Solvation and pairwise association in a 2D fluid

It is shown that it is possible: (a) to derive the 2D scaled particle theory formula of the reversible work of cavity creation using a geometric approach; (b) to obtain the solvation Gibbs energy in a 2D Lennard-Jones fluid; (c) to calculate the solvent contribution to the solvophobic interaction of two Lennard-Jones disks on the basis of geometric arguments. The solvent-excluded surface area associated with cavity creation decreases significantly upon pairwise association, leading to a marked increase in the configurational/translational entropy of solvent disks.     

Configuration-specific kinetic theory applied to the elastic collisions of hard spherical molecules

Classical trajectory simulations can be used to glean a wealth of information on the geometric details of gas-phase molecular collision events for which the standard theoretical treatment lacks the ability to predict. For instance, the standard treatment gives no information on configuration-specific collision parameters. A configuration-specific parameter is defined here as the average value for a collision parameter that is exclusive to either an ensemble of front-end or an ensemble of rear-end molecular collisions. This paper presents statistical results of simulation "measurements" on several configuration-specific parameters, including the configuration-specific collision frequencies. The simulations use single-component systems of hard spherical molecules confined within a spherical boundary. To complement the simulation effort, a systematic mathematical analysis for the configuration-specific parameters is presented. This analysis uses the Maxwell-Boltzmann distribution of molecular speeds as usual, but exploits the distinction between front-end and rear-end collision space, and uses the line-of-centers speed rather than the relative speed. The configuration-specific expressions derived from this analysis are in very good agreement with the simulation measurements for every molecular collision parameter studied in this work.     

Effect of binding on escape from cavity through narrow tunnel

When a diffusing particle escapes from a spherical cavity through a narrow, not too long tunnel, the escape kinetics is essentially single-exponential. The presence of reversible binding sites on the cavity wall leads to retention of the particle in the system and converts the single-exponential kinetics into bi-exponential. We develop a theory that describes these effects. The theory shows how the delay time and the average number of binding events depend on the geometric and kinetic parameters of the system. To study the effect of the cavity shape, we also analyze the kinetics when the particle escapes from a cylindrical cavity with reversible binding sites.     

Molecular dynamics simulation of entropy driven ligand escape process in heme pocket

Molecular dynamics simulations were performed to investigate the gate effect of protein motion on the escape of O(2) from the heme pocket. The existing geometric entropy in a spherical cavity pushes the ligand toward the cavity surface, and then the ligand escape along the cavity surface is controlled by the gate size and gate modulation, i.e., protein dynamics regulate the gating behavior, which is an inherent feature of proteins such as myoglobin. Our simulation results confirm that the ligand escape process is basically entropy driven.     

溶剂化变色法测定有机分子β的若干问题

溶剂化变色法是测定有机分子超极化率．的一种半定量方法,已为许多实验室采用并取得了较好的结果．它的理论依据是描述有机分子产值的双能级模型【小式中：P。、11。分别为分子的基态和激发态偶极矩,。e。和11e。则分别为基态和激发态的跃迁频率和跃迁偶极矩．这包括三个方面     

Two interacting particles in a spherical pore

In this work we analytically evaluate, for the first time, the exact canonical partition function for two interacting spherical particles into a spherical pore. The interaction with the spherical substrate and between particles is described by an attractive square-well and a square-shoulder potential. In addition, we obtain exact expressions for both the one particle and an averaged two particle density distribution. We develop a thermodynamic approach to few-body systems by introducing a method based on thermodynamic measures [I. Urrutia, J. Chem. Phys. 134, 104503 (2010)] for nonhard interaction potentials. This analysis enables us to obtain expressions for the pressure, the surface tension, and the equivalent magnitudes for the total and Gaussian curvatures. As a by-product, we solve systems composed of two particles outside a fixed spherical obstacle. We study the low density limit for a many-body system confined to a spherical cavity and a many-body system surrounding a spherical obstacle. From this analysis we derive the exact first order dependence of the surface tension and Tolman length. Our findings show that the Tolman length goes to zero in the case of a purely hard wall spherical substrate, but contains a zero order term in density for square-well and square-shoulder wall-fluid potentials. This suggests that any nonhard wall-fluid potential should produce a non-null zero order term in the Tolman length.     

High-order discretization schemes for biochemical applications of boundary element solvation and variational electrostatic projection methods

A series of high-order surface element discretization schemes for variational boundary element methods are introduced. The surface elements are chosen in accord with angular quadrature rules for integration of spherical harmonics. Surface element interactions are modeled by Coulomb integrals between spherical Gaussian functions with exponents chosen to reproduce the exact variational energy and Gauss's law for a point charge in a spherical cavity. The present work allows high-order surface element expansions to be made for variational methods such as the conductorlike screening model for solvation and the variational electrostatic projection method for generalized solvent boundary potentials in molecular simulations.     

Electrophoresis of a charge-regulated sphere at an arbitrary position in a charged spherical cavity

The electrophoresis of a charge-regulated spherical particle at an arbitrary position in a charged spherical cavity is modeled under conditions of low surface potential (<25 mV) and weak applied electric field (<25 kV/m). The charged cavity allows us to simulate the effect of electroosmotic flow, and the charge-regulated nature of the particle permits us to model various types of surface. The problem studied previously is reanalyzed based on a more rigorous electric force formula. In particular, the influences of various types of charged conditions on the electrophoretic behavior of a particle and the roles of all the relevant forces acting on the particle are examined in detail. Several new results are found. For instance, the mobility of a particle has a local minimum as the thickness of a double layer varies, which is not seen in the cases where the surface of a particle is maintained at a constant potential and at a constant charge density.     

A unique spherical molecular host with D2d symmetry. A novel intramolecular kinetic equilibrium in metal ion complexation between two crown ethers

[formula: see text] A spherical host with D2d symmetry consisting of a tetrathia[3.3.3.3]paracyclophane and two 18-crown-6 moieties was synthesized. Its crystal structure shows a central cavity with a diameter of 1.96 A and a depth of 6.75 A. A Na+ ion could rest in the cavity center but prefers core binding to external binding in one of the crown units. An intramolecular kinetic equilibrium was reached with the Na+ ion switching between the two crown units with an energy barrier of 14.1 +/- 3 kcal/mol.     

Dimerization of argon and the properties of its small clusters

Statistical thermodynamic means are used to study the bound state of a small cluster A_N (2 ≤ N ≤ 5) of Lennard-Jones particles in a spherical cavity. The statistical sum is calculated by the Monte Carlo method. For the dimer, integration is reduced to quadratures. The integration region contains only phase space points corresponding to the bound cluster state. Dimerization constant 2A = A₂ is calculated via the probability of finding a molecule in the bound state using the example of argon.     

蛋白质-蛋白质分子对接中打分函数研究进展

分子对接是研究分子间相互作用与识别的有效方法.其中,用于近天然构象挑选的打分函数的合理设计对于对接中复合物结构的成功预测至关重要.本文回顾了蛋白质-蛋白质分子对接组合打分函数中一些主要打分项,包括几何互补项、界面接触面积、范德华相互作用能、静电相互作用能以及统计成对偏好势等打分项的计算方法.结合本研究小组的工作,介绍了目前普遍使用的打分方案以及利用与结合位点有关的信息进行结构筛选的几种策略,比较并总结了常用打分函数的特点.最后,分析并指出了当前蛋白质-蛋白质对接打分函数所存在的主要问题,并对未来的工作进行了展望.     

Comparison of electrical mixture rules for composites

Firstly the basic theoretical methods of calculating the dielectric properties of heterogeneous mixtures are discussed. These are the mean field and effective medium theories and integral methods. Formulae are presented for systems containing parallel oriented ellipsoids and for randomly oriented ellipsoidal systems. Theoretical formulae are divided into two sub-groups: symmetric equations for statistical mixtures and asymmetric equations for matrix-inclusion type composites. In the former case only the relative amount of the components is important, in the second case phase inversion results in a change of the dielectric properties.Formulae are compared numerically using spherical and spheroidal systems with sharply different components (permittivity ratio is 1 100). In the case of asymmetric formulae the effect of phase inversion is studied as well. Percolation behaviour predicted by the equations is demonstrated and discussed. Functional shapes are compared in relation to the theoretical differences.Finally, experimental data are compared with the theoretical results, advantages and drawbacks of the various formulae are discussed. For spherical systems the simplest mean field formula yields somewhat worse values than effective medium or integral equations. The Looyenga equation does not work very well if the permittivity difference is high. For nonspherical systems the fit is better in general, even the simplest formula works satisfactorily. The shape independence predicted by the Looyenga theory for randomly oriented ellipsoids is in conflict with experimental data.     

分子动力学模拟纳米尺寸限制体系下氩溶液中I2的振动能量弛豫

利用平衡态分子动力学方法(EMD)模拟了纳米尺寸限制球壳内I2在Ar溶液中的振动能量转移. 计算并讨论了I2振动能量弛豫时间T1随球壳半径、溶剂密度的变化规律. 通过分子间相互作用分析, 在原子、分子水平上, 揭示了随着球壳半径的减小, T1呈逐渐增大趋势的原因. 结果表明, 球壳的几何限制效应和表面作用对受限溶液密度分布的影响较大, 从而导致溶质振动弛豫的显著变化. 此外, 非限制体系模拟显示, 非平衡态分子动力学(NEMD)方法可以得到与平衡态分子动力学方法较一致的振动能量弛豫时间T1.     

Mobility matrix of a spherical particle translating and rotating in a viscous fluid confined in a spherical cell, and the rate of escape from the cell

The mobility matrix of a spherical particle moving in a spherical cavity, filled with a viscous incompressible fluid, and with no-slip boundary condition at the wall of the cavity, is evaluated from the Oseen tensor for the cavity by the method used by Lorentz for a particle near a planar wall. For the case that the particle is a rigid sphere with no-slip boundary condition the comparison with exact calculations shows that the approximation is quite accurate, provided the radius of the particle is small relative to that of the cavity, and provided the particle is not too close to the wall. The translational mobility is used to derive the diffusion tensor of a Brownian particle via an Einstein relation. The approximate result for the diffusion tensor is employed to estimate the rate of escape of a Brownian particle from a cavity with semipermeable wall.     

Computational evidence for stable inorganic fullerene-like structures of ceramic and semiconductor materials

Theoretical electronic structure techniques have become an indispensible and powerful means for predicting molecular properties and designing new materials. Based on a density functional approach and guided by geometric considerations we provide evidence for some specific inorganic fullerene-like cage molecules of ceramic and semiconductor materials which exhibit high energetic stability and point group symmetry as well as nearly perfect spherical shape.     

Excluded volume effect for large and small solutes in water

The cavitation effect, i.e., the process of the creation of a void of excluded volume in bulk solvent (a cavity), is considered. The cavitation free energy is treated in terms of the information theory (IT) approach [Hummer, G.; Garde, S.; Garcia, A. E.; Paulaitis, M. E.; Pratt, L. R. J. Phys. Chem. B 1998, 102, 10469]. The binomial cell model suggested earlier is applied as the IT default distribution p(m) for the number m of solute (water) particles occupying a cavity of given size and shape. In the present work, this model is extended to cover the entire range of cavity size between small ordinary molecular solutes and bulky biomolecular structures. The resulting distribution consists of two binomial peaks responsible for producing the free energy contributions, which are proportional respectively to the volume and to the surface area of a cavity. The surface peak dominates in the large cavity limit, when the two peaks are well separated. The volume effects become decisive in the opposite limit of small cavities, when the two peaks reduce to a single-peak distribution as considered in our earlier work. With a proper interpolation procedure connecting these two regimes, the MC simulation results for model spherical solutes with radii increasing up to R = 10 A [Huang, D. H.; Geissler, P. L.; Chandler, D. J. Phys. Chem. B 2001, 105, 6704] are well reproduced. The large cavity limit conforms to macroscopic properties of bulk water solvent, such as surface tension, isothermal compressibility and Tolman length. The computations are extended to include nonspherical solutes (hydrocarbons C1-C6).     

Modeling the phase behavior of H2S+n-alkane binary mixtures using the SAFT-VR+D approach

A statistical associating fluid theory for potential of variable range has been recently developed to model dipolar fluids (SAFT-VR+D) [Zhao and McCabe, J. Chem. Phys. 2006, 125, 104504]. The SAFT-VR+D equation explicitly accounts for dipolar interactions and their effect on the thermodynamics and structure of a fluid by using the generalized mean spherical approximation (GMSA) to describe a reference fluid of dipolar square-well segments. In this work, we apply the SAFT-VR+D approach to real mixtures of dipolar fluids. In particular, we examine the high-pressure phase diagram of hydrogen sulfide+n-alkane binary mixtures. Hydrogen sulfide is modeled as an associating spherical molecule with four off-center sites to mimic hydrogen bonding and an embedded dipole moment (micro) to describe the polarity of H2S. The n-alkane molecules are modeled as spherical segments tangentially bonded together to form chains of length m, as in the original SAFT-VR approach. By using simple Lorentz-Berthelot combining rules, the theoretical predictions from the SAFT-VR+D equation are found to be in excellent overall agreement with experimental data. In particular, the theory is able to accurately describe the different types of phase behavior observed for these mixtures as the molecular weight of the alkane is varied: type III phase behavior, according to the scheme of classification by Scott and Konynenburg, for the H2S+methane system, type IIA (with the presence of azeotropy) for the H2S+ethane and+propane mixtures; and type I phase behavior for mixtures of H2S and longer n-alkanes up to n-decane. The theory is also able to predict in a qualitative manner the solubility of hydrogen sulfide in heavy n-alkanes.     

Effect of a charged boundary on electrophoresis: a sphere at an arbitrary position in a spherical cavity

The effect of the presence of a charged boundary on the electrophoretic behavior of a particle is investigated by considering a sphere at an arbitrary position in a spherical cavity under conditions of low surface potential and weak applied electric field. Previous analyses are modified by using a more realistic electrostatic force formula and several interesting results, which are not reported in the literature, are observed. We show that the qualitative behavior of a particle depends largely on its position, its size relative to that of a cavity, and the thickness of the electric double layer. In general, the presence of a cavity has the effect of increasing the conventional hydrodynamic drag on a particle through a nonslip condition on the former. Also, a decrease in the thickness of the double layer surrounding a sphere has the effect of increasing the electrostatic force acting on its surface so that its mobility increases. However, this may not be the case when an uncharged particle in placed in a positively charged cavity, where the electroosmotic flow plays a role; for example, the mobility can exhibit a local maximum and the direction of electrophoresis can change.