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A simple effective model for STDP: from spike pairs and triplets to rate-encoding plasticity
BMC Neurosciencevolume 16, Article number: P87 (2015)
In the present work  we propose an effective model formulating synaptic potentiation and depression in terms of two interacting traces, representing the fraction of open NMDA receptors and the Ca2+ concentration in the post-synaptic neuron, respectively. These two traces then determine the evolution of the synaptic strength. We first confirm that the standard pairwise STDP curve is obtained for low frequency trains of pairs of pre- and post-synaptic spikes and we then evaluate triplet effects (see Figure 1), comparing the model's results to experimental data from hippocampal culture [2, 3]. Finally, we evaluate the model's predictions for spike trains of different frequencies and degrees of correlation, observing that a BCM-like rule for plasticity as a function of the pre-and post-synaptic firing rates is recovered when employing uncorrelated poisson trains of pre- and postsynaptic spikes.
Having a low number of parameters and being composed of only polynomial differential equations, the model is able nonetheless to reproduce key features of LTP and LTD. Moreover, since the parameters of the model are easily related to the dynamical properties of the synapse, we believe the model constitutes a useful tool to study extended neural networks from a dynamical system's point of view.
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Wang HX, Gerkin RC, Nauen DW, Bi GQ: Coactivation and timing-dependent integration of synaptic potentiation and depression. Nat Neurosci. 2005, 8: 87-193.
The support of the German Science Foundation (DFG) and the German Academic Exchange Service (DAAD) are acknowledged.