Anti-correlations in the degree distribution increase stimulus detection performance in noisy spiking neural networks

Abstract

Neuronal circuits in the rodent barrel cortex are characterized by stable low firing rates. However, recent experiments show that short spike trains elicited by electrical stimulation in single neurons can induce behavioral responses. Hence, the underlying neural networks provide stability against internal fluctuations in the firing rate, while simultaneously making the circuits sensitive to small external perturbations. Here we studied whether stability and sensitivity are affected by the connectivity structure in recurrently connected spiking networks. We found that anti-correlation between the number of afferent (in-degree) and efferent (out-degree) synaptic connections of neurons increases stability against pathological bursting, relative to networks where the degrees were either positively correlated or uncorrelated. In the stable network state, stimulation of a few cells could lead to a detectable change in the firing rate. To quantify the ability of networks to detect the stimulation, we used a receiver operating characteristic (ROC) analysis. For a given level of background noise, networks with anti-correlated degrees displayed the lowest false positive rates, and consequently had the highest stimulus detection performance. We propose that anti-correlation in the degree distribution may be a computational strategy employed by sensory cortices to increase the detectability of external stimuli. We show that networks with anti-correlated degrees can in principle be formed by applying learning rules comprised of a combination of spike-timing dependent plasticity, homeostatic plasticity and pruning to networks with uncorrelated degrees. To test our prediction we suggest a novel experimental method to estimate correlations in the degree distribution.Electronic supplementary materialThe online version of this article (doi:10.1007/s10827-016-0629-1) contains supplementary material, which is available to authorized users.

Flexible Frequency Switching in Adult Mouse Visual Cortex Is Mediated by Competition Between Parvalbumin and Somatostatin Expressing Interneurons

“…To be more explicit, the values corresponding to interneuron projections (P PV→A con , P SOM→A con , g PV→A rec , g SOM→A rec , A ∈ {PC, PV, SOM}) have been collected from Pfeffer et al (2013) and those assigned to PC projection parameters (P PC→A con , g PC→A rec , A ∈ {PC, PV, SOM}) have been derived from Jouhanneau et al (2018). The synaptic time constants of the interneurons (τ PV rec , τ SOM rec ) are inspired by Safari et al (2017), that is, we use the same proportion between the two as proposed by the study, but scale them toward smaller values to make them more comparable to the synaptic time constant of the PCs (τ PC rec ); this latter value has been acquired from Stern et al (1992) and is in accordance with an earlier modeling study to the mouse V1 (Martens, Houweling, & Tiesinga, 2017). In addition, σ PC→SOM = 1 2 and σ B→PC = σ B→PV = 1 6 where B ∈ {PC, PV, SOM}, which reflects the experimental finding that intralaminar projections to PC and PV cells are more spatially restricted than the ones to SOM cells.…”

“…This model merely had two neuron classes: excitatory and inhibitory neurons. Another example investigated how stimulus detection performance can be enhanced in noisy spiking neural networks; this model consisted of the same neuron types as have been included in this study (Martens et al, 2017). Still, we are not the first to investigate the coexistence of oscillations through a spiking neuron network model comprising three distinct cell types: one model that was based on the hippocampus already demonstrated that the coexistence of theta and gamma oscillations requires a balance in the effective strengths of the different inhibitory neurons in the network (Gloveli et al, 2005).…”

Balance between inhibitory cell types is necessary for flexible frequency switching in adult mouse visual cortex

“…This model merely comprised two neuron classes: excitatory and inhibitory neurons. Another example investigated how stimulus detection performance can be enhanced in noisy spiking neural networks; this model consisted of the same neuron types as have been included in this study [59]. Still, we are not the first to investigate the coexistence of oscillations through a spiking neuron network model comprising three distinct cell types: one model that was based on the hippocampus already demonstrated that coexistence of θ and gamma oscillations requires a balance in the effective strengths of the different inhibitory neurons in the network [60].…”

Dynamics of Structured Networks of Winfree Oscillators

“…We first consider the effects of correlating an oscillator's in- and out-degree. This general question has been considered by a number of authors studying different types of oscillators (LaMar and Smith, 2010 ; Vasquez et al, 2013 ; Martens et al, 2017 ; Nykamp et al, 2017 ; Vegué and Roxin, 2019 ) and experimental evidence for within-neuron degree correlations is given in Vegué et al ( 2017 ). Our derivation follows Laing and Bläsche ( 2020 ).…”