Theory Of Energy Representation Research Articles

Free-energy decomposition of salt effects on the solubilities of small molecules and the role of excluded-volume effects.

The roles of cations and anions are different in the perturbation on solvation, and thus, the analyses of the separated contributions from cations and anions are useful to establish molecular pictures of ion-specific effects. In this work, we investigate the effects of cations, anions, and water separately in the solvation of n-alcohols and n-alkanes by free-energy decomposition. By utilising energy-representation theory of solvation, we address the contributions arising from the direct solute-solvent interactions and the excluded-volume effects. It is found that the change in solvation of n-alcohols and n-alkanes upon addition of salt depends primarily on the anion species. The direct interaction between the anion and solute is in agreement with the Setschenow coefficient in terms of the ranking of salting-in and salting-out for n-alkanes, which corresponds to the extent of accumulation of the anion on the solute surface. For each of the n-alcohols and n-alkanes examined, the excluded-volume component in the Setschenow coefficient is well correlated to the (total) Setschenow coefficient when the salt effects are concerned. The ranking of the excluded-volume component in the variation of the salt species is parallel to the water contribution, which is correlated further to the change in the water density upon the addition of the salt.

Chain-Increment Approach to the Mutual Miscibility of Polymers with All-Atom Molecular Simulation

The mutual miscibility of polymers was addressed with all-atom molecular dynamics (MD) simulation and the energy-representation theory of solvation. The chain-increment method was extended to polymer mixtures, and the mixing free energy was related to the incremental free energy for the constituent polymer species that is the free-energy change of turning on the interaction of a monomer in the tagged polymer chain with the surrounding molecules. The free energy was then computed for the mixing of polyethylene (PE) and poly(vinylidene difluoride) (PVDF) and of poly(vinyl alcohol) (PVA) and polyvinylpyrrolidone (PVP). It was seen that the incremental free energy is insensitive to the location of the monomer in the inner part of the polymer chain and depends on the mixing ratio of the polymer system in parallel with the average interaction energy of the incremented monomer with the surrounding polymers. The intermolecular interactions of each polymer species were further analyzed at atomic resolution. The PVDF–PVDF interaction was found to become less favorable (more positive) upon addition of PE in the mixture of PE and PVDF, making them immiscible with each other. PVP favors PVA more than PVP, on the other hand, leading to the miscibility of PVA and PVP. The connection of our formulation of the mixing free energy with the Flory–Huggins expression is also described.

Anion-cation contrast of small molecule solvation in salt solutions.

The contributions from anions and cations from salt are inseparable in their perturbation of molecular systems by experimental and computational methods, rendering it difficult to dissect the effects exerted by the anions and cations individually. Here we investigate the solvation of a small molecule, caffeine, and its perturbation by monovalent salts from various parts of the Hofmeister series. Using molecular dynamics and the energy-representation theory of solvation, we estimate the solvation free energy of caffeine and decompose it into the contributions from anions, cations, and water. We also decompose the contributions arising from the solute–solvent and solute-ions interactions and that from excluded volume, enabling us to pin-point the mechanism of salt. Anions and cations revealed high contrast in their perturbation of caffeine solvation, with the cations salting-in caffeine via binding to the polar ketone groups, while the anions were found to be salting-out via perturbations of water. In agreement with previous findings, the perturbation by salt is mostly anion dependent, with the magnitude of the excluded-volume effect found to be the governing mechanism. The free-energy decomposition as conducted in the present work can be useful to understand ion-specific effects and the associated Hofmeister series.

Solvation energetics of proteins and their aggregates analyzed by all-atom molecular dynamics simulations and the energy-representation theory of solvation.

Solvation is a controlling factor for the structure and function of proteins. This article addresses the effects of solvation from an energetic perspective for the fluctuations and cosolvent-induced changes in protein structures and the equilibrium of aggregate formation for a peptide. A theoretical framework to analyze the solvation effects with an explicit solvent is introduced by adopting the energy-representation theory of solvation, and the connection of the solvation free energy to the protein structure and the aggregation tendency is quantitatively described in combination with all-atom molecular dynamics simulations. The interaction components that govern the solvation effects on the structural variations of proteins are further identified through correlation analysis, and a computational scheme to assess the shift of an aggregation equilibrium due to the addition of a cosolvent is provided.

Energy-Representation Theory of Solutions: Its Formulation and Application to Soft, Molecular Aggregates

Abstract The energy-representation theory of solutions is developed to address the dissolution of a molecule in homogeneous fluid as well as the partitioning into such nanoscale structures as micelle and lipid membrane and the physisorption onto gas-liquid and solid-liquid interfaces in a unified manner as solvation in an extended sense. The present review describes the formulation of the solution theory with illustrative applications to the peptide configuration in lipid membrane, the water dissolution into polymer, and the physisorption on urea crystal in contact with liquid water. The solution theory in the energy representation is a density-functional scheme formulated by adopting the solute-solvent pair interaction energy as a one-dimensional coordinate for distribution functions and provides an approximate functional for the solvation free energy in terms of energy distribution functions in the reference-solvent and solution systems of interest. Each of the solute and solvent molecules is treated as a single unit as a whole, and due to this feature, a species with intramolecular flexibility and a solvent system with nano-scale inhomogeneity or interface can be analyzed in a common framework. The role of water is pointed out in determining the configuration of a peptide in lipid membrane, and the dissolution of water into polymer medium is described at chemical accuracy. Some directions of future developments are also discussed.

Free-energy analysis of the hydration and cosolvent effects on the β-sheet aggregation through all-atom molecular dynamics simulation.

Energetics was analyzed for the aggregation of an 11-residue peptide. An all-atom molecular dynamics simulation was conducted with explicit solvent, and the energy-representation theory of solution was employed to compute the solvation free energies of the peptide and its aggregates. The aggregation in the pure-water solvent was observed to be inhibited by the solvation. The driving force of aggregate formation is the interactions among the peptide molecules, and the sum of the intra-aggregate and solvation terms per monomer is more favorable for larger aggregates. The effect of the cosolvent was then examined by focusing on the mixtures of water with urea and dimethyl sulfoxide (DMSO). It was actually shown that the derivative of the excess chemical potential of a flexible solute species with respect to the cosolvent concentration is determined exactly by the corresponding derivative of the free energy of solvation. The cosolvent effect on the equilibrium of aggregate formation can thus be addressed by comparing the solvation free energies with and without the cosolvent, and both the urea and DMSO cosolvents were found to inhibit the aggregation. The cosolvent-induced change in the solvation free energy was further decomposed into the contributions from the cosolvent and water. Their dependencies on the degree of aggregation were seen to be weak for large aggregates, and the roles of the electrostatic, van der Waals, and excluded-volume components in the solvation energetics were discussed.

Free-energy analysis of physisorption on solid-liquid interface with the solution theory in the energy representation.

Physisorption of urea on its crystal in contact with water was subject to energetics analysis with all-atom molecular dynamics simulation. The transfer free energy of urea to an adsorption site was treated in the framework of the energy-representation theory of solutions, which allows a fast computation of the free energy in an inhomogeneous environment with solid-liquid interface. The preference of adsorption was then compared between the (001) and (110) faces, and it was found that the physisorption is more favorable on (001) than on (110) in correspondence to the hydrogen bonding between the adsorbed urea and the crystal urea. Among the terrace configurations of adsorption, the attractive interaction governs the preferable site with a minor role of the repulsive interaction. The effect of an edge was also treated by examining the terrace and step and was shown to be strongly operative on the (110) face when the CO group of the adsorbed urea points toward the edge. The present work demonstrates that the solution theory can be a framework for analyzing the energetics of physisorption and addressing the roles of the crystal and liquid at the interface through the systematic decomposition of free energy.

Free-Energy Analysis of Peptide Binding in Lipid Membrane Using All-Atom Molecular Dynamics Simulation Combined with Theory of Solutions.

All-atom molecular dynamics (MD) simulations are performed to examine the stabilities of a variety of binding configurations of alamethicin, a 20-amino-acid amphipathic peptide, in the bilayers of 1-palmitoyl-2-oleoyl phosphatidylcholine (POPC) and 1,2-dimyristoyl- sn-glycero-3-phosphatidylcholine (DMPC). The binding free energy of alamethicin is calculated through a combination of MD simulation and the energy-representation theory of solutions, and it is seen that the transmembrane configuration is stable in both membranes. A surface-bound state is also found to be stable due to the balance between the attractive and repulsive interactions of the peptide with lipid and water, and the key role of water is pointed out for the stability in the interfacial region. A difference between the POPC and DMPC systems is noted when the polar C-terminal domain is buried in the hydrophobic region of the membrane. In POPC, the peptide is unfavorably located with that configuration due to the loss of electrostatic interaction between the peptide and lipid.

Drastic Compensation of Electronic and Solvation Effects on ATP Hydrolysis Revealed through Large-Scale QM/MM Simulations Combined with a Theory of Solutions.

Hydrolysis of adenosine triphosphate (ATP) is the "energy source" for a variety of biochemical processes. In the present work, we address key features of ATP hydrolysis: the relatively moderate value (about -10 kcal/mol) of the standard free energy, ΔGhyd, of reaction and the insensitivity of ΔGhyd to the number of excess electrons on ATP. We conducted quantum mechanical/molecular mechanical simulation combined with the energy-representation theory of solutions to analyze the electronic-state and solvation contributions to ΔGhyd. It was revealed that the electronic-state contribution in ΔGhyd is largely negative (favorable) upon hydrolysis, due to the reduction of electrostatic repulsion accompanying the breakage of the P-O bond. In contrast, the solvation effect was found to be strongly more favorable on the reactant side. Thus, we showed that a drastic compensation of the two opposite effects takes place, leading to the modest value of ΔGhyd at each number of excess electrons examined. The computational analyses were also conducted for pyrophosphate ions (PPi), and the parallelism between the ATP and PPi hydrolyses was confirmed. Classical molecular dynamics simulation was further carried out to discuss the effect of the solvent environment; the insensitivity of ΔGhyd to the number of excess electrons was seen to hold in solvent water and ethanol.

Computation of the free energy due to electron density fluctuation of a solute in solution: A QM/MM method with perturbation approach combined with a theory of solutions

We developed a perturbation approach to compute solvation free energy Δμ within the framework of QM (quantum mechanical)/MM (molecular mechanical) method combined with a theory of energy representation (QM/MM-ER). The energy shift η of the whole system due to the electronic polarization of the solute is evaluated using the second-order perturbation theory (PT2), where the electric field formed by surrounding solvent molecules is treated as the perturbation to the electronic Hamiltonian of the isolated solute. The point of our approach is that the energy shift η, thus obtained, is to be adopted for a novel energy coordinate of the distribution functions which serve as fundamental variables in the free energy functional developed in our previous work. The most time-consuming part in the QM/MM-ER simulation can be, thus, avoided without serious loss of accuracy. For our benchmark set of molecules, it is demonstrated that the PT2 approach coupled with QM/MM-ER gives hydration free energies in excellent agreements with those given by the conventional method utilizing the Kohn-Sham SCF procedure except for a few molecules in the benchmark set. A variant of the approach is also proposed to deal with such difficulties associated with the problematic systems. The present approach is also advantageous to parallel implementations. We examined the parallel efficiency of our PT2 code on multi-core processors and found that the speedup increases almost linearly with respect to the number of cores. Thus, it was demonstrated that QM/MM-ER coupled with PT2 deserves practical applications to systems of interest.

Interaction-component analysis of the urea effect on amino acid analogs

Transfer energetics from pure water to a urea-water mixture is examined for a set of amino acid analog solutes by using molecular dynamics simulation and free-energy calculation. The free energy of transfer from pure-water solvent to 8 M urea-water mixed solvent is calculated for each solute, and the urea-water mixture is shown to be a more favorable solvent than pure water. The correlation of the transfer free energy is then examined against the corresponding changes upon transfer of the average sum of solute-solvent interaction energy and its electrostatic and van der Waals components. A strong correlation is observed against the change in solute-solvent energy, with a dominant contribution from the van der Waals component for neutral solutes. The electrostatic component exhibits a weak correlation due to the compensation between the contributions from urea and water. The transfer free energy is further decomposed into the contributions from urea and water within an approximate framework of the energy-representation theory of solvation. It is found that urea makes a favorable contribution to the transfer free energy. The contribution from water depends on the hydrophobicity/hydrophilicity of the solute. Urea and water act cooperatively for hydrophobic solute, and are competitive against each other for hydrophilic solute. The effect of excluded volume is also addressed, and is seen to be minor in the transfer energetics due to the compensation between the contributions from urea and water.

Free-energy analysis of the electron-density fluctuation in the quantum-mechanical/molecular-mechanical simulation combined with the theory of energy representation

The relationship is investigated for QM/MM (quantum-mechanical/molecular-mechanical) systems between the fluctuations of the electronic state of the QM subsystem and of the solvation effect due to the QM-MM interaction. The free-energy change due to the electron-density fluctuation around its average is highlighted, and is evaluated through an approximate functional formulated in terms of distribution functions of the many-body coupling (pairwise non-additive) part of the QM-MM interaction energy. A set of QM/MM simulations are conducted in MM water solvent for QM water solute in ambient and supercritical conditions and for QM glycine solute in the neutral and zwitterionic forms. The variation of the electronic distortion energy of the QM solute in the course of QM/MM simulation is then shown to be compensated by the corresponding variation of the free energy of solvation. The solvation free energy conditioned by the electronic distortion energy is further analyzed with its components. It is found that the many-body contribution is essentially equal between the free energy and the average sum of solute-solvent interaction energy.

The QM/MM‐ER studies for the origin of the antioxidative properties of MCI‐186 in aqueous solutions

AbstractThe anionic derivative of the pharmaceutical compound 3‐methyl‐1‐phenyl‐2‐pyrazolin‐5‐one (MCI‐186) is known to deactivate the free radicals in biological systems by donating its excess electron. For the purpose to investigate the mechanism that the MCI‐186 anion exhibits the antioxidative activity in aqueous solutions, we have performed a series of quantum mechanical/molecular mechanical (QM/MM) simulations based on the density functional theory in combination with the theory of energy representation (QM/MM‐ER). For the computational convenience, MCI‐186 has been modeled by 1,3‐dimethyl‐2‐pyrazolin‐5‐one (DMP) by substituting the phenyl group in MCI‐186 by a methyl one. We have applied the QM/MM‐ER approach to compute free energy change δGaq associated with the electron detachment from DMP anion in water. To make comparisons, we have also performed the simulations for a natural radical scavenger, ascorbic acid modeled by 3,4‐dihydroxy‐furan‐2‐one (DHF). In the QM/MM‐ER approach, the distribution functions of the solute–solvent interaction energy, which serve as fundamental variables to describe the free energy, are to be constructed with the QM/MM force field. The free energy changes δGaq were computed as 99.1, 108.3 kcal/mol for DMP and DHF anions, respectively, whereas that for hydroxyl anion OH− taken as a reference system was evaluated as 138.9 kcal/mol. Thus, it was revealed that the free energies δGaq for DMP and DHF anions are much smaller than that for hydroxyl anion, which directly indicates the high activities of the molecules as electron donors. We found that the small δGaq values can be mainly attributed to the small values in the absolutes of the solvation free energies. The fractional charge analyses provided the evidence that the delocalization of the excess charge on the solute gives rise to the destabilization of these radical scavengers in the solute–solvent interaction. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Hydration effects on the reaction with an open-shell transition state: QM/MM-ER study for the dehydration reaction of alcohol in hot water

The reaction mechanism for the dehydration of 1,4-butanediol in hot water has been investigated by means of the hybrid quantum mechanical/molecular mechanical approach combined with the theory of energy representation (QM/MM-ER). We have assumed that the proton transfers along the hydrogen bonds of the water molecules catalyze the reaction, where the transition state (TS) forms a singlet biradical electronic structure. It has been revealed by the simulation that the biradical electronic state at the TS changes to zwitterionic structure in solution due to the hydration of the polar solvent. Such the electronic structure change gives rise to the substantial stabilization of the TS in hot water. As a result, the water-catalytic path becomes more favorable in aqueous solution than another possible path that proceeds without proton transfers as opposed to the reaction mechanism in the gas phase. Furthermore, the activation free energy computed by the present method is in excellent agreement with the experimental result.

Computation of the free energy change associated with one-electron reduction of coenzyme immersed in water: A novel approach within the framework of the quantum mechanical/molecular mechanical method combined with the theory of energy representation

The isoalloxazine ring (flavin ring) is a part of the coenzyme flavin adenine dinucleotide and acts as an active site in the oxidation of a substrate. We have computed the free energy change Deltamicro(red) associated with one-electron reduction of the flavin ring immersed in water by utilizing the quantum mechanical/molecular mechanical method combined with the theory of energy representation (QM/MM-ER method) recently developed. As a novel treatment in implementing the QM/MM-ER method, we have identified the excess charge to be attached on the flavin ring as a solute while the remaining molecules, i.e., flavin ring and surrounding water molecules, are treated as solvent species. Then, the reduction free energy can be decomposed into the contribution Deltamicro(red)(QM) due to the oxidant described quantum chemically and the free energy Deltamicro(red)(MM) due to the water molecules represented by a classical model. By the sum of these contributions, the total reduction free energy Deltamicro(red) has been given as -80.1 kcal/mol. To examine the accuracy and efficiency of this approach, we have also conducted the Deltamicro(red) calculation using the conventional scheme that Deltamicro(red) is constructed from the solvation free energies of the flavin rings at the oxidized and reduced states. The conventional scheme has been implemented with the QM/MM-ER method and the calculated Deltamicro(red) has been estimated as -81.0 kcal/mol, showing excellent agreement with the value given by the new approach. The present approach is efficient, in particular, to compute free energy change for the reaction occurring in a protein since it enables ones to circumvent the numerical problem brought about by subtracting the huge solvation free energies of the proteins in two states before and after the reduction.

Computation of the reduction free energy of coenzyme in aqueous solution by the QM/MM-ER method

In a recent development we proposed a quantum chemical approach to compute free energy change for chemical reactions in condensed phases by combining the QM/MM method with the theory of energy representation (QM/MM-ER). We extend in this Letter the novel approach to compute reduction free energy of isoalloxazine ring of FAD (flavin adenine dinucleotide) immersed in water within the framework of the QM/MM-ER method. The characteristic feature of our approach is that the excess electron to be attached on the FAD is identified as a solute. The reduction free energy has been obtained as −80.1 kcal/mol in the aqueous solution.

Investigation of the dominant hydration structures among the ionic species in aqueous solution: Novel quantum mechanics/molecular mechanics simulations combined with the theory of energy representation

In the present work, we have performed quantum chemical calculations to determine preferable species among the ionic complexes that are present in ambient water due to the autodissociation of water molecule. First, we have formulated the relative population of the hydrated complexes with respect to the bare ion (H(3)O(+) or OH(-)) in terms of the solvation free energies of the relevant molecules. The solvation free energies for various ionic species (H(3)O(+), H(5)O(2) (+), H(7)O(3) (+), H(9)O(4) (+) or OH(-), H(3)O(2) (-), H(5)O(3) (-), H(7)O(4) (-), H(9)O(5) (-)), categorized as proton or hydroxide ion in solution, have been computed by employing the QM/MM-ER method recently developed by combining the quantum mechanical/molecular mechanical (QM/MM) approach with the theory of energy representation (ER). Then, the computed solvation free energies have been used to evaluate the ratio of the populations of the ionic complexes to that of the bare ion (H(3)O(+) or OH(-)). Our results suggest that the Zundel form, i.e., H(5)O(2) (+), is the most preferable in the solution among the cationic species listed above though the Eigen form (H(9)O(4) (+)) is very close to the Zundel complex in the free energy, while the anionic fragment from water molecules mostly takes the form of OH(-). It has also been found that the loss of the translational entropy of water molecules associated with the formation of the complex plays a role in determining the preferable size of the cluster.

Novel quantum mechanical/molecular mechanical method combined with the theory of energy representation: Free energy calculation for the Beckmann rearrangement promoted by proton transfers in the supercritical water

The Beckmann rearrangement of acetone oxime promoted by proton transfers in the supercritical water has been investigated by means of the hybrid quantum mechanical/molecular mechanical approach combined with the theory of energy representation (QM/MM-ER) recently developed. The transition state (TS) structures have been explored by ab initio calculations for the reaction of hydrated acetone oxime on the assumption that the reaction is catalyzed by proton transfers along the hydrogen bonds connecting the solute and the solvent water molecules. Up to two water molecules have been considered as reactants that take part in the proton transfers. As a result of the density functional theory calculations with B3LYP functional and aug-cc-pVDZ basis set, it has been found that participation of two water molecules in the reaction reduces the activation free energy by -12.3 kcal/mol. Furthermore, the QM/MM-ER simulations have revealed that the TS is more stabilized than the reactant state in the supercritical water by 2.7 kcal/mol when two water molecules are involved in the reaction. Solvation free energies of the reactant and the TS have been decomposed into terms due to the electronic polarization of the solute, electron density fluctuation, and others to elucidate the origin of the stabilization of the TS as compared with the reactant. It has been revealed that the promotion of the chemical reaction due to the hydration mainly originates from the interaction between the nonpolarized solute and the solvent water molecules at the supercritical state.

Computational Study on the Relative Acidity of Acetic Acid by the QM/MM Method Combined with the Theory of Energy Representation

We have applied the quantum mechanical/molecular mechanical (QM/MM) method combined with the theory of energy representation (ER) to study the acidity of acetic acid in aqueous solution. We have focused our attention on the relative acidity DeltapK(a) of the molecule with respect to water solvent to circumvent the ambiguity of the solvation free energies of the molecular species referred to as proton. The value of DeltapK(a) for the acetic acid has been computed as -11.5 when we adopt the free energy change in the gas phase obtained by the B3LYP functional, which is in excellent agreement with the experimental value of -11.0. It has been demonstrated that the QM/MM-ER approach recently developed gives an adequate description for the solvation free energies related to the acidity/basicity calculations of organic molecules.

A QM/MM study combined with the theory of energy representation: Solvation free energies for anti/ syn acetic acids in aqueous solution

The solvation free energies for acetic acids in the anti/ syn conformations in water solution have been computed by the novel QM/MM approach combined with the theory of energy representation (QM/MM-ER). To examine the accuracy of the methodology, we have compared the results with those given by experiments and other theoretical calculations. The solvation free energies computed by the QM/MM-ER approach are in reasonable agreement with corresponding experimental values. The free energy difference between the anti and syn conformers also agrees well with the results of AM1/TIP3P or RISM-SCF calculations.