Abstract
The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (arameter stimation in a on-mensionalized -system with onstraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.Electronic supplementary materialThe online version of this article (doi:10.1007/s11538-014-9960-8) contains supplementary material, which is available to authorized users.
Highlights
Comprehensive methods using high-throughput analytical instruments have made it possible to simultaneously measure cellular metabolite concentrations (Fiehn 2002; Sawada et al 2009; Weckwerth 2003)
Some important metabolites may be undetectable by simultaneous analytical methods used in metabolomics, so that the mathematical model constructed on the basis of available experimental data may lack essential information
The agreement between the calculated results and time-series data is not perfect but satisfactory. This indicates that the solutions to the S-system equations can depict time-transient behaviors analogous to the time-series data, even when arbitrary constant values are used for the kinetic orders, implying that the behavior of the metabolite concentrations is strongly governed by the network structure of a metabolic reaction system
Summary
Comprehensive methods using high-throughput analytical instruments have made it possible to simultaneously measure cellular metabolite concentrations (or their relative quantities referenced by peak intensities or heights) (Fiehn 2002; Sawada et al 2009; Weckwerth 2003) Using these measured values to construct a mathematical model would enable us to carry out the in silico simulation of metabolic behaviors in various conditions. The simplification of mathematical modeling using power-law representations, such as saturable and synergistic (S)-system or generalized mass action (GMA)-system representations in the framework of biochemical systems theory (BST) (Savageau 1969a,b, 1970; Shiraishi and Savageau 1992; Voit 2013), probably has the potential to overcome the above problems This is because such modeling techniques allow us to straightforwardly formulate the mathematical equations that describe the timetransient behaviors of metabolite concentrations in a metabolic reaction network by means of only a metabolic pathway map comprised enzymatic reactions and regulatory relationships. Kinetic orders are fixed at a value of 0.5 or −0.5, and the remaining rate constants are estimated by fitting calculated values to measured metabolite concentrations
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