Boosting of neural circuit chaos at the onset of collective oscillations

Abstract

Cortical networksin vivoexhibit highly irregular spiking activity to repeated stimuli. One source of such variability is network chaos, ever-present in spiking network models. In order to reliably and robustly represent and transmit information, cortical networks must implement active mechanisms to quench undesired changes in spiking patterns. Neuronal oscillations have been proposed as a mechanism to flexibly gate information flow across the cortex, but whether these collective rhythms would actually contribute to quenching spiking unreliability and tame network chaos by synchronizing activity, or on the contrary, intensify chaos by acting as a common drive to the network, is not easily predictable. Here we investigate the dynamical properties of network models with respect to two known control parameters regulating collective oscillatory activity: delayed re-current inhibition and an external periodic drive. To do so, we advanced the tractability of large spiking networks of exactly solvable neuronal models by developing a strategy that allows for exact characterization of the dynamics on the attractor of effectively delayed network models in a system with fixed and finite degrees of freedom. We find that, below the transition to collective oscillations, neuronal networks have a stereotypical dependence on the delay so far only described for scalar systems and low-dimensional maps. We demonstrate that the emergence of internally generated oscillations induces a complete dynamical reconfiguration, by increasing the dimensionality of the chaotic attractor, the speed at which nearby trajectories separate from one another, and the rate at which the network produces entropy. Our results suggest that simple temporal dynamics of the mean activity can have a profound effect on the structure of the spiking patterns and therefore on the information processing capability of neuronal networks.Significance StatementRecordingsin vivoshow that spiking patterns in response to repeated stimuli in cortex are highly variable. Here we investigate whether collective oscillations, either internally generated through delayed recurrent inhibition or by external feed-forward drive, are able to quench chaotic variability by structuring spiking patterns or if they contribute to intensifying chaos. We develop a strategy that allowed us to completely characterize the dynamics of delayed spiking circuit models by means of classic ergodic theory measures. We find that chaos is intensified at the onset of collective oscillations, but that transient oscillatory input, where the dynamics are most resembling those found in biological networks, has only a mild effect on chaos and hence on network variability.