In vivo potency revisited - Keep the target in sight

Potency is a central parameter in pharmacological and biochemical sciences, as well as in drug discovery and development endeavors. It is however typically defined in terms only of ligand to target binding affinity also in in vivo experimentation, thus in a manner analogous to in in vitro studies. As in vivo potency is in fact a conglomerate of events involving ligand, target, and target-ligand complex processes, overlooking some of the fundamental differences between in vivo and in vitro may result in serious mispredictions of in vivo efficacious dose and exposure. The analysis presented in this paper compares potency measures derived from three model situations. Model A represents the closed in vitro system, defining target binding of a ligand when total target and ligand concentrations remain static and constant. Model B describes an open in vivo system with ligand input and clearance (Cl(L)), adding in parallel to the turnover (ksyn, kdeg) of the target. Model C further adds to the open in vivo system in Model B also the elimination of the target-ligand complex (ke(RL)) via a first-order process. We formulate corresponding equations of the equilibrium (steady-state) relationships between target and ligand, and complex and ligand for each of the three model systems and graphically illustrate the resulting simulations. These equilibrium relationships demonstrate the relative impact of target and target-ligand complex turnover, and are easier to interpret than the more commonly used ligand-, target- and complex concentration-time courses. A new potency expression, labeled L50, is then derived. L50 is the ligand concentration at half-maximal target and complex concentrations and is an amalgamation of target turnover, target-ligand binding and complex elimination parameters estimated from concentration-time data. L50 is then compared to the dissociation constant Kd (target-ligand binding affinity), the conventional Black & Leff potency estimate EC50, and the derived Michaelis-Menten parameter Km (target-ligand binding and complex removal) across a set of literature data. It is evident from a comparison between parameters derived from in vitro vs. in vivo experiments that L50 can be either numerically greater or smaller than the Kd (or Km) parameter, primarily depending on the ratio of kdeg-to-ke(RL). Contrasting the limit values of target R and target-ligand complex RL for ligand concentrations approaching infinity demonstrates that the outcome of the three models differs to a great extent. Based on the analysis we propose that a better understanding of in vivo pharmacological potency requires simultaneous assessment of the impact of its underlying determinants in the open system setting. We propose that L50 will be a useful parameter guiding predictions of the effective concentration range, for translational purposes, and assessment of in vivo target occupancy/suppression by ligand, since it also encompasses target turnover - in turn also subject to influence by pathophysiology and drug treatment. Different compounds may have similar binding affinity for a target in vitro (same Kd), but vastly different potencies in vivo. L50 points to what parameters need to be taken into account, and particularly that closed-system (in vitro) parameters should not be first choice when ranking compounds in vivo (open system).