The game of the pentose phosphate cycle

Sugar rearrangement in the pentose phosphate cycle for transformation of six pentoses into five hexoses is analysed by abstraction to a mathematical model consisting of the resolution of a logical mathematical game of optimization. In the model, the problem is to arrive at five boxes containing six balls each, having started with six boxes containing five balls each, where boxes simulate the sugars and balls simulate the carbons in each. This is achieved by means of transferring two or three balls from any box to any other in each step, according to transketolase and transaldolase (or aldolase) mechanisms which account for sugar interconversions in the living cell. A hypothesis of simplicity is imposed in order to arrive at the objective with the least number of steps and with the least number of balls in the intermediary boxes. A symmetrical solution is obtained, demonstrating that this is the simplest solution, which is the procedure carried out by biological systems. The same treatment is applied for sugar rearrangement in the non-oxidative phase of the Calvin cycle in photosynthesis and the analysis of the "L-type" of pentose phosphate cycle is also treated, obtaining similar solutions in both cases, which allow us to make some physiological reflections.