تجزیه و تحلیل حساسیت برای کاهش مدل های سوخت و ساز پیچیده

Two different model reduction strategies are studied in order to test their applicability to reduce complex metabolism models. Using a model of one pre-identified model set describing complex metabolic dynamics after glucose pulse stimulation, a model reduction method based on the parameter tuning importance is compared with a pca based approach. Up to 49 of 122 parameters are rejected without significant changes of the simulated trajectories and of the flux distribution. Applying the reduction procedure to 12 other dynamic models reveals a general model structure inconsistency within the description of the pentose phosphate pathway. That points out the need of additional experiments to reproduce metabolite courses especially of this metabolic pathway. Thus the sensitivity based model reduction procedure is qualified as a promising tool for the model structure check and can be very useful for the entire model validation process which also includes the critical analysis of the data sets underlying the models.

The well known, widely-used procaryote Escherichia coli K12 possesses approximately 4800 genes encoding 2500 proteins [1]. Several hundreds or even thousands of them are expressed and active at the same time sharing a pool of a comparable number of metabolites, co-factors, nucleotides, etc. Despite this complexity, numerous approaches have been studied up to now to quantitatively describe the cellular metabolism. Stoichiometric models based on flux balance analysis [2], metabolic flux analysis using intensive labelling information [3] or structured metabolism models considering in vitro derived enzyme kinetics [4] are only some of the examples that aim at covering metabolism complexity by modelling. These approaches have in common that they do not use information about in vivo enzyme kinetics although the knowledge about kinetic and thermodynamic properties of all macromolecules in living cells would offer the possibilities of a modern metabolic engineering [5]. In their pioneering work Rizzi et al. [6] aimed at identifying in vivo enzyme kinetic data for Saccharomyces cerevisiae by performing glucose pulse experiments. Cells which were cultivated under glucose-limited conditions, were stimulated by a glucose pulse which caused a sudden increase of cellular glucose uptake. As a result, intracellular metabolite pools changed significantly which was monitored during a few minutes time-window by rapid cell sampling combined with immediate metabolism inactivation. Because a series of rapid samples was taken, courses of intracellular metabolite changes were observed which were the basis for the subsequent model identification considering 22 metabolite balances and 99 parameters describing yeast's central metabolism. In the following, similar experiments were performed using E. coli [7] and Zymomonas mobilis [8]. However, potential pitfalls of the procedure become obvious when the model identifiability and resulting model accuracies are taken into account. The underlying data sets consist of intracellular metabolite concentrations which are only accessible with sophisticated analytical approaches (for instance using LC–MS/MS) considering a significant number of sample preparation steps [9]. As a consequence, dynamically changing metabolite levels of an `average' cell (neglecting any cell distributions in the population) are given which can possess significant measurement errors. To build up the structured metabolism model, well-known enzyme databases like (BRENDA [10], ExPASy [11], etc.) are typically used which have the intrinsic problem that their information is usually derived from in vitro enzyme kinetic experiments. The application of these `in vitro' approaches for the modelling of in vivo enzyme kinetics turned out to be complicated. Lacking or contradicting enzyme information together with limited experimental possibilities caused the formulation of competing enzyme kinetic equations which need to be identified and qualified within the model identification process. Furthermore, it should be considered that the experimental data sets may not be optimal with respect to the identifiability of all parameters in the complex ODE system [12]. Model reduction thus represents an important step to eliminate redundant parameters and to uncover the most important control mechanisms of the metabolism models. Following this aim, the contribution focusses on the presentation of alternative, classical model reduction approaches which were used to analyze complex metabolism models. Starting basis for the model reduction study are 13 metabolism models. They were selected due to their good fitting quality from in total approximately 200 different models which were formulated recently [13] for the description of the metabolism dynamics in E. coli K12 after a glucose pulse [14]. For the sake of clarity, the main reduction results for the selected set of models are summarized briefly whereas the different statistical methods are compared in more detail on the basis of one model. In the following, parameter sensitivity analysis will be based on the criterium of tuning importance as well as on principal component analysis (pca). It will be shown that both approaches lead to comparable results which means that model predictions are still very similar to the original, non-reduced model and the model itself is mechanistically correct. Hence, using the pca approach, the opportunity for an automatic model reduction is given.

The analysis of the two different model reduction approaches showed that both procedures basically discard the same parameters. However, the pca approach offers the opportunity to be used as a self-controlled routine, meaning that this procedure can be repeated automatically until a predefined upper-limit of the error-functional ζ is achieved. Using the parameter tuning importance, no unique criterium could be identified because even parameters with small parameter tuning importance caused significant model prediction discrepancies. Therefore, this procedure must be performed step-by-step critically studying each model reduction result. The model reduction procedure based on the two methods enabled to identify severe redundancies and structure problems in the models used. The structure problems in turn indicated the need of additional experiments to reproduce the trajectories of distinct metabolites within the pentose phosphate pathway. This shows the powerfulness of the sensitivity analysis for the validation of mechanistic models in an iterative cycle between data analysis, model building and experimental design.