Theory occupancy

Occupancy theory is the predominant receptor theory and is closely related to the enzyme model of Michaelis and Menten. 

Clark developed occupancy theory in the 1920s and 1930s.23 He built his theory on the premise that a response (E) arises only when a receptor is occupied by a ligand, that is, from a ligand-receptor complex (RL). The response is directly proportional to [RL] (Equation 5.3). 

The receptor itself can be present in one of two states free (R) or bound in a ligand-receptor complex (RL) (Equation 5.4). 

The maximal response (Emax) will be reached if all the receptors are bound and no receptors are free (Equation 5.5). 

Through algebraic substitutions and rearrangements of Equations 5.4, 5.6, and 5.7, Equation 5.8 can be derived. 

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The law of mass action has been successfully applied to many drug dose-response relationships since the early work of Clark. The systematic relation between the dose of a drug and the magnitude of its response is based on three assumptions (1) response is proportional to the level of receptor occupancy (occupancy theory), (2) one drug molecule combines with one receptor site, and (3) a negligible fraction of total drug is combined with the receptors. These assumptions must also apply to Beidler s equation. 

The biological or functional response to receptor activation can be assumed to be directly proportional to the number of receptors (R) occupied by a given ligand (L) at equilibrium. This assumption is termed the occupancy theory of drug response. The equation describing this phenomenon was proposed as ... 

Biological response to drug binding, OCCUPANCY THEORY OF DRUG ACTION... 

OCCUPANCY THEORY OF DRUG ACTION OCTAHEDRAL COORDINATION OCTANOL DEHYDROGENASE trans-OCTAPRENYLTRANSTRANSFERASE OCTOPINE DEHYDROGENASE D-Octopine synthase,... 

The classical occupation theory of Clark rests on the assumption that drugs interact with independent binding sites and activate them, resulting in a biological response that is proportional to the amount of drug-receptor complex formed. The response ceases when this complex dissociates. Assuming a bimolecular reaction, one can write... 

To accommodate some or all of these phenomena, several alternatives to the occupation theory have been proposed. None of them is entirely satisfactory, and some have no physicochemical basis. 

In contrast to the assumption made in the classical occupation theory, the agonist in the two-state model does not activate the receptor but shifts the equilibrium toward the R form. This explains why the number of occupied receptors does not equal the number of activated receptors. 

Therefore, based on Clark s occupancy theory, EC50 equals KD. Both occur at the point of inflection of a response versus log [ligand] plot (Figure 5.19). 

Clark s simple version of occupancy theory to explain partial agonists, has led researchers to expand and improve the model of occupancy theory.26... 

In the 1950s, Ariens27 and Stephenson28 independently developed modifications to extend Clark s occupancy theory. Ariens introduced the concept of intrinsic activity, denoted by the variable e (Equation 5.13). 

Intrinsic efficacy is the efficacy, or activity, per unit receptor. By including the idea of intrinsic efficacy, Stephenson explained how tissues with the same concentrations of a receptor can give rise to different dose-response graphs. The full results of Stephenson s contributions to occupancy theory are summarized in Equation 5.18.26... 

At the start of this section, we derived Equation 5.8 to model dose-response relationships. This equation is elegantly simple and essentially identical to the Michaelis-Menten equation from our studies on enzymes. Receptors, however, are more diverse and more complicated than enzymes. Clark s straightforward equation models few receptors accurately, and Stephenson s equation (5.18) has emerged as the best available description of occupancy theory. While Stephenson s additions may result in a more accurate model, the simplicity of Clark s original theory remains attractive. Many receptor studies still rely on Clark s model and work around its deficiencies as best as possible. 

While occupancy theory is far and away the most widely used model for describing dose-response curves, other theories do exist. One example is allosteric theory. At the center of allosteric theory, sometimes called the two-state model, is the idea that a receptor can exist in conformations that either cause a response (relaxed state) or do not cause a response (tensed state).29 These conformations, represented by T and R, are in equilibrium (Scheme 5.7). 

Another alternative to occupancy theory is rate theory. Rate theory was developed by Paton through examination of receptors that bind stimulants.30 Paton proposed that a response is caused by the act of binding, not the state of being bound or free (Scheme 5.8). This seemingly subtle difference shifts the theory away from KD and toward kon and fcoff, the rate constants of association and dissociation. Interestingly, at equilibrium, KD is equal to koa/kon (Equations 5.19-5.21). For this reason, occupancy and rate theory are closely related. 

The pioneering work of Clark (1), Aliens (2), Stephenson (3), and Fuchgott (4) provided a foundation for modem drug discovery based on the concepts embodied in classic occupation theory as presented in Equation 1 ... 

Simple mathematical calculations by the first pharmacologists in the 1930s indicated that structurally specific drugs exert their action in very small doses and do not act on all molecules of the body but only on certain ones, those that constitute the drug receptors. For example, Clark [407] calculated that ouabain applied to the cells of the heart ventricle, isolated from the toad, would cover only 2.5% of the cellular surface. These observations prompted Clark [407,408] to apply the mathematical approaches used in enzyme kinetics to the effects of chemicals on tissues, and this formed the basis of the occupancy theory for drug-receptor interaction. Thus, pharmacological receptor models preceded accurate knowledge of receptors by many years. 

According to the occupancy theory, which has evolved chronologically from the original work of Clark [407,408], the drug effect is a function of two processes ... 

Time is not an independent variable in the presented models. Dynamic behavior is either a consequence of the pharmacokinetics or the observed lag time by means of the effect compartment. Dynamic models from the occupancy theory and described by differential equations, such as (10.4), are scarce [428,429]. 

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