Hidden Markov Model of Cortical Synaptic Plasticity: Derivation of the Learning Rule

Cortical synaptic plasticity depends on the relative timing of preand postsynaptic spikes and also on the temporal pattern of presynaptic spikes and of postsynaptic spikes. We study the hypothesis that cortical synaptic plasticity does not associate individual spikes, but rather whole firing episodes, and depends only on when these episodes start and how long they last, but as little as possible on the timing of individual spikes. Here we present the mathematical background for such a study. Standard methods from hidden Markov models are used to define what “firing episodes” are. Estimating the probability of being in such an episode requires not only the knowledge of past spikes, but also of future spikes. We show how to construct a causal learning rule, which depends only on past spikes, but associates preand postsynaptic firing episodes as if it also knew future spikes. We also show that this learning rule agrees with some features of synaptic plasticity in superficial layers of rat visual cortex (Froemke and Dan, Nature 416:433, 2002).