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Poisson-Like Spiking in Circuits with Probabilistic Synapses

Figure 5

The mechanism for Poisson-like variability in a network with probabilistic synapses.

(a) Scheme of the transformation between input variance in the spike counts of the presynaptic spike trains and output variance of the post-synaptic currents in an open loop network with probabilistic synapses. (b) Precise balancing of two competing forces in a closed-loop network: the integration step tends to lower spiking variance, while the probabilistic synaptic step increases spiking variability. (c) Output variance (solid red line) and the variance of the spike train, (dashed) increase linearly as a function of input variance for fixed input firing rates. Solid line is vertically shifted respect to the dashed line due to the increase of variance by probabilistic synapses, which is uniform for all input variances. The equilibrium point of the network (red point) corresponds to the state where the input and output variances match. (d) The equilibrium point moves linearly with firing rate because the vertical shift induced by probabilistic synapses increases linearly with rate. (e) Spike count variance increases linearly with rate, leading to Fano factor constancy.

doi: https://doi.org/10.1371/journal.pcbi.1003522.g005