Hill coefficient inhibition

Figure 5.5 Concentration-response plots for enzyme inhibition with Hill coefficients (h) of 1 (A) and 3 (B). Data simulated using Equation (5.4).

To account for differences in the Hill coefficient, enzyme inhibition data are best ht to Equation (5.4) or (5.5). In measuring the concentration-response function for small molecule inhibitors of most target enzymes, one will hnd that the majority of compounds display Hill coefficient close to unity. However, it is not uncommon to hnd examples of individual compounds for which the Hill coefficient is signihcandy greater than or less than unity. When this occurs, the cause of the deviation from expected behavior is often reflective of non-ideal behavior of the compound, rather than a true reflection of some fundamental mechanism of enzyme-inhibitor interactions. Some common causes for such behavior are presented below. 

The second common cause of a low Hill coefficient is a partitioning of the inhibitor into an inactive, less potent, or inaccessible form at higher concentrations. This can result from compound aggregation or insolubility. As the concentration of compound increases, the equilibrium between the accessible and inaccessible forms may increase, leading to a less than expected % inhibition at the higher concentrations. This will tend to skew the concentration-response data, resulting in a poorer... 

Compound Identification Number IC50 (pM) Standard Error (SE) of Fit or Standard Deviation (SD) from Multiple, Independent Determinations Hill Coefficient Maximum % Inhibition Attained Comments... 

For example, if the Hill coefficient (h) is unity, and we wish to achieve 25% inhibition, the fraction velocity would be 0.75, and its reciprocal (voM) would be 1.33. Plugging this into Equation (5.9), we find that 25% inhibition is obtained at a concentration of inhibitor equal to 1/3 IC50. Table 5.3 summarizes the four inhibitor concentrations needed to achieve the desired inhibition levels (again, at [5] = KM) when the Hill coefficient is unity and 3.0. 

Table 5.3 Concentrations of inhibitor, relative to the IC50, required for different levels of inhibition for concentration-response plots displaying Hill coefficients (h) of 1.0 and 3.0...

Similar to Eq. (67), the first reaction (incorporating the enzyme phosphofructo-kinase) exhibits a Hill-type inhibition by its substrate ATP [126]. The overall ATP utilization v3 (ATP) is modeled by a saturable Michaelis Menten function. The system is specified by five kinetic parameters (with Gx lumped into Vm ), the Hill coefficient n, and the total concentration, 4 / = [ATP] + [ADP]. Note that the model is not intended to capture biological realism, rather it serves as a paradigmatic example to identify dynamic behavior in metabolic pathways. 

The overall influence of ATP on the rate V (ATP) is measured by a saturation parameter C (—oo, 1]. Note that, when using Eq. (139) as an explicit rate equation, the saturation parameter implicitly specifies a minimal Hill coefficient min > C necessary to allow for the reverse transformation of the parameters. The interval 6 [0,1] corresponds to conventional Michaelis Menten kinetics. For = 0, ATP has no net influence on the reactions, either due to complete saturation of a Michaelis Menten term or, equivalently, due to an exact compensation of the activation by ATP as a substrate by its simultaneous effect as an inhibitor. For < 0, the inhibition by ATP supersedes the activation of the reaction by its substrate ATP. 

A fourth pattern of interaction (enzymes of group D) between allosteric activator and inhibitor is seen with barley endosperm. The ADPGIc PPase, which is poorly-activated by 3PGA, is inhibited by Pi (Table 4.2). However, 3PGA lowers (up to 3-fold) the S0 5 for ATP (i.e. the apparent affinity of ATP is increased) and the Hill coefficient.75 At 0.1 mM ATP, activation by 3PGA is about 4-fold 2.5 mM Pi reverses the effect. Thus, in barley endosperm, the prime effect of 3PGA or Pi may be to either increase or decrease the apparent affinity of the enzyme for the substrate, ATP. 

Figure 19.7. Competition curves for two compounds versus a known radioligand. (Top) These data represent the competition of two compounds with a known radioligand (in this case a radioligand that labels the dopamine D receptor, a member of the G protein-coupled superfamily). It is important to note not only the left-right difference between Compound A and Compound B, but also the difference in the shape of their competition curves. (Bottom) A Hill plot [based on Eq. (19.20)] of the competition curves shown in the top figure provides two pieces of data. First, the slopes of the lines are different (Compound A = -1.0 Compound B = -0.6), which has important mechanistic meaning that is discussed in Section 19.3.4b. Hill plots also allow more precise estimation of IC50s. By definition, at 50% inhibition, the Hill coefficient is 0. As shown, one can estimate the IC50 for each compound from this plot.

Figure 2.6. Influence of I mM DTT on the inhibition of the binding of I nM [3H]mepyramine by mepyramine and histamine in guinea-pig cerebellar membranes. Values for the ICS0 estimate and Hill coefficient (a) were obtained by non-linear regression [112].

Tfc4 Fragment Global Kjj TFIIIB Inhibition nM SEa nH Hill Coefficient... 

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