The tricarboxylic acid cycle in Dictyostelium discoideum. IV. Resolution of discrepancies between alternative methods of analysis.

Experimental studies of enzyme kinetics in vitro and metabolic fluxes in vivo have been used by Wright and her colleagues to develop a detailed kinetic model of the tricarboxylic acid cycle in Dictyostelium discoideum. This model has recently been been analyzed by two different methods (Albe, K. R., and Wright, B. E. (1992) J. Biol. Chem. 267, 3106-3114; Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22926-22933 in an effort to determine the response of individual fluxes and metabolite concentrations to changes in levels of the enzymes that constitute the system. Individual responses were found to differ significantly in magnitude as well as in sign. Perhaps the most glaring difference concerns the influence of the enzyme succinate dehydrogenase on the flux through the cycle; in one study, it has the maximum influence, whereas, in the other, it has absolutely no influence. In this paper, we provide a resolution of these discrepancies. We have reconstructed the methodology of Albe and Wright and have been able to reproduce their results in detail. We show that their methodology does not yield a valid steady state analysis, and, consequently, that the conclusions drawn from their analysis must be called into question. First, they concluded that their model is realistic and predictive. It is now clear that their model is ill-determined and has a steady state only for unrealistically narrow conditions. Second, they concluded that their analysis is valid for variations of less than 2% in the levels of the enzymes because they could satisfy summation relationships considered to be mathematically inevitable. It is now clear that these relationships are neither necessary nor sufficient for establishing the validity of an analysis or the appropriateness of a biochemical model. Third, they concluded on the basis of their empirical methodology that certain enzymes are most important in influencing flux through the cycle. It is now clear that these results are inaccurate because of deficiencies in their methodology. Finally, they concluded that steady state analyses cannot be carried out experimentally because of the small variations required in enzyme levels. It is now clear that the requirement for such small variations reflects the ill-determined character of the underlying model and is not a necessary property of the real system.