Kinetic and thermodynamic principles determining the structural design of ATP-producing systems

It is theoretically analysed whether the structural design of ATP-producing pathways, in particular the design of glycolysis, may be explained by optimization principles. On the basis of kinetic and thermodynamic principles conclusions are derived concerning the stoichiometry of these pathways in states of high ATP production rates. One of the extensions to previous investigations is that the concentrations of the adenine nucleotides are taken into account as variable quantities. This necessitates the consideration of an interaction of the ATP-producing system I with an external ATP-consuming system II. A great variety of pathways is studied which differ in the number and location of ATP-consuming reactions, ATP-producing reactions and reactions involving inorganic phosphate. The corresponding number of possible pathways may be calculated in an explicit manner as a function of the number of those reactions which do not couple to ATP or inorganic phosphate. The kinetics of the individual reactions are described by linear or bilinear functions of reactant concentrations and all rate equations are expressed in terms of equilibrium constants and characteristic times. A thermodynamical analysis of the two coupled systems yields upper and lower limits for the concentration of ATP and an explicit expression for the maximal difference between the number of ATP-producing and ATP-consuming reactions of system I. The following results of the optimization are obtained. (i) The ATP production rate always increases if the ATP-producing reactions as well as those reactions characterized by an uptake of inorganic phosphate are shifted as far as possible towards the end of system I. (ii) Explicit conditions for the optimal location of the ATP-consuming reactions are presented. The results are discussed in the context of characteristic times as well as in terms of enzyme kinetic parameters. (iii) For two sets of characteristic times the resulting stoichiometries and their corresponding steady-state fluxes are investigated in detail. One of these stoichiometries shows a close correspondence to contemporary standard glycolysis. (iv) It is shown that most possible pathways result in a very low steady-state flux, that is, the optimal stoichiometry is characterized by a significant selective advantage. (v) The standard free energy profile of a pathway with an optimal stoichiometry is discussed. It differs significantly from the free energy profiles of nonoptimized pathways. (C) 1998 Society for Mathematical Biology.