Pharmacodynamic Models of Indirect Effects and Irreversible Inactivation with Turnover: Applicability to Mechanism-Based Modeling of Gene Silencing and Targeted Protein Degradation

Indirect response (IDR) and turnover with inactivation (TI) comprise two arrays of mechanism-based pharmacodynamic (PD) models widely used to describe delayed drug effects. IDR Model-IV (stimulation of response loss) and TI (irreversible loss) have been described with discerning "signature" profiles; classical IDR-IV response-time profiles display slow declines where peak response shifts later with increasing dose, whereas TI profiles feature steep response declines with earlier-shifting nadirs. Herein, we demonstrate mathematical convergence of IDR-IV and TI models upon implementation with identical linear versus nonlinear pharmacologic effect terms. Time of peak response in IDR-IV can in fact shift earlier or later depending on PK or PD parameters (e.g., kel, Smax) and effect type. A generalized dynamic model linking mRNA and protein turnover is proposed. Applicability of IDR-IV and TI, with either linear or nonlinear terms acting on degradation/catabolism/loss of response, is demonstrated through model-fitting PK-PD effects of three proteolysis-targeting chimeras (PROTACs) and two ligand-conjugated small interfering RNAs (siRNA). This work clarifies mathematical properties, convergence, and expected responses of IDR-IV and TI, demonstrates their applicability for targeted gene-silencing and protein-degrading agents, and illustrates how well-designed in vivo studies covering broad dose ranges with richly sampled time-points can influence PK-PD model structure and parameter resolution.