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.

Vibrissa motoneurons (vMNs) generate rhythmic firing that controls whisker movements, even without cortical, cerebellar, or sensory inputs. vMNs receive serotonergic modulation from brain stem areas, which mainly increases their persistent sodium conductance ( gNaP) and, possibly, phasic input from a putative central pattern generator (CPG). In response to serotonergic modulation or just-suprathreshold current steps, vMNs fire at low rates, below the firing frequency of exploratory whisking. In response to periodic inputs, vMNs exhibit nonlinear suprathreshold resonance in frequency ranges of exploratory whisking. To determine how firing patterns of vMNs are determined by their 1) intrinsic ionic conductances and 2) responses to periodic input from a putative CPG and to serotonergic modulation, we construct and analyze a single-compartment, conductance-based model of vMNs. Low firing rates are supported in extended regimes by adaptation currents and the minimal firing rate decreases with gNaP and increases with M-potassium and h-cation conductances. Suprathreshold resonance results from the locking properties of vMN firing to stimuli and from reduction of firing rates at low frequencies by slow M and afterhyperpolarization potassium conductances. h conductance only slightly affects the suprathreshold resonance. When a vMN is subjected to a small periodic CPG input, serotonergically induced gNaP elevation may transfer the system from quiescence to a firing state that is highly locked to the CPG input. Thus we conclude that for vMNs, the CPG controls firing frequency and phase and enables bursting, whereas serotonergic modulation controls transitions from quiescence to firing unless the CPG input is sufficiently strong.

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 SummaryCortical 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 PLOS Computational Biology |