Using dynamic sensitivities to characterize metabolic reaction systems

Metabolite concentrations in cells are governed by enzyme kinetics in the metabolic reaction system. One can analyze how these concentrations depend on system variables such as enzyme activities by computing system sensitivities, which generally vary with time. Dynamic sensitivities, i.e., time-varying sensitivities, reflect the time-dependent response of the metabolic reaction network to perturbations. Unfortunately, dynamic sensitivity profiles are not commonly used in the analysis of metabolic reaction systems. In the present study, we demonstrate the use of dynamic logarithmic gains, i.e., normalized time-varying sensitivities, to gain insights into the dynamic behavior of metabolic networks. A biosynthetic reaction model of aromatic amino acids proposed by other researchers is used as a case study. The model system is analyzed using the dynamic logarithmic gains in parallel with simulations of the time-transient behavior of metabolite concentrations and metabolic fluxes. The result indicates that the influences of independent variables are most pronounced just after perturbations and the effects of perturbations on metabolite concentration at early times can be larger than those at steady state. These findings suggest that it is important to perform dynamic sensitivity analysis in addition to steady-state analysis. Furthermore, the rankings of the bottleneck ranking indicators, defined as the product of dynamic logarithmic gain and metabolite concentration, for three desired amino acids reveal that the degree of bottleneck for each enzyme changes with time. In conclusion, the dynamic logarithmic gains are not only useful for analyzing metabolic reaction systems but also can offer additional insights on the transient behavior of the system over steady state sensitivities, leading to a proper design of metabolic systems.ISSN:0025-5564ISSN:1879-313

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

Time-series data of metabolite concentrations for the simplified model of glycolysis in Lactococcus lactis.

<p>(a) Glucose concentration. (b) Glucose-6-phosphate concentration. (c) Fructose-1,6-bisphosphate concentration. (d) Lactate concentration. (e) Acetate concentration.</p

Comparison of metabolic reaction networks of the glycolysis pathway in Lactococcus lactis predicted by our approach and taken from KEGG.

<p>(a) illustrates the pathway predicted by our approach whereas (b) illustrates the pathway taken from KEGG and the red characters in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0051212#pone-0051212-g006" target="_blank">Figure 6B</a> indicate metabolites considered in our prediction model.</p

Proposed algorithm for metabolic reaction network identification.

<p>Proposed algorithm for metabolic reaction network identification.</p

First iteration values for rate constants and kinetic orders in the generic inhibition and activation model.

*<p>The significantly large kinetic orders are underlined.</p

Time-series data of metabolite concentrations for the generic inhibition and activation model.

<p>Time-series data of metabolite concentrations for the generic inhibition and activation model.</p

Probable metabolic reaction network of the glycolysis pathway in <i>Lactococcus lactis</i> predicted by Granger causality.

<p>Probable metabolic reaction network of the glycolysis pathway in <i>Lactococcus lactis</i> predicted by Granger causality.</p