Asynchronous Rate Chaos in Spiking Neuronal Circuits

The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results.Author Summary: Cortical circuits exhibit complex temporal patterns of spiking and are exquisitely sensitive to small perturbations in their ongoing activity. These features are all suggestive of an underlying chaotic dynamics. Theoretical works have indicated that a rich dynamical reservoir can endow neuronal circuits with remarkable computational capabilities. Nevertheless, the mechanisms underlying chaos in circuits of spiking neurons remain unknown. We combine analytical calculations and numerical simulations to investigate this fundamental issue. Our key result is that chaotic firing rate fluctuations on the time scales of the synaptic dynamics emerge generically from the network collective dynamics. Our results pave the way in the study of the physiological mechanisms and computational significance of chaotic states in neuronal networks.