Calculation of free energy surfaces using the methods of thermodynamic perturbation theory

A molecular dynamics method for determining the free energy difference between systems separated in configuration space has been developed. With this new approach, which is based on thermodynamic perturbation techniques, potentials of mean force for conformational changes may be calculated. As a test of the method, the potential of mean force and radial distribution function for liquid argon have been computed. The results are in good agreement with those obtained from an ordinary simulation.     

Thermodynamic and structural properties of methanol-water solutions using nonadditive interaction models

We study bulk structural and thermodynamic properties of methanol-water solutions via molecular dynamics simulations using novel interaction potentials based on the charge equilibration (fluctuating charge) formalism to explicitly account for molecular polarization at the atomic level. The study uses the TIP4P-FQ potential for water-water interactions, and the CHARMM-based (Chemistry at HARvard Molecular Mechanics) fluctuating charge potential for methanol-methanol and methanol-water interactions. In terms of bulk solution properties, we discuss liquid densities, enthalpies of mixing, dielectric constants, self-diffusion constants, as well as structural properties related to local hydrogen bonding structure as manifested in radial distribution functions and cluster analysis. We further explore the electronic response of water and methanol in the differing local environments established by the interaction of each species predominantly with molecules of the other species. The current force field for the alcohol-water interaction performs reasonably well for most properties, with the greatest deviation from experiment observed for the excess mixing enthalpies, which are predicted to be too favorable. This is qualitatively consistent with the overestimation of the methanol-water gas-phase interaction energy for the lowest-energy conformer (methanol as proton donor). Hydration free energies for methanol in TIP4P-FQ water are predicted to be -5.6 +/- 0.2 kcal/mol, in respectable agreement with the experimental value of -5.1 kcal/mol. With respect to solution microstructure, the present cluster analysis suggests that the microscale environment for concentrations where select thermodynamic quantities reach extremal values is described by a bipercolating network structure.     

Structure and thermodynamics of polymeric liquids: Polymer kirkwood integral equation method

A statistical mechanical theory is employed to predict the structural and thermodynamic properties of polymeric liquids. The theory consists of a coupled set of self-consistent integral equations for the pair correlation functions which relates the polymer structure to molecular interaction potentials. In this article, the essentials of the method are reviewed and the results are shown in comparison with other theories and simulation data. Quantitative agreements are found between the results of the theory and those of the simulations for a wide range of density and temperature.     

A simple method for evaluation of the self-consistency of the radial distribution functions and the orientation of water molecules in the first coordination sphere from the results of molecular dynamics calculations

A simple method for determination of the angular orientation of water molecules in the first coordination sphere from the radial distribution functions is proposed. A comparative analysis of the ability of the model potentials of pair interaction to take into account the effects of manybody interactions (MBI) was performed. The responses of the model pair potentials to the MBI effects in the first and second coordination spheres were found to be poorly correlated with each other. It was concluded that it is necessary to derive a new analytical type of potential functions of pair interaction. Published inIzvestiya Akademii Nauk. Seriya Khimicheskaya. No. 11, pp. 1842–1846. November. 2000.     

Representability problems for coarse-grained water potentials

The use of an effective intermolecular potential often involves a compromise between more accurate, complex functional forms and more tractable simple representations. To study this choice in detail, we systematically derive coarse-grained isotropic pair potentials that accurately reproduce the oxygen-oxygen radial distribution function of the TIP4P-Ew water model at state points over density ranges from 0.88 to 1.30 g/cm3 and temperature ranges from 235 to 310 K. Although by construction these effective potentials correctly represent the isothermal compressibility of TIP4P-Ew water, they do not accurately resolve other thermodynamic properties such as the virial pressure, the internal energy, or thermodynamic anomalies. Because at a given state point the pair potential that reproduces the pair structure is unique, we have therefore explicitly demonstrated that it is impossible to simultaneously represent the pair structure and several key equilibrium thermodynamic properties of water with state-point dependent radially symmetric pair potentials. We argue that such representability problems are related to, but different from, more widely acknowledged transferability problems and discuss in detail the implications this has for the modeling of water and other liquids by coarse-grained potentials. Nevertheless, regardless of thermodynamic inconsistencies, the state-point dependent effective potentials for water do generate structural and dynamical anomalies.     

Anisotropic united atom model including the electrostatic interactions of benzene

An optimization including electrostatic interactions has been performed for the parameters of an anisotropic united atoms intermolecular potential for benzene for thermodynamic and transport property prediction using Gibbs ensemble, isothermal-isobaric (NPT) Monte Carlo, and molecular dynamic simulations. The optimization procedure is based on the minimization of a dimensionless error criterion incorporating various thermodynamic data (saturation pressure, vaporization enthalpy, and liquid density) at ambient conditions and at 350 and 450 K. A comprehensive comparison of the new model is given with other intermolecular potentials taken from the literature. Overall thermodynamic, structural, reorientational, and translational dynamic properties of our optimized model are in very good agreement with experimental data. The new model also provides a good representation of the liquid structure, as revealed by three-dimensional spatial density functions and carbon-carbon radial distribution function. Shear viscosity variations with temperature and pressure are very well reproduced, revealing a significant improvement with respect to nonpolar models.     

Monte Carlo simulation of water solvent with biomolecules: Serine and the corresponding zwitterion

Monte Carlo simulation results are reported for clusters consisting of 250 water molecules surrounding serine, both in the neutral form and in two zwitterionic conformers (in order to gain some insight into conformational effects). Calculations were carried out at 300 K and using two-body potentials obtained by means of quantum-mechanical calculations. The spatial dependence of the average interaction energies was investigated. The solvation structure was investigated by means of radial distribution functions and probability density maps, which showed a few water molecules directly solvating the hydrophilic groups and, beyond them, a more or less rich and complex hydrogen-bonded network of solvent molecules.     

Calorimetric indication of the molten globule-like state of cytochrome c induced by n-alkyl sulfates at low concentrations

The molten globule state has been proposed as a major intermediate of protein folding. However it has proven difficult to obtain thermodynamic data characterizing this state. To explore an alternative approach for characterization of the molten globule state, n-alkyl sulfates induced formation of the molten globule state of horse cytochrome c at pH 2 was studied by isothermal titration calorimetry (ITC). Titration of the acid unfolded state of cytochrome c with sodium octyl sulfate, sodium dodecyl sulfate or sodium tetradecyl sulfate, generated an exothermic reaction for formation of the molten globule state. The effects of various n-alkyl sulfates on the acid unfolded state of cytochrome c demonstrated that the increased alkyl chain length enhanced the exothermic values of calorimetric enthalpy and induced a more compact molten globule states. The heat contents agreed well with the conformational transition measured by molar ellipticity at 222 nm ([θ]₂₂₂) and Stoke radius (Rs) values. These results emphasize that isothermal titration calorimetry provides a reasonable alternative method for characterization of the molten globule state.     

The properties of off-shell coulomb radial wavefunctions

Approximations to exact wave functions for the scattering of few-particle systems often involve components corresponding to the interaction of two of the particles “off the energy-shell”. Several examples arising in the collision of ions and photons with atoms are given. An expansion in partial waves leads to an off-shell radial wave function. The defining differential equation is solved here numerically with particular emphasis on the behaviour arising from two-body potentials of long-range Coulomb form. The transition to shell of the radial wave functions, Jost functions and solutions andT-matrix elements is discussed for both short-range and Coulomb potentials. It is shown that the approximation of a Coulomb potential by a shorter-range form involves little error when sufficiently far off the energy shell.     

DNA与表面活性剂相互作用研究(Ⅱ)--基于构象变化的分子水平研究

综述了DNA在稀溶液中与表面活性剂在分子水平上的相互作用的研究进展。介绍了DNA与表面活性剂的两阶段键合过程以及伴生的DNA由线圈向小球的构象变化及其理论解释。同时阐述了相关的对其微观构象变化的研究方法，如热变性实验、荧光光谱、荧光显微技术、动静态光散射等。对DNA与表面活性剂形成的复合物作为基因转染载体的前景及限制因素作了简要介绍。     

Structural transitions in liquid cesium

Two series of models of liquid cesium at temperatures of 493 and 623 K and pressures lower than 18 GPa are constructed by means of molecular dynamics using the potential of the embedded atom model. The thermodynamic properties of the models, pair correlation functions, pair radial distribution functions, structure factors, coordination numbers, and distributions of the Voronoi polyhedra and Delaunay simplexes are analyzed. No indications of structural transitions in liquid cesium of the first-order phase transition type are observed near a pressure of 3.9 GPa. Divergences from the results of some X-ray diffraction studies could be due to incorrect determination of the coordination numbers via the standard method because of the strong asymmetry of the first peaks of the pair radial distribution functions.     

On Coarse-Graining by the Inverse Monte Carlo Method: Dissipative Particle Dynamics Simulations Made to a Precise Tool in Soft Matter Modeling

We present a promising coarse-graining strategy for linking micro- and mesoscales of soft matter systems. The approach is based on effective pairwise interaction potentials obtained from detailed atomistic molecular dynamics (MD) simulations, which are then used in coarse-grained dissipative particle dynamics (DPD) simulations. Here, the effective potentials were obtained by applying the inverse Monte Carlo method [Lyubartsev and Laaksonen, Phys. Rev. E. 52, 3730 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. In our first application of the method, the effective potentials were used in DPD simulations of aqueous NaCl solutions. With the same computational effort we were able to simulate systems of one order of magnitude larger than the MD simulations. The results from the MD and DPD simulations are in excellent agreement.     

液态水的分子动力学模拟

用分子动力学(MD)模拟方法在150~376K的温度范围内对液态水的微正则系统进行了研究。考察了液态水的结构及其性质。模拟采用了由从头算得出的柔性水-水相互作用势MCYL。对时间和空间的平均得出了液态中水分子几何构型及温度改变所引起的液态水结构变化。对径向分布函数gOH, gOO, gHH及配位数的分析表明, 在所考察的温度范围内, 每个水分子与相邻分子形成的氢键数为2~3, 水分子在参与的2个氢键中同时作为授受体。结合对振动谱的研究表明在低温时液态水形成的网络结构可能随温度的升高而形成小的簇结构。     

Molecular Dynamics Simulation of Mg2+ and Ca2+ Ions in Water

Molecular dynamics simulations of single Mg²⁺ and Ca²⁺ ions in water have been carried out. Different ion-water potentials from the literature have been used, whereas the same water potential, a rigid simple point charged model, has been considered in all the simulations. Structural, thermodynamic, and dynamic properties have been calculated, and the results for different potentials have been compared with available experimental data. The study includes ion–water radial distribution functions, coordination numbers, solution enthalpies, hydration free energies, self-diffusion coefficients, and reorientational times of water molecules in the hydration shells.     

A united-residue force field for off-lattice protein-structure simulations. I. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data

A two-stage procedure for the determination of a united-residue potential designed for protein simulations is outlined. In the first stage, the long-range and local-interaction energy terms of the total energy of a polypeptide chain are determined by analyzing protein-crystal data and averaging the all-atom energy surfaces. In the second stage (described in the accompanying article), the relative weights of the energy terms are optimized so as to locate the native structures of selected test proteins as the lowest energy structures. The goal of the work in the present study is to parameterize physically reasonable functional forms of the potentials of mean force for side-chain interactions. The potentials are of both radial and anisotropic type. Radial potentials include the Lennard-Jones and the shifted Lennard-Jones potential (with the shift parameter independent of orientation). To treat the angular dependence of side-chain interactions, three functional forms of the potential that were designed previously to describe anisotropic systems are evaluated: Berne-Pechukas (dilated Lennard-Jones); Gay-Berne (shifted Lennard-Jones with orientation-dependent shift parameters); and Gay-Berne-Vorobjev (the same as the preceding one, but with one more set of variable parameters). These functional forms were used to parameterize, within a short-distance range, the potentials of mean force for side-chain pair interactions that are related by the Boltzmann principle to the pair correlation functions determined from protein-crystal data. Parameter determination was formulated as a generalized nonlinear least-squares problem with the target function being the weighted sum of squares of the differences between calculated and “experimental” (i.e., estimated from protein-crystal data) angular, radial-angular, and radial pair correlation functions, as well as contact free energies. A set of 195 high-resolution nonhomologous structures from the Protein Data Bank was used to calculate the “experimental” values. The contact free energies were scaled by the slope of the correlation line between side-chain hydrophobicities, calculated from the contact free energies, and those determined by Fauchere and Pliška from the partition coefficients of amino acids between water and n-octanol. The methylene group served to define the reference contact free energy corresponding to that between the glycine methylene groups of backbone residues. Statistical analysis of the goodness of fit revealed that the Gay-Berne-Vorobjev anisotropic potential fits best to the experimental radial and angular correlation functions and contact free energies and therefore represents the free-energy surface of side-chain-side-chain interactions most accurately. Thus, its choice for simulations of protein structure is probably the most appropriate. However, the use of simpler functional forms is recommended, if the speed of computations is an issue. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 849–873, 1997     

The structure of binary liquids. The Kirkwood-Buff theory of liquid mixtures,illustrated on the basis of the systems water/methanol,water/ethanol,and cyclohexane/2,3-dimethylbutane,as a link between thermodynamic data and x-ray and neutron scattering results

With the help of the Kirkwood-Buff theory of liquid mixtures it is demonstrated that there is a close relationship between, on the one hand, x-ray and neutron scattering intensities from liquid mixtures and, on the other hand, certain thermodynamic properties of the systems considered. This relationship can be utilized without having to specify the intermolecular interaction potential and without having to perform computer simulation calculations. In the present paper the Kirkwood-Buff theory is applied to liquid water and to the binary systems H₂O/MeOH, H₂O/EtOH, and cyclohexane/2,3-dimethyl-butane. On the basis of these examples it is explained that, from the thermodynamic quantities used, the detailed shape of the various molecular radial distribution functions cannot be established. However, in principle this information could well be obtained from the x-ray and neutron scattering intensities of the liquids that are being studied, provided an acceptable procedure could be found to isolate the different radial distribution functions. In this respect the information extracted from thermodynamic data would be essential since, in the first place, it provides a valuable way of normalization of the scattered intensity, and, in the second place, for multicomponent liquids it puts forward specific conditions to be satisfied by the various radial distribution functions.     

Semiflexible amphiphilic polymers: cylindrical-shaped, collagenlike, and toroidal structures

A coarse-grained model is used to study the conformational properties of semiflexible polymers with amphiphilic monomer units containing both hydrophilic and hydrophobic interaction sites. The hydrophobically driven conformational transitions are studied using molecular dynamics simulations for the chains of varying stiffness, as characterized by intrinsic Kuhn segment lengths that vary over a decade. It is shown that the energy of hydrophobic attraction required for the realization of the coil-to-globule transition increases with increasing chain stiffness. For rather stiff backbone, the coil-to-globule transition corresponds to a first order phase transition. We find that depending on the chain stiffness, a variety of thermodynamically stable anisometric chain morphologies are possible in a solvent selectively poor for hydrophobic sites of amphiphilic monomer units. For flexible chains, the amphiphilic polymer forms a cylindrical globule having blob structure with nearly spherical blobs. With increasing stiffness, the number of blobs composing the globule decreases and the shape of blobs transforms into elongated cylinder. Further increase in stiffness leads to compaction of macromolecules into a collagenlike structure when the chain folds itself several times and different strands wind round each other. In this state, the collagenlike structures coexist with toroidal globules, both conformations having approximately equal energies.     

Nature of the cytochrome c molten globule

We have employed fluorescence energy transfer (FET) kinetics to probe unfolded and molten globule states of five dansyl (Dns) variants of Saccharomyces cerevisiae iso-1 cytochrome c. The covalently bound Fe(III) heme group quenches Dns fluorescence by energy transfer; measurements of FET kinetics yielded distributions of D-A distances (P(r)) for these states. The P(r) distributions and corresponding mean force potentials (U(r)) show that the cytochrome c molten globule is a highly structured state with a substantial number of native interactions. Wide P(r) distributions directly reflect the dynamic nature and conformational diversity of this molten globule. P(r) distributions for the "burst-phase" refolding intermediate suggest that the equilibrium cytochrome c molten globule is not a suitable model for early intermediates formed during protein refolding.