Figure 2.

Spiking neuronal network implementation of the delta rule. (A) The microcircuit implementing the delta rule consists of interconnected pools of neurons (circles). Numbers in the circles signify the number of neurons in each pool. Numbers next to the connections indicate maximum total conductance through that pathway in nS. The connections have a sparsity of s = 0.3. Not shown are the non-specific external connections made to each neuron in pools M and O. Each individual post-synaptic neuron in those pools gets its own Poisson spike train with rate r_ϵ = 100 Hz that excites it through an excitatory synapse with conductances of 0.42 nS and 0.6 nS, respectively. (B) The spiking plasticity rule at the plastic inhibitory synapses implements a form of the BCM rule. Synapses depress (dashed red lines) or potentiate (solid green lines) depending on whether the post-synaptic firing rate, r_M, is respectively less than (or greater than) some threshold rate r_θ (thick line). By controlling r_M to be below r_θ when the delta rule (thin line) predicts depression, and vice versa when the delta rule predicts potentiation, this microcircuit approximates the delta rule. (C) Responses of the model neurons to DC current injection. Once the neurons exceed a certain threshold current, their firing rate is approximately linear, which leads to an overall linearity of this microcircuit.