A calcium-influx-dependent plasticity model exhibiting multiple STDP curves.

Hebbian plasticity means that if the firing of two neurons is correlated, then their connection is strengthened. Conversely, uncorrelated firing causes a decrease in synaptic strength. Spike-timing-dependent plasticity (STDP) represents one instantiation of Hebbian plasticity. Under STDP, synaptic changes depend on the relative timing of the pre- and post-synaptic firing. By inducing pre- and post-synaptic firing at different relative times the STDP curves of many neurons have been determined, and it has been found that there are different curves for different neuron types or synaptic sites. Biophysically, strengthening (long-term potentiation, LTP) or weakening (long-term depression, LTD) of glutamatergic synapses depends on the post-synaptic influx of calcium (Ca2+): weak influx leads to LTD, while strong, transient influx causes LTP. The voltage-dependent NMDA receptors are the main source of Ca2+ influx, but they will only open if a post-synaptic depolarisation coincides with pre-synaptic neurotransmitter release. Here we present a computational mechanism for Ca2+-dependent plasticity in which the interplay between the pre-synaptic neurotransmitter release and the post-synaptic membrane potential leads to distinct Ca2+ time-courses, which in turn lead to the change in synaptic strength. It is shown that the model complies with classic STDP results, as well as with results obtained with triplets of spikes. Furthermore, the model is capable of displaying different shapes of STDP curves, as observed in different experimental studies.