Optimal selection of metabolic fluxes for in vivo measurement. II. Application to Escherichia coli and hybridoma cell metabolism.

A method of analysis was presented in part I of this series for determining the fluxes in a biochemical network that are the optimal choices for experimental measurement. This algorithm is applied to two important biological models: Escherichia coli and a hybridoma cell line (167.4G5.3). Our results show that potentially poor choices for in vivo measurement of metabolic fluxes exist for both model systems. For the subset of reactions in E. coli that was studied, the condition number of the augmented stoichiometric matrix reveals that a 60-fold amplification of experimental error during computations is possible. The biochemical network of the hybridoma cell is more complex than the E. coli system, and thus results in much larger possible error amplification--up to 100,000-fold. The physiological situations appear to have sensitivities that are less than 1/4 to 1/10 of those estimated by the condition number, and the maximum sensitivities are proportional to the condition number. These maximum sensitivities calculated using estimates of the fluxes and the worst possible error vector are upper bounds on the system's actual sensitivity. By examining the effect of measurement error on the sensitivity, the most probable sensitivity is calculated. These results indicate that an approximate two-fold increase in sensitivity of the E. coli system is likely when the worst set of fluxes are measured rather than the best set. The most likely sensitivity of the hybridoma system can range three orders of magnitude, depending on the set of fluxes that are measured. The propagation of experimental error during computations can be diminished for both systems by increasing the number of flux measurements over and above the minimum number of experimental measurements. The findings from these two model systems indicate that the calculation of the condition number can be a useful method for efficient experimental design, and that the usefulness of this method increases as the order of the system increases.