Cooperative binding system

A related cooperative binding system is shown in Figure 11.5. A crown ether derived macrocycle only binds a squaraine dye when sodium cations are present in the solution. The sodium cations bridge the dye and the crown ether oxygens inside the macrocyclic... 

Usually non-cooperative and non-Unear binding isotherms were observed in alkaloid-B-DNA complexation and the data were fitted to a theoretical curve drawn according to the excluded site model [126] developed by McGhee and von Hippel [127] for a non-Unear non-cooperative ligand binding system using the following equation ... 

When a ligand can complex more than one cation, the question arises of possible cooperative binding. There are many definitions of cooperativity but they are all consistent with the following criterion (Connors, 1987). A system is... 

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. 

In order to compute the binding isotherm (Section 2.1) of any system, one must know all the microstates of the system. This cannot be done for even the smallest binding system. However, in order to understand the origin of cooperativity and the mechanism by which ligands cooperate, it is sufficient to consider simple models having only a few macrostates. This understanding will be helpful for the selection of methods to extract information from experimental data, and for the meaningful interpretation of this information. 

This is also equivalent to a mixture of two different binding systems. However, here we stress the case of a mixture that is obtained from an equilibrated system. It is only in such a case that one might misinterpret spurious cooperativity as genuine see Section 4.8 for an experimental example. 

In two-site systems, there is only one correlation function which characterizes the cooperativity of the system. In systems with more than two identical sites, for which additivity of the higher-order correlations is valid, it is also true that the pair correlation does characterize the cooperativity of the system. This is no longer valid when we have different sites or nonadditivity effects. In these cases there exists no single correlation that can be used to characterize the system, hence the need for a quantity that measures the average correlation between ligands in a general binding system. There have been several attempts to define such a quantity in the past. Unfortunately, these are valid only for additive systems, as will be shown below. 

It is clear that neither Wyman s nor Minton and Saroff s measures do justice to aU types of cooperativities in the system, and certainly cannot account for variation in cooperativity at different stages of the binding process. In the next subsection we define a new measure of the average correlation in any binding system, and show how to extract this quantity from experimental data. 

Thus, all cooperativities in this limit are positive, as expected from a two-state binding system. 

In 1985 I was glad to see T. L. Hill s volume entitled Cooperativity Theory in Biochemistry, Steady State and Equilibrium Systems. This was the first book to systematically develop the molecular or statistical mechanical approach to binding systems. Hill demonstrated how and why the molecular approach is so advantageous relative to the prevalent phenomenological approach of that time. On page 58 he wrote the following (my italics) ... 

The main objective of this book is to understand the molecular origin of cooperativity and its relation to the actual function of biochemical binding systems. 

Even when the term cooperativity is confined to binding systems, it has been defined in a variety of ways. This has led to some inconsistencies and even to conflicting results. 

In summary, although each of the aforementioned books does touch upon some aspects of cooperativity in binding systems, none of them explores the details of the mechanisms of cooperativity on a molecular level. In this respect I feel that the present book fills a gap in the literature. I hope it will help the reader to gain insight into the mechanism of cooperativity, one of the cleverest and most intricate tricks that nature has evolved to regulate biochemical processes. 

The book is organized in nine chapters and eleven appendices. Chapters 1 and 2 introduce the fundamental concepts and definitions. Chapters 3 to 7 treat binding systems of increasing complexity. The central chapter is Chapter 4, where all possible sources of cooperativity in binding systems are discussed. Chapter 8 deals with regulatory enzymes. Although the phenomenon of cooperativity here is manifested in the kinetics of enzymatic reactions, one can translate the description of the phenomenon into equilibrium terms. Chapter 9 deals with some aspects of solvation effects on cooperativity. Here, we only outline the methods one should use to study solvation effects for any specific system. 

A graphical procedure used to determine, in cooperative systems, values for L (the ratio of the T to R state in the absence of any binding ligand in the Monod-Wyman-Changeux model) and n (the stoichiometry of binding) in exclusive binding systems (c = 0 where c = i.e., the ratio of the intrinsic dissociation constants for... 

On this occasion, we would like to emphasize that so-called cooperative phenomena or allosteric phenomena are not characteristic of biological systems alone but are often observed also in synthetic polymer systems. For example, we cite Fig. 25, which shows the adsorption of metal ions on a synthetic polymer ligand112. The adsorption of Cu ions on the polymer ligand is sigmoidal. This cooperative binding of metal ions is easily understood by following Scheme 12. 

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