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Abstract:
Introduction
The determination of in vivo enzyme kinetic parameters from Stimulus-Response-Experiments has shown to be limited to only a small number of parameters. Even if the data from several experiments is gathered, it is not possible to identify all (mechanistic) model parameters [1, 3]. In case of stationary metabolic flux analysis, the use of 13C labeling has proven to increase the information content significantly [4]. Metabolic steady state experiments at instationary labeling are currently evaluated and will further refine the resolution of the flux distribution. Thus, a metabolic and isotopic stimulus should increase the accuracy of kinetic parameter estimation. A simulation study is used to examine the information contained in the labeling transients for the enzyme kinetic parameter identification.
Model Structure and Simulation
Accepting the common assumptions, especially homogeneity of the intracellular metabolites, the dynamic state of a metabolic network is described by the concentrations c, the kinetic rate equations v with the parameters a and solving the differential equation dc/dt=Nv(a,c). The labeling state of the metabolites is described by their isotopomer distributions x, that depend on the network fluxes and the given input substrates ainp: dx/dt = F inp c,c together the network concentrations and labeling states can be characterized by the isotopomer concentrations (xc).
A simple cyclic reaction network is used to estimate the information gain by using 13C labeled substrates. Different scenarios regarding the availability and precision of measurements (assuming LC-MS/MS) as well as different input substrate mixtures are studied. All simulations are carried out using the software MMT2 [2]. The scenarios are compared by statistical measures like the parameter covariance and the D criterium.
Conclusions
Using 13C labeled substrates and intracellular measurements of the transient labeling state, it is possible to significantly increase the accuracy of the kinetic parameter estimation. Interestingly, also the correlations of the parameters strongly decrease. When only measuring the concentrations, an observed concentration increase can be explained by an increased influx or a decreased efflux. Adding the isotopic transients to the concentration courses give clues on the pool exchanges. With the labeling transients the pool exchange can be identified more directly as the labeling increase depends on the labeling influx. Thus, the labeling measurements deliver further important constraints.
Comparing the experiment with labeled substrate to its reference counterpart without labeling shows a six fold increase in parameter estimation accuracy. In particular, the mean standard deviations are drastically decreased. Missing concentration measurements seem to be tolerable as long as the mass isotopomer distributions can be measured. Looking at the mean standard deviations of the parameters, only a loss of 10% in accuracy is observed.
The results obtained from the example network should be transferable to real size metabolic networks. In the case of isotopically instationary experiments under metabolic steady-state conditions a similar example network was used to estimate the information gain and the conclusions drawn have shown to be valid also for realistic networks.
References
[1] Degenring, D., Frömel, C., Dikta, G., and Takors., R. (2004). Sensitivity analysis for the reduction of complex metabolism models. J Proc Contr, 14(7):729-745.
[2] Haunschild, M. D., Wahl, S. A., von Lieres, E., Qeli, E., Freisleben, B., Takors, R., and Wiechert, W. (2004). MMT 2: supporting the modeling process for rapid sampling experiments. In Liao, J., editor, Metabolic Engineering V, Lake Tahoe, California, September 2004.
[3] Wahl, S., Haunschild, M., Oldiges, M., and Wiechert, W. (accepted). Unraveling the regulatory structure of biochemical networks using stimulus response experiments and large scale model selection. IEE Proc Syst Biol.
[4] Wiechert, W. (2001). C-13 metabolic flux analysis. Met Eng, 3(3):195-206.
