Global optimization of the Michaelis–Menten parameters using physiologically-based pharmacokinetic (PBPK) modeling and chloroform vapor uptake data in F344 rats

Abstract

Objective: To quantify metabolism, a physiologically based pharmacokinetic (PBPK) model for a volatile compound can be calibrated with the closed chamber (i.e. vapor uptake) inhalation data. Here, we introduce global optimization as a novel component of the predictive process and use it to illustrate a procedure for metabolic parameter estimation.

Materials and methods: Male F344 rats were exposed in vapor uptake chambers to initial concentrations of 100, 500, 1000, and 3000 ppm chloroform. Chamber time-course data from these experiments, in combination with optimization using a chemical-specific PBPK model, were used to estimate Michaelis–Menten metabolic constants. Matlab^® simulation software was used to integrate the mass balance equations and to perform the global optimizations using MEIGO (MEtaheuristics for systems biology and bIoinformatics Global Optimization – Version 64 bit, R2016A), a toolbox written for Matlab®. The cost function used the chamber time-course data and least squares to minimize the difference between data and simulation values.

Results and discussion: The final values estimated for V_max (maximum metabolic rate) and K_m (affinity constant) were 1.2 mg/h and a range between 0.0005 and 0.6 mg/L, respectively. Also, cost function plots were used to analyze the dose-dependent capacity to estimate V_max and K_m within the experimental range used. Sensitivity analysis was used to assess identifiability for both parameters and show these kinetic data may not be sufficient to identify K_m.

Conclusion: In summary, this work should help toxicologists interested in optimization techniques understand the overall process employed when calibrating metabolic parameters in a PBPK model with inhalation data.

Keywords:

• Physiologically based pharmacokinetic (PBPK) model
• numerical optimization
• Michaelis–Menten equation
• chloroform
• optimization

Acknowledgments

The authors wish to thank Ms. Maribel Bruno for her thoughtful comments and edits. Mr. Williams reports support from Oak Ridge Institute for Science and Education (ORISE) during the conduct of the study. We also wish to thank our internal reviewers, Dr. Dustin Kapraun and Dr. Gregory Honda, and internal management for their thoughtful comments that have resulted in significant improvements to this manuscript. We would like to acknowledge the valuable contributions of Dr. Hui-Min Yang with the generation and collection of the vapor uptake and partition coefficient data. We are grateful to the MEIGO optimization research group in Vigo, Spain for allowing us to use their global optimization software (http://nautilus.iim.csic.es/∼gingproc/meigom.html).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

U.S. Environmental Protection Agency National Health and Environmental Health Effects Research Laboratory. The information in this document has been funded wholly by the U.S. Environmental Protection Agency. It has been subjected to review by the National Health and Environmental Effects Research Laboratory and approved for publication. Approval does not signify that the contents reflect the views of the Agency, nor does the mention of trade names or commercial products constitute endorsement or recommendation for use.