Dynamics of self-sustained asynchronous-irregular activity in random networks of spiking neurons with strong synapses.

Birgit Kriener,Tom Tetzlaff,Hans E Plesser,Marc-Oliver Gewaltig,Gaute T Einevoll,Hã¥Kon Enger

doi:10.3389/fncom.2014.00136

Abstract

Random networks of integrate-and-fire neurons with strong current-based synapses can, unlike previously believed, assume stable states of sustained asynchronous and irregular firing, even without external random background or pacemaker neurons. We analyze the mechanisms underlying the emergence, lifetime and irregularity of such self-sustained activity states. We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network. Thus, by increasing the synaptic coupling strength, the system can become bistable: In addition to the quiescent state, a second stable fixed-point at moderate firing rates can emerge by a saddle-node bifurcation. Inherently generated fluctuations of the population firing rate around this non-trivial fixed-point can trigger transitions into the quiescent state. Hence, the trade-off between the magnitude of the population-rate fluctuations and the size of the basin of attraction of the non-trivial rate fixed-point determines the onset and the lifetime of self-sustained activity states. During self-sustained activity, individual neuronal activity is moreover highly irregular, switching between long periods of low firing rate to short burst-like states. We show that this is an effect of the strong synaptic weights and the finite time constant of synaptic and neuronal integration, and can actually serve to stabilize the self-sustained state.

Highlights

The sustained activity of populations of spiking neurons, even in the absence of external input, is observed in many circumstances, amongst them spontaneously active neurons in cell cultures, in vitro slice preparations and even in toto preparations of whole brain parts, such as cortical slabs (Burns and Webb, 1979; Timofeev et al, 2000) or the entire hippocampus (Ikegaya et al, 2013)
We show how taking this into account in a simple escape rate model can explain the observed lifetimes of the persistent activation as a function of the network coupling parameters g and J: If the fluctuations are too strong, the system can escape the basin of attraction and activity spontaneously breaks down, while for other g-J-pairs the escape probability becomes very small and the system is virtually stable on biologically relevant time scales
We investigate the transition in the dynamic behavior that random networks of inhibitory and excitatory leaky integrate-and-fire (LIF) neurons undergo when the synaptic coupling strength J is increased

Summary

Introduction

The sustained activity of populations of spiking neurons, even in the absence of external input, is observed in many circumstances, amongst them spontaneously active neurons in cell cultures (see e.g., Marom and Shahaf, 2002; Wagenaar et al, 2006), in vitro slice preparations (see e.g., Plenz and Aertsen, 1996; Mao et al, 2001; Cossart et al, 2003; Shu et al, 2003) and even in toto preparations of whole brain parts, such as cortical slabs (Burns and Webb, 1979; Timofeev et al, 2000) or the entire hippocampus (Ikegaya et al, 2013) Another prominent phenomenon in this context is the existence of up and down states in striatum and cortex, i.e., states in which neurons switch between two preferred membrane potentials: In the so-called down-state membrane potentials are close to the resting value, corresponding to a quiescent state, while in the so-called up-states membrane potentials are at a depolarized level that allows for the emission of spikes.

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Conclusion