PENDISC: A Simple Method for Constructing a Mathematical Model from Time-Series Data of Metabolite Concentrations

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.

PASMet: a web-based platform for prediction, modelling and analyses of metabolic systems

“…The data for five metabolites in the glycolysis pathway are included: glucose (Glc), glucose 6-phosphate (G6P), fructose bisphosphate (FBP), lactate (Lac) and acetate (Ace). To test the Construction function, a simple but stiff model of the aspartate-family amino acid biosynthesis pathway in Arabidopsis thaliana ( 23 ) (aspartate model) was prepared. The 21-point time-series data of metabolite concentrations in this biosynthesis pathway encompass seven metabolites: aspartate-4-phosphate (A4P, x 1 ), aspartate-semialdehyde (ASA, x 2 ), lysine (LYS, x 3 ), homoserine (HS, x 4 ), O -phospho-homoserine (OPH, x 5 ), threonine (THR, x 6 ) and isoleucine (ILE, x 7 ).…”

“…In addition to time-series data, Construction also needs information on the metabolic pathway and its regulation to symbolically build mathematical formulations. Although the Construction is applicable to estimate parameters of kinetic equations such as Michaelis–Menten kinetics, its performance is predominant for equations which contain a small number of parameters such as the S-system equations on the basis of BST, especially, simplified equations using the PENDISC method ( 23 ). Although there is no input limits on the number of parameters to be estimated, it is recommended to decrease the number of parameters as much as possible.…”

Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data

“…Numerous approaches to estimate parameter values using S-system formulation together with time series data of metabolic concentrations have been proposed. This includes alternative regression (Chou, 2006 ), automated procedure (Marino and Eberhard, 2006 ), Newton flow (Kutalik et al, 2007 ), automated smoother for decoupling (Vilela et al, 2007 ), neutral (Vilela et al, 2009 ), two-phase dynamic (Jia et al, 2011 ), estimation of dynamic flux profiles (Chou and Voit, 2012 ), Newton-Raphson (Iwata et al, 2014 ), and PENDISC method (Sriyudthsak et al, 2014a ). In addition, approximate estimation methods for large-scale analysis include coarse (Iwata et al, 2013 ) and U-system (Sriyudthsak et al, 2014b ) approaches, which were proposed for predicting coarse metabolic parameters, including those of unmeasurable metabolites.…”

Improved Representation of Biological Information by Using Correlation as Distance Function for Heatmap Cluster Analysis

“…To better understand the complexity of living organisms, the omic sciences such as genomics [1], transcriptomics [2] [3], proteomics [4], metabolomics [5] [6] [7], and phenomics [8] are continuously developing new technologies that generate a large amount of digital data from nucleic acids, proteins, and metabolites. Bioinformatic [9], chemometric [10], cell fractionation [11], and biostatistical methods [12] are optimized in parallel, to automatize data mining, so that biological meaningful conclusions can be drawn from the vast amounts of numbers and letters. Raw data from the omic experiments need to be analysed and converted into figures, models, and other visual representations to be shared among the scientific community.…”