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.
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