Pharmacodynamic modeling of time‐dependent transduction systems

The past decade has seen a marked expansion of the development and application of mechanism-based pharmacokinetic/pharmacodynamic (PK/PD) models for quantitating the time course of drug responses. A general conceptual scheme that depicts the major processes controlling drug effects is depicted in Fig 1.1 The potential for drug distribution into a biophase as a rate-limiting step controlling some effects was pointed out by Furchgott2 and Segre,3 and the application of a linking compartment in pharmacodynamics was popularized by Sheiner et al.4 The biosensor process represents the mechanism of action of the drug whereby either receptor binding or turnover of endogenous mediators may be altered. The former can be quantitated with an array of equations reflecting reversible binding of agonist or antagonist to receptors,5 whereas the latter may require use of indirect response models.6,7 Some mechanisms involve irreversible inactivation of cells or enzymes such as those used for chemotherapeutic agents8 or drugs such as aspirin9 or omeprazole.10 Bound receptors or endogenous mediators often activate additional biochemical or physiologic steps with such transduction processes leading to the observed response.11 Further, there may occur diverse counterregulation, depletion, or tolerance mechanisms that can modify the observed response.12 A highly mechanistic characterization of pharmacologic responses in relation to dose, time, and other factors requires direct measurement of the diverse steps controlling the action of the drug. This may be feasible with invasive animal studies such as our receptor and gene-mediated models for corticosteroids13; however, the modeling of clinical drug responses has severe limitations. Most typically it is desirable and often feasible to capture a capacity constant such as the maximum induced response (Emax), a sensitivity constant such as the equilibrium dissociation constant (KD) or related biophase concentration (EC50), the Hill coefficient (γ) if necessary, and perhaps a time constant (τ) that may reflect a major rate-limiting step causing a delay in responses separate from the pharmacokinetics of the drug. Either the rate constant for biophase distribution (keo) or the constant for loss of the response variable in indirect response models (kout) is thus the fourth parameter often generally sought where relevant from clinical data. General expectations in quantitating pharmacodynamic data are that the model applied will be as mechanistically relevant as possible, it will capture the major rate-limiting step or steps in control of drug responses, and it will reflect as many doses, routes, or regimens as possible to allow maximal interpretive and predictive capability. The purpose of this report is to point out the need and feasibility of considering transduction processes and a simplified nonlinear transduction model as the third major class of PK/PD models for characterizing various drug responses with time delays.