Kristel Bernaerts | Search PubMed

PubMed2002

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

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.

Azospirillum brasilense↗

PubMed2002

Optimal temperature input design for estimation of the square root model parameters: parameter accuracy and model validity restrictions.

As part of the model building process, parameter estimation is of great importance in view of accurate prediction making. Confidence limits on the predicted model output are largely determined by the parameter estimation accuracy that is reflected by its parameter estimation covariance matrix. In view of the accurate estimation of the Square Root model parameters, Bernaerts et al. have successfully applied the techniques of optimal experiment design for parameter estimation [Int. J. Food Microbiol. 54 (1-2) (2000) 27]. Simulation-based results have proved that dynamic (i.e., time-varying) temperature conditions characterised by a large abrupt temperature increase yield highly informative cell density data enabling precise estimation of the Square Root model parameters. In this study, it is shown by bioreactor experiments with detailed and precise sampling that extreme temperature shifts disturb the exponential growth of Escherichia coli K12. A too large shift results in an intermediate lag phase. Because common growth models lack the ability to model this intermediate lag phase, temperature conditions should be designed such that exponential growth persist even though the temperature may be changing. The current publication presents (i) the design of an optimal temperature input guaranteeing model validity yet yielding accurate Square Root model parameters, and (ii) the experimental implementation of the optimal input in a computer-controlled bioreactor. Starting values for the experiment design are generated by a traditional two-step procedure based on static experiments. Opposed to the single step temperature profile, the novel temperature input comprises a sequence of smaller temperature increments. The structural development of the temperature input is extensively explained. High quality data of E. coli K12 under optimally varying temperature conditions realised in a computer-controlled bioreactor yield accurate estimates for the Square Root model parameters. The latter is illustrated by means of the individual confidence intervals and the joint confidence region.

Bioreactors↗