BCM and Membrane Potential: Alternative Ways to Timing Dependent Plasticity

The Bienenstock-Cooper-Munroe (BCM) rule is one of the best-established learning formalisms for neural tissue. However, as it is based on pulse rates, it can not account for recent spike-based experimental protocols that have led to spike timing dependent plasticity (STDP) rules. At the same time, STDP is being challenged by experiments exhibiting more complex timing rules (e.g. triplets) as well as simultaneous rateand timing dependent plasticity. We derive a formulation of the BCM rule which is based on the instantaneous postsynaptic membrane potential as well as the transmission profile of the presynaptic spike. While this rule is neither directly rate nor timing based, it can replicate BCM, conventional STDP and spike triplet experimental data, despite incorporating only two state variables. Moreover, these behaviors can be replicated with the same set of only four free parameters, avoiding the overfitting problem of more involved plasticity rules.