A dispersion model for cellular signal transduction cascades

Purpose. The purpose of this study was to evaluate the ability of the dispersion model to describe pharmacokinetic-pharmacodynamic data containing contributions from signal transduction cascades. Methods. The partial differential equations and appropriate boundary conditions describing the dispersion model for signal transduction were obtained. Explicit analytical solutions to the dispersion equation were not available, and a numerical approach was necessary. Solutions were obtained by numerical inversion of the output Laplace transform. Generalized least square fitting was used to obtain parameter estimates for a variety of experimental data sets. Results. The parameters of the dispersion model estimate the relative roles of diffusion, convection, and chemical reaction in signal transduction. The model is capable of describing messenger RNA and protein expression kinetics induced by drug action. Conclusions. The dispersion model may find potential applications in pharmacokinetic-pharmacodynamic models involving delayed drug effects mediated by transcriptional changes.