asurements. As the amplitude of each calcium spike increased, the curve of relative activity between calcineurin and CaMKII shifted towards lower frequencies, indicating large calcium input size increased the proportion of active CaMKII at low frequencies. At 200 Hz of calcium spikes, the final ratio of calcineurin versus CaMKII activity remained the same across different calcium input sizes, meaning that the level of activated CaMKII at high frequency stimulation is independent of the calcium input size. This situation is similar as when we varied calcium spike number. However, simulations with larger calcium input size reached this final ratio more rapidly than those with smaller input size. Sabatini et al. argued that NMDA-receptorinduced Ca2+ influx at resting membrane potential triggers LTD, but induces LTP when coupled with postsynaptic membrane depolarization because of the large amplitude of calcium input. Combined with our simulation results, a more complete picture might be that a large amplitude of calcium influx more easily induces LTP, because it relies less on high spiking frequencies. Thus, high frequencies of calcium inputs provide a mechanism to produce transient but potent calcium elevations in order to activate CaMKII. This is important when each individual calcium influx is not large enough, or when the number of calcium inputs is limited. In parallel, a large DMXB-A chemical information amount of calcium ions entering into the spine can lower the threshold frequency required for strongly activating CaMKII. Therefore, the total amount of input calcium ions contributes to the sensitivity of the system towards decoding frequencies, and determines above which frequency CaMKII can overcome calcineurin, therefore when LTP can be triggered rather 7 Calcium Spikes Modulate Synaptic Plasticity than LTD. However, the maximal extent to which CaMKII can be activated seems independent of the actual quantity of calcium ions, though it may depend on other factors, such as the availability of calmodulin, and phosphatase inhibitors. CaMKII autophosphorylation amplifies sensitivity of CaMKII towards calcium input frequency Calcium Spikes Modulate Synaptic Plasticity This autophosphorylation 
plays a crucial role in regulating the direction of synaptic plasticity. DARPP-32 interacts with PP1 through two domains, which contribute to both low affinity binding and inhibition. Upon binding both sites, the affinity between DARPP-32 and PP1 is increased to a nanomolar range. In our model, a relatively low affinity was used, representing the average inhibitory effect of different PP1 inhibitors, under basal conditions. However, when the affinity between DARPP-32 and PP1 was increased by 10-fold , with basal DARPP-32 phosphorylation unchanged, the activation of CaMKII effectively rose during low frequency calcium stimulation. Moreover, the activated area of CaMKII was more than 14 times larger than that of calcineurin in the high frequency range, which was more than 3 fold increase when compared with the ratio obtained in the low affinity simulation. This indicates that, although CaMKII activation outpaces PP1 activation at high frequency stimulation, PP1 still plays an important role in shaping CaMKII response to calcium. The potency of PP1, which is controlled by DARPP-32, not only determines the sensitivity of the CaMKII frequency response, but also the extent to which CaMKII can be activated by high frequency calcium inputs. Because DARPP-32 is a hub of kinases and p