Graphic rule for drug metabolism systems.

Using graphic rules to deal with kinetic systems is an elegant approach by combining the graph representation (schematic representation) and rigorous mathematical derivation. It bears the following advantages: (1) providing an intuitive picture or illuminative insights; (2) helping grasp the key points from complicated details; (3) greatly simplifying many tedious, laborious, and error-prone calculations; and (4) able to double-check the final results. In this mini review, the non-steady state graphic rule in enzyme-catalyzed kinetics and protein-folding kinetics was extended to cover drug-metabolic systems. As a demonstration, a step-by-step illustration is presented showing how to use the graphic rule to derive the concentrations of the parent drug and its metabolites vs. time for the seliciclib, vildagliptin, and cyclin-dependent kinase inhibitor (AG-024322) metabolic systems, respectively. It can be seen from these paradigms that the graphic rule is particularly useful to analyze complicated drug metabolic systems and ensure the correctness of the derived results. Meanwhile, the intuitive feature of graphic representation may facilitate analyzing and classifying drug metabolic systems; e.g., according to their directed graphs, the metabolism of seliciclib and the metabolism of vildagliptin can be categorized as 0-->5 mechanism while that of AG-024322 as 0-->4-->3 mechanism.

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