Heterogeneous plasticity rules generate diverse structures in recurrent networks

How do local changes at individual synapses give rise to structured recurrent connectivity? Experiments have revealed diverse forms of spike-timing-dependent plasticity (STDP) across the brain, making it difficult to predict which circuit structures different rules will generate. We developed an analytical framework mapping excitatory Hebbian, anti-Hebbian, and symmetric STDP rules to directed three-neuron motifs. Individual homogeneous rules generate restricted subsets of motifs, and no single rule produces all motifs. Combining different rules generates motifs inaccessible to individual rules and yields the full motif repertoire, and these predictions generalize to larger recurrent networks. The mapping is nevertheless highly non-unique, with distinct rules and parameters producing similar motif distributions, including distributions compatible with experimental connectivity. Thus, circuit structure constrains candidate plasticity rules but does not uniquely identify them. Finally, networks with similar motif distributions can nonetheless differ in their firing rates and pairwise correlations, suggesting that activity may provide an additional constraint on candidate plasticity rules.