Toward a Unified Model of Passive Drug Permeation II: The Physiochemical Determinants of Unbound Tissue Distribution with Applications to the Design of Hepatoselective Glucokinase Activators

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Abstract
In this work, we leverage a mathematical model of the underlying physiochemical properties of tissues and physicochemical properties of molecules to support the development of hepatoselective glucokinase activators. Passive distribution is modeled via a Fick-Nernst-Planck approach, using in vitro experimental data to estimate the permeability of both ionized and neutral species. The model accounts for pH and electrochemical potential across cellular membranes, ionization according to Henderson-Hasselbalch, passive permeation of the neutral species using Fick’s law, and passive permeation of the ionized species using the Nernst-Planck equation. The mathematical model of the physiochemical system allows derivation of a single set of parameters governing the distribution of drug molecules across multiple conditions both in vitro and in vivo. A case study using this approach in the development of hepatoselective glucokinase activators via organic anion-transporting polypeptide–mediated hepatic uptake and impaired passive distribution to the pancreas is described. The results for these molecules indicate the permeability penalty of the ionized form is offset by its relative abundance, leading to passive pancreatic exclusion according to the Nernst-Planck extension of Fickian passive permeation. Generally, this model serves as a useful construct for drug discovery scientists to understand subcellular exposure of acids or bases using specific physiochemical properties.

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