Heinrich R., Stephani A.
Humboldt-University Berlin, Theoretical Biophysics Invalidenstrasse 42, D-10115 Berlin, Germany, E-mail: reinhart=heinrich@rz.hu-berlin.de
It is theoretically analyzed whether the structural design of cellular energy metabolism, in particular the design of glycolysis, may be explained by evolutionary optimization principles. Using kinetic and thermodynamic principles conclusions are derived concerning the stoichiometry of these pathways in states of high ATP production rate. In extensions to previous investigations [1] 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 with an external ATPase. A great variety of pathways is studied which differ in the number and the 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. The following results of the optimization are obtained: (i) The ATP production rate always increases if the ATP producing reactions are shifted as far as possible towards the end of system I; (ii) the optimal location of the ATP consuming reactions depend on the characteristic times of the participating reactions; (iii) some optimal stoichiometries show a close correspondance to contemporary standard glycolysis, that is, ATP consumption takes place in the upper part of the chain (hexokinase and phosphofructokinase) and ATP production in the lower part of the chain (phosphoglyceratekinase and pyruvatekinase); (iv) the optimal stoichiometry is characterized by a significant selective advantage; (v) the standard free energy profile of the pathway with an optimal stoichiometry differs significantly from the free energy profiles of nonoptimized pathways, vi) Genetic Algorithms are an efficient tool for the determination of the optimal reaction sequences, vii) flux control in optimized pathway differs significantly from that in nonoptimized pathways (for details see [2]).
  1. R. Heinrich, F. Montero, E. Klipp, T. G. Waddell, and E. MelŠ¹ndez - Hevia (1997) Theoretical Approaches to the Evolutionary Optimization of Glycolysis; Thermodynamic and Kinetic Constraints, Eur. J. Biochem., 243, 191-201.
  2. A. Stephani and R. Heinrich (1998) Kinetic and Thermodynamic Principles Determining the Structural Design of ATP Producing Systems, Bull Math.Biol., in press