Figure 2

The effects of noise on an enzymatic futile cycle. The cycle is formed by the phosphorylation of a protein X to form X* through the action of a kinase, E+, which may or may not be subject to noise in its activity. Each curve is a plot of the stationary-state concentration of X*, from the system shown schematically in the inset, as a function of the average forward enzyme activity <E+>. The variable p is related to the noise power and determines the effective noise distribution around <E+>; p = 0 corresponds, for example, to approximately normally distributed noise whereas the other values correspond to different distribution shapes. The (black) curve labeled 'det' is the deterministic solution when E+ is not subject to noise. Whereas the deterministic system defined by p = 0 is monostable, the system with noise can be bistable and oscillate stochastically. From an analysis in [31].