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

Effects of degree distributions in random networks of type-I neurons

We consider large networks of theta neurons and use the Ott-Antonsen ansatz to derive degree-based mean-field equations governing the expected dynamics of the networks. Assuming random connectivity, we investigate the effects of varying the widths of the in- and out-degree distributions on the dynamics of excitatory or inhibitory synaptically coupled networks and gap junction coupled networks. For synaptically coupled networks, the dynamics are independent of the out-degree distribution. Broadening the in-degree distribution destroys oscillations in inhibitory networks and decreases the range of bistability in excitatory networks. For gap junction coupled neurons, broadening the degree distribution varies the values of parameters at which there is an onset of collective oscillations. Many of the results are shown to also occur in networks of more realistic neurons.

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

Neuronal networks in rodent primary visual cortex (V1) can generate oscillations in different frequency bands depending on the network state and the level of visual stimulation. High-frequency gamma rhythms, for example, dominate the network's spontaneous activity in adult mice but are attenuated upon visual stimulation, during which the network switches to the beta band instead. The spontaneous local field potential (LFP) of juvenile mouse V1, however, mainly contains beta rhythms and presenting a stimulus does not elicit drastic changes in network oscillations. We study, in a spiking neuron network model, the mechanism in adult mice allowing for flexible switches between multiple frequency bands and contrast this to the network structure in juvenile mice that lack this flexibility. The model comprises excitatory pyramidal cells (PCs) and two types of interneurons: the parvalbumin-expressing (PV) and the somatostatinexpressing (SOM) interneuron. In accordance with experimental findings, the pyramidal-PV and pyramidal-SOM cell subnetworks are associated with gamma and beta oscillations, respectively. In our model, they are both generated via a pyramidal-interneuron gamma (PING) mechanism, wherein the PCs drive the oscillations. Furthermore, we demonstrate that large but not small visual stimulation activates SOM cells, which shift the frequency of resting-state gamma oscillations produced by the pyramidal-PV cell subnetwork so that beta rhythms emerge. Finally, we show that this behavior is obtained for only a subset of PV and SOM interneuron projection strengths, indicating that their influence on the PCs should be balanced so that they can compete for oscillatory control of the PCs. In sum, we propose a mechanism by which visual beta rhythms can emerge from spontaneous gamma oscillations in a network model of the mouse V1; for this mechanism to reproduce V1 dynamics in adult mice, balance between the effective strengths of PV and SOM cells is required.

Dynamics of Structured Networks of Winfree Oscillators

Winfree oscillators are phase oscillator models of neurons, characterized by their phase response curve and pulsatile interaction function. We use the Ott/Antonsen ansatz to study large heterogeneous networks of Winfree oscillators, deriving low-dimensional differential equations which describe the evolution of the expected state of networks of oscillators. We consider the effects of correlations between an oscillator's in-degree and out-degree, and between the in- and out-degrees of an “upstream” and a “downstream” oscillator (degree assortativity). We also consider correlated heterogeneity, where some property of an oscillator is correlated with a structural property such as degree. We finally consider networks with parameter assortativity, coupling oscillators according to their intrinsic frequencies. The results show how different types of network structure influence its overall dynamics.

The effects of within-neuron degree correlations in networks of spiking neurons

We consider the effects of correlations between the in- and out-degrees of individual neurons on the dynamics of a network of neurons. By using theta neurons, we can derive a set of coupled differential equations for the expected dynamics of neurons with the same in-degree. A Gaussian copula is used to introduce correlations between a neuron's in- and out-degree, and numerical bifurcation analysis is used determine the effects of these correlations on the network's dynamics. For excitatory coupling, we find that inducing positive correlations has a similar effect to increasing the coupling strength between neurons, while for inhibitory coupling it has the opposite effect. We also determine the propensity of various two- and three-neuron motifs to occur as correlations are varied and give a plausible explanation for the observed changes in dynamics.

Sensitivity to Stimulus Irregularity Is Inherent in Neural Networks

Behavior is controlled by complex neural networks in which neurons process thousands of inputs. However, even short spike trains evoked in a single cortical neuron were demonstrated to be sufficient to influence behavior in vivo. Specifically, irregular sequences of interspike intervals (ISIs) had a more reliable influence on behavior despite their resemblance to stochastic activity. Similarly, irregular tactile stimulation led to higher rates of behavioral responses. In this study, we identify the mechanisms enabling this sensitivity to stimulus irregularity (SSI) on the neuronal and network levels using simulated spiking neural networks. Matching in vivo experiments, we find that irregular stimulation elicits more detectable network events (bursts) than regular stimulation. Dissecting the stimuli, we identify short ISIs-occurring more frequently in irregular stimulations-as the main drivers of SSI rather than complex irregularity per se. In addition, we find that short-term plasticity modulates SSI. We subsequently eliminate the different mechanisms in turn to assess their role in generating SSI. Removing inhibitory interneurons, we find that SSI is retained, suggesting that SSI is not dependent on inhibition. Removing recurrency, we find that SSI is retained due to the ability of individual neurons to integrate activity over short timescales ("cell memory"). Removing single-neuron dynamics, we find that SSI is retained based on the short-term retention of activity within the recurrent network structure ("network memory"). Finally, using a further simplified probabilistic model, we find that local network structure is not required for SSI. Hence, SSI is identified as a general property that we hypothesize to be ubiquitous in neural networks with different structures and biophysical properties. Irregular sequences contain shorter ISIs, which are the main drivers underlying SSI. The experimentally observed SSI should thus generalize to other systems, suggesting a functional role for irregular activity in cortex.