Indirect pharmacodynamic models for responses with circadian removal

Rhythmicity in baseline responses over a 24-h period for an indirect pharmacological effect R(t) can arise from either a periodic time-dependent input rate k _in (t) or a periodic time-dependent loss constant k _out (t). If either k _in (t) or k _out (t) follows some nonstationary biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. Indirect response models assuming time-dependent input rates [ k _in (t) ] have been utilized to capture drug effects on various physiological responses such as hormone suppression, immune cell trafficking, and gene expression in tissues. This paradigm was extended to consider responses with circadian-controlled loss [ k _out (t) ] mechanisms. Theoretical equations describing this model are presented and simulations were performed to examine expected response behaviors. The model was able to capture the chronobiology and pharmacodynamics of applicable drug responses, including the uricosuric effects of lesinurad in humans, suppression of the beta amyloid (Aβ) peptide by a gamma-secretase inhibitor in mouse brain, and the modulation of extracellular dopamine by a dopamine transporter inhibitor in rat brain. This type of model has a mechanistic basis and shows utility for capturing drug responses displaying nonstationary baselines controlled by removal mechanism(s).