Abstract
Neuronal networks in rodent barrel cortex are characterized by stable low baseline firing rates. However, they are sensitive to the action potentials of single neurons as suggested by recent single-cell stimulation experiments that reported quantifiable behavioral responses in response to short spike trains elicited in single neurons. Hence, these networks are stable against internally generated fluctuations in firing rate but at the same time remain sensitive to similarly-sized externally induced perturbations. We investigated stability and sensitivity in a simple recurrent network of stochastic binary neurons and determined numerically the effects of correlation between the number of afferent (“in-degree”) and efferent (“out-degree”) connections in neurons. The key advance reported in this work is that anti-correlation between in-/out-degree distributions increased the stability of the network in comparison to networks with no correlation or positive correlations, while being able to achieve the same level of sensitivity. The experimental characterization of degree distributions is difficult because all pre-synaptic and post-synaptic neurons have to be identified and counted. We explored whether the statistics of network motifs, which requires the characterization of connections between small subsets of neurons, could be used to detect evidence for degree anti-correlations. We find that the sample frequency of the 3-neuron “ring” motif (1→2→3→1), can be used to detect degree anti-correlation for sub-networks of size 30 using about 50 samples, which is of significance because the necessary measurements are achievable experimentally in the near future. Taken together, we hypothesize that barrel cortex networks exhibit degree anti-correlations and specific network motif statistics.
Highlights
Rodents can be trained to use their whiskers to detect an object that predicts a reward and respond with licking to obtain this reward (Huber et al, 2012)
We explored whether the statistics of network motifs, which requires the characterization of connections between small subsets of neurons, could be used to detect evidence for degree anti-correlations
The mean-field limit, corresponding to an infinite network, is studied by considering the dynamics of a network where each neuron has the same firing rate, each neuron has the same number of synaptic inputs, i.e., in-degree, and there is no stochasticity
Summary
Rodents can be trained to use their whiskers to detect an object that predicts a reward and respond with licking to obtain this reward (Huber et al, 2012). An important question is how many neurons need to be activated for the subject to reliably detect the stimulation and whether some cell types are more sensitive than others. Answers to these questions may come from nanostimulation experiments in which a single neuron is activated through juxtacellular stimulation (Houweling and Brecht, 2008). These experiments show that adding trains of 10-15 action potentials in a single cortical neuron can be detected, but the reliability of detection is low and reaction times are long compared to microstimulation
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