The metabolic productivity of the cell factory

It is widely accepted that some performance function has been optimized during the evolution of metabolic pathways. One can study the nature of such a function by analogy with the industrial manufacturing world, in which there have been efforts over recent decades to optimize production chains, and in which it is now accepted that fluxes are not the only important system variables that determine process efficiency, because inventory turnover must also be considered. Inspired by the parallels between living cells and manufacturing factories, we propose that fluxes and transit time may have simultaneously been major targets of natural selection in the optimization of the design, structure and kinetic parameters of metabolic pathways. Accordingly we define the ratio of flux to transit time as a performance index of productivity in metabolic systems: it measures the efficiency with which stocks are administered, and facilitates comparison of a pathway in different steady states or in different tissues or organisms. For a linear chain of two enzymes, at a fixed total equilibrium constant, we have analysed the variation of flux, transit time and productivity index as functions of the equilibrium constants of the two steps. The results show that only the productivity index has a maximum, which represents a good compromise in optimizing flux and transit time. We have extended control analysis to the productivity index and derived the summation theorem that applies to it. For linear chains of different length with maximum productivity index values, the distribution of control coefficients with regard to the three parameters has a characteristic profile independent of the length of the chain. Finally, this control profile changes when other variables are optimized, and we compare the theoretical results with the control profile of the first steps of glycolysis in rat liver.