accurate pKa values. In particular, calculations performed on a series of 13 differently substituted phenols provided reliable results, with a mean absolute error of 0.3. Furthermore, the model achieves accurate results with -CN and -NO₂ substituents, which are usually excluded from computational pKa studies, enabling easy and reliable pKa determination in a wide range of phenols.     

A study on orientation and absorption spectrum of interfacial molecules by using continuum model

In this work, a numerical procedure based on the continuum model is developed and applied to the solvation energy for ground state and the spectral shift against the position and the orientation of the interfacial molecule. The interface is described as a sharp boundary separating two bulk media. The polarizable continuum model (PCM) allows us to account for both electrostatic and nonelectrostatic solute-solvent interactions when we calculate the solvation energy. In this work we extend PCM to the interfacial system and the information about the position and orientation of the interfacial molecule can be obtained. Based on the developed expression of the electrostatic free energy of a nonequilibrium state, the numerical procedure has been implemented and used to deal with a series of test molecules. The time-dependent density functional theory (TDDFT) associated with PCM is used for the electron structure and the spectroscopy calculations of the test molecules in homogeneous solvents. With the charge distribution of the ground and excited states, the position- and orientation-dependencies of the solvation energy and the spectrum have been investigated for the interfacial systems, taking the electrostatic interaction, the cavitation energy, and the dispersion-repulsion interaction into account. The cavitation energy is paid particular attention, since the interface portion cut off by the occupation of the interfacial molecule contributes an extra part to the stabilization for the interfacial system. The embedding depth, the favorable orientational angle, and the spectral shift for the interfacial molecule have been investigated in detail. From the solvation energy calculations, an explanation has been given on why the interfacial molecule, even if symmetrical in structure, tends to take a tilting manner, rather than perpendicular to the interface.     

Thermochemistry of arylselanyl radicals and the pertinent ions in acetonitrile

Reduction and oxidation potentials of a series of parasubstituted phenylselanyl radicals, XC(6)H(4)Se(*), have been measured using photomodulated voltammetry in acetonitrile. The thermodynamic significance of these data was substantiated through a study of the oxidation process of the pertinent selenolates in linear sweep voltammetry. Both the reduction and the oxidation potentials correlate linearly with the Hammett substituent coefficients sigma and sigma(+) leading in the latter case to slopes, rho(+), of 2.5 and 3.8, respectively. Through comparison of these slopes with those published previously for the O- and S-centered analogues, it is revealed that the pi-interaction becomes progressively smaller as the size of the radical center increases in the order O, S, and Se. Solvation energies of the pertinent selenolates and selanylium ions have been extracted from thermochemical cycles incorporating the measured electrode potentials for XC(6)H(4)Se(*) as well as electron affinities and ionization potentials obtained from theoretical calculations at the B3LYP/6-31+G(d) level. The extracted data show the expected overall substituent dependency for both kinds of ions; that is, the absolute value of the solvation energy decreases as the charge becomes more delocalized. The data have also been compared with solvation energies computed using the polarizable continuum model (PCM). Interestingly, we find that, while the model seems to work well for selenolates, it underestimates the solvation of selanylium ions in acetonitrile by as much as 25 kcal mol(-)(1). These large deviations are ascribed to the fact that the PCM method does not take specific solvent effects into account as it treats the solvent as a continuum described solely by its dielectric constant. Gas-phase calculations show that the arylselanylium ions can coordinate covalently to one or two molecules of acetonitrile in strong Ritter-type adducts. When this strong interaction is included in the solvation energy calculations by means of a combined supermolecule and PCM approach, the experimental data are reproduced within a few kcal mol(-)(1). Although the energy difference of the singlet and triplet spin states of the arylselanylium ions is small for the gas-phase structures, the singlet cation is undoubtedly the dominating species in solution because the triplet cation lacks the ability to form covalent bonds.     

Theoretical studies of 31P NMR spectral properties of phosphanes and related compounds in solution

Selected theoretical methods, basis sets and solvation models have been tested in their ability to predict (31)P NMR chemical shifts of large phosphorous-containing molecular systems in solution. The most efficient strategy was found to involve NMR shift calculations at the GIAO-MPW1K/6-311++G(2d,2p)//MPW1K/6-31G(d) level in combination with a dual solvation model including the explicit consideration of single solvent molecules and a continuum (PCM) solvation model. For larger systems it has also been established that reliable (31)P shift predictions require Boltzmann averaging over all accessible conformations in solution.