ted by Ca2+ and Ca2+/ calmodulin. Calcineurin is a heterodimer, consisting the Calcium Spikes Modulate Synaptic Plasticity frequency calcium input actually means smaller quantity of calcium ions, comparing with high-frequency calcium input. Finally and most importantly, as far as the authors know, there is no model that systematically compares the activities of phosphatase and kinase upon stimulation of different calcium spike DHA web frequencies, while keeping the total amount of calcium ions constant. The study presented here is based on a published allosteric model of calmodulin. In this model, Stefan et al. depicted various properties of calmodulin, including the cooperativity of calcium binding, different affinities for calcium binding sites, and the activity of calcium-unsaturated calmodulin. The authors also proposed that the differential activation of calcineurin and CaMKII is based on the static concentration of calcium elevation. However, this model does not take into account the binding of calcium ions to the regulatory subunit of calcineurin, the autophosphorylation of CaMKII, and the negative regulation by calcineurin of the activation of CaMKII. Most importantly, the activation of calcineurin and CaMKII by calcium spikes has not been assessed. We expanded the model of Stefan et al. to include inter-holoenzyme autophosphorylation of CaMKII, using a rate based on the probability of having an active neighboring subunit at each simulation step. The activation of calcineurin by binding calcium ions and activated calmodulin has also been modeled in greater detail. In addition, we included reactions describing the dephosphorylation of CaMKII by PP1, the inhibition of PP1 by DARPP-32, and the dephosphorylation of DARPP-32 by calcineurin. We modeled the calcium spikes according to experimental measurements, with explicit binding and dissociation reactions involving calcium buffer proteins. We systematically compare the effects of calcium input frequency, duration and amplitude on the activities of both CaMKII and calcineurin. Results Modeling calcium spikes and simulation design The transient changes of free calcium concentration in the spine are shaped by many factors including calcium sources, calcium extrusion mechanisms, and distribution of calcium buffer proteins. In this study, we focused on the calcium spikes induced by synaptic stimulation. Using the model described in the methods section, we showed that a single calcium input of 34560 molecules induced free intracellular calcium transients reaching the peak level of 0.7 micromolar, within 10 milliseconds, followed by a decay to basal levels within 220 milliseconds. Such a spike is in agreement with the amplitude and time course of NMDA receptor mediated calcium transients in an individual spine in partially depolarized conditions. This single input was repeated to induce a train of calcium spikes, with varied intervals, to 
form signals with different frequencies. First, we modulated the calcium signal purely on frequency, without changing the number of inputs or the input size. This generated either a prolonged low frequency stimulation, or a relatively short-lived high frequency stimulus. In total, 41 different frequencies, ranging from 0.1 Hz to 200 Hz, were studied. For each frequency, 100 calcium inputs were created after the system reached steady state. Filled arrow: yield, bar arrow: inhibition or dephosphorylation, R: calmodulin in active state, T: calmodulin in inactive st
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