Collective stochastic coherence in recurrent neuronal networks

Abstract

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behavior in the slow oscillation regime exhibited by a cerebral cortex network under dynamical conditions resembling slow-wave sleep and anaesthesia. Computational analysis of a biologically realistic network model reveals that an intermediate level of background noise leads to quasi-regular dynamics. We verify this prediction experimentally in cortical slices subject to varying amounts of extracellular potassium, which modulates neuronal excitability and thus synaptic noise. The model also predicts that this effectively regular state should exhibit noise-induced memory of the spatial propagation profile of the collective oscillations, which is also verified experimentally. Taken together, these results allow us to construe the enhanced regularity observed experimentally in the brain as an instance of collective stochastic coherence.Recurrent networks are directed graphs with cyclic paths that can exhibit self-sustained collective dynamics. When the network nodes are threshold elements, a sufficiently large background noise will render their activity stochastic. Yet, the collective behavior of the network is frequently highly regular in time. This raises the question of how the stochastic nature of the network elements coexists with the quasi-deterministic character of the collective dynamics. While coupling has long been proposed as a regularizing mechanism for interacting sloppy oscillators [1,2], the situation is much less clear when the individual elements are not intrinsic oscillators, but exhibit noise-driven pulsatile dynamics, such as in excitable elements. A relevant instance of this situation is given by neuronal networks.Here we study the interplay between noise and collective dynamics in networks of neurons from the cerebral cortex operating in the state of slow oscillations, a dynamical regime that has been suggested as the default activity of the cortex [3]. In this physiological state, typical of slow wave sleep and anesthesia [4], the membrane potential of cortical neurons alternates at frequencies of the order of 1 Hz between the so-called UP and DOWN states [5,6]. UP states are characterized by a depolarization of the membrane voltage towards the spiking threshold and a sustained firing activity of the neurons, similar to their dynamics during wakefulness. In contrast, in the DOWN states neurons are mostly silent and exhibit a hyperpolarized membrane voltage. The fact that UP and DOWN states exist spontaneously in vitro [7,8], in the absence ...

Attractor competition enriches cortical dynamics during awakening from anesthesia

“…These results suggest that during the first part of the transition from deep to light levels of anesthesia (from D1 to D2) the SO not only became faster but also more regular, since the interquartile range, representing the range of the frequencies visited around this median value, was reduced. This increased regularity of SO is highly suggestive that there is an optimal level of the network excitability to express this rhythm, as it has been reported for the cortex in vitro (Sancristóbal et al, 2016). We explore this quantitatively in our computer model (see below).…”

“…We observed that while the Up state duration remained almost constant with a small tendency to increase, the Down state duration decreased monotonically, at some point converging to duration values very similar to those of the Up state, resulting into an increase in frequency and regularity of the SO ( Figure 2C). Remarkably, a similar stability of the Up state duration and the changes of the Down state duration has been also found in vitro when the network excitability is modulated both by extracellular potassium concentration (Sancristóbal et al, 2016) and by applying exogenous electric fields (D'Andola et al, 2018) suggesting that regular SO is an attractive dynamical regime for the isolated cortex (Sanchez -Vives et al, 2017).…”

Collective excitability in a mesoscopic neuronal model of epileptic activity

“…While in many cases coupling merely coordinates dynamical regimes that are already present in the isolated elements, in others it underlies the emergence of novel behaviors that would not exist in the absence of interaction between the elements [4,5]. In the brain, examples of such emergent behavior exist at the microscopic scale of networks of neurons, in the form of, for instance, collective oscillations arising from a balance between excitation and inhibition [6,7] and recurrent up/down dynamics [8]. Much less is known, however, about the emergent behavior of the brain at the mesoscopic level of coupled brain areas.…”

Fast reversible learning based on neurons functioning as anisotropic multiplex hubs

“…-Since the pioneering work of Donald Hebb [1], seven decades ago, the common hypothesis in the dynamics of neural networks [2][3][4][5][6] is that the network links, the synapses, are the building blocks of our brain which are responsible for the learning process [7,8]. The basic idea proposed by Hebb was that neurons that fire together, wire together, indicating a local dynamical learning rule to imprint changes in the strengths of the synapses.…”