Molecular origin of anticooperativity in hydrophobic association

The structuring of water molecules in the vicinity of nonpolar solutes is responsible for hydrophobic hydration and association thermodynamics in aqueous solutions. Here, we studied the potential of mean force (PMF) for the formation of a dimer and trimers of methane molecules in three specific configurations in explicit water to explain multibody effects in hydrophobic association on a molecular level. We analyzed the packing and orientation of water molecules in the vicinity of the solute to explain the effect of ordering of the water around nonpolar solutes on many-body interactions. Consistent with previous theoretical studies, we observed cooperativity, manifested as a reduction of the height of the desolvation barrier for the trimer in an isosceles triangle geometry, but for linear trimers, we observed only anticooperativity. A simple mechanistic picture of hydrophobic association is drawn. The free energy of hydrophobic association depends primarily on the difference in the number of water molecules in the first solvation shell of a cluster and that in the monomers of a cluster; this can be approximated by the molecular surface area. However, there are unfavorable electrostatic interactions between the water molecules from different parts of the solvation shell of a trimer because of their increased orientation induced by the nonpolar solute. These electrostatic interactions make an anticooperative contribution to the PMF, which is clearly manifested for the linear trimer where the multibody contribution due to changes in the molecular surface area is equal to zero. The information theory model of hydrophobic interactions of Hummer et al. also explains the anticooperativity of hydrophobic association of the linear trimers; however, it predicts anticooperativity with a qualitatively identical distance dependence for nonlinear trimers, which disagrees with the results of simulations.     

A consistent integral equation theory for hard spheres

The standard integral equation approach is used to extract the bridge function and other correlation functions of hard spheres fluid. To achieve this, we first use a recent consistent closure relation proposed by Bomont et al. [J. Chem. Phys. 119, 2188 (2003)] that has already proven to be accurate to describe the Lennard-Jones fluid properties. Second, we take advantage of the coherent scheme derived by Bomont [J. Chem. Phys. 119, 11484 (2003)] to calculate the excess chemical potential, the entropy and some relative transport properties. Very good agreement is obtained for structural quantities and thermodynamic properties as compared to exact data at densities ranging from 0.1 to 0.9.     

Mercedes-Benz water molecules near hydrophobic wall: integral equation theories vs Monte Carlo simulations

Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes-Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied.     

Treatment of charged solutes in three-dimensional integral equation theory

Periodicity artifacts, which occur within three-dimensional reference interaction site model integral equation theory for net-charged solute systems, are analyzed and corrected by means of a renormalization procedure for long range interactions. The method is formulated for solute-solvent and solute-solute variants of the theory. Both dielectric and electrolyte solvents are considered. Comparison of the results for atomic ions with one-dimensional reference computations shows that structural and thermodynamic artifacts are efficiently removed.     

Prediction of tautomer ratios by embedded-cluster integral equation theory

The “embedded cluster reference interaction site model” (EC-RISM) approach combines statistical-mechanical integral equation theory and quantum-chemical calculations for predicting thermodynamic data for chemical reactions in solution. The electronic structure of the solute is determined self-consistently with the structure of the solvent that is described by 3D RISM integral equation theory. The continuous solvent-site distribution is mapped onto a set of discrete background charges (“embedded cluster”) that represent an additional contribution to the molecular Hamiltonian. The EC-RISM analysis of the SAMPL2 challenge set of tautomers proceeds in three stages. Firstly, the group of compounds for which quantitative experimental free energy data was provided was taken to determine appropriate levels of quantum-chemical theory for geometry optimization and free energy prediction. Secondly, the resulting workflow was applied to the full set, allowing for chemical interpretations of the results. Thirdly, disclosure of experimental data for parts of the compounds facilitated a detailed analysis of methodical issues and suggestions for future improvements of the model. Without specifically adjusting parameters, the EC-RISM model yields the smallest value of the root mean square error for the first set (0.6 kcal mol⁻¹) as well as for the full set of quantitative reaction data (2.0 kcal mol⁻¹) among the SAMPL2 participants.     

Conformational effect on small angle neutron scattering behavior of interacting polyelectrolyte solutions: a perspective of integral equation theory

We present small angle neutron scattering (SANS) measurements of deuterium oxide (D(2)O) solutions of linear and star sodium poly(styrene sulfonate) (NaPSS) as a function of polyelectrolyte concentration. Emphasis is on understanding the dependence of their SANS coherent scattering cross section I(Q) on the molecular architecture of single polyelectrolyte. The key finding is that for a given concentration, star polyelectrolytes exhibit more pronounced characteristic peaks in I(Q), and the position of the first peak occurs at a smaller Q compared to their linear counterparts. Based on a model of integral equation theory, we first compare the SANS experimental I(Q) of salt-free polyelectrolyte solutions with that predicted theoretically. Having seen their satisfactory qualitative agreement, the dependence of counterion association behavior on polyelectrolyte geometry and concentration is further explored. Our predictions reveal that the ionic environment of polyelectrolyte exhibits a strong dependence on polyelectrolyte geometry at lower polyelectrolyte concentration. However, when both linear and star polyelectrolytes exceed their overlap concentrations, the spatial distribution of counterion is found to be essentially insensitive to polyelectrolyte geometry due to the steric effect.     

Reformulation of the nth order poisson equation in strong electrolyte solution theory using the kirkwood integral equations

A Poisson equation for the nth order mean potential has previously been derived in the case of the primitive model of an electrolyte solution using the Kirkwood integral equations. We generalise this analysis to the case of an arbitrary short range pair potential between the ions.     

Criticality of a liquid-vapor interface from an inhomogeneous integral equation theory

A microscopic theory is developed to study the liquid-vapor interfacial properties of simple fluids with ab initio treatment of the inhomogeneous two-body correlation functions, without any interpolation. It consists of the inhomogeneous Ornstein-Zernike equation coupled with the Duh-Henderson-Verlet closure and the Lovett-Mou-Buff-Wertheim equation. For the liquid-vapor interface of the Lennard-Jones fluid, we obtained the density profile and the surface tension, as well as their critical behaviour. In particular, we identified non-classical critical exponents. The theory accurately predicts the phase diagram and the interfacial properties in a very good agreement with simulations. We also showed that the method leads to true capillary-wave asymptotics in the macroscopic limit.     

Protein inclusion in lipid membranes: a theory based on the hypernetted chain integral equation

A theory for describing the structure of the hydrocarbon chains around a protein inclusion embedded in a lipid bilayer is developed on the basis of the hypernetted chain integral equation formalism for liquids. The exact lateral density-density response function of the hydrocarbon core, which is extracted from a molecular dynamics simulation of a pure lipid bilayer, is used as input to the theory. Numerical calculations show that the average lipid order is perturbed over a distance of 25 to 30 A around a hard repulsive cylinder of 5 A radius representing an alpha-helical polyleucine protein inclusion. The lipid-mediated protein-protein interaction is calculated and is shown to be non-monotonic, being repulsive at an intermediate range but attractive at short range. It is found that the lipid matrix contributes a free energy well of 8 kBT to the association of two cylindrical inclusions.     

An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.     

Structure and effective interactions in polymer nanocomposite melts: an integral equation theory study

The polymer reference interaction site model from integral equation theory is used to investigate the structure and effective interactions in polymer nanocomposite melts where strong nanoparticle-monomer interactions are principally considered in this work. For finite particle volume fraction, the compromise for the interference between polymers and nanoparticles results in an optimum particle volume fraction for nanoparticle dispersion in polymer melts. At constant particle volume fraction, the effects of degree of polymerization become insignificant when it reaches a threshold value, below which quantitative effects on the organization states of polymer nanocomposite melts are found and help nanoparticles to well disperse in polymer. The aggregation of large nanoparticles decreases with the increase of the nanoparticle-monomer attraction strength. These observations may provide useful information for the development of new polymer materials.     

键能的分子轨道理论研究 1: 理论公式

从LCAO-MO出发, 给出了一个计算键能的近似方法, 即EAB(i)-∑∑CaiSabCbiεi为第i个占据分子轨道(MO)中的一对电子对A-B键键能的贡献。对所有分子轨道求和即为该键的键能: EAB=∑EAB(i)。按该方法, 不仅可以计算各种不同分子中每两个相键连原子间的键能, 还可以从MO及AO角度分析每一具体键, 如σ, π, δ键的键能以及各AO对键能的贡献。该方法虽有别于求键焓和平衡离解能De, 但计算结果和De的实验值甚相符合。通过对键能的分析研究, 能较好地揭示原子间的相互作用关系及化学键的强弱, 从而可进一步探讨化学反应活性, 反应速率等化学性质。     

Selective ion binding by protein probed with the statistical mechanical integral equation theory

Selective ion binding by human lysozyme and its mutants is probed with the three-dimensional interaction site model theory which is the statistical mechanical integral equation theory. Preliminary and partial results of the study have been already published (Yoshida, N. et al. J. Am. Chem. Soc. 2006, 128, 12042-12043). The calculation was carried out for aqueous solutions of three different electrolytes, CaCl2, NaCl, and KCl, and for four different mutants of the human lysozyme: wild type, Q86D, A92D, and Q86D/A92D, which have been studied experimentally. The discussion of this article focuses on the cleft that consists of amino acid residues from Q86 to A92. For the wild type of protein in the aqueous solutions of all the electrolytes studied, there are no distributions observed for the ions inside the cleft. The Q86D mutant shows essentially the same behavior with that of the wild type. The A92D mutant shows strong binding ability to Na+ in the recognition site, which is in accord with the experimental results. There are two isomers of the Q86D/A92D mutant, e.g., apo-Q86D/A92D and holo-Q86D/A92D. Although both isomers exhibit the binding ability to the Na+ and Ca2+ ions, the holo isomer shows much greater affinity compared with the apo isomer. Regarding the selective ion binding of the holo-Q86D/A92D mutant, it shows greater affinity to Ca2+ than to Na+, which is also consistent with the experimental observation.     

A description of phase equilibria in nonideal systems with the use of integral equation theory

Integral equation theory for partial distribution functions was used to consider a method for calculations of vapor-liquid phase equilibrium conditions in binary Lennard-Jones systems with substantial deviations from the Berthelot-Lorentz mixing rules. Possible sources of errors in pressure and chemical potential values and methods for refining the results were analyzed. The required accuracy of calculations can be reached using two parameters only, one in the closure to the Ornstein-Zernike equation and the other in the equation for the chemical potential. These parameters are determined independently from two thermodynamic equations.     

A comparative analysis of models for hydration free energy calculations using the RISM theory of integral equations

Rigorous calculations and a detailed analysis of the free energies of hydration were performed using the RISM (reference interaction site model) approach for 96 compounds of various chemical natures. A comparison of all the existing models for calculation of hydration free energy, including models that use corrections and semiempirical parameters, was performed for the first time. The applicability ranges of all the models under consideration were determined. It was shown that the PWC model based on jointly using the RISM and chemoinformatics approaches gave most accurate hydration free energy values. This model allows the free energy of hydration to be predicted with high accuracy and, at the same time, does not require the use of substantial computer resources.     

Thermodynamic and structural properties of repulsive hard-core Yukawa fluid: integral equation theory, perturbation theory and Monte Carlo simulations

The thermodynamic and structural properties of purely repulsive hard-core Yukawa particles in the fluid state are determined through Monte Carlo simulation and modeled using perturbation theory and integral equation theory in the mean spherical approximation (MSA). Systems of particles with Yukawa screening lengths of 1.8, 3.0, and 5.0 are examined with results compared to variations of MSA and perturbation theory. Thermodynamic properties were predicted well by both theories in the fluid region up to the fluid-solid phase boundary. Further, we found that a simplified exponential version of the MSA is the most accurate at predicting radial distribution function at contact. Radial distribution function of repulsive hard-core Yukawa particles are also reported. The results show that methods based on MSA and perturbation theory that are typically applied to the attractive hard-core Yukawa potential can also be extended to the purely repulsive hard-core Yukawa potential.     

Studies on fluids and their mixtures using the Born-Green-Yvon integral equation technique

We have developed the Born-Green-Yvon (BGY) integral equation theory for investigating the equilibrium properties of fluids and their mixtures both on the lattice and in the continuum. Using the continuum theory we have studied hard sphere fluids over a range in density having chain lengths between one and fifty sites. We have also investigated the collapse transition of a square well chain and a square well ring, each having up to four hundred sites, and have predicted the theta temperature for these systems. Turning to the case of a dilute (hard-sphere) solution we have been able to show the effect of solvation on a hard sphere chain, and captured the dependence of this effect on the ratio of hard sphere diameters of the solvent and chain segments. In all the continuum studies we have found good to excellent agreement with simulation results. We have also derived a lattice BGY theory which, while less sophisticated than the continuum version, has the advantage of producing simple closed-form expressions for thermodynamic properties of interest. This theory is capable of exhibiting the full range of miscibility behaviour observed experimentally, including upper and lower critical solution temperatures and closed-loop phase diagrams. We find that the theory does an excellent job of fitting to different kinds of experimental data and, making use of the parameters derived from fits to pure component data alone, we have been able to predict properties ranging from pure fluid vapour pressures and critical temperatures to changes in the volume and enthalpy on mixing as well as coexistence curves for solutions.