Mathematical Modelling of Enzymatic Reactions , Simulation and Parameter Estimation

MATHEMATICAL MODELLING OF ENZYMATIC REACTIONS, SIMULATION AND PARAMETER ESTIMATION Süreyya Özöğür M.Sc., Department of Scientific Computing Supervisor: Prof. Dr. Bülent Karasözen January 2005, 75 pages A deep and analytical understanding of the human metabolism grabbed attention of scientists from biology, medicine and pharmacy. Mathematical models of metabolic pathways offer several advances for this deep and analytical understanding due to their incompensable potential in predicting metabolic processes and anticipating appropriate interventions when required. This thesis concerns mathematical modelling analysis and simulation of metabolic pathways. These pathways include intracellular and extracellular compounds such as enzymes, metabolites, nucleotides and cofactors. Experimental data and available knowledge on metabolic pathways are used in constituting a mathematical model. The models are either in the form of nonlinear ordinary differential equations (ODE’s) or differential algebraic equations (DAE’s). These equations are composed of kinetic parameters such as kinetic rate constants, initial rates and concentrations of metabolites. The nonlinear nature of enzymatic reactions and large number of parameters cause trouble in efficient simulation of those iii reactions. Metabolic engineering tries to simplify these equations by reducing the number of parameters. In this work, an enzymatic system which includes Creatine Kinase, Hexokinase and Glucose 6-Phosphate Dehydrogenase (CKHK-G6PDH) is modelled in the form of DAE’s, solved numerically and the system parameters are estimated. The numerical results are compared with the results from an existing work 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 genetic algorithm (GA) for parameter estimation provides much more clear results to the experimental values of the metabolite, especially, with NADPH.