Solvent Effects on Cooperativity

All binding processes in real-life systems occur in some solvent. The solvent is, in general, a mixture of many components, including water electrolytes and nonelectrolytes. At present, it is impossible to account for all possible solvent effects, even when the solvent is pure water. Yet, the solvent, whether a single or multi-component, cannot be ignored. Any serious molecular theory of cooperativity must deal with solvent effects. We shall see in this chapter that this is not an easy task even when the solvent is inert, such as argon, or a simple hydrocarbon liquid.  

In all the theoretical developments in the previous chapters we have assumed that the systems operate in vacuum (except for the case of alkylated succinic acid. Section 4.8). This assumption has enormously simplified the theory. Strictly speaking, all we have learned so far about cooperativity applies only to vacuum systems. One might justifiably wonder whether we have not wasted our time and effort in studying systems that do not exist in reality. In fact, we shall soon see that the introduction of the solvent does change the theory of cooperativity. But the changes are such that the formal structure of the results obtained for the vacuum system is preserved. Formally, if g (l, 1) is the pair correlation function discussed 

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Cooper, M. A. NMR Spectra of Some Iodo- and Bromofluorobenzenes. Novel Solvent Effect on Ortho Fluorine-Fluorine Couplings. Org. Mag. Res. 1969, 363. 

Colombo et al. (1992) examined the water effect on the cooperativity of hemoglobin. They found that about 60 water molecules are involved in the transition between the oxy and the deoxy conformations of hemoglobin. Unfortunately, this paper does not discuss the solvent effect on the free energies involved in the cooperativity of hemoglobin. 

Before we examine some specific solvation effects on cooperativity we must first consider various aspects of the solvation Gibbs energy of a macromolecule a. We present here one possible decomposition of AG which will be useful for our purposes. Consider a globular protein a which, for simplicity, is assumed to be compactly packed so that there are no solvent molecules within some spherical region to which we refer as the hard core of the protein. The interaction energy between a and the fth solvent molecule (the solvent is presmned to be water, w) is written as... 

Summary of Cooperative Ligand and Solvent Effects ON Thiocyanate Coordination... 

Hunter CA, Mismaca MC, Turega SM. Solvent effects on chelate cooperativity. Chem Sci. 2012 3 589-601. 

For some of the systems in the data set, the effect of solvent on the value of EM has been investigated. Solvent can have a significant influence on the properties of the individual interactions present in supramolecular complexes.Fiowever, these solvent effects can be accounted for by using reference complexes that are studied in the same solvent as the cooperative system. In other words, solvent effects on cancel out in the determination of EM. The value of EM might therefore be expected to be solvent independent. ... 

Cooper, K.A., Dhar, M.L., Hughes, E.D., Ingold, C.K., MacNulty, B.J. and Woolf, L.I., Mechanism of elimination reactions. Part VII. Solvent effects on rates and product-proportions in uni- and bi-molecular substitution and elimination reactions of allq l halides and sulphonium salts in hydroxylic solvents, J. Chem. Soc. 2043-2049 (1948). 

Theoretically, the problem has been attacked by various approaches and on different levels. Simple derivations are connected with the theory of extrathermodynamic relationships and consider a single and simple mechanism of interaction to be a sufficient condition (2, 120). Alternative simple derivations depend on a plurality of mechanisms (4, 121, 122) or a complex mechanism of so called cooperative processes (113), or a particular form of temperature dependence (123). Fundamental studies in the framework of statistical mechanics have been done by Riietschi (96), Ritchie and Sager (124), and Thorn (125). Theories of more limited range of application have been advanced for heterogeneous catalysis (4, 5, 46-48, 122) and for solution enthalpies and entropies (126). However, most theories are concerned with reactions in the condensed phase (6, 127) and assume the controlling factors to be solvent effects (13, 21, 56, 109, 116, 128-130), hydrogen bonding (131), steric (13, 116, 132) and electrostatic (37, 133) effects, and the tunnel effect (4,... 

Guo, H., and M. Karplus. 1994. Solvent Influence on the Stability of the Peptide Hydrogen Bond A Supramolecular Cooperative Effect. J. Phys. Chem. 98, 7104-7105. 

First, we remove the solvent and consider only the system of adsorbent and ligand molecules. We make this simplification not because solvent effects are unimportant or negligible. On the contrary, they are very important and sometimes can dominate the behavior of the systems. We do so because the development of the theory of cooperativity of a binding system in a solvent is extremely complex. One could quickly lose insight into the molecular mechanism of cooperativity simply because of notational complexity. On the other hand, as we shall demonstrate in subsequent chapters, one can study most of the aspects of the theory of cooperativity in unsolvated systems. What makes this study so useful, in spite of its irrelevance to real systems, is that the basic formalism is unchanged by introducing the solvent. The theoretical results obtained for the unsolvated system can be used almost unchanged, except for reinterpretation of the various parameters. We shall discuss solvated systems in Chapter 9. 

Perhaps the simplest two-site cooperative systems are small molecules having two binding sites for protons, such as dicarboxylic acids and diamines. Despite their molecular simplicity, most of these molecules do not conform with the modelistic assumptions made in this chapter. Therefore, their theoretical treatment is much more intricate. The main reasons for this are (1) there is, in general, a continuous range of macrostates (2) the direct and indirect correlations are both strong and intertwined, so that factorization of the correlation function is impossible. In addition, as with any real biochemical system, the solvent can have a major effect on the binding properties of these molecules. 

Clearly, for any specific order of turning on the interaction U lc, X,), we shall obtain a different expansion on the rhs of Eq. (9.4.2). In the particular expansion written on the rhs of Eq. (9.4.2) we have classified all the functional groups on the surface of a (i.e., those FGs that are exposed to the solvent) into different classes. The first consists of all the FGs that are independently solvated. The second consists of all pairs of correlated FGs, and so on. We shall see in the next two sections that this particular form of expansion of AG is convenient for a qualitative analysis of the types of solvent effect we may expect on cooperativity. 

We shall now examine the effect of size on the cooperativity. We use the model of Section 4.5, for which we found the formal expression for the ligand-ligand pair correlation 1, 1) in Eq. (9.3.16). The solvent effect enters this expression via three factors, which we shall examine separately. 

The response of solvent to an electrical field depends on the intrinsic dipole moment of its molecules, but depends also on cooperative effects of adjacent dipoles, when these are correlated in the Uquid. 

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