Evaluating the robustness of a biochemical network model

Mathematical models of robust biological systems are expected to be robust against small variations in the model´s parameters. In this paper, we investigate the robustness of the model proposed by Laub and Loomis for the molecular network underlying adenosine 3´,5´-cycle monophosphate (cAMP) oscillations observed in populations of Dictyostelium cells 4 hours after the initiation of development. This is performed by using bifurcation analysis. In particular, we reduce the problem to study the persistence of the periodic orbit that arises from Hopf bifurcation as one key parameter is varied. By introducing an optimization problem, we determine the maximum allowed parameter variation under which the oscillatory behavior of the system persists. We obtain maximum allowed variation of 0.51% and show that this bound is tight.