Empirical Hill equation

Most hemoglobins, however, do not obey the simple mass action equation (Equation 7.2) and instead obey the empirical Hill equation ... 

It was noted earlier that Michaelis-Menten kinetics and its linear transformations are not valid for allosteric enzymes. Instead, the Hill equation, an equation originally empirically developed to describe the cooperative binding of Oz to hemoglobin (Chapter 7), is used. The expression describing such a straight-line plot is... 

Although the maximum-effect pharmacodynamic models are empirically based/ they do incorporate the concept of a maximum effect predicted by the drug-receptor interactions described earlier. The Hill equation/ which takes the same form as the equation describing drug effect as a function of receptor occupancy/ relates a continuous drug effect to the drug concentration at the effect site as shown ... 

Plasma concentration (C) and intensity (7) of the pharmacological response often follow an empirical relationship, known as the Hill equation ... 

The Hill equation has only limited applicability as a model to predict the expression of agonism, because the parameters from this empirical equation depend on both drug-specific and system-related properties, complicating the extrapolation and prediction from in vitro to in vivo systems. With a fully mechanistic model, Zuideveld was better able to predict the in vivo affinity and efficacy of 5-HTia receptor agonists from in vitro receptor binding assay. 

This equation is formally analogous to Hill s empirical equation (Hill, 1910) which is employed to rationalize allosteric interactions in multienzyme systems. 

From the practical point of view, the following empirical equation of Hill [6] is more convenient. 

Data of densities of liquids are empirical in nature, but the effects of temperature, pressure, and composition can be estimated suitable methods are described by Reid et al. (Properties of Gases and Liquids, McGraw Hill, New York, 1977), the API Refining Data Book (American Petroleum Institute, Washington, DC, 1983), and the AIChE Data Prediction Manual (1984-date). The densities of gases are represented by equations of state of which the simplest is that of ideal gases from this the density is given by ... 

According to the recommendations, in quantitative measurements of biological activity drug action is expressed in terms of the effect, E, produced when an agonist, A, is applied at a concentration [A]. The relationship between E and [A] can often be described empirically by Hill s equation, which has the form ... 

Many different equations have been used to interpret monolayer—multilayer isotherms [7, 11, 18, 21, 22] (e.g., the equations associated with the names Langmuir, Vohner, HiU-de Boer, Fowler-Guggenheim, Brunauer-Emmett-Teller, and Frenkel-Halsey-Hill). Although these relations were originally based on adsorption models, they are generally applied to the experimental data in an empirical manner and they all have Hmitations of one sort or another [7, 10, 11]. 

In addition to the well-known monolayer equations already referred to (e.g., the Langmuir, Hill—de Boer and virial equations), there are others such as those associated with the names of Freundlich, Sips, and Toth, which have been applied to physisorption isotherms on microporous solids [11]. These relatively simple, empirical equations are useful for the interpolation and extrapolation of chemical engineering data, but they are not capable of throwing any new light... 

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