Kinetic Modeling

Kinetic models provide the most powerful method for understanding flux distributions under both steady-state and non–steady-state conditions, but they are totally dependent on the availability of accurate kinetic data for each enzymecatalyzed step in the network (Wiechert, 2002). The difficulty of assembling such information means that kinetic models are generally restricted to fragments of the metabolic network, for example, glycolysis in yeast (Pritchard and Kell, 2002; Teusink et al., 2000), and to date the only kinetic models that attempt to cover the complete network of a cell have been set up for the metabolically specialized red blood cell, with its greatly reduced metabolic network (Jamshidi et al., 2001; Mulquiney and Kuchel, 2003). Small-scale kinetic models are a more realistic target for the analysis of plant metabolism and, as documented elsewhere (Morgan and Rhodes, 2002), there has been sustained interest in the development of such models since the publication of an influential model of C₃ photosynthesis (Farquhar et al., 1980).

One application of such models in a metabolic engineering context is in rationalizing and understanding the behavior of transgenic plants with altered levels of particular enzymes. Kinetic models can be used to predict the flux control coefficients of individual enzymes, and these can be compared with the values obtained empirically. This approach can be illustrated by an analysis of the Calvin cycle that included starch synthesis, starch degradation, and triose phosphate export from the chloroplast to the cytosol (Poolman et al., 2000). The calculated flux control coefficients showed that the control distribution varied between fluxes—for example, the CO₂ assimilation flux was predicted to be largely determined by the activities of ribulose 1,5-bisphosphate carboxylase/oxygenase (Rubisco) and sedoheptulose-1,7-bisphosphatase (SBPase), and to be largely independent of the activity of the triose phosphate translocator—and it was concluded that the predictions were broadly consistent with the observations that have been made on transgenic plants. This conclusion provides some reassurance that the model is a reasonable, though still imperfect, representation of the experimental system, but the real value of the approach probably lies not so much in how close the fit can be, but in providing insights into the operation of the pathway. Thus, this modeling exercise highlighted the previously largely neglected role of SBPase in the assimilation process, and it reinforced the view that the manipulation of a single selected enzyme is unlikely to increase the assimilatory capacity of the pathway (Poolman et al., 2000).

This leads to the second major application for kinetic models in metabolic engineering, which is their use as predictive tools for generating hypotheses about flux limitation in a metabolic network and thus providing the basis for a rational engineering strategy. A good example of this approach can be found in an analysis of the synthesis of glycine betaine in transgenic tobacco expressing choline monooxygenase (McNeil et al., 2000a,b). In this work, the aim was to identify the constraints on the synthesis of glycine betaine as part of a program to engineer stress tolerance into tobacco through the production of an osmoprotectant. The first stage in the analysis was to establish which of three parallel, interconnected pathways were used for the synthesis of choline from ethanolamine in tobacco (McNeil et al., 2000a). This objective was achieved by incubating the system with ¹⁴C- and ³³P-labeled precursors and monitoring the time course for the redistribution of the label into the intermediates of choline synthesis. With a knowledge of the corresponding pool sizes, it was then possible to construct a flux model that described the labeling kinetics for each precursor and thus to deduce that the predominant pathway involved N-methylation of phosphoethanolamine (McNeil et al., 2000a). This led to the suggestion that overexpression of phosphoethanolamine N-methyltransferase would be a rational target for improving the endogenous choline supply for glycine betaine synthesis. Subsequently, further modeling of [¹⁴C]choline-labeling experiments revealed two more constraints— inadequate capacity for choline uptake into the chloroplast and excessive choline kinase activity—both of which work against the provision of substrate for choline monooxygenase. It was concluded that the failure of the engineered plants to accumulate significant levels of glycine betaine was due to multiple causes and that it would be necessary to address all of them to obtain a glycine betaine concentration comparable to that found in natural accumulators (McNeil et al., 2000b).

These examples demonstrate the utility of kinetic modeling as a procedure for probing relatively small metabolic networks. They also highlight the way in which the properties of the network conspire against simple engineering solutions, a conclusion that is consistent with the wealth of empirical data on flux control coefficients that has been accumulated in recent years and the theoretical predictions of metabolic control analysis (see next section).