Solute-water radial distribution function

For an understanding of protein-solvent interactions it is necessary to explore the modifications of the dynamics and structure of the surrounding water induced by the presence of the biopolymer. The theoretical methods best suited for this purpose are conventional molecular dynamics with periodic boundary conditions and stochastic boundary molecular dynamics techniques, both of which treat the solvent explicitly (Chapt. IV.B and C). We focus on the results of simulations concerned with the dynamics and structure of water in the vicinity of a protein both on a global level (i.e., averages over all solvation sites) and on a local level (i.e., the solvent dynamics and structure in the neighborhood of specific protein atoms). The methods of analysis are analogous to those commonly employed in the determination of the structure and dynamics of water around small solute molecules.163 In particular, we make use of the conditional protein solute -water radial distribution function,... 

Fig. 3.49. Comparison of the weighted Cf-water radial distribution function from an MD simulation of a 1.1 M MgCl2 solution (solid line) with results from neutron diffraction studies of a 5.32 /WNaCI(o), a3 /WNiCl2 (x), and a 9.95 MUCI ( ) solution (1 A = 0.1 nm). (Reprinted from P. Bopp, NATO ASI Series 206-. 237,1987.)...

Figure 48. Solute-solvent radial distribution functions and running coordination numbers. The radial distribution (the solid line using the left scale) and the running coordination number (the dashed line using the right scale) are plotted versus distance in angstroms for the distribution of water oxygens around apolar atoms (o) Asp-48 Cs (b) Ser-72 O3 (c) Asn-46 C 3 and ((i) Gly-71 C .

For a solution, the radial distribution function will typically have a structure as shown in Figure 14.6 for a simulation of a benzene radical anion in water. ... 

An analysis of the structure of the dilute aqueous solution of methane was also developed in terms of quasicomponent distribution functions and stereographic views of significant molecular structures. The coordination number of methane in this system was calculated on the basis of 5.38, fixed at the first minimum In the methane-water radial distribution function. A plot of the mole fraction of methane molecules x (K) vs. their corresponding water coordination number is given in Figure 7. 

Figure 11. Calculated cation-water radial distribution function ui. center of mass separation R for the dilute aqueous solution of lithium at T = 25°C...

We have recently carried out Monte Carlo computer simulation of dilute aqueous solutions of the monatomic cations Li, Na and K and the monatomic anions F and Cl using the KPC-HF functions for the ion-water interaction and the MCY-CI potential for the water-water interaction. The temperature of the systems was taken to be 25° and the density chosen to be commensurate with the partial molar volumes as reported by Millero. - The calculated average quantities are based on from 600- 900K configurations after equilibration of the systems. The calculated ion-water radial distribution functions are given for the dilute aqueous solutions of Li", K" ", Na" ", F and Cl" in Figures 11-15, respectively. 

After this computer experiment, a great number of papers followed. Some of them attempted to simulate with the ab-initio data the properties of the ion in solution at room temperature [76,77], others [78] attempted to determine, via Monte Carlo simulations, the free energy, enthalpy and entropy for the reaction (24). The discrepancy between experimental and simulated data was rationalized in terms of the inadequacy of a two-body potential to represent correctly the n-body system. In addition, the radial distribution function for the Li+(H20)6 cluster showed [78] only one maximum, pointing out that the six water molecules are in the first hydration shell of the ion. The Monte Carlo simulation [77] for the system Li+(H20)2oo predicted five water molecules in the first hydration shell. A subsequent MD simulation [79] of a system composed of one Li+ ion and 343 water molecules at T=298 K, with periodic boundary conditions, yielded... 

Thus, effects of the surfaces can be studied in detail, separately from effects of counterions or solutes. In addition, individual layers of interfacial water can be analyzed as a function of distance from the surface and directional anisotropy in various properties can be studied. Finally, one computer experiment can often yield information on several water properties, some of which would be time-consuming or even impossible to obtain by experimentation. Examples of interfacial water properties which can be computed via the MD simulations but not via experiment include the number of hydrogen bonds per molecule, velocity autocorrelation functions, and radial distribution functions. 

The structure of the adsorbed ion coordination shell is determined by the competition between the water-ion and the metal-ion interactions, and by the constraints imposed on the water by the metal surface. This structure can be characterized by water-ion radial distribution functions and water-ion orientational probability distribution functions. Much is known about this structure from X-ray and neutron scattering measurements performed in bulk solutions, and these are generally in agreement with computer simulations. The goal of molecular dynamics simulations of ions at the metal/water interface has been to examine to what degree the structure of the ion solvation shell is modified at the interface. 

The probability of cavity formation in bulk water, able to accommodate a solute molecule, by exclusion of a given number of solvent molecules, was inferred from easily available information about the solvent, such as the density of bulk water and the oxygen-oxygen radial distribution function [65,79]. 

In short, our S-MC/QM methodology uses structures generated by MC simulation to perform QM supermolecular calculations of the solute and all the solvent molecules up to a certain solvation shell. As the wave-function is properly anti-symmetrized over the entire system, CIS calculations include the dispersive interaction[35]. The solvation shells are obtained from the MC simulation using the radial distribution function. This has been used to treat solvatochromic shifts of several systems, such as benzene in CCI4, cyclohexane, water and liquid benzene[29, 37] formaldehyde in water(28, 38] pyrimidine in water and in CCl4(31] acetone in water[39] methyl-acetamide in water[40] etc. 

Figure 17-12. Radial distribution functions (RDFs) of the oxygen of water solvent around the nitrogen in the neutral glycine (NF). The solid line is for the solute with average electron density and the broken line is for the solute with a set of point charges...

We conclude that the proximal radial distribution function (Fig. 1.11) provides an effective deblurring of this interfacial profile (Fig. 1.9), and the deblurred structure is similar to that structure known from small molecule hydration results. The subtle differences of the ( ) for carbon-(water)hydrogen exhibited in Fig. 1.11 suggest how the thermodynamic properties of this interface, fully addressed, can differ from those obtained by simple analogy from a small molecular solute like methane such distinctions should be kept in mind together to form a correct physical understanding of these systems. 

Following the notation of Section 7.6, specifically p. 160, A is the distance of closest approach of the solvent (water) center to the hard spherical solute. The left side of Eq. (8.25) is the differential work done in expanding the solute sphere against the solvent pressure. G (A), introduced on p. 121, Eq. (5.70), is the contact value of the radial distribution function of solvent centers from the position of a hard-spherical solute. G (A) then gives molecular-scale structural information to obtain that solvent pressure, and Eig. 8.13 shows the current best information on that molecular-scale pressure (Ashbaugh and Pratt, 2004). 

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