Identification of metabolic system parameters using global optimization methods

Background: The problem of estimating the parameters of dynamic models of complex biological systems from time series data is becoming increasingly important. Methods and results: Particular consideration is given to metabolic systems that are formulated as Generalized Mass Action (GMA) models. The estimation problem is posed as a global optimization task, for which novel techniques can be applied to determine the best set of parameter values given the measured responses of the biological system. The challenge is that this task is nonconvex. Nonetheless, deterministic optimization techniques can be used to find a global solution that best reconciles the model parameters and measurements. Specifically, the paper employs branch-and-bound principles to identify the best set of model parameters from observed time course data and illustrates this method with an existing model of the fermentation pathway in Saccharomyces cerevisiae. This is a relatively simple yet representative system with five dependent states and a total of 19 unknown parameters of which the values are to be determined. Conclusion: The efficacy of the branch-and-reduce algorithm is illustrated by the S. cerevisiae example. The method described in this paper is likely to be widely applicable in the dynamic modeling of metabolic networks.