Preferential interaction parameter

If the system separates, it can be extended to a model for the interface between two solutions by introducing ions. In the basic case the system contains a salt composed of cations and anions which is preferentially solvated by the solvent 5], but badly solvable in solution 2, and a salt K2A2 that is preferentially dissolved in solvent 2. This can be achieved by choosing suitable interaction parameters between the ions and the two solvents. 

The nearest-neighbor interactions of the ions with the solvents have to be chosen such that the ions and are preferentially solvated in solvent 1, K2 and Aj in solvent 2. The simplest choice is to set the interaction of and A with Si equal u, and with solvent S2 equal to —u, where m < 0. Similarly, the interactions of K2 and A2 with Si and S2 are —u and u, respectively. Of course, nonsymmetrical choices are also possible, and are discussed in the original paper. The interaction parameter u determines the energy of transfer of the ion between the two pure solvents, which is 2mu. 

In the case of a neutral gel, the values a and Q change smoothly as Qo increases, while in the case of a polyelectrolyte network the jumpwise collapse takes place. Note that the composition of the mixture in the swollen network practically coincides with Q0, whereas a significant difference between solvent compositions in the collapsed network and solution exists. The enrichment of the sample by good solvent can be very considerable. An analysis shows that this redistribution increases with the growth of interaction parameter Xab °f solvent components. The reason for this is the following with an increase of Xab. the tendency to phase separation becomes stronger and preferential solvation of... 

Preferential Solvation. Examination of the data of Figure 2 in terms of Equation 3 shows that below 65% chloroethanol, (dmi/dm2)r, io.ni is positive, while above this point it becomes negative. Negative values of this interaction parameter indicate a deficiency of component 1 in the immediate vicinity of molecules of component 2—i.e., preferential hydration of component 2. The extent of hydration is given by Equation 5. 

Thus, in small-angle x-ray scattering, measurement of the molecular weight of a macromolecule in concentrated solvent requires knowledge of the preferential interaction parameter. This can be measured by techniques such as differential refractometry, densimetry, and isopiestic vapor phase equilibrium measurements. For densimetry,... 

Fig. 13. Preferential interaction parameter vs lyotropic number for lysozyme on (° ) bovine serum albumin and ( ) Toyopearl.

Fig. 3.36 Segment density profiles from a Monte Carlo computer simulation of adsorption of a BAB triblock at a planar interface, where the hydrophobic B block is preferentially adsorbed (Balazs and Lewandowski 1990). Profiles are plotted for different A segment-surface interaction parameters, AS, with Xas = 0 and a chain length - 30 units.

To circumvent the above problems with mass action schemes, it is necessary to use a more general thermodynamic formalism based on parameters known as interaction coefficients, also called Donnan coefficients in some contexts (Record et al, 1998). This approach is completely general it requires no assumptions about the types of interactions the ions may make with the RNA or the kinds of environments the ions may occupy. Although interaction parameters are a fundamental concept in thermodynamics and have been widely applied to biophysical problems, the literature on this topic can be difficult to access for anyone not already familiar with the formalism, and the application of interaction coefficients to the mixed monovalent-divalent cation solutions commonly used for RNA studies has received only limited attention (Grilley et al, 2006 Misra and Draper, 1999). For these reasons, the following theory section sets out the main concepts of the preferential interaction formalism in some detail, and outlines derivations of formulas relevant to monovalent ion-RNA interactions. Section 3 presents example analyses of experimental data, and extends the preferential interaction formalism to solutions of mixed salts (i.e., KC1 and MgCl2). The section includes discussions of potential sources of error and practical considerations in data analysis for experiments with both mono- and divalent ions. 

There is a substantial literature on the thermodynamics of three-component systems—water, protein, and second solute. For a review of early work, methods, and theory, with emphasis on sedimentation experiments, see Kuntz and Kauzmann (1974). Timasheff and colleagues (see Lee et ai, 1979, and references cited therein) have developed a beautiful formalism for treating the thermodynamic nonideality of three-component systems in terms of the preferential interaction parameter... 

Now, the key thermodynamic aspects of this mechanism (reviewed in [4,78,79]) will be examined in more detail. Setting component 1 = principal solvent (here water), component 2 = protein, and component 3 = solute (e.g., sucrose or PEG), the preferential interaction of component 3 with a protein is expressed, within close approximation, by the parameter (5m3/5m2) jj at constant temperature and pressure, where p, and m, are the chemical potential and molal concentration of component /, respectively. A positive value of this interaction parameter indicates an excess of component 3 in the vicinity of the protein over the bulk concentration (i.e., preferential binding of the solute). A negative value for this parameter indicates a deficiency of component 3 in the protein domain. Component 3 (the solute) is preferentially excluded and component 1 (water) is in excess in the protein domain. 

The preferential interaction parameter is a direct expression of changes in the free energy of the system induced by component 3 and has the relation ... 

The term on the left-hand side of the equation defines the change in protein chemical potential as a function of solute concentration. The first term on the right-hand side of the equation is the preferential interaction parameter, which was defined earlier. The second term is the solute self-interaction parameter, which will be described in detail later. Equation (1) indicates that those compounds that are excluded (i.e., (5" 3/5m2) j < 0) from the surface of the protein will have posi-... 

This effect correlated with the interaction parameters, x> and with the solubility parameters, 8, of the different reagents (9, 10). For example, in Figure 1, the evolution of A, which is characteristic of the preferential solvation, and the evolution of AC, which is the difference in composition between grafted and non-grafted SAN, are plotted as functions of the acrylonitrile volume fraction (II). 

Prior to Harwood s work, the existence of a Bootstrap effect in copolymerization was considered but rejected after the failure of efforts to correlate polymer-solvent interaction parameters with observed solvent effects. Kamachi, for instance, estimated the interaction between polymer and solvent by calculating the difference between their solubility parameters. He found that while there was some correlation between polymer-solvent interaction parameters and observed solvent effects for methyl methacrylate, for vinyl acetate there was none. However, it should be noted that evidence for radical-solvent complexes in vinyl acetate systems is fairly strong (see Section 3), so a rejection of a generalized Bootstrap model on the basis of evidence from vinyl acetate polymerization is perhaps unwise. Kratochvil et al." investigated the possible influence of preferential solvation in copolymerizations and concluded that, for systems with weak non-specific interactions, such as STY-MMA, the effect of preferential solvation on kinetics was probably comparable to the experimental error in determining the rate of polymerization ( 5%). Later, Maxwell et al." also concluded that the origin of the Bootstrap effect was not likely to be bulk monomer-polymer thermodynamics since, for a variety of monomers, Flory-Huggins theory predicts that the monomer ratios in the monomer-polymer phase would be equal to that in the bulk phase. 

Polymer blends may be characterized in terms of the temperature dependence of the Flury-Huggins interaction parameter (j)- In the case of an upper critical solution temperature (UCST) blend, / decreases with temperature, and the blend remains miscible. For phase separation to occur in a UCST blend, the temperature must be lower than the critical solution temperature. In the case of a lower critical solution temperature (LCST) blend, x increases with temperature, and thus phase separation occurs above the critical solution temperature. The ability of CO2 to mimic heat means that miscibility is enhanced in the case of UCST blends, and for the case of LCST blends the miscibihty is depressed. Ramachandrarao et al. [132] explained this phenomenon by postulating a dilation disparity occurring at higher CO2 concentration as a result of the preferential affinity of CO2 to one of the components of the blend, inducing free-volume and packing disparity. 

Kang, M. and P. E. Smith. 2007. Preferential interaction parameters in biological systems by Kirkwood-Buff theory and computer simulation. Fluid Phase Equilibria. 256, 14. Kang, M. and P. E. Smith. 2008. Kirkwood-Buff theory of four and higher component mixtures. Journal of Chemical Physics. 128, 244511. 

Smith, P. E. 2006a. Chemical potential derivatives and preferential interaction parameters in biological systems from Kirkwood-Buff theory. Biophysical Journal. 91, 849. 

Smith, P. E. 2006b. Equilibrium dialysis data and the relationships between preferential interaction parameters for biological systems in terms of Kirkwood-Buff integrals. Journal of Physical Chemistry B. 110, 2862. 

As expected,preferential sorption was observed, with the essential distinction of molar volumes Vi and Vj of components of the mixed solvent (hexane-DBP, DOS-DEP). For swelling of the crosslinked elastomer SCN-26 in the mixture of components, having similar molar volumes Vj and Vj (e.g., amyl acetate-dimethyl phthalate) the preferential sorption of components of SL is practically absent. Influence of Vj and V2 and the influence of double interaction parameters on the sorption of binary liquids by crosslinked elastomers was examined by the method of mathematical experiment. Therewith the set of equations describing swelling of crosslinked elastomers in binary mixture, similar to the equations obtained by Bristow from the Flory-Rehner theory and from the work of Schulz and Flory, were used ... 

---