Stability and Competition in Multi-spike Models of Spike-Timing Dependent Plasticity

Spike-timing dependent plasticity (STDP) is a widespread plasticity mechanism in the nervous system. The simplest description of STDP only takes into account pairs of pre- and postsynaptic spikes, with potentiation of the synapse when a presynaptic spike precedes a postsynaptic spike and depression otherwise. In light of experiments that explored a variety of spike patterns, the pair-based STDP model has been augmented to account for multiple pre- and postsynaptic spike interactions. As a result, a number of different “multi-spike” STDP models have been proposed based on different experimental observations. The behavior of these models at the population level is crucial for understanding mechanisms of learning and memory. The challenging balance between the stability of a population of synapses and their competitive modification is well studied for pair-based models, but it has not yet been fully analyzed for multi-spike models. Here, we address this issue through numerical simulations of an integrate-and-fire model neuron with excitatory synapses subject to STDP described by three different proposed multi-spike models. We also analytically calculate average synaptic changes and fluctuations about these averages. Our results indicate that the different multi-spike models behave quite differently at the population level. Although each model can produce synaptic competition in certain parameter regions, none of them induces synaptic competition with its originally fitted parameters. The dichotomy between synaptic stability and Hebbian competition, which is well characterized for pair-based STDP models, persists in multi-spike models. However, anti-Hebbian competition can coexist with synaptic stability in some models. We propose that the collective behavior of synaptic plasticity models at the population level should be used as an additional guideline in applying phenomenological models based on observations of single synapses.Author Summary: Synaptic plasticity is believed to underlie learning and memory by competitive strengthening and weakening of synapses in neural networks. However, the ability to form new memories while maintaining the old ones involves an intricate balance between synaptic stability and competition. In one of the most widespread such mechanisms, spike-timing dependent plasticity (STDP), the temporal order of pre- and postsynaptic spiking across a synapse determines whether it is strengthened or weakened. Early description of STDP only took into account pairs of pre- and postsynaptic spikes. However, more recent experimental results showed that the “pair-based” description is not sufficient to fully account for synaptic modifications under STDP, and motivated more complex “multi-spike” STDP models. While the conditions under which the pair-based STDP leads to synaptic stability and/or competition are well studied, it is not clear when and how multi-spike STDP models lead to synaptic stability and competition. Here, we address these questions through numerical simulation and analysis of a population of plastic excitatory synapses that converge to a neuron. We show that different multi-spike STDP models can induce synaptic stability and competition under radically different conditions, which have important implications in relating learning and memory to biophysical properties of synapses.