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

Influence of experimental errors on the determination of flux control coefficients from transient metabolic concentrations

The influence of experimental errors on the determination of flux control coefficients from transient metabolite concentrations with the method proposed by Delgado and Liao [(1992) Biochem. J. 282, 919-927] has been investigated by using Monte Carlo simulations. The method requires least-squares fitting of the transient metabolite concentrations. Three different fitting methods have been evaluated. Simulated metabolite concentrations of a fictive metabolic pathway were scattered randomly, emulating experimental errors, before performing the fits. This was repeated a large number of times; the mean values and standard deviations of the resulting control coefficients are reported. The results show that the proposed method for determining control coefficients is too sensitive to experimental errors to be practicable, with theoretically justified fitting methods. This is in particular due to the high degree of correlation between the concentrations. An alternative ad hoc fitting method produced biased mean values of the estimates of the control coefficients, but with remarkably low standard deviations

A general formalism for metabolic control analysis

A general formalism for Metabolic Control Analysis is derived using general sensitivity analysis and structural information of the metabolic pathway inherent in the stoichiometry matrix. The equations derived provide a general procedure for calculating the control coefficients from the elasticity coefficients using matrix algebra, and is valid for any pathway stoichiometry. The procedure diminishes the risk of deriving erroneous relations and is, due to its generality, well suited for computer handling. The formalism is mathematically stringent and is a complement to the original theorems of Metabolic Control Analysis, which were derived using ad hoc reasoning. (C) 1997 Elsevier Science Ltd

MIST - A user-friendly metabolic simulator

The Metabolic Interactive Simulation Tool, MIST, is a software package, running under Microsoft Windows 3.1, which can be used for dynamic simulations, stoichiometric calculations and control analysis of metabolic pathways. The pathways can be of any complexity and are defined by the user in a simple, interactive way. The user-defined enzymatic rate equations can be compiled either by an external or an internal compiler. Simulations of pathways compiled by an external compiler run significantly faster, but since these compilers are commercial software, they are not distributed together with MIST. The simulations are performed by numerical integration of a set of ordinary differential equations. The integration can be done by either an explicit fourth-order Runge-Kutta algorithm or a semiimplicit third-order Runge-Kutta algorithm, both with adjustable step size. The second algorithm can be used if the set of differential equations is stiff Vector-based drawing facilities are included in the program, with which results can be presented in graphs. Results of simulations, including graphics, can be stored in files. MIST is a very user-friendly, flexible and yet powerful program, with the mathematical details regarding models, simulations and calculations hidden from the user. This makes it suitable for scientists and students with limited computer experience

Optimization of a blueprint for in vitro glycolysis by metabolic real-time analysis

Recruiting complex metabolic reaction networks for chemical synthesis has attracted considerable attention but frequently requires optimization of network composition and dynamics to reach sufficient productivity. As a design framework to predict optimal levels for all enzymes in the network is currently not available, state-of-the-art pathway optimization relies on high-throughput phenotype screening. We present here the development and application of a new in vitro real-time analysis method for the comprehensive investigation and rational programming of enzyme networks for synthetic tasks. We used this first to rationally and rapidly derive an optimal blueprint for the production of the fine chemical building block dihydroxyacetone phosphate (DHAP) via Escherichia coli’s highly evolved glycolysis. Second, the method guided the three-step genetic implementation of the blueprint, yielding a synthetic operon with the predicted 2.5-fold–increased glycolytic flux toward DHAP. The new analytical setup drastically accelerates rational optimization of synthetic multienzyme networks.