Co-operative Co-evolutionary Approach for Flux Balance in Bacillus subtilis

Flux balance analysis of the metabolic network of Bacillus subtilis was employed to investigate flux distribution with maximizing ATP and ATP per sum of all flux values. The first objective function, which is to maximize ATP, is a conventional linear objective function and is performed with a hill-climbing algorithm. The second, which is to maximize ATP per sum of all flux values, is a non-linear objective function and is performed with a co-operative co-evolutionary genetic algorithm (CCGA). The effects of co-substrate supplementation; i.e. serine, cysteine, aspartate and threonine, are investigated. Employing two different objective functions predicts different effect of substrate supplementation. The optimization results according to the first objective function suggest that no improvement can be gained by substrate supplementation, while those according to the second objective function suggest that the introduction of each alternative substrate can lead to an improvement in ATP production. Exploration of alternative objective functions by CCGA is illustrated to generate more flux scenarios.