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 non-autonomous dynamical system in the framework of non-autocatalytic, 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 (10⁴ 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. Received: 25 April 1994/Accepted in revised form: 16 December 1994