Reversible metabolism of vitamin K-vitamin K epoxide: modeling considerations and limitations

Understanding the pharmacokinetics of reversible metabolism

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.

Ethnic differences in the population pharmacokinetics and pharmacodynamics of warfarin

Ethnic differences in warfarin maintenance doses have been documented amongst the three major Asian ethnic groups (Chinese, Malay and Indian) in Singapore. Studies have shown that cytochrome P450 2C9 (CYP2C9) polymorphisms alone did not entirely account for these differences. Recent reports suggest that VKORC1 (subunit of vitamin K epoxide reductase) haplotypes are more predictive of warfarin response. Population pharmacokinetic/pharmacodynamic (PK/PD) modelling techniques were employed to characterise the PK and PD of warfarin in a healthy volunteer study of 16 Chinese and Indian subjects following a single 25 mg dose of warfarin. To further investigate the underlying differences in warfarin response, a semi-mechanistic modelling approach (using an indirect response model for PCA activity) incorporating the vitamin K cycle was attempted using population methods with Bayesian inference. All eight Indian subjects had H7H7 VKORC1 haplotypes and three had either *2/wt or *3/wt CYP2C9 genotypes. Six Chinese subjects had H1H1 VKORC1 haplotypes and one had H1H7. All Chinese subjects were homozygous wt/wt for CYP2C9. Simulations to steady state were performed to examine warfarin response in subjects with different CYP2C9 and VKORC1 polymorphisms. The presence of a single *2 or *3 CYP2C9 allele reduced mean [SE (standard error)] S-warfarin clearance by 35% from 0.276 (0.04) to 0.180 (0.11) l/h. Subjects with VKORC1 haplotype groups of H7H7 had increased mean (SE) C (50,S) (concentration of S-warfarin required to achieve 50% of maximum effect) of 479 (7.3) compared to 206 (6.7) ng/ml in subjects with the H1H1 groups. For subjects with the H1H7 haplotype, mean (SE) C (50,S) increased 1.4 times to 288 (1.3) ng/ml compared to subjects with H1H1 haplotypes. Steady state simulations showed that whilst CYP2C9 polymorphisms affect the PK of warfarin, VKORC1 haplotypes may be better predictors of warfarin response. Since 90% of Chinese subjects had the VKORC1 H1 haplotype and 100% of Indian subjects the H7 haplotype in this study, ethnic differences in warfarin response in this study appear to be linked to differences in VKORC1 haplotypes.