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]).

- 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.
- A. Stephani and R. Heinrich (1998) Kinetic and Thermodynamic Principles Determining the Structural Design of ATP Producing Systems, Bull Math.Biol., in press