Transitions between asynchronous and synchronous states: a theory of correlations in small neural circuits

Volume-transmitted GABA waves pace epileptiform rhythms in the hippocampal network

Mechanisms that entrain and pace rhythmic epileptiform discharges remain debated. Traditionally, the quest to understand them has focused on interneuronal networks driven by synaptic GABAergic connections. However, synchronized interneuronal discharges could also trigger the transient elevations of extracellular GABA across the tissue volume, thus raising tonic conductance (Gtonic) of synaptic and extrasynaptic GABA receptors in multiple cells. Here, we monitor extracellular GABA in hippocampal slices using patch-clamp GABA "sniffer" and a novel optical GABA sensor, showing that periodic epileptiform discharges are preceded by transient, region-wide waves of extracellular GABA. Neural network simulations that incorporate volume-transmitted GABA signals point to a cycle of GABA-driven network inhibition and disinhibition underpinning this relationship. We test and validate this hypothesis using simultaneous patch-clamp recordings from multiple neurons and selective optogenetic stimulation of fast-spiking interneurons. Critically, reducing GABA uptake in order to decelerate extracellular GABA fluctuations-without affecting synaptic GABAergic transmission or resting GABA levels-slows down rhythmic activity. Our findings thus unveil a key role of extrasynaptic, volume-transmitted GABA in pacing regenerative rhythmic activity in brain networks.

Modulation of Spectral Representation and Connectivity Patterns in Response to Visual Narrative in the Human Brain

The regional brain networks and the underlying neurophysiological mechanisms subserving the cognition of visual narrative in humans have largely been studied with non-invasive brain recording. In this study, we specifically investigated how regional and cross-regional cortical activities support visual narrative interpretation using intracranial stereotactic electroencephalograms recordings from thirteen human subjects (6 females, and 7 males). Widely distributed recording sites across the brain were sampled while subjects were explicitly instructed to observe images from fables presented in “sequential” order, and a set of images drawn from multiple fables presented in “scrambled” order. Broadband activity mainly within the frontal and temporal lobes were found to encode if a presented image is part of a visual narrative (sequential) or random image set (scrambled). Moreover, the temporal lobe exhibits strong activation in response to visual narratives while the frontal lobe is more engaged when contextually novel stimuli are presented. We also investigated the dynamics of interregional interactions between visual narratives and contextually novel series of images. Interestingly, the interregional connectivity is also altered between sequential and scrambled sequences. Together, these results suggest that both changes in regional neuronal activity and cross-regional interactions subserve visual narrative and contextual novelty processing.

Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model

Despite their biological plausibility, neural network models with asymmetric weights are rarely solved analytically, and closed-form solutions are available only in some limiting cases or in some mean-field approximations. We found exact analytical solutions of an asymmetric spin model of neural networks with arbitrary size without resorting to any approximation, and we comprehensively studied its dynamical and statistical properties. The network had discrete time evolution equations and binary firing rates, and it could be driven by noise with any distribution. We found analytical expressions of the conditional and stationary joint probability distributions of the membrane potentials and the firing rates. By manipulating the conditional probability distribution of the firing rates, we extend to stochastic networks the associating learning rule previously introduced by Personnaz and coworkers. The new learning rule allowed the safe storage, under the presence of noise, of point and cyclic attractors, with useful implications for content-addressable memories. Furthermore, we studied the bifurcation structure of the network dynamics in the zero-noise limit. We analytically derived examples of the codimension 1 and codimension 2 bifurcation diagrams of the network, which describe how the neuronal dynamics changes with the external stimuli. This showed that the network may undergo transitions among multistable regimes, oscillatory behavior elicited by asymmetric synaptic connections, and various forms of spontaneous symmetry breaking. We also calculated analytically groupwise correlations of neural activity in the network in the stationary regime. This revealed neuronal regimes where, statistically, the membrane potentials and the firing rates are either synchronous or asynchronous. Our results are valid for networks with any number of neurons, although our equations can be realistically solved only for small networks. For completeness, we also derived the network equations in the thermodynamic limit of infinite network size and we analytically studied their local bifurcations. All the analytical results were extensively validated by numerical simulations.