Binding equation, derivation

The derivation of equilibrium ligand binding equations for this model involves the following assumptions First, the protein is oligomeric and contains a finite number of identical subunits (called protomers). Second, the protein exists in two different symmetrical states (historically re-... 

The side chains of amino acid residues in a protein may be changed at will by protein engineering (Chapter 14) and the consequent effects on binding and catalysis studied directly. This is the subject of Chapter 15, where it will be seen how the equations derived so far actually hold in practice and are used to analyze the data. There is direct evidence for enzyme-transition state complementarity. 

Equation 75 (as all others derived from rapid equilibrium assumptions) is really an equilibrium binding equation that gives the ratio of occupied to total sites. We obtain a velocity equation by assuming that the velocity is proportional to the concentration of occupied sites. In other words, a velocity equadon is obtained when we equate Ys to v/Vm xi... 

Eq. 4 is derived based on an exact solution to the binding equation for E and I. Thus, the fit of Eq. 4 to inhibition data results in an estimate of both /l and IC50 value. The kinetics of tight-binding inhibitors are presented in more detail in ref. 12. 

It is important to note, and should always be remembered, that all the rate and binding equations for cooperative and allosteric enzymes were derived under rapid equilibrium assumption. Therefore, all kinetic models for the cooperative phenomena can be equally well applied to enzyme reactions that are in the rapid equilibrium and to the binding of ligands to enzymes and proteins. 

Correct titration curves for the contribution of unbound retinol (15) and analyze either by a linearization method (15) or by curve-fitting to an equation derived from binding theory (Eq. 1 see Note 10). 

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