Genetic-algorithm selection of a regulatory structure that directs flux in a simple metabolic model.

A genetic algorithm (GA) is used to optimize parameters for allosteric regulation of enzymes in a model of a metabolic futile cycle, in which two metabolites are interconverted by a pair of irreversible enzymatic reactions. The cycle is regulated by end products of the surrounding pathway. The optimization criterion for the GA is the proper direction of chemical flux in the regulated cycle toward one or the other end product in response to a simple, time-dependent model of biochemical "need" based on externally imposed variation of the end product concentrations. An energetic cost, to be held to a minimum, is also imposed on the operation of the cycle. The best-performing individuals selected by the GA are found to switch rapidly the direction of net flux according to need. In different "environments" (specific time courses of end product concentrations), the GA produces better- or poorer-performing individuals. In some cases "generalists" and "specialists" are produced. The present approach provides, purely as a consequence of formally specifying the task of flux direction, the new result of numerical confirmation, in a simple model, of the intuition that negative feedback and reciprocal regulation are important for good flux direction in arbitrary environments, and gives rise to a diversity of structures, suggestive of the results of biological evolution.