Kybernetika 57 no. 6, 1005-1018, 2021

Biochemical network of drug-induced enzyme production: Parameter estimation based on the periodic dosing response measurement

Volodymyr Lynnyk, Štěpán Papáček and Branislav RehákDOI: 10.14736/kyb-2021-6-1005

Abstract:

The well-known bottleneck of systems pharmacology, i. e., systems biology applied to pharmacology, refers to the model parameters determination from experimentally measured datasets. This paper represents the development of our earlier studies devoted to inverse (ill-posed) problems of model parameters identification. The key feature of this research is the introduction of control (or periodic forcing by an input signal being a drug intake) of the nonlinear model of drug-induced enzyme production in the form of a system of ordinary differential equations. First, we tested the model features under periodic dosing, and subsequently, we provided an innovative method for a parameter estimation based on the periodic dosing response measurement. A numerical example approved the satisfactory behavior of the proposed algorithm.

Keywords:

parameter estimation, dynamical system, systems pharmacology, biochemical network, input-output regulation, fast Fourier transform

Classification:

92C45, 34A34, 65F60, 65K10

References:

  1. H. A. Barton, W. A. Chiu, R. W. Setzer, M. E. Andersen, A. J. Bailer, F. Y. Bois, R. S. DeWoskin, S. Hays, G. Johanson, N. Jones, G. Loizou, R. C. MacPhail, C. J. Portier, M. Spendiff and Y.-M. Tan: Characterizing uncertainty and variability in physiologically based pharmacokinetic models: State of the science and needs for research and implementation. Toxicolog. Sci. 99 (2007), 2, 395-402.   CrossRef
  2. F. Y. Bois: Applications of population approaches in toxicology. Toxicology Letters 120 (2001), 1-3, 385-394.   DOI:10.1016/S0378-4274(01)00270-3
  3. A. Cintrón-Arias, H. T. Banks, A. Capaldi and A. L. Lloyd: A sensitivity matrix based methodology for inverse problem formulation. J. Inverse and Ill-posed Problems 17 (2009), 6.   CrossRef
  4. H. Clewell and M. Andersen: Risk assessment extrapolations and physiological modeling. Toxicology and Industr. Health 1 (1985), 111-–131.   CrossRef
  5. H. J. Clewell, P. R. Gentry, T. R. Covington, R. Sarangapani and J. G. Teeguarden: Evaluation of the potential impact of age- and gender-specific pharmacokinetic differences on tissue dosimetry. Toxicolog. Sci. 79 (2004), 2, :381-393.   DOI:10.1590/S1678-31662004000300006
  6. R. Clewell, M. Andersen and H. Barton: A consistent approach for the application of pharmacokinetic modeling in cancer and noncancer risk assessment. Environmental Health Perspectives 110 (2002), 85–-93.   DOI:10.1289/ehp.0211085
  7. J. Duintjer Tebbens, C. Matonoha, A. Matthios and Š. Papáček: On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy. Appl. Math. 64 (2019), 2, 253-277.   CrossRef
  8. A. Galetin, H. Burt, L. Gibbons and J. B. Houston: Prediction of time-dependent CYP3A4 drug-drug interactions: impact of enzyme degradation, parallel elimination pathways, and intestinal inhibition. Drug Metabolism and Disposition 34 (2005), 1, 166-175.   DOI:10.1124/dmd.105.006874
  9. D. S. Gerhard Michal: Biochemical Pathways: An Atlas of Biochemistry and Molecular Biology. Second edition. Wiley, 2012.   CrossRef
  10. L. E. Gerlowski and R. K. Jain: Physiologically based pharmacokinetic modeling: Principles and applications. J. Pharmaceut. Sci. 72 (1983), 10, 1103-1127.   DOI:10.1002/jps.2600721003
  11. J. Huang: Nonlinear output regulation: theory and applications. Advances in design and control. Society for Industrial and Applied Mathematics, Philadelphia, 2004.   CrossRef
  12. G. Jia, G. Stephanopoulos and R. Gunawan: Incremental parameter estimation of kinetic metabolic network models. BMC Systems Biology 6 (2012), 142, 1799–-1819.   DOI:10.1007/s11538-010-9508-5
  13. K. Krishnan: Characterization and Application of Physiologically Based Pharmacokinetic Models in Risk Assessment. Technical Report, World Health Organization, 2010.   CrossRef
  14. N. S. Luke, M. J. DeVito, I. Shah and H. A. El-Masri: Development of a quantitative model of pregnane X receptor (PXR) mediated xenobiotic metabolizing enzyme induction. Bull. Math. Biol. 72 (2010), 7, 1799–-1819.   CrossRef
  15. MATLAB: Simulink Toolbox. Simulation and Model-Based Design. The MathWorks Inc., Natick 2020.   CrossRef
  16. Š. Papáček, S. Čelikovský, B. Rehák and D. Štys: Experimental design for parameter estimation of two time-scale model of photosynthesis and photoinhibition in microalgae. Math. Computers Simul. 80 (2010), 6, 1302-1309.   DOI:10.1016/j.matcom.2009.06.033
  17. Š. Papáček, V. Lynnyk and B. Rehák: Regulatory network of drug-induced enzyme production: parameter estimation based on the periodic dosing response measurement. In: Programs and Algorithms of Numerical Mathematics 20, Institute of Mathematics, Czech Academy of Sciences, 2021.   CrossRef
  18. B. Rehák: Alternative method of solution of the regulator equation: L2-space approach. Asian J. Control 14 (2011), 4, 1150-1154.   DOI:10.1002/asjc.416
  19. B. Rehák and S. Čelikovský: Numerical method for the solution of the regulator equation with application to nonlinear tracking. Automatica 44 (2008), 5, 1358-1365.   DOI:10.1016/j.automatica.2007.10.015
  20. B. Rehák, S. Čelikovský and Š. Papáček: Model for photosynthesis and photoinhibition: Parameter identification based on the harmonic irradiation $O_{2}$ response measurement. IEEE Trans. Automat. Control 53 (Special Issue) (2008), 101-108.   DOI:10.1080/04597220801912762
  21. B. Rehák, S. Čelikovský, J. Ruiz-León and J. Orozco-Mora: A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem. Kybernetika 45 (2009), 427-444.   CrossRef
  22. A. Rostami-Hodjegan and G. Tucker: `In silico' simulations to assess the `in vivo' consequences of `in vitro' metabolic drug{\textendash}drug interactions. Drug Discovery Today: Technologies 1 (2004), 4, 441-448.   DOI:10.1016/j.ddtec.2004.10.002
  23. M. Rowland, C. Peck and G. Tucker: Physiologically-based pharmacokinetics in drug development and regulatory science. Ann. Rev. Pharmacology and Toxicology 51 (2011), 1, 45-73.   DOI:10.1146/annurev-pharmtox-010510-100540
  24. N. Sakamoto and B. Rehák: Iterative methods to compute center and center-stable manifolds with application to the optimal output regulation problem. In: IEEE Conference on Decision and Control and European Control Conference, 2011.   CrossRef
  25. L. Svecova, R. Vrzal, L. Burysek, E. Anzenbacherova, L. Cerveny, J. Grim, F. Trejtnar, J. Kunes, M. Pour, F. Staud, P. Anzenbacher, Z. Dvorak and P. Pavek: Azole antimycotics differentially affect rifampicin-induced pregnane X receptor-mediated CYP3A4 gene expression. Drug Metabolism and Disposition 36 (2007), 2, 339-348.   DOI:10.1124/dmd.107.018341
  26. P. Zhao, M. Rowland and S.-M. Huang: Best practice in the use of physiologically based pharmacokinetic modeling and simulation to address clinical pharmacology regulatory questions. Clinical Pharmacology and Therapeutics 92 (2012), 17-–20.   DOI:10.1038/clpt.2012.68