Ca2+/calmodulin-dependent protein kinase II (CaMKII) is concentrated in brain, and is particularly enriched in synaptic structures where it comprises 20-50% of all proteins. The abundant nature of CaMKII and its ability to phosphorylate a wide range of substrate proteins, including itself, earmarks it as a protein kinase that may have a vital role in neuronal information processing and memory. A computer model of CaMKII is investigated that incorporates recent findings about the geometrical arrangement of subunits, the mechanism of Ca(2+)-dependent subunit activation, and Ca(2+)-independent autophosphorylation. The model is framed as a system of nonlinear differential equations. It is demonstrated numerically that (1) CaMKII is tuned to be activated by stimulation protocols associated with the induction of long-term potentiation; (2) the observed slow dissociation of trapped Ca2+/calmodulin may require the autonomy site to be protected from dephosphorylation; and (3) Ca(2+)-independent kinase activity is expressed in a manner akin to a graded switch. The model validates current theories concerning how CaMKII may be a Ca2+ pulse frequency detector, a molecular switch, or a mediator of the threshold for long-term synaptic plasticity.