Switching dynamics and the transient memory storage in a model enzyme network involving Ca2+/calmodulin-dependent protein kinase II in synapses.

The signal processing through a chain of phosphorylation-dephosphorylations mediated by a pair of enzymes, Ca2+/calmodulin-dependent protein kinase II and the associated phosphatase, is formulated as a nonautonomous dynamical system in the framework of nonautocatalytic, intraholoenzyme reaction dynamics. A classification of switching characteristics of the system is made in the parameter space comprising the three controllable system parameters: an input-pulse intensity and initial concentrations of the two associated enzymes. It is found that a region of parameter space exists termed the transition zone, that exhibits a quasi-switching behaviour characterized by a signal storage time being prolonged by more than several orders of magnitude (10(4) times in certain cases) for the increase of two orders of magnitude in the input signal intensity. The effect of alterations of certain rate constants on the quasi-switching property is explored. It is numerically demonstrated that the Ca2+/calmodulin-dependent kinase II-related phosphatase is the most important key enzyme for regulating the signal storage time.