During the acquisition of memories, influx of Ca2+ into the postsynaptic spine through the pores of activated N-methyl-D-aspartate-type glutamate receptors triggers processes that change the strength of excitatory synapses. The pattern of Ca2+influx during the first few seconds of activity is interpreted within the Ca2+-dependent signaling network such that synaptic strength is eventually either potentiated or depressed. Many of the critical signaling enzymes that control synaptic plasticity,including Ca2+/calmodulin-dependent protein kinase II (CaMKII), are regulated by calmodulin, a small protein that can bindup to 4 Ca2+ ions. As a first step toward clarifying how the Ca2+-signaling network decides between potentiation or depression, we have created a kinetic model of the interactions of Ca2+, calmodulin, and CaMKII that represents our best understanding of the dynamics of these interactions under conditions that resemble those in a postsynaptic spine. We constrained parameters of the model from data in the literature, or from our own measurements, and then predicted time courses of activation and autophosphorylation of CaMKII under a variety of conditions. Simulations showed that species of calmodulin with fewer than four bound Ca2+ play a significant role in activation of CaMKII in the physiological regime,supporting the notion that processing of Ca2+ signals in a spine involves competition among target enzymes for binding to unsaturated species of CaM in an environment in which the concentration of Ca2+ is fluctuating rapidly. Indeed, we showed that dependence of activation on the frequency of Ca2+ transients arises from the kinetics of interaction of fluctuating Ca2+with calmodulin/CaMKII complexes. We used parameter sensitivity analysis to identify which parameters will be most beneficial to measure more carefully to improve the accuracy of predictions. This model provides a quantitative base from which to build more complex dynamic models of postsynaptic signal transduction during learning.