Poisson-Like Spiking in Circuits with Probabilistic Synapses

Abstract

Neuronal activity in cortex is variable both spontaneously and during stimulation, and it has the remarkable property that it is Poisson-like over broad ranges of firing rates covering from virtually zero to hundreds of spikes per second. The mechanisms underlying cortical-like spiking variability over such a broad continuum of rates are currently unknown. We show that neuronal networks endowed with probabilistic synaptic transmission, a well-documented source of variability in cortex, robustly generate Poisson-like variability over several orders of magnitude in their firing rate without fine-tuning of the network parameters. Other sources of variability, such as random synaptic delays or spike generation jittering, do not lead to Poisson-like variability at high rates because they cannot be sufficiently amplified by recurrent neuronal networks. We also show that probabilistic synapses predict Fano factor constancy of synaptic conductances. Our results suggest that synaptic noise is a robust and sufficient mechanism for the type of variability found in cortex.

Cortical reliability amid noise and chaos

“…3,4). Chaotic network dynamics without synaptic noise have been extensively studied [22][23][24] , and it has been suggested that synaptic noise generates high neural variability in postsynaptic neurons 18,46 . However, this is the first time that the interplay between stochastic synaptic transmission and chaotic network dynamics has been seen and understood.…”

“…The universal presence of synaptic noise suggests that cortical neurons respond far less reliably to presynaptic inputs than to current injections. It has been shown, moreover, that a simplified cortical network model with stochastic synapses can provide a sufficient explanation for variable spiking 18 . Furthermore, in vitro, some types of inhibitory neurons exhibit stochastic firing types.…”

Note on the coefficient of variations of neuronal spike trains

“…The question how to achieve large CV values has been studied in computer simulations (Softky and Koch 1993;Troyer and Miller 1997;Christodoulou and Bugmann 2000;Stiefel et al 2013;Lengler et al 2013;Moreno-Bote 2014), in random walk models (Shadlen and Newsome 1998;Salinas and Sejnowski 2000), in Ornstein-Uhlenback models (Feng and Brown 1999;Fusi and Mattia 1999;Moreno-Bote 2014), and in other models (Terman et al 2013). In contrast to most other approaches, our model allows exact mathematical solutions.…”

Memristors Empower Spiking Neurons With Stochasticity

“…However, this approach is less attractive due to the lack of a direct control over the stochastic properties of each neuron in such network (e.g., the voltage-dependent inhomogeneous Poissonian spiking rate cannot be straightforwardly mapped onto such network, and can be only approximated [19]). Moreover, it was shown that Poissonian statistics generated by a network itself is usually stable only for a limited input range if no additional noise generation mechanism is used [75].…”