Economy of design in metabolic pathways: further remarks on the game of the pentose phosphate cycle.

Sugar rearrangement in the pentose phosphate cycle and other related pathways were previously analysed by abstraction to a mathematical game of optimization based on certain hypotheses concerning enzymatic mechanisms of living cells (Meléndez-Hevia & Isidoro, 1985, J. theor. Biol. 117, 251-263). The solution of that problem shows that the metabolic pathway, as occurs in cells, is the simplest solution of the operative problem. However, in that work, only the number of carbons in every sugar was considered. In the present paper, all structural features of the sugars and reaction mechanisms are taken into consideration, and the problem is again considered by abstraction to a mathematical model which includes all structural features of the sugars as well as all structural requirements of the enzymes in the hypotheses of the mechanisms. As in the above-mentioned paper, the hypothesis of simplicity is also imposed in order to achieve the objective (to convert six ribulose 5-phosphate into five glucose 6-phosphate) in the least number of steps (or with the least number of free intermediates), and the least number of carbons in the intermediates. It is concluded that the optimal, or simplest, solution of this problem is the same procedure as that occurring in living cells. The Calvin cycle in photosynthesis and the "L-type" of the pentose phosphate cycle are also analysed arriving at similar conclusions in both cases. These results suggest some reflections about the logic in the design of metabolic pathways, and the possible role of the hypothesis of simplicity in cell evolution.