Estimation of kinetic parameters in an S-system equation model for a metabolic reaction system using the Newton–Raphson method

• The performance of Newton–Raphson method is elucidated for parameter estimation.
• Decoupled S-system equations are used for parameter estimation.
• The method converges rapidly and gives very accurate values.
• The method can estimate parameters from time-series data with noise.

Metabolic reaction systems can be modeled easily in terms of S-system type equations if their metabolic maps are available. This study therefore proposes a method for estimating parameters in decoupled S-system equations on the basis of the Newton–Raphson method and elucidates the performance of this estimation method. Parameter estimation from the time-course data of metabolite concentrations reveals that the parameters estimated are highly accurate, indicating that the estimation algorithm has been constructed correctly. The number of iterations is small and the calculation converges in a very short time (usually less than 1 s). The method is also applied to time course data with noise and found to estimate parameters efficiently. Results indicate that the present method has the potential to be extended to a method for estimating parameters in large-scale metabolic reaction systems.