Hill coefficients binding

A linear form of the Hill equation is used to evaluate the cooperative substrate-binding kinetics exhibited by some multimeric enzymes. The slope n, the Hill coefficient, reflects the number, nature, and strength of the interactions of the substrate-binding sites. A... 

DERIVATION OF THE HILL COEFFICIENT (OR SLOPE) AS A DETERMINANT OF THE NUMBER OF BINDING SITES FOR AN AGONIST (NEUROTRANSMITTER) ON ITS RECEPTOR... 

Figure 5.6 Biphasic concentration-response plot for an enzyme displaying a high- and low-affinity binding interaction with an inhibitor. In panel A, the data are fit to Equation (5.4) and the best fit suggests a Hill coefficient of about 0.46. In panel B, the data are fitted to an equation that accounts for two, nonidentical binding interactions Vj/v0 = (a/(l + ([/]/ICs0))) + ((1 - a)/(l+([t]/IC(o)))> where a is an amplitude term for the population with high binding affinity, reflected by IC , and IC 0 is the IC50 for the lower affinity interaction. (See Copeland, 2000, for further details.)...

Hill plots are often used in pharmacology, where y may be either the fractional response of a tissue or the amount of a ligand bound to its binding site, expressed as a fraction of the maximum binding, and x is the concentration. It is sometimes found (especially when tissue responses are measured) that the Hill coefficient differs markedly from unity. What might this mean ... 

The Hill plot for binding would be nonlinear with a Hill coefficient given by ... 

The prevalent receptor model for the excitatory amino acid is a tetrameric complex. As mentioned in the text, there is evidence that the channel conductance depends on the number of subunits that bind a ligand. Estimate the EC50 value and Hill coefficient for a dose-response curve assuming that the occupation at each subunit has a Kd value of 1 pi I, an % of 1, and that activation induces a transition to an active state independent of the state of the other subunits ... 

Finally, we note that the fact that we have four different correlations in this system, some possibly of different signs, renders meaningless the characterization of the cooperativity of the system by a single number (as is frequently done using the Hill coefficient, see Section 4.3). We shall introduce in Section 5.8 a measure of the average cooperativity in a system, a quantity that may vary widely, even in its sign, as the binding process proceeds. 

Fig. 1. Ligand binding behavior of a hypothetical protein exhibiting a Hill coefficient of 2 or 4.

Fig. 3. Ligand binding behavior of a hypothetical protein exhibiting a unit Hill coefficient of (hh = 1). Such behavior would be expected (a) for the case of a protein with only a single binding site or (b) for the case of an oligomeric protein containing n independent and noninteracting binding sites.

The main plots used in enzyme kinetics and receptor binding studies are the Scatchard plot, the Lineweaver-Burk plot, and the linearization for estimation of the Hill coefficient. This chapter gives a short survey of these transformations of enzyme kinetics or receptor binding data. 

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