Learning and memory formation are processes which are still not fully understood. It is widely believed that synaptic plasticity is the most important neural substrate for both. However, it has been observed that large-scale theta band oscillations in the mammalian brain are beneficial for learning, and it is not clear if and how this is linked to synaptic plasticity. Also, the underlying dynamics of synaptic plasticity itself have not been completely uncovered yet, especially for non-linear interactions between multiple spikes. Here, we present a new and simple dynamical model of synaptic plasticity. It incorporates novel contributions to synaptic plasticity including adaptation processes. We test its ability to reproduce non-linear effects on four different data sets of complex spike patterns, and show that the model can be tuned to reproduce the observed synaptic changes in great detail. When subjected to periodically varying firing rates, already linear pair based spike timing dependent plasticity (STDP) predicts a specific susceptibility of synaptic plasticity to pre- and postsynaptic firing rate oscillations in the theta-band. Our model retains this band-pass property, while for high firing rates in the non-linear regime it modifies the specific phase relation required for depression and potentiation. For realistic parameters, maximal synaptic potentiation occurs when the postsynaptic is trailing the presynaptic activity slightly. Anti-phase oscillations tend to depress it. Our results are well in line with experimental findings, providing a straightforward and mechanistic explanation for the importance of theta oscillations for learning.
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