Figure 1.

Leaky integration with a single biophysical neuron. a, Diagram illustrating the connectivity of a “network” consisting of a single neuron (N = 1). The diagram shows that the neuron receives stimulus input as well as input from synaptic connections to itself, and the decoder x̂(t) “reads-out” the computation from the spike trains of the network. b, Schematic of how the network is derived in the case of a single neuron. The upper plots show the decoded signal x̂(t) (red traces) plotted against the actual signal x(t) (dashed black lines) along with the neurons' voltage trace (bottom). For the examples in this figure, the network is performing leaky integration on a box function input. In the first column, we illustrate the output of a single neuron from the LIF framework of Boerlin et al. (2013). In the second column, we alter how the stimulus information is read-out from the spike-times of the network (first arrow) which results in an LIF network without instantaneous (δ-function) synaptic dynamics. Going from the second to third columns, we add spike-generating, HH-type ionic currents to the voltage dynamics. The fourth column illustrates how the addition of the compensating synaptic kernel affects the output of the decoder.