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The current model for the tricarboxylic acid cycle in Dictyostelium discoideum is based on extensive experimental studies of enzyme kinetics in vitro and of metabolite fluxes measured in vivo. In the previous papers (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22912-22918; 22919-22925; 22926-22933; 22934-22943) of this series we have carried out extensive analyses of the current model within the framework of biochemical systems theory with a view toward understanding the behavior of the integrated system. The model was found to be ill determined with respect to at least three of its features. In this paper we propose a minimal modification in the model that is consistent with previous experimental data but also includes recycling of amino acids for protein synthesis, one of the neglected features identified as important in the previous analysis. We again perform an analysis within the framework of biochemical systems theory to determine the systemic consequences of this change. The results show that the robustness of the modified model, as determined by the parameter sensitivities, is improved by 2 orders of magnitude over that of the previous model. Analysis of the dynamics shows that the turnover times for the pools of alanine, glutamate, and aspartate are reduced by 2 orders of magnitude and made more physiologically realistic. The distribution of flux is no longer rigidly fixed, and problems previously centered on the metabolism of pyruvate have been partially alleviated. Continued discrepancies lead us to question the degree to which kinetic data obtained with purified enzymes in vitro faithfully reflect the kinetic behavior of the integrated enzyme system in vivo. We must continue to re-examine the manner in which the kinetics of reactions in vivo are represented and to reassess the physical conditions that prevail in vitro and in vivo. Results in this paper direct our attention toward specific aspects of the system where these efforts should be focused. Thus, a minimal modification of the previous model has led to several improvements that make it more representative of the tricarboxylic acid cycle in D. discoideum, and the analysis in this paper leads to further predictions for improving the model.

When kinetic models of complex biochemical systems are reconstructed from knowledge of the component reactions that have been characterized in vitro, or when values must be assumed for some of the parameters, errors are invariably encountered, and, as a consequence, the resulting model is frequently internally inconsistent. The simplest and most basic manifestations of such logical inconsistency are the failure of the model to exhibit a steady state or to yield a steady state that is in agreement with the actual steady state of the integrated system, or to yield a steady state that is dynamically stable. Models that are consistent may nonetheless be lacking in robustness, which is manifested as a pathological sensitivity to small changes in the values of their parameters. In this paper, we examine the current model of the tricarboxylic acid cycle in Dictyostelium discoideum (see Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22912-22918) with regard to these basic indicators of model quality. This may be viewed as a preliminary analysis; the object is to determine whether or not the model is reasonable and worthy of a more refined analysis and, if not, to diagnose the areas in need of modification before further analysis is undertaken. The results demonstrate that the current model of the tricarboxylic acid cycle is self-consistent and possesses a steady state that is in agreement with experimental evidence. However, the results also suggest that this model is not very robust. The high sensitivities of parameters influencing pyruvate metabolism indicate that the experimental characterization of these reactions might be fruitfully re-examined. These high sensitivities lead us to predict that this model of the tricarboxylic acid cycle should be accurate only over a very narrow range in variation of the independent variables. This is verified by the results presented in the following paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22926-22933).

The examination of model robustness in the previous paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22919-22925 led to the suggestion that the current model for the tricarboxylic acid cycle in Dictyostelium discoideum is ill-determined with respect to one or more of the features reflecting pyruvate metabolism. This conclusion is further supported here by results of steady state and dynamic analyses. The tricarboxylic acid cycle, according to the current model, is poised on a knife's edge with its behavior rigidly determined; any alteration of the system's components leads to nonviable behavior, as exemplified by explosive accumulation of pyruvate and loss of steady state in response to a minute change in the level of malate dehydrogenase. With the additional results in this paper, we are able to refine the diagnosis of the problem and suggest three different areas of the current model that might profitably be re-examined by experiment. These include the kinetics of the reactions at the malate branch point, the turnover times for the alanine, glutamate, and aspartate pools in vivo, and the dynamic mass balances for the cofactor NAD. We also suggest a minimal modification in the current model that could alleviate or circumvent some of these problems.

Enzyme systems within living cells have recently been shown to be highly ordered structures that violate classic assumptions of the Michaelis-Menten formalism, which originally was developed for the characterization of isolated reactions in vitro. This evidence suggests that a thorough examination of alternative kinetic formalisms for integrated biochemical systems is in order. The purpose of this series of papers is to assess the utility of an alternative power-law formalism by carrying out a detailed comparative analysis of a relatively large, representative system--the tricarboxylic acid cycle of Dictyostelium discoideum. This system was chosen because considerable experimental information already has been synthesized into a detailed kinetic model of the intact system. In this first paper, we set the stage for subsequent analysis within the framework of the power-law formalism: we review the underlying theory, emphasizing recent developments, formulate the model in terms that are convenient for the analysis to follow, and develop the system representation in both the Michaelis-Menten and power-law forms. In the second paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22919-22925), these alternative representations are shown to be internally consistent and locally equivalent. The third paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22926-22933) provides a complete analysis of the steady state behavior and also treats the dynamic behavior of the model.