Theta rhythmicity enhances learning in adaptive STDP

Abstract

The classical STDP window captures changes of a synaptic weight in response to the relative timing of a pre and a postsynaptic spike (see e.g. Bi and Poo, 1998). Due to its static nature, however, it cannot account for nonlinear interactions between spikes. Several theoretical studies offer dynamic formulations for STDP, for example by modulating the synaptic weight change by variables like synaptic calcium concentration (Shouval et al., 2002) or somatic depolarisation (Clopath et al., 2010), or by introducing spike triplet interactions (Pfister and Gerstner, 2006). Here, we propose a new model which is formulated as a set of differential equations (Schmiedt et al., 2010). The weight change is given by a differential Hebbian learning rule, which reproduces the STDP window for spike pairs. To account for the effects of repeated neuronal firing on the synaptic weight, we introduce modulations of the spike impact, which act on exponential traces of the spiking activity. We found that this model captures a series of experiments on STDP with complex spike pattern in cortex (Froemke et al., 2006) and hippocampus (Wang et al., 2005). When applied to continuous firing rates, our approach allows us to analyze the effects of given time courses of firing rates on the synaptic weight change, i.e. the filter properties of STDP. For sinusoidal modulations of baseline firing rates we find the strongest weight changes for modulation frequencies in the theta band, which plays a key role in learning. Furthermore, weight modifications in the hippocampus are predicted to be most prominent for baseline rates of around 5Hz in striking agreement with experimental findings.This suggests that STDP-dependent learning is mediated by theta oscillations and modulated by the background firing rate which are both testable predictions of our theory.