A mathematical model is presented of autophosphorylation of Ca2+/calmodulin-dependent protein kinase (CaMKII) and its dephosphorylation by a phosphatase. If the total concentration of CaMKII subunits is significantly higher than the phosphatase Michaelis constant, two stable steady states of the CaMKII autophosphorylation can exist in a Ca2+ concentration range from below the resting value of the intracellular [Ca2+] to the threshold concentration for induction of long-term potentiation (LTP). Bistability is a robust phenomenon, it occurs over a wide range of parameters of the model. Ca2+ transients that switch CaMKII from the low-phosphorylated state to the high-phosphorylated one are in the same range of amplitudes and frequencies as the Ca2+ transients that induce LTP. These results show that the CaMKII-phosphatase bistability may play an important role in long-term synaptic modifications. They also suggest a plausible explanation for the very high concentrations of CaMKII found in postsynaptic densities of cerebral neurons.
Zhabotinsky, A. M. (2000). Bistability in the Ca2+/calmodulin-dependent protein kinase-phosphatase system. Biophysical Journal, 79(5), 2211–2221. https://doi.org/10.1016/S0006-3495(00)76469-1