Regular ArticleMetabolic Pathway Characterization from Transient Response Data Obtained In Situ: Parameter Estimation in S-system Models
Abstract
The actual values of internal metabolites and fluxes can be measured by a number of experimental techniques and they provide important information for evaluating the properties of a metabolic pathway in situ. In this paper we propose a strategy to properly exploit this information. The suggested approach permits estimation of a set of parameters on the whole system so that a useful model can be constructed and used to describe its components and systemic properties and to predict its behavior under new conditions. A simulated reference pathway is provided to validate this method and to show its utility in metabolic studies.
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Kinetic modeling of batch fermentation for mixed-sugar to ethanol production
2010, Journal of the Taiwan Institute of Chemical EngineersWe analyze the growth dynamics of Saccharomyces diastaticus LORRE 316 utilizing mixed-sugar to produce ethanol and glycerol, using three alternative modeling frameworks, namely S-system, lin-log model and Monod's model. The S-system and lin-log model have identical steady-state solutions, but differ in their representation of transients. The global/local optimization method was applied to determine optimal parameter values for each model. Hybrid differential evolution with data collocation was first applied to determine a satisfied solution. Such a global search phase could avoid yielding a premature estimate and alleviate computational burden. The optimal estimate obtained from the global search phase was then served as the initial starting point for a local optimization method to obtain the refined solution. From experimental observation, the dynamical prediction using the S-system is more acceptable than those of the lin-log model and Monod's model.
Unraveling the functional interaction structure of a biomolecular network through alternate perturbation of initial conditions
2007, Journal of Biochemical and Biophysical MethodsVarious approaches attempting to infer the functional interaction structure of a hidden biomolecular network from experimental time-series measurements have been developed; however, due to both experimental limitations and methodological complexities, a large majority of these approaches have been unsuccessful. In particular, with respect to the elucidation of such networks, there are (i) a dimensionality problem: too many network nodes with too few available sampling points, (ii) a computational complexity problem: exponential complexity if a priori information is unavailable for regulatory nodes, and (iii) an experimental measurement problem: no guidelines for an appropriate experimental design for distinguishing direct and indirect influences among network nodes. Here, we sought to develop a new methodology capable of identifying the correct functional interaction structure with only a few sampling points through relatively simple computations. We also attempted to provide guidelines for an experimental design capable of supporting this methodology by taking proper measurements of the direct influences among the network nodes.
In the present study, we considered an experiment where measurements were taken at two sampling time points with alternate perturbation (up-regulation or down-regulation) of initial conditions while keeping the same initial conditions for unperturbed network nodes, and propose a new method of identifying the functional interaction structure from such measurements. The proposed method is able to avoid the dimensionality problem caused by the practically limited number of sampling time points, and does not suffer from the computational complexity problem, as it only uses a simple algebra based on the Mean Value Theorem (see Supplementary mathematical descriptions) without any other complicated computation. In addition, we provide a detailed guideline for an experimental design that can take proper measurements of the direct influences among the network nodes through perturbation of initial conditions. The proposed method is particularly useful for cases investigating the local interaction structure around a specific network node of interest. An example, based on simulated data, is provided to illustrate the proposed method.
Power-law modeling based on least-squares criteria: Consequences for system analysis and simulation
2000, Mathematical BiosciencesThe power-law formalism was initially derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The resulting models, either as generalized mass action (GMA) or as S-systems models, allow to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. This approach has been succesfully used as a modeling tool in many applications from cell metabolism to population dynamics. Without leaving the general formalism, we recently proposed to derive the power-law representation in an alternative way that uses least-squares (LS) minimization instead of the traditional derivation based on Taylor series [B. Hernández-Bermejo, V. Fairén, A. Sorribas, Math. Biosci. 161 (1999) 83–94]. It was shown that the resulting LS power-law mimics the target rate-law in a wider range of concentration values than the classical power-law, and that the prediction of the steady-state using the LS power-law is closer to the actual steady-state of the target system. However, many implications of this alternative approach remained to be established. We explore some of them in the present work. Firstly, we extend the definition of the LS power-law within a given operating interval in such a way that no preferred operating point is selected. Besides providing an alternative to the classical Taylor power-law, that can be considered a particular case when the operating interval is reduced to a single point, the LS power-law so defined is consistent with the results that can be obtained by fitting experimental data points. Secondly, we show that the LS approach leads to a system description, either as an S-system or a GMA model, in which the systemic properties (such as the steady-state prediction or the log-gains) appear averaged over the corresponding interval when compared with the properties that can be computed from Taylor-derived models in different operating points within the considered operating range. Finally, we also show that the LS description leads to a global, accurate description of the system when it is submitted to external forcing.
Modeling metabolic dynamics. From cellular processes to organ and whole body responses
1998, Progress in Biophysics and Molecular BiologyApplication of biochemical systems theory to metabolism in human red blood cells: Signal propagation and accuracy of representation
1996, Journal of Biological ChemistryHuman erythrocytes are among the simplest of cells. Many of their enzymes have been characterized kinetically using steady-state methods in vitro, and several investigators have assembled this kinetic information into mathematical models of the integrated system. However, despite its relative simplicity, the integrated behavior of erythrocyte metabolism is still complex and not well understood. Errors will inevitably be encountered in any such model because of this complexity; thus, the construction of an integrative model must be considered an iterative process of assessment and refinement. In a previous study, we selected a recent model of erythrocyte metabolism as our starting point and took it through three stages of model assessment and refinement using systematic strategies provided by biochemical systems theory. At each stage deficiencies were diagnosed, putative remedies were identified, and modifications consistent with existing experimental evidence were incorporated into the working model. In this paper we address two issues: the propagation of biochemical signals within the metabolic network, and the accuracy of kinetic representation. The analysis of signal propagation reveals the importance of glutathione peroxidase, transaldolase, and the concentration of total glutathione in determining systemic behavior. It also reveals a highly amplified diversion of flux between the pathways of pentose phosphate and nucleotide metabolism. In determining the range of accurate representation based on alternative kinetic formalisms we discovered large discrepancies. These were identified with the behavior of the model represented within the Michaelis-Menten formalism. This model fails to exhibit a nominal steady state when the activity of glutathione peroxidase is decreased by as little as 9%. Our current understanding, as embodied in this working model, is in need of further refinement, and the results presented in this paper suggest areas of the model where such effort might profitably be concentrated.
Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: Model validation and dynamic behavior
1995, Mathematical BiosciencesIn the first two papers of this series (immediately preceding, this issue), we characterized the steady-state properties of a model of a fermentation pathway in Saccharomyces cerevisiae in four experimental conditions. In each of these conditions, the pictures obtained by metabolic control analysis and biochemical systems theory were coincident, which illustrates the relatedness of the two approaches. In this paper we analyze the quality of this description by means of the tools available within biochemical systems theory, and we show that in some of the experimental conditions studied the system is poorly characterized. The most critical condition corresponds to the immobilization of the cells at pH 5.5, in which the kinetic characterization appears to be inaccurate. Furthermore, sensitivity analysis and the study of the local steady-state stability identify the most critical parameters. The results of these analyses are confirmed by the predictions of the dynamic response of the model using its S-system representation. This illustrates the utility of these tools and warns against using the steady-state characterization without testing its validity.