Assessing the completeness of a QSP model for azathioprine metabolism

Introduction: A QSP model for azathioprine metabolism was developed from known mechanistic pathways and expert opinion. The model was intended to predict the concentrations of 6-thioguanine nucleotides (TGN) and 6-methyl mercaptopurine (MMP) under different clinical scenarios [1-3]. The model was able to predict 6-TGN and 6-MMP for typical individuals but it was unable to predict elevated concentrations of MMP and TGN as expected under atypical scenarios. The aim of this work was to assess model completeness by determining whether a set of parameter values exist that can support both typical and atypical data under the current model structure.

Methods:  An adaptive random (global) search algorithm was implemented to evaluate possible sets of parameter vectors. The Vmax and KM values for 44 enzymes and transporter activities were sampled from a left truncated normal distribution centered on values extracted from the literature and a σ= 1000 times the literature parameter value. The value of σ was adjusted during the search until σ =10-7. For atypical clinical outcomes the Vmax values of some of the enzymes were allowed to vary independently (to simulate enzyme polymorphisms) for different scenarios. The parameter vector that minimised the absolute value of relative difference of the model prediction from the observed data was kept as the best set. If no values of the parameter vector yielded simulation values within 10% of the observed then the model was considered to be structurally incomplete.

Results: The global search did not find a set of parameters that could predict both typical and atypical clinical scenarios. The best set parameter vector could not predict TGN concentrations associated with bone marrow toxicity.

Discussion: The results indicated that the model structure cannot predict data for all possible scenarios (normal and atypical). This suggests that the current knowledge of the pathways of the system is insufficient and therefore the current model is incomplete. Further work is required to find potential (as yet unrecognised) pathways contributing to the metabolic fate of azathioprine.

References:

  1. Derijks et al (2004) Pharmacokinetics of 6-mercaptopurine in patients with inflammatory bowel disease: Implications for therapy, Ther Drug Monit 26: 311-8.
  2. Goldenberg et al (2004) The utility of 6-thioguanine metabolite levels in managing patients with inflammatory bowel disease. Am J Gastroenterol 99: 1744-8.
  3. Sparrow et al (2005) Allopurinol safely and effectively optimizes tioguanine metabolites in inflammatory bowel disease patients not responding to azathioprine and mercaptopurine Aliment Pharmacol Ther 22: 441-6.