The inhibitory control of traveling waves in cortical networks

Propagating waves of activity can be evoked and can occur spontaneously in vivo and in vitro. We examine the properties of these waves as inhibition varies in a cortical slice and then develop several computational models. We first show that in the slice, inhibition controls the velocity of propagation as well as the magnitude of the local field potential. We introduce a spiking model of sparsely connected excitatory and inhibitory theta neurons which are distributed on a one-dimensional domain and illustrate both evoked and spontaneous waves. The excitatory neurons have an additional spike-frequency adaptation current which limits their maximal activity. We show that increased inhibition slows the waves down and limits the participation of excitatory cells in this spiking network. Decreased inhibition leads to large amplitude faster moving waves similar to those seen in seizures. To gain further insight into the mechanism that control the waves, we then systematically reduce the model to a Wilson-Cowan type network using a mean-field approach. We simulate this network directly and by using numerical continuation to follow traveling waves in a moving coordinate system as we vary the strength and spread of inhibition and the strength of adaptation. We find several types of instability (bifurcations) that lead to the loss of waves and subsequent pattern formation. We approximate the smooth nonlinearity by a step function and obtain expressions for the velocity, wave-width, and stability. Author summaryStimuli and other aspects of neuronal activity are carried across areas in the brain through the concerted activity of recurrently connected neurons. The activity is controlled through negative feedback from both inhibitory neurons and intrinsic currents in the excitatory neurons. Evoked activity often appears in the form of a traveling pulse of activity. In this paper we study the speed, magnitude, and other properteis of these waves as various aspects of the negative feedback are altered. Inhibition enables information to be readily transmitted across distances without the neural activity blowing up into a seizure-like state.