The game of the pentose phosphate cycle: a mathematical approach to study the optimization in design of metabolic pathways during evolution.

The optimization of the pathway structure of the pentose phosphate cycle is studied by means of abstraction to a model designed as a mathematical game of combinatorial optimization. The objective of the game is to convert pentoses into hexoses, which is the aim of the non-oxidative phase of the metabolic cycle, and it includes two kinds of hypotheses: (a) the hypothesis of the mechanisms based on the enzyme mechanisms available to cells, and (b) the hypothesis of simplicity which establishes that the optimal solution must have the least number of steps and the least number of carbons in every intermediate. A mathematical proof of the optimal solution of this problem is given, and it is demonstrated that such a solution is the same as occurs in cells. The Calvin cycle and the "L-type" of the pentose cycle are also studied by a similar method, and equivalent results are obtained. These results point out the role which the hypothesis of simplicity may have played in the evolution of metabolic pathways.