Activation entropy of electron transfer reactions

We report microscopic calculations of free energies and entropies for intramolecular electron transfer reactions. The calculation algorithm combines the atomistic geometry and charge distribution of a molecular solute obtained from quantum calculations with the microscopic polarization response of a polar solvent expressed in terms of its polarization structure factors. The procedure is tested on a donor–acceptor complex in which ruthenium donor and cobalt acceptor sites are linked by a four-proline polypeptide. The reorganization energies and reaction energy gaps are calculated as a function of temperature by using structure factors obtained from our analytical procedure and from computer simulations. Good agreement between two procedures and with direct computer simulations of the reorganization energy is achieved. The microscopic algorithm is compared to the dielectric continuum calculations. We found that the strong dependence of the reorganization energy on the solvent refractive index predicted by continuum models is not supported by the microscopic theory. Also, the reorganization and overall solvation entropies are substantially larger in the microscopic theory compared to continuum models.     

Impact of the solvent on the conformational isomerism of calix[4]arenes: a study based on continuum solvation models

The influence of solvation on the conformational isomerism of calix[4]arene and p-tert-butylcalix[4]arene has been investigated by using the continuum model reported by Miertus, Scrocco, and Tomasi (MST). The quantum mechanical (QM) and semiclassical (SC) formalisms of the MST model have been considered for two different solvents (chloroform and water). The suitability of the QM-MST and SC-MST methods has been examined by comparison with previous results derived from classical molecular dynamics (MD) simulations with explicit solvent molecules. The application of the continuum model to the solute configurations generated by using in vacuo classical MD simulations provides a fast strategy to evaluate the effects of the solvent on the conformational preferences of calixarenes. These encouraging results allow us to propose the use of continuum models to solutes with complex molecular structures, which are traditionally studied by MD simulations.     

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.     

Implicit solvent models: Combining an analytical formulation of continuum electrostatics with simple models of the hydrophobic effect

The recent development of approximate analytical formulations of continuum electrostatics opens the possibility of efficient and accurate implicit solvent models for biomolecular simulations. One such formulation (ACE, Schaefer & Karplus, J. Phys. Chem., 1996, 100:1578) is used to compute the electrostatic contribution to solvation and conformational free energies of a set of small solutes and three proteins. Results are compared to finite-difference solutions of the Poisson equation (FDPB) and explicit solvent simulations and experimental data where available. Small molecule solvation free energies agree with FDPB within 1–1.5 kcal/mol, which is comparable to differences in FDPB due to different surface treatments or different force field parameterizations. Side chain conformation free energies of aspartate and asparagine are in qualitative agreement with explicit solvent simulations, while 74 conformations of a surface loop in the protein Ras are accurately ranked compared to FDPB. Preliminary results for solvation free energies of small alkane and polar solutes suggest that a recent Gaussian model could be used in combination with analytical continuum electrostatics to treat nonpolar interactions. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 322–335, 1999     

Dynamics of water in the hydration layer of a partially unfolded structure of the protein HP-36

Atomistic molecular dynamics simulations of the folded native structure and a partially unfolded molten globule structure of the protein villin headpiece subdomain or HP-36 have been carried out with explicit solvent to explore the effects of unfolding on the dynamical behavior of water present in the hydration layers of different segments (three alpha-helices) of the protein. The calculations revealed that the unfolding of helix-2 influences the translational and rotational motions of water present in the hydration layers of the three helices in a heterogeneous manner. It is observed that a correlation exists between the unfolding of helix-2 and the microscopic kinetics of protein-water hydrogen bonds formed by its residues. This in turn has an influence on the rigidity of the hydration layers of the helices in the unfolded structure versus that in the folded native structure. These results should provide a microscopic explanation to recent solvation dynamics experiments on folded native and unfolded structures of proteins.     

Stability of ion triplets in ionic liquid/lithium salt solutions: Insights from implicit and explicit solvent models and molecular dynamics simulations

Binding energies of ion triplets formed in ionic liquids by Li⁺ with two anions have been studied using quantum‐chemical calculations with implicit and explicit solvent supplemented by molecular dynamics (MD) simulations. Explicit solvent approach confirms variation of solute‐ionic liquid interactions at distances up to 2 nm, resulting from structure of solvation shells induced by electric field of the solute. Binding energies computed in explicit solvent and from the polarizable continuum model approach differ largely, even in sign, but relative values generally agree between these two models. Stabilities of ion triplets obtained in quantum‐chemical calculations for some systems disagree with MD results; the discrepancy is attributed to the difference between static optimized geometries used in quantum chemical modeling and dynamic structures of triplets in MD simulations. © 2015 Wiley Periodicals, Inc.     

The importance of excluded solvent volume effects in computing hydration free energies

Continuum dielectric methods such as the Born equation have been widely used to compute the electrostatic component of the solvation free energy, DeltaG(solv)(elec), because they do not need to include solvent molecules explicitly and are thus far less costly compared to molecular simulations. All of these methods can be derived from Gauss Law of Maxwell's equations, which yields an analytical solution for the solvation free energy, DeltaG(Born), when the solute is spherical. However, in Maxwell's equations, the solvent is assumed to be a structureless continuum, whereas in reality, the near-solute solvent molecules are highly structured unlike far-solute bulk solvent. Since we have recently reformulated Gauss Law of Maxwell's equations to incorporate the near-solute solvent structure by considering excluded solvent volume effects, we have used it in this work to derive an analytical solution for the hydration free energy of an ion. In contrast to continuum solvent models, which assume that the normalized induced solvent electric dipole density P(n) is constant, P(n) mimics that observed from simulations. The analytical formula for the ionic hydration free energy shows that the Born radius, which has been used as an adjustable parameter to fit experimental hydration free energies, is no longer ill defined but is related to the radius and polarizability of the water molecule, the hydration number, and the first peak position of the solute-solvent radial distribution function. The resulting DeltaG(solv)(elec) values are shown to be close to the respective experimental numbers.     

Computational study on the properties and structure of methyl lactate

A theoretical study on the properties and molecular level structure of the very important green solvent methyl lactate is carried out in the gas phase and methanol and water solutions, with the solvent treated both explicitly and as a continuum. Torsional barriers giving rise to different conformers by rotation of the hydroxyl and methyl groups were analyzed using density functional theory (DFT) to establish the most stable conformer both in gas phase and solution. DFT computations on lactate dimers were also done to study short-range features, and the effect of the surrounding solvent on intra- and intermolecular hydrogen bonding was analyzed according to the polarizable continuum model approach. We have also studied lactate/water and lactate/methanol small clusters together with the corresponding binding energies. Moreover, classical molecular dynamics simulations (MD) were carried out to study medium- and large-range effects at lower computational cost. MD simulations at different pressure and temperature conditions on pure lactate were carried out, and mixtures with water and methanol of different compositions were also studied. Structural information, analyzed through the radial distribution functions, together with dynamic aspects of pure and mixed fluids were considered. The intramolecular hydrogen bonding ability of methyl lactate together with the possibility of homo- and hetero-intermolecular association determines the behavior of this molecule in pure fluids or in mixed.     

FACTS: Fast analytical continuum treatment of solvation

An efficient method for calculating the free energy of solvation of a (macro)molecule embedded in a continuum solvent is presented. It is based on the fully analytical evaluation of the volume and spatial symmetry of the solvent that is displaced from around a solute atom by its neighboring atoms. The two measures of solvent displacement are combined in empirical equations to approximate the atomic (or self) electrostatic solvation energy and the solvent accessible surface area. The former directly yields the effective Born radius, which is used in the generalized Born (GB) formula to calculate the solvent-screened electrostatic interaction energy. A comparison with finite-difference Poisson data shows that atomic solvation energies, pair interaction energies, and their sums are evaluated with a precision comparable to the most accurate GB implementations. Furthermore, solvation energies of a large set of protein conformations have an error of only 1.5%. The solvent accessible surface area is used to approximate the nonpolar contribution to solvation. The empirical approach, called FACTS (Fast Analytical Continuum Treatment of Solvation), is only four times slower than using the vacuum energy in molecular dynamics simulations of proteins. Notably, the folded state of structured peptides and proteins is stable at room temperature in 100-ns molecular dynamics simulations using FACTS and the CHARMM force field.     

On the solvation of the Zn2+ ion in methanol: a combined quantum mechanics, molecular dynamics, and EXAFS approach

The solvation properties of the Zn(2+) ion in methanol solution have been investigated using a combined approach based on molecular dynamics (MD) simulations and extended X-ray absorption fine structure (EXAFS) experimental results. The quantum mechanical potential energy surface for the interaction of the Zn(2+) ion with a methanol molecule has been calculated taking into account the effect of bulk solvent by the polarizable continuum model (PCM). The effective Zn-methanol interactions have been fitted by suitable analytical potentials, and have been utilized in the MD simulation to obtain the structural properties of the solution. The reliability of the whole procedure has been assessed by comparing the theoretical structural results with the EXAFS experimental data. The structural parameters of the first solvation shells issuing from the MD simulations provide an effective complement to the EXAFS experiments.     

Equilibrium solvation in quadrupolar solvents

We present a microscopic theory of equilibrium solvation in solvents with zero dipole moment and nonzero quadrupole moment (quadrupolar solvents). The theory is formulated in terms of autocorrelation functions of the quadrupolar polarization (structure factors). It can be therefore applied to an arbitrary dense quadrupolar solvent for which the structure factors are defined. We formulate a simple analytical perturbation treatment for the structure factors. The solute is described by coordinates, radii, and partial charges of constituent atoms. The theory is tested on Monte Carlo simulations of solvation in model quadrupolar solvents. It is also applied to the calculation of the activation barrier of electron transfer reactions in a cleft-shaped donor-bridge-acceptor complex dissolved in benzene with the structure factors of quadrupolar polarization obtained from molecular-dynamics simulations.     

Simulation studies of the protein-water interface. II. Properties at the mesoscopic resolution

We report molecular dynamics (MD) simulations of three protein-water systems (ubiquitin, apo-calbindin D(9K), and the C-terminal SH2 domain of phospholipase C-gamma1), from which we compute the dielectric properties of the solutions. Since two of the proteins studied have a net charge, we develop the necessary theory to account for the presence of charged species in a form suitable for computer simulations. In order to ensure convergence of the time correlation functions needed for the analysis, the minimum length of the MD simulations was 20 ns. The system sizes (box length, number of waters) were chosen so that the resulting protein concentrations are comparable to experimental conditions. A dielectric component analysis was carried out to analyze the contributions from protein and water to the frequency-dependent dielectric susceptibility chi(omega) of the solutions. Additionally, an even finer decomposition into protein, two solvation shells, and the remaining water (bulk water) was carried out. The results of these dielectric decompositions were used to study protein solvation at mesoscopic resolution, i.e., in terms of protein, first and second solvation layers, and bulk water. This study, therefore, complements the structural and dynamical analyses at molecular resolution that are presented in the companion paper. The dielectric component contributions from the second shell and bulk water are very similar in all three systems. We find that the proteins influence the dielectric properties of water even beyond the second solvation shell, in agreement with what was observed for the mean residence times of water molecules in protein solutions. By contrast, the protein contributions, as well as the contributions of the first solvation shell, are system specific. Most importantly, the protein and the first water shell around ubiquitin and apo-calbindin are anticorrelated, whereas the first water shell around the SH2 domain is positively correlated.     

有机π共轭配体溶剂化效应与分子间相互作用的理论研究

采用可极化的连续介质模型(PCM), 运用密度泛函理论(DFT), 在B3LYP/6-31+G^**水平下研究了溶剂极性对有机π共轭配体N,N'-Bis-(3-pyridyl)ethylene-bis-urea(BPEBU)中syn-anti构象的分子几何和电子结构的影响, 并借助分子动力学模拟的方法, 采用明确溶剂模型研究了溶质-溶剂分子间的相互作用. 密度泛函理论计算结果表明, 随着溶剂极性的增强, BPEBU中尿素基上的CO键和N-H键以及吡啶环上的C-N键被明显极化, 使羰基氧原子和吡啶氮原子的电负性明显增强, 尿素基的N-H键上氢原子的正电荷也显著增加. 分子动力学模拟统计的结果表明, 在极性较强的乙醇溶液中, 有明确的O…H-O, N…H-O和N-H…O等3种氢键作用存在, 而在丙酮溶液中, 只有N…H-O一种氢键作用存在, 而且与乙醇溶液中的N…H-O作用相比要弱些. 另外, 采用密度泛函理论方法结合连续/明确的混合溶剂模型, 优化得到了溶质-溶剂三聚体的超分子簇结构, 与分子动力学模拟的第一溶剂层中的超分子结构相比, 两者定性一致.     

Solvent effects on electronic structures and chain conformations of alpha-oligothiophenes in polar and apolar solutions

Solvent effects on electronic structures and chain conformations of alpha-oligothiophenes nTs (n = 1 to 10) are investigated in solvents of n-hexane, 1,4-dioxane, carbon tetrachloride, chloroform, and water by using density functional theory (DFT) and molecular dynamics (MD) simulations. Both implicit and explicit solvent models are employed. The polarized continuum model (PCM) calculations and MD simulations demonstrate the weak solvent effects on the electronic structures of alpha-oligothiophenes. The lowest dipole-allowed vertical excitation energies of nTs, obtained from time-dependent DFT/PCM calculations at the B3LYP/6-31G(d) level, exhibit a red shift as the solvent polarity increases, in agreement with experiments. The studied solvents have little impact on the state order of the low-lying excited states provided that the nTs are kept in C2h or C2v symmetry. The MD simulations demonstrate that the chain conformations are distorted to some extent in polar and nonpolar solvents. A qualitative picture of the distribution of solvent molecules around the solvated nTs is drawn by means of radial and spatial distribution functions. The S...H-O and pi...H-O solute-solvent interactions are insignificant in aqueous solution.     

Potential of mean force of water–proton bath and molecular dynamic simulation of proteins at constant pH

An advanced implicit solvent model of water–proton bath for protein simulations at constant pH is presented. The implicit water–proton bath model approximates the potential of mean force of a protein in water solvent in a presence of hydrogen ions. Accurate and fast computational implementation of the implicit water–proton bath model is developed using the continuum electrostatic Poisson equation model for calculation of ionization equilibrium and the corrected MSR6 generalized Born model for calculation of the electrostatic atom–atom interactions and forces. Molecular dynamics (MD) method for protein simulation in the potential of mean force of water–proton bath is developed and tested on three proteins. The model allows to run MD simulations of proteins at constant pH, to calculate pH‐dependent properties and free energies of protein conformations. The obtained results indicate that the developed implicit model of water–proton bath provides an efficient way to study thermodynamics of biomolecular systems as a function of pH, pH‐dependent ionization‐conformation coupling, and proton transfer events. © 2012 Wiley Periodicals, Inc.     

Density functional theory study of uranium(VI) aquo chloro complexes in aqueous solution

Mixed uranyl aquo chloro complexes of the type [UO2(H2O)xCly]2-y (y = 1, 2, 3, 4; x + y = 4, 5) have been optimized at the BLYP, BP86, and B3LYP levels of density functional theory in vacuo and in a polarizable continuum modeling bulk water (PCM) and have been studied at the BLYP level with Car-Parrinello molecular dynamics (MD) simulations in the gas phase and in explicit aqueous solution. Free binding energies were evaluated from static PCM data and from pointwise thermodynamic integration involving constrained MD simulations in water. The computations reveal significant solvent effects on geometric and energetic parameters. Based on the comparison of PCM-optimized or MD-averaged uranyl-ligand bond distances with EXAFS-derived values, the transition between five- and four-coordination about uranyl is indicated to occur at a Cl content of y = 2 or 3.