Method Of Energy Representation Research Articles

Adsorption Energetics of Amino Acid Analogs on Polymer/Water Interfaces Studied by All-Atom Molecular Dynamics Simulation and a Theory of Solutions.

Energetics of adsorption was addressed with all-atom molecular dynamics simulation on the interfaces of poly(2-methoxyethyl acrylate) (PMEA), poly(methyl methacrylate) (PMMA), and poly(butyl acrylate) (PBA) with water. A wide variety of adsorbate solutes were examined, and the free energy of adsorption was computed with the method of energy representation. It was found that the adsorption free energy was favorable (negative) for all the combinations of solute and polymer, and among PMEA, PMMA, and PBA, the strongest adsorption was observed on PMMA for the hydrophobic solutes and on PMEA for the hydrophilic ones. According to the decomposition of the adsorption free energy into the contributions from polymer and water, it was seen that the polymer contribution is larger in magnitude with the solute size. The total free energy of adsorption was correlated well with the solvation free energy in bulk water only for hydrophobic solutes. The roles of the intermolecular interaction components such as electrostatic, van der Waals, and excluded-volume were further studied, and the electrostatic component was influential only in determining the polymer dependences of the adsorption propensities of hydrophilic solutes. The extent of adsorption was shown to be ranked by the van der Waals component in the solute-polymer interaction separately over the hydrophilic and hydrophobic solutes, with the excluded-volume effect from water pointed out to also drive the adsorption.

Chain-Increment Method for Free-Energy Computation of a Polymer with All-Atom Molecular Simulations

A chain-increment method is developed to approach the chemical potential of a polymer with an all-atom model. The method relies on the structural feature that the polymer consists of repeated monomers, and the interactions with the surrounding molecules are introduced sequentially for the monomers in the tagged polymer. The solution theory in the energy representation is then adopted in combination with all-atom molecular simulations to compute the free energy of chain increment. This scheme identifies the incremented monomer as the solute and the surrounding molecules as the solvent, and the incremental free energy is obtained as a solvation free energy for the solute and solvent thus identified. The chain-increment method is applied to polyethylene (PE) in water and the polymer melts of PE, polypropylene, poly(methyl methacrylate), and poly(vinylidene difluoride). It is found for PE in water that the free energy of chain increment computed approximately by the energy-representation method stays constant...

Aerosol-OT Surfactant Forms Stable Reverse Micelles in Apolar Solvent in the Absence of Water.

Normal micelle aggregates of amphiphilic surfactant in aqueous solvents are formed by a process of entropically driven self-assembly. The self-assembly of reverse micelles from amphiphilic surfactant in a nonpolar solvent in the presence of water is considered to be an enthalpically driven process. Although the formation of normal and reverse surfactant micelles has been well characterized in theory and experiment, the nature of dry micelle formation, from amphiphilic surfactant in a nonpolar solvent in the absence of water, is poorly understood. In this study, a theory of dry reverse micelle formation is developed. Variation in free energy during micelle assembly is derived for the specific case of aerosol-OT surfactant in isooctane solvent using atomistic molecular dynamics simulation analyzed using the energy representation method. The existence and thermodynamic stability of dry reverse micelles of limited size are confirmed. The abrupt occurrence of monodisperse aggregates is a clear signature of a critical micelle concentration, commonly observed in the formation of normal surfactant micelles. The morphology of large dry micelles provides insight into the nature of the thermodynamic driving forces stabilizing the formation of the surfactant aggregates. Overall, this study provides detailed insight into the structure and stability of dry reverse micelles assembly in a nonpolar solvent.

Energetics of cosolvent effect on peptide aggregation.

The cosolvent effect on the equilibrium of peptide aggregation is reviewed from the energetic perspective. It is shown that the excess chemical potential is stationary against the variation of the distribution function for the configuration of a flexible solute species and that the derivative of the excess chemical potential with respect to the cosolvent concentration is determined by the corresponding derivative of the solvation free energy averaged over the solute configurations. The effect of a cosolvent at low concentrations on a chemical equilibrium can then be addressed in terms of the difference in the solvation free energy between pure-water solvent and the mixed solvent with the cosolvent, and illustrative analyses with all-atom model are presented for the aggregation of an 11-residue peptide by employing the energy-representation method to compute the solvation free energy. The solvation becomes more favorable with addition of the urea or DMSO cosolvent, and the extent of stabilization is smaller for larger aggregate. This implies that these cosolvents inhibit the formation of an aggregate, and the roles of such interaction components as the electrostatic, van der Waals, and excluded-volume are discussed.

Fractional sparse energy representation method for ISAR imaging

Inverse synthetic aperture radar (ISAR) is an effective radar imaging technology to obtain high-resolution images of manoeuvring targets. To improve the cross-range resolution of ISAR images, a fractional sparse energy representation method is proposed for ISAR imaging of rotating targets by combining fractional Fourier transform with sparse representation technique. Experimental results demonstrate that the proposed algorithms can efficiently realise high-quality imaging in addition to robustness against noise.

Structure and permeability of ionomers studied by atomistic molecular simulation combined with the theory of solutions in the energy representation.

Ionomers play a key role in forming the catalyst layer of polymer electrolyte fuel cells. In the present work, we performed atomistic molecular dynamics simulations and free-energy calculations with the energy-representation method for sulfonated polyethersulfone (SPES) and its derivatives toward the rational design of ionomers for carbon alloy catalysts. It was observed that H2O aggregates strongly in the branched SPES systems with fluorocarbons and is located homogeneously in the systems without fluorocarbons. The O2 permeability was then examined within the framework of the solubility-diffusion mechanism. The permeability was seen to be large for the branched SPES with fluorocarbons, indicating that the performance of ionomers as a permeation medium for O2 may be tuned by the flexibility and branching of the polymer chain.

Physical driving force of actomyosin motility based on the hydration effect.

We propose a driving force hypothesis based on previous thermodynamics, kinetics and structural data as well as additional experiments and calculations presented here on water-related phenomena in the actomyosin systems. Although Szent-Györgyi pointed out the importance of water in muscle contraction in 1951, few studies have focused on the water science of muscle because of the difficulty of analyzing hydration properties of the muscle proteins, actin, and myosin. The thermodynamics and energetics of muscle contraction are linked to the water-mediated regulation of protein-ligand and protein-protein interactions along with structural changes in protein molecules. In this study, we assume the following two points: (1) the periodic electric field distribution along an actin filament (F-actin) is unidirectionally modified upon binding of myosin subfragment 1 (M or myosin S1) with ADP and inorganic phosphate Pi (M.ADP.Pi complex) and (2) the solvation free energy of myosin S1 depends on the external electric field strength and the solvation free energy of myosin S1 in close proximity to F-actin can become the potential force to drive myosin S1 along F-actin. The first assumption is supported by integration of experimental reports. The second assumption is supported by model calculations utilizing molecular dynamics (MD) simulation to determine solvation free energies of a small organic molecule and two small proteins. MD simulations utilize the energy representation method (ER) and the roughly proportional relationship between the solvation free energy and the solvent-accessible surface area (SASA) of the protein. The estimated driving force acting on myosin S1 is as high as several piconewtons (pN), which is consistent with the experimentally observed force.

Assessing the accuracy of integral equation theories for nano-sized hydrophobic solutes in water.

Integral equation theories provide an efficient route for computing the solvation free energy (SFE) of molecular systems in water. The accuracy of those theories is usually tested against small molecules via comparison of SFE with reference data. However, tests against larger molecules in the nanometer regime are scarce in literature despite recent applications to such systems. Here, we thus study the accuracy and validity of a commonly used integral equation theory, namely, a three-dimensional reference interaction site model (3D-RISM), by considering the following problems: (1) solvation of a small to large Lennard-Jones particle, (2) binding of planar hydrophobic systems with varying size and hydrophobicity, and (3) self-assembly of amphiphilic molecules into a nanocapsule. The energy representation method is also utilized for comparison. The results show that the 3D-RISM method works successfully for small molecules, while the accuracy degrades systematically with system size and hydrophobicity. The size-dependent error in SFE does not cancel adequately between two solute configurations, resulting in a substantial error in the free energy difference. It is also shown that the free energy profiles for hydrophobic association exhibit a fictitious high-energy barrier, suggesting that care must be taken for studying such systems. The numerical difficulties observed above are discussed based on the relation between hypernetted-chain approximation, classical density functional theory with quadratic expansion, and the size-dependent error arising from the cavity region of the system.

Interaction-component analysis of the effects of urea and its alkylated derivatives on the structure of T4-lysozyme.

The effects of urea and its alkylated derivatives on the structure of T4-lysozyme were analyzed from the standpoint of energetics. Molecular dynamics simulations were conducted with explicit solvent, and the energy-representation method was employed to compute the free energy of transfer of the protein from pure-water solvent to the mixed solvents of water with urea, methylurea, 1,1-dimethylurea, and isopropylurea. Through the decomposition of the transfer free energy into the cosolvent and water contributions, it was observed that the former is partially cancelled by the latter and governs the total free energy of transfer. To determine the interaction component responsible for the transfer energetics, the correlations of the transfer free energy were also examined against the change in the solute-solvent interaction energy upon transfer and the corresponding changes in the electrostatic, van der Waals, and excluded-volume components. It was then found over the set of protein structures ranging from native to (partially) unfolded ones that the transfer free energy changes in parallel with the van der Waals component even when the cosolvent is alkylated. The electrostatic and excluded-volume components play minor roles in the structure modification of the protein, and the denaturing ability of alkylurea is brought by the van der Waals interaction.

Ermod: fast and versatile computation software for solvation free energy with approximate theory of solutions.

ERmod is a software package to efficiently and approximately compute the solvation free energy using the method of energy representation. Molecular simulation is to be conducted at two condensed-phase systems of the solution of interest and the reference solvent with test-particle insertion of the solute. The subprogram ermod in ERmod then provides a set of energy distribution functions from the simulation trajectories, and another subprogram slvfe determines the solvation free energy from the distribution functions through an approximate functional. This article describes the design and implementation of ERmod, and illustrates its performance in solvent water for two organic solutes and two protein solutes. Actually, the free-energy computation with ERmod is not restricted to the solvation in homogeneous medium such as fluid and polymer and can treat the binding into weakly ordered system with nano-inhomogeneity such as micelle and lipid membrane. ERmod is available on web at http://sourceforge.net/projects/ermod.

Free-energy analysis of water affinity in polymer studied by atomistic molecular simulation combined with the theory of solutions in the energy representation

Affinity of small molecule to polymer is an essential property for designing polymer materials with tuned permeability. In the present work, we develop a computational approach to the free energy ΔG of binding a small solute molecule into polymer using the atomistic molecular dynamics (MD) simulation combined with the method of energy representation. The binding free energy ΔG is obtained by viewing a single polymer as a collection of fragments and employing an approximate functional constructed from distribution functions of the interaction energy between solute and the fragment obtained from MD simulation. The binding of water is then examined against 9 typical polymers. The relationship is addressed between the fragment size and the calculated ΔG, and a useful fragment size is identified to compromise the performance of the free-energy functional and the sampling efficiency. It is found with the appropriate fragment size that the ΔG convergence at a statistical error of ∼0.2 kcal/mol is reached at ∼4 ns of replica-exchange MD of the water-polymer system and that the mean absolute deviation of the computational ΔG from the experimental is 0.5 kcal/mol. The connection is further discussed between the polymer structure and the thermodynamic ΔG.

Simple and exact approach to the electronic polarization effect on the solvation free energy: Formulation for quantum-mechanical/ molecular-mechanical system and its applications to aqueous solutions

We present a simple and exact numerical approach to compute the free energy contribution δμ in solvation due to the electron density polarization and fluctuation of a quantum-mechanical solute in the quantum-mechanical/molecular-mechanical (QM/MM) simulation combined with the theory of the energy representation (QM/MM-ER). Since the electron density fluctuation is responsible for the many-body QM-MM interactions, the standard version of the energy representation method cannot be applied directly. Instead of decomposing the QM-MM polarization energy into the pairwise additive and non-additive contributions, we take sum of the polarization energies in the QM-MM interaction and adopt it as a new energy coordinate for the method of energy representation. Then, it is demonstrated that the free energy δμ can be exactly formulated in terms of the energy distribution functions for the solution and reference systems with respect to this energy coordinate. The benchmark tests were performed to examine the numerical efficiency of the method with respect to the changes in the individual properties of the solvent and the solute. Explicitly, we computed the solvation free energy of a QM water molecule in ambient and supercritical water, and also the free-energy change associated with the isomerization reaction of glycine from neutral to zwitterionic structure in aqueous solution. In all the systems examined, it was demonstrated that the computed free energy δμ agrees with the experimental value, irrespective of the choice of the reference electron density of the QM solute. The present method was also applied to a prototype reaction of adenosine 5'-triphosphate hydrolysis where the effect of the electron density fluctuation is substantial due to the excess charge. It was demonstrated that the experimental free energy of the reaction has been accurately reproduced with the present approach.

Free-Energy and Structural Analysis of Ion Solvation and Contact Ion-Pair Formation of Li+ with BF4– and PF6– in Water and Carbonate Solvents

Free energy of contact ion-pair (CIP) formation of lithium ion with BF(4)(-) and PF(6)(-) in water, propylene carbonate (PC), dimethyl carbonate (DMC) are quantitatively analyzed using MD simulations combined with the energy representation method. The relative stabilities of the mono-, bi-, and tridentate coordination structures are assessed with and without solvent, and water, PC, and DMC are found to favor the CIP-solvent contact. The monodentate structure is typically most stable in these solvents, whereas the configuration is multidentate in vacuum. The free energy of CIP formation is not simply governed by the solvent dielectric constant, and microscopic analyses of solute-solvent interaction at a molecular level are then performed from energetic and structural viewpoints. Vacant sites of Li(+) cation in CIP are solvated with three carbonyl oxygen atoms of PC and DMC solvent molecules, and the solvation is stronger for the monodentate CIP than for the multidentate. Energetically favorable solute-solvent configurations are shown to be spatially more restricted for the multidentate CIP, leading to the observation that the solvent favors the monodentate coordination structure.

2PT185 The chroride ion uptake mechanism in pharaonis halorhodopisin as studied by the energy representation method(The 50th Annual Meeting of the Biophysical Society of Japan)

2PT185 The chroride ion uptake mechanism in pharaonis halorhodopisin as studied by the energy representation method(The 50th Annual Meeting of the Biophysical Society of Japan)

Solvation effect on the structural change of a globular protein: A molecular dynamics study

AbstractTo investigate the relationship between structural change and the solvation effect, we estimated the solvation free energy or excess chemical potential (ECP) of a globular protein by the energy representation method for the protein structure obtained by a molecular dynamic simulation. A large fluctuation of ECP was detected. The estimated ECP along the first principal component axis of protein fluctuation was accompanied with “open–close” structural change, which indicated a smooth and progressive change in ECP. By performing a global water density analysis in the grid space, the water density at the hydration site had a strong correlation with the ECP. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Communication: Free-energy analysis of hydration effect on protein with explicit solvent: Equilibrium fluctuation of cytochrome c

The relationship between the protein conformation and the hydration effect is investigated for the equilibrium fluctuation of cytochrome c. To elucidate the hydration effect with explicit solvent, the solvation free energy of the protein immersed in water was calculated using the molecular dynamics simulation coupled with the method of energy representation. The variations of the protein intramolecular energy and the solvation free energy are found to compensate each other in the course of equilibrium structural fluctuation. The roles of the attractive and repulsive components in the protein-water interaction are further examined for the solvation free energy. The attractive component represented as the average sum of protein-water interaction energy is dominated by the electrostatic effect and is correlated to the solvation free energy through the linear-response-type relationship. No correlation with the (total) solvation free energy is seen, on the other hand, for the repulsive component expressed as the excluded-volume effect.

Hydration property of globular proteins: An analysis of solvation free energy by energy representation method

Molecular dynamics simulations and solvation free energy calculations of five globular proteins (BPTI, RNase A, Lysozyme, β-lactoglobulin A, and α-chymotrypsinogen A) have been carried out to elucidate the hydration properties. Solvation free energies of the proteins with explicit solvent were estimated by energy representation (ER) method. The calculated solvation free energies were correlated with the solvent accessible surface area of hydrophilic portion, being consistent with the hydrophilic property of the proteins. These results showed that the ER method should be a powerful tool for estimating the hydration property of proteins, showing a progress of the free energy calculation with explicit solvent.

End-point calculation of solvation free energy of amino-acid analogs by molecular theories of solution

The computational efficiency is improved for the solvation free energy when the calculation is restricted to the initial and final states of the solute insertion process (pure solvent and solution systems of interest). We explore the possibility of such ‘end-point’ calculations and assess the performance of several approximate free-energy functionals against benchmarks for amino-acid analogs in water. The performance is the best and the second, respectively, for the method of energy representation and the RISM (reference interaction site model)/partial-wave expansion supplemented by semi-empirical corrections for the excluded-volume and hydrogen-bonding effects, while the chemical accuracy is not achieved for the others.

Free-Energy Analysis of Solvation with the Method of Energy Representation

A new theory of solutions, the method of energy representation, is introduced by adopting the solute-solvent interaction energy as the coordinate of distribution functions. The density-functional theory is formulated over the energy coordinate, and an approximate functional for the solvation free energy is given in terms of energy distribution functions in the solution and reference solvent systems. The method of energy representation greatly expands the scope of solution theory and is amenable to supercritical fluid, flexible molecules with intramolecular degrees of freedom, inhomogeneous system, and quantum-mechanical/molecular-mechanical (QM/MM) system. Through the combination with molecular simulation, the functional for the solvation free energy is demonstrated to perform well for nonpolar, polar, and ionic solutes in water over a wide range of thermodynamics conditions, with drastic reduction of the computational demand compared to the standard free-energy perturbation and thermodynamic integration methods. As an application to inhomogeneous system involving flexible species, the molecular binding into micelle and membrane is analyzed by treating micelle and membrane as a mixed solvent system consisting of water and amphiphilic molecule.

Free-Energy Analysis of Solvation with the Method of Energy Representation

Free-Energy Analysis of Solvation with the Method of Energy Representation