Kirkwood-Buff integrals water

Keywords Fluctuation theory Kirkwood-Buff integrals A/,A -dimethylformamide Methanol Water Binary mixtures Ternary mixtures... 

It was shown by us J. Phys. Chem. B, 2006, 110, 12707) that the excess (deficit) of any species i around a central molecule j in a binary mixture is not provided by c,Gy (where c, is the molar concentration of species i in the mixture and Gy are the Kirkwood-Buff integrals) as usually considered and that an additional term, involving a volume F which is inaccessible to molecules of species i because of the presence of the central molecule j, must be included. In this paper, the new expression is applied to various binary mixtures and used to establish a simple criterion for preferential solvation in a binary system. First, it is applied to binary Lennard-Jones fluids. The conventional expression for the excess (deficit) in binary mixtures, c,Gy, provides always deficits around any central molecule in such fluids. In contrast, the new expression provides excess for one species and deficit for the other one. In addition, two kinds of binary mixtures involving weak (argon/krypton) and strong (alcohols/water) mtermolecular interactions were considered. 

Let us apply eqns (13), (14) and (15) to a real system and compare the results. Fig. 2 provides such a comparison for the binary system isopropanol (l)-water (2) (The Kirkwood-Buff integrals were taken from literature and the van der Waals volumes were calculated as suggested in ref. 39-41). Fig. 2 shows that the excesses (deficits) calculated using all three equations (eqns (13), (14) and (15)) provide quite comparable results for both central isopropanol and water molecules. The differences between the excesses (deficits) calculated with eqns (13) and (14) are small. 

The Kirkwood—Buff integrals for the mixture water-electrolyte, when one assumes ideal behavior in the dilute region, can be expressed as follows ... 

The Kirkwood-Buff integrals Gn and G13 in the binary mixture water (1) -1- sodium chloride (3) were taken from reference [71]. The values obtained for G12 and G23 from Eqs. (27) and (28) were used to calculate the excesses (or deficits) number of water and sodium chloride molecules in the vicinity of a gas molecule. 

The Kirkwood-Buff integrals G 2 and G23 and the excesses (or deficits) numbers Anu and A 32 in a binary mixture water (l)+gas (2)+sodium chloride (3) ... 

The knowledge of the Kirkwood-Buff integrals for dilute mixtures can be very helpful in the analysis of the local water/cosolvent composition in the vicinity of a solute molecule. Ultimately, it can provide information about the effect of various cosolvents on the protein behavior in aqueous solutions. 

FIG. 1. The Kirkwood-Buff integrals Gj2 and G23 for an infinitely dilute protein (2) in water (l)+cosolvent (3) mixture. The solid line represents G 2 and G23 for the reference mixture calculated using Eqs. (20) and (21). The numerical values of and are so close to each other that at the scale of the figure they superpose on a single curve. The symbol ( ) represents Gj2 and the symbol (O) represents G23. The values of Gj2 and G23 were calculated by solving Eqs. (3) and (5). 

The results of the calculations are presented in Figs. 1-3 and Table I. Fig. 1(a) presents the Kirkwood-Buff integrals Gj2 and G23 for an infinitely dilute ribonuclease A (2) in water (l)-i-glycerol (3) rnixmres. All the Kirkwood-Buff integrals have negative values. However, G12 and G23 have different sign deviations from Gp and The same... 

Similar results regarding the Kirkwood-Buff integrals Gp and G23, and excesses or deficits of water and cosolvent in the vicinity of a protein molecule were obtained for an infinitely dilute ribonuclease A (2) in water (1) -t trehalose (3) mixture [See Figs. 1(b) and 2(b)]. Again, our calculations demonstrate that in the vicinity of ribonuclease A at high... 

In the present paper the Kirkwood-Buff theory of ternary solutions was apphed to infinitely dilute proteins in aqueous mixed solvents. Novel expressions for the Kirkwood-Buff integrals G]2, G23, and G]3, and the preferential binding parameter r23 have been derived and used to calculate the various properties of infinitely dilute proteins in aqueous mixed solvents. In particular, the Kirkwood-Buff integrals Gi2 and G23, the excess (or deficit) of water and cosolvent, and the derivatives of the activity coefficients of a protein and cosolvent were calculated for five different mixtures involving infinitely dilute proteins in various aqueous mixed solvents. 

Indeed, Gn and Gi3 are much smaller than the Kirkwood-Buff integrals for the pairs involving the protein (IG12I and IG23I). Table 1 provides their values for the system water (1) + lysozyme (2) -I- urea (3) (pH 7.0, 20°C). 

Experimental data regarding 7 and V2 are available in the literature for many water/protein/cosolvent systems [4-14,18-20,22]. The Kirkwood-Buff integrals Gu and G13 are for the binary mixture water/cosolvent and ean be ealeulated as de-seribed in the literature [24-28]. The Kirkwood-Buff integrals Gi2 and G23 can be calculated Ifom Eqs. (3) and (6) using experimental data for 7 Tj, Vi and V3. 

Kirkwood-Buff integrals and the excess (or deficit) number of molecules of water and PEG around a protein molecule... 

The Kirkwood-Buff integrals and the excess (or deficit) number of molecules of water and PEG around a protein molecule were calculated for 3-lactoglobulin (p-LG), bovine serum albumin (BSA), lysozyme, chymotrypsinogen and ribo-nuclease A (RNase A). Experimental data regarding and V2 for these systems are available in the literature [11,12,14]. The partial molar volumes V and E3 in the aqueous solutions of PEGs were calculated using the experimental data and the correlations suggested in Ref [51]. 

E. Matteoli, L. Lepori, Solute—solute interactions in water II. An analysis through the Kirkwood—Buff integrals for 14 organic solutes, J. Chem. Phys. 80 (1984) 2856-2863. 

Equations 3 and 5 allow one to calculate the Kirkwood-Buff integrals G12 and G23 using experimental data regarding the preferential binding parameters r2 and the partial molar volume of a protein at infinite dilution in a mixed solvent 49-50,52 jjjg Kirkwood—Buff integrals Gn and Go can be evaluated on the basis of the properties of protein-free mixed solvent water + cosolvent. It should be mentioned that recently the Kirkwood—Buff theory was used to analyze the effects of various cosolvents on the properties of aqueous protein solutions. " ... 

Marcus Y, Ben-Naim A (1985) A study of the structure of water and its dependence on solutes, based on the isotope effects on solvation thermodynamics. J Chem Phys 83 4744 475 MatteoU E (1997) a study on Kirkwood-Buff integrals and preferential solvation in mixtures with small deviations from ideality and/or with size mismatch of components. Importance of a proper reference system. 1 Phys Chem B 101 9800-9810. 

MatteoU E, Lepori L (1984) Solute-solute interactions in water. II. An analysis through the Kirkwood-Buff integrals for 14 organic solutes. 1 Chem Phys 80 2856-2863... 

The first term in the square brackets is generally small compared with the other two and may be neglected. Salting-in then occurs in systems where Ve° > Vw, i.e., for bulky ions having a molar volume larger than that of pure water, but otherwise salting-out occurs. Mazo (2006) in an equivalent derivation used the measured ne to evaluate the Kirkwood-Buff integral Gne not otherwise accessible. 

Survey of the Properties of Water 81 Kirkwood- Buff Integrals... 

For concreteness, suppose that at this stage we have the inequality/XL < /XH-Then,ifwe re-introduce our catalyst, water molecules will flow from the state of the high to the state of the low chemical potential. This means that adding dNs increases the number of L-cules. Figure 3.18 shows schematically the two stages of the process of adding one solute s to water. We start with an equilibrated system with composition Ni and Nh- In the first step a solute is added to the frozen-in water, i.e. Nl and Nh are unaltered. Next, we allow the system to relax to the new equilibrium condition, which is now characterized by the composition N , N. In the next subsection, we turn to the mathematical expression for the derivatives on the left-hand side of (3.7.4) in terms of the Kirkwood-Buff integrals. 

From E. Matteoli and L. Lepori, 1984, Solute-Solute Interactions in Water, 2, An Analysis through the Kirkwood-Buff Integrals for 14 Organic Solutes, Journal of Chemical Physics, 80, 2856. 

FIGURE 5.3 The Kirkwood-Buff integrals (Gy, units of cmVmol) as a function of integration distance for the A -methylacetamide (NMA) -i- water system at %ma = 0-1 for th S force fields. The thin horizontal line is the experimental value. The multiple lines correspond to five 20-nanosecond subaverages for each force field. 

Matteoli, E. and L. Lepori. 1990. The ternary system water + 1-propanol + urea at 298.15 K. Activity coefficients, partial molal volumes and Kirkwood-Buff integrals. Journal of Molecular Liquids. 47, 89. 

ZieUciewicz, J. 1995b. Solvation of DMF in the Ai,Ai-dimethytfoimaniide + alcohol + water mixtures investigated by means of the Kirkwood-Buff integrals. Journal of Physical... 

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