Robust detection and verification of linear relationships to generate metabolic networks using estimates of technical errors

Background  

The size and magnitude of the metabolome, the ratio between individual metabolites and the response of metabolic networks is controlled by multiple cellular factors. A tight control over metabolite ratios will be reflected by a linear relationship of pairs of metabolite due to the flexibility of metabolic pathways. Hence, unbiased detection and validation of linear metabolic variance can be interpreted in terms of biological control. For robust analyses, criteria for rejecting or accepting linearities need to be developed despite technical measurement errors. The entirety of all pair wise linear metabolic relationships then yields insights into the network of cellular regulation.     

A biologically inspired validity measure for comparison of clustering methods over metabolic data sets

In the biological domain, clustering is based on the assumption that genes or metabolites involved in a common biological process are coexpressed/coaccumulated under the control of the same regulatory network. Thus, a detailed inspection of the grouped patterns to verify their memberships to well-known metabolic pathways could be very useful for the evaluation of clusters from a biological perspective. The aim of this work is to propose a novel approach for the comparison of clustering methods over metabolic data sets, including prior biological knowledge about the relation among elements that constitute the clusters. A way of measuring the biological significance of clustering solutions is proposed. This is addressed from the perspective of the usefulness of the clusters to identify those patterns that change in coordination and belong to common pathways of metabolic regulation. The measure summarizes in a compact way the objective analysis of clustering methods, which respects coherence and clusters distribution. It also evaluates the biological internal connections of such clusters considering common pathways. The proposed measure was tested in two biological databases using three clustering methods.     

Chemical basis of metabolic network organization

Although the metabolic networks of the three domains of life consist of different constituents and metabolic pathways, they exhibit the same scale-free organization. This phenomenon has been hypothetically explained by preferential attachment principle that the new-recruited metabolites attach preferentially to those that are already well connected. However, since metabolites are usually small molecules and metabolic processes are basically chemical reactions, we speculate that the metabolic network organization may have a chemical basis. In this paper, chemoinformatic analyses on metabolic networks of Kyoto Encyclopedia of Genes and Genomes (KEGG), Escherichia coli and Saccharomyces cerevisiae were performed. It was found that there exist qualitative and quantitative correlations between network topology and chemical properties of metabolites. The metabolites with larger degrees of connectivity (hubs) are of relatively stronger polarity. This suggests that metabolic networks are chemically organized to a certain extent, which was further elucidated in terms of high concentrations required by metabolic hubs to drive a variety of reactions. This finding not only provides a chemical explanation to the preferential attachment principle for metabolic network expansion, but also has important implications for metabolic network design and metabolite concentration prediction.     

Identification of a Metabolic Reaction Network from Time-Series Data of Metabolite Concentrations

Recent development of high-throughput analytical techniques has made it possible to qualitatively identify a number of metabolites simultaneously. Correlation and multivariate analyses such as principal component analysis have been widely used to analyse those data and evaluate correlations among the metabolic profiles. However, these analyses cannot simultaneously carry out identification of metabolic reaction networks and prediction of dynamic behaviour of metabolites in the networks. The present study, therefore, proposes a new approach consisting of a combination of statistical technique and mathematical modelling approach to identify and predict a probable metabolic reaction network from time-series data of metabolite concentrations and simultaneously construct its mathematical model. Firstly, regression functions are fitted to experimental data by the locally estimated scatter plot smoothing method. Secondly, the fitted result is analysed by the bivariate Granger causality test to determine which metabolites cause the change in other metabolite concentrations and remove less related metabolites. Thirdly, S-system equations are formed by using the remaining metabolites within the framework of biochemical systems theory. Finally, parameters including rate constants and kinetic orders are estimated by the Levenberg–Marquardt algorithm. The estimation is iterated by setting insignificant kinetic orders at zero, i.e., removing insignificant metabolites. Consequently, a reaction network structure is identified and its mathematical model is obtained. Our approach is validated using a generic inhibition and activation model and its practical application is tested using a simplified model of the glycolysis of Lactococcus lactis MG1363, for which actual time-series data of metabolite concentrations are available. The results indicate the usefulness of our approach and suggest a probable pathway for the production of lactate and acetate. The results also indicate that the approach pinpoints a probable strong inhibition of lactate on the glycolysis pathway.