Excess coordination numbers

Figure 7-4. Excess coordination number plots for (a) MEP (three-water-bridge) [27] and (b) PMF (H64 in ) [14] simulations for the proton transfer in CAII. Note that the MEP calculation follows a very concerted mechanism while PMF simulation follows a step-wise proton hole mechanism...

Excess Coordination Number and Preferential Exclusion Parameter... 

Using this definition, one can clearly see the inhomogeneous profile of the/ -dependent KB integral and the excess coordination number of the solvent species, which reflect the spatial/structural characteristics around/of each individual solute molecule. 

Multiplying the KBIs by number densities (concentrations) one obtains an alternative picture of the integrals. The qnantities, = p,Gy, have been referred to as excess coordination numbers and quantify the change in the nnmber of j molecules observed in an open volume of solution on introduction of a central i molecule from that observed for the same volume of bulk solution in the absence of the i molecule (Newman 1994). 

The inversion of KB theory to provide fluctuating quantities or KBIs in terms of thermodynamic quantities leads to the following expression for the excess coordination numbers,... 

As it is well known, the KB theory allows one to calculate the excess (or deficit) number (or excess coordination number) of moles of j in the whole space around a central molecule i,... 

The results indicate that several of the FFs are competitive with the KBFF models for one of the systems, but none exhibited the overall balance between solute-solute, solute-solvent, and solvent-solvent distributions for aU the solutes as provided by the KBFF models. The NMA and water results are particularly concerning due to the central role of peptide-peptide interactions in determining the balance between folded and unfolded protein conformations. The observation that all the FFs display a significantly more positive solute-solute excess coordination number compared to... 

FIGURE 5.2 Comparisons of the excess coordination numbers for mixtures of methanol + water, benzene + methanol, N-methylacetamide + water, and zwitterionic glycine + water using the Kirkwood-Buff force field and the biomolecular force field that best reproduced the excess coordination numbers for each system. Please note the different y-axis scales. Error bars show the estimated standard deviation obtained from five 20-nanosecond subaverages. (See color insert.)... 

Hess and Van der Vegt (2009) studied cation-binding affinity with carboxylate ions. They computed the excess coordination numbers, V, defined in Section 1.1.5 in Chapter 1, for water (w) or cations (c) about cations. 

All the above answers have significant meaning (Shimizu 2004). Answer 1 has provided a long-awaited modernization of the field, away from stoichiometric binding models and other similar approaches. Answer 2 has provided a breakthrough in our ability to probe solute-solvent interactions from thermodynamic measuranents, via the combination of two thermodynamic measurements hitherto interpreted independently. Now the excess coordination numbers can be obtained directly from... 

FIGURE 11.3 Exclusion does indicate an absence of binding. It does lead to a negative contribution to the excess coordination number, as shown here, as well as in Equation 11.3. 

We have seen that FST has finally brought a molecular understanding of biomolecular solvation in the presence of cosolvents. It has paved a way toward an experimental determination of the excess coordination numbers. Now, the practical question is how can we estimate the change of hydration that accompanies a biomolecular process FST provides a clear answer to this question through partial molar volume measurements, commonly called volumetric analysis (Shimizu 2004). 

This means that the excess coordination number can directly be obtained from the partial molar volume measurements. 

The excess coordination number obtained via FST consists of two contributions (Shimizu 2004 Chalikian 2011). The first contribution is the excluded volume, namely, the contribution from the region into which the solvent molecules cannot penetrate. The second is the contribution due to the change of water distribution in the solvation shell. If one is interested in the latter, then the excluded volume contribution should be subtracted out. Admittedly, the estimation of the excluded volume at present is a rough estimation at best it nevertheless has provided some useful insight into biomolecular hydration (Chalikian 2003, 2011). Therefore, I employ the method proposed by Chalikian and coworkers in the estimation of the excluded volume Fg. This requires the calculation of the following two factors the first is the inaccessibility of solvent molecules to biomolecules to intrinsic (core) volume F, and the second is thermal volume (volume inaccessible due to thermal motion) F. The former is calculated from the van der Waals volumes of the molecule, the second is estimated from the solvent-accessible surface area. The contribution of the above two to the excess coordination number is -c Fg = -c, (F, + F ). Thus, we obtain the solvation-shell contribution to the excess hydration number. 

The fact that OSA overestimates the excess coordination number can be explained from the experimental data. This is illustrated by comparing the osmolyte-induced equilibrium shift with the pressure-induced shift, The former... 

This means that the contribution from the excess coordination number, AA21, is negligibly small, in stark contrast to the supposition of OSA (Shimizu and Boon 2004 Gee and Smith 2009). 

FIGURE 11.5 Schematic diagram showing what the osmotic stress analysis actually measures not the hydration change, but the change of cosolvent exclnsion. The meshed area represents the region into which the osmolytes cannot penetrate. This provides a negative contribution to the excess coordination number. 

The preferential hydration parameter, V21, defined below, can be expressed by the excess coordination numbers through FST (Shulgin and Ruckenstein 2005a),... 

FIGURE 11.9 Preferential hydration parameter (solid) and the excess coordination number of PEG (dotted) around ribonuclease. Consequently, the contribution from protein-water interaction is negligibly small. 

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