Sensitivity function-based model reduction: A bacterial gene expression case study.

Abstract

Mathematical models used to predict the behavior of genetically modified organisms require 1). a (rather) large number of state variables, and 2). complicated kinetic expressions containing a large number of parameters. Since these models are hardly identifiable and of limited use in model-based optimization and control strategies, a generic methodology based on sensitivity function analysis is presented to reduce the model complexity at the level of the kinetics, while maintaining high prediction power. As a case study to illustrate the method and results obtained, the influence of the dissolved oxygen concentration on the cytN gene expression in the bacterium Azospirillum brasilense Sp7 is modeled. As a first modeling approach, available mechanistic knowledge is incorporated into a mass balance equation model with 3 states and 14 parameters. The large differences in order of magnitude of the model parameters identified on the available experimental data indicate 1). possible structural problems in the kinetic model and, associated with this, 2). a possibly too high number of model parameters. A careful sensitivity function analysis reveals that a reduced model with only seven parameters is almost as accurate as the original model.