Fig 3. Network motifs that affect the STDP dynamics.

A. The first term in Eq 3 is proportional to the average firing rates of the pre and post synaptic neurons. B. General form of a structural motif, contributing to the STDP dynamics in the synapse W_ij (dashed line). A source neuron k (red line) projects to the post synaptic neuron i (green) via α synapses, and to the pre synaptic neuron j (black) via β synapses. The contribution is proportional to the firing rate of the source neuron r_k and to the product of all synaptic efficacies along the two paths. The expression (W^α)_ik r_k(W^β)_jk is a sum over all paths that start from neuron k and reach the post synaptic neuron i via α synapses and the pre synaptic neuron j via β synapses. C-H: Examples of six motifs that affect STDP in the synapse W_ij (dashed line), by inducing time dependent coupling between neurons j and i. Black arrows indicate synapses that participate in the motifs. C. One of the first order motifs contains the direct synapse from j to i (α = 1, β = 0). The source neuron is the pre synaptic neuron j. D. The other first order motif contains the opposite synapse from i to j (α = 0, β = 1). Here the source neuron is the post synaptic neuron i. E. One of the second order motifs (α = 1, β = 1). Here the source neuron is some other neuron in the network that projects directly both to i and j. F. Additional example for a second order motif (α = 2, β = 0). The source neuron is the pre synaptic neuron j, that projects to the post synaptic neuron i through one intermediate neuron. G. Example of a third order motif (α = 2, β = 1). The source neuron projects directly to the pre synaptic neuron j and via one intermediate neuron to the post synaptic neuron i. H. Additional example of a third order motif (α = 3, β = 0). The pre synaptic neuron j is the source neuron, that projects to the post synaptic neuron i via two intermediate neurons.