TRANSIT COMPARTMENTS VERSUS GAMMA-DISTRIBUTION FUNCTION TO MODEL SIGNAL-TRANSDUCTION PROCESSES IN PHARMACODYNAMICS

Delayed effects for pharmacodynamic responses can be observed for many signal transduction processes. Three approaches are summarized in thi s report to describe such effects caused by cascading steps: stochasti c process model, gamma distribution function, and transit compartment model. The gamma distribution function, a probability density function of the waiting time for the final step in a stochastic process model, is a function of time with two variables: number of compartments N, a nd the expected number of compartments occurring per unit time k. The parameter k is equal to 1/tau, where tau is the mean transit time in t he stochastic process model. Effects of Nand k on the gamma distributi on function were examined. The transit compartment model can link the pharmacokinetic profile of the tested compound, receptor occupancy, an d cascade steps for the signal transduction process. Time delays are d escribed by numbers of steps, the mean transit time tau, and the ampli fication or suppression of the process as characterized by a power coe fficient gamma. The effects of N, tau, and gamma on signal transductio n profiles are shown. The gamma distribution function can be utilized to estimate Nand k values when the final response profile is available , but it is less flexible than transit compartments when dose-response relationships, receptor dynamics, and efficiency of the transduction process are of concern. The transit compartment model is useful in pha rmacokinetic/pharmacodynamic modeling to describe precursor/product re lationships in signal transduction process.