Transl Clin Pharmacol.  2019 Jun;27(2):52-58. 10.12793/tcp.2019.27.2.52.

Understanding the pharmacokinetics of reversible metabolism

• Cho S
• Yoon YR

• KMID: 2457571
• DOI: http://doi.org/10.12793/tcp.2019.27.2.52

Abstract

This tutorial introduces the mathematical skills required to obtain exact and approximate solutions for reversible reactions and provides graphical insights to help understand the pharmacokinetics of reversible metabolism. The matrix method provides an easy way to derive the exact solution for the amount of each species as a function of time. The plots of the exact solutions reveal some characteristic features of the pharmacokinetic profiles of the reversible metabolism. We also describe two approximation approaches, steady-state approximation, and equilibrium approximation, to simplify the solutions. The skills and knowledge acquired through this tutorial will provide a basis for understanding more complex reversible reaction systems.

Keyword

Equilibrium approximation; Matrix Method; Pharmacokinetics; Reversible Metabolism; Steady-state approximation

MeSH Terms

Metabolism*
Methods
Pharmacokinetics*

Figure

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  Figure 1 (a) Linear and (b) semi-logarithmic plots of the amount-time curves of A, B, or C in the reversible reaction, A k1⇄k2  B k3→ C, where k1 = 10, k2 = 0.1, and k3 = 1. The abscissa and ordinate denote the time and the amount of each species, respectively, in arbitrary unit. See text for details.

• 

  Figure 2 (a) Linear and (b) semi-logarithmic plots of the amount-time curves of A, B, or C in the reversible reaction, A k1⇄k2  B k3→ C, where k1 = 5, k2 = 4, and k3 = 2. The abscissa and ordinate denote time and the amount of each species, respectively, in arbitrary unit. See text for details.

• 

  Figure 3 (a) Linear and (b) semi-logarithmic plots of the amount-time curves of A, B, or C in the reversible reaction, A k1⇄k2  B k3→ C, where k1 = 1, k2 = 5, and k3 = 0.2. The abscissa and ordinate denote time and the amount of each species, respectively, in arbitrary unit. See text for details.

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  Figure 4 Linear plots of the amount-time curves of A, B, or C for the cases of (a) k1 = 0.1, k2 = 1, and k3 = 5, corresponding to the steady-state approximation, and (b) k1 = 10, k2 = 1, and k3 = 0.1, corresponding to the equilibrium approximation. The solid and dashed lines represent the exact and approximate solutions, respectively. The abscissa and ordinate denote time and the amount of each species, respectively, in arbitrary unit. See text for details.

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