Dynamic metabolic control theory. A methodology for investigating metabolic regulation using transient metabolic data

Optimization-based metabolic control analysis

In this work, a novel optimization-based metabolic control analysis (OMCA) method is introduced for reducing data requirement for metabolic control analysis (MCA). It is postulated that using the optimal control approach, the fluxes in a metabolic network are correlated to metabolite concentrations and enzyme activities as a state-feedback control system that is optimal with respect to a homeostasis objective. It is then shown that the optimal feedback gains are directly related to the elasticity coefficients (ECs) of MCA. This approach requires determination of the relative "importance" of metabolites and fluxes for the system, which is possible with significantly reduced experimental data, as compared with typical MCA requirements. The OMCA approach is applied to a top-down control model of glycolysis in hepatocytes. It is statistically demonstrated that the OMCA model is capable of predicting the ECs observed experimentally with few exceptions. Further, an OMCA-based model reconciliation study shows that the modification of four assumed stoichiometric coefficients in the model can explain most of the discrepancies, with the exception of elasticities with respect to the NADH/NAD ratio.

A method for estimation of elasticities in metabolic networks using steady state and dynamic metabolomics data and linlog kinetics

Background

Dynamic modeling of metabolic reaction networks under in vivo conditions is a crucial step in order to obtain a better understanding of the (dis)functioning of living cells. So far dynamic metabolic models generally have been based on mechanistic rate equations which often contain so many parameters that their identifiability from experimental data forms a serious problem. Recently, approximative rate equations, based on the linear logarithmic (linlog) format have been proposed as a suitable alternative with fewer parameters.

Results

In this paper we present a method for estimation of the kinetic model parameters, which are equal to the elasticities defined in Metabolic Control Analysis, from metabolite data obtained from dynamic as well as steady state perturbations, using the linlog kinetic format. Additionally, we address the question of parameter identifiability from dynamic perturbation data in the presence of noise. The method is illustrated using metabolite data generated with a dynamic model of the glycolytic pathway of Saccharomyces cerevisiae based on mechanistic rate equations. Elasticities are estimated from the generated data, which define the complete linlog kinetic model of the glycolysis. The effect of data noise on the accuracy of the estimated elasticities is presented. Finally, identifiable subset of parameters is determined using information on the standard deviations of the estimated elasticities through Monte Carlo (MC) simulations.

Conclusion

The parameter estimation within the linlog kinetic framework as presented here allows the determination of the elasticities directly from experimental data from typical dynamic and/or steady state experiments. These elasticities allow the reconstruction of the full kinetic model of Saccharomyces cerevisiae, and the determination of the control coefficients. MC simulations revealed that certain elasticities are potentially unidentifiable from dynamic data only. Addition of steady state perturbation of enzyme activities solved this problem.

Determination of elasticities, concentration and flux control coefficients from transient metabolite data using linlog kinetics

This paper presents a practical approach to estimate the kinetic parameters of a metabolic network from in vivo kinetics experiments. This method is based on the linlog kinetics format (Visser and Heijnen, 2003, Metab. Eng. 5(3), 164-176; Wu et al., 2004, Eur. J. Biochem. 271, 3348-3359), of which the kinetic parameters, called elasticities, are estimated by an iterative linear optimization followed by non-linear optimization, from transient metabolite concentration data which are directly obtainable from rapid pulse experiments. In this way, not only the parameters are estimated but also a full kinetic model, based on linlog kinetics, is developed. The obtained elasticities also allow immediate calculation of all control coefficients. As an in silico case study, the estimation of elasticities of a linear pathway is presented. The method is shown to be able to estimate the elasticities quite accurately and to be robust toward errors in the metabolite data originating from sampling and measurement inaccuracy. The method allows experimental redesign to get more accurate estimated parameters and accommodates various types of experimentally applied disturbances in the pathway: changes in independent metabolites, dependent metabolites or enzyme levels/activities.

Metabolic control in integrated biochemical systems

Traditional analyses of the control and regulation of steady-state concentrations and fluxes assume the activities of the enzymes to be constant. In living cells, a hierarchical control structure connects metabolic pathways to signal-transduction and gene-expression. Consequently, enzyme activities are not generally constant. This would seem to compromise analyses of control and regulation at the metabolic level. Here, we investigate the concept of metabolic quasi-steady state kinetics as a means of applying metabolic control analysis to hierarchical biochemical systems. We discuss four methods that enable the experimental determination of metabolic control coefficients, and demonstrate these by computer simulations. The best method requires extra measurement of enzyme activities, two others are simpler but are less accurate and one method is bound only to work under special conditions. Our results may assist in evaluating the relative importance of transcriptomics and metabolomics for functional genomics.