Dynamical Modeling of Enzymatic Reactions, Simulation and Parameter Estimation with Genetic Algorithm
Ozogur S., Celep A. Gulcin, Karasozen, B., Yıldırım, N., and Weber, G.
Proceedings of International Symposium on Health and Bioinformatics, November, 2005
A deep and analytical understanding of the human metabo-lism grabbed attention of scientists from biology, medicine and pharmacy. Mathematical models of metabolic pathways offer several advances for this deep and analytical under-standing due to their incompensable potential in predicting metabolic processes and anticipating appropriate interven-tions when required. This study concerns mathematical modelling analysis and simulation of metabolic pathways. These pathways include intracellular and extracellular com-pounds such as enzymes, metabolites, nucleotides and co-factors. Experimental data and available knowledge on metabolic pathways are used in constituting a mathematical model. The models are either in the form of nonlinear ordi-nary differential equations (ODE's) or differential algebraic equations (DAE's). These equations are composed of kinetic parameters such as kinetic rate constants and initial concen-trations of metabolites. The nonlinear nature of enzymatic reactions and large number of parameters cause trouble in efficient and predictive simulation of those reactions. Meta-bolic engineering tries to simplify these equations by reduc-ing the number of parameters. In this work, an enzymatic system which includes Creatine Kinase, Hexokinase and Glucose 6-Phosphate Dehydrogenase (CK-HK-G6PDH) is modelled in the form of DAE's, solved numerically and the system parameters are estimated. The numerical results are compared with the published in vitro experimental data in literature. We demonstrate that our solution method based on direct solution of the CK-HK-G6PDH system significantly differs from simplified solutions. We also show that a ge-netic algorithm (GA) for parameter estimation provides much more clear results to the experimental values of the metabolite, especially, with NADPH in terms of conver-gence.