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Long-term depression (LTD) and long-term potentiation (LTP) of granule-Purkinje cell synapses are persistent synaptic alterations induced by high and low rises of the intracellular calcium ion concentration ([Ca 2+ ]), respectively. The occurrence of LTD involves the activation of a positive feedback loop formed by protein kinase C, phospholipase A 2 , and the extracellular signal-regulated protein kinase pathway, and its expression comprises the reduction of the population of synaptic AMPA receptors. Recently, a stochastic computational model of these signalling processes demonstrated that, in single synapses, LTD is probabilistic and bistable. Here, we expanded this model to simulate LTP, which requires protein phosphatases and the increase in the population of synaptic AMPA receptors. Our results indicated that, in single synapses, while LTD is bistable, LTP is gradual. Ca 2+  induced both processes stochastically. The magnitudes of the Ca 2+  signals and the states of the signalling network regulated the likelihood of LTP and LTD and defined dynamic macroscopic Ca 2+  thresholds for the synaptic modifications in populations of synapses according to an inverse Bienenstock, Cooper and Munro (BCM) rule or a sigmoidal function. In conclusion, our model presents a unifying mechanism that explains the macroscopic properties of LTP and LTD from their dynamics in single synapses.

Stochastic Induction of Long-Term Potentiation and Long-Term Depression