Continuous and lurching traveling pulses in neuronal networks with delay and spatially decaying connectivity

Propagation of discharges in cortical and thalamic systems, which is used as a probe for examining network circuitry, is studied by constructing a one-dimensional model of integrate-and-fire neurons that are coupled by excitatory synapses with delay. Each neuron fires only one spike. The velocity and stability of propagating continuous pulses are calculated analytically. Above a certain critical value of the constant delay, these pulses lose stability. Instead, lurching pulses propagate with discontinuous and periodic spatio-temporal characteristics. The parameter regime for which lurching occurs is strongly affected by the footprint (connectivity) shape; bistability may occur with a square footprint shape but not with an exponential footprint shape. For strong synaptic coupling, the velocity of both continuous and lurching pulses increases logarithmically with the synaptic coupling strength gsyn for an exponential footprint shape, and it is bounded for a step footprint shape. We conclude that the differences in velocity and shape between the front of thalamic spindle waves in vitro and cortical paroxysmal discharges stem from their different effective delay; in thalamic networks, large effective delay between inhibitory neurons arises from their effective interaction via the excitatory cells which display postinhibitory rebound.

Leading role of thalamic over cortical neurons during postinhibitory rebound excitation

The postinhibitory rebound excitation is an intrinsic property of thalamic and cortical neurons that is implicated in a variety of normal and abnormal operations of neuronal networks, such as slow or fast brain rhythms during different states of vigilance as well as seizures. We used dual simultaneous intracellular recordings of thalamocortical neurons from the ventrolateral nucleus and neurons from the motor cortex, together with thalamic and cortical field potentials, to investigate the temporal relations between thalamic and cortical events during the rebound excitation that follows prolonged periods of stimulus-induced inhibition. Invariably, the rebound spike-bursts in thalamocortical cells occurred before the rebound depolarization in cortical neurons and preceded the peak of the depth-negative, rebound field potential in cortical areas. Also, the inhibitory-rebound sequences were more pronounced and prolonged in cortical neurons when elicited by thalamic stimuli, compared with cortical stimuli. The role of thalamocortical loops in the rebound excitation of cortical neurons was shown further by the absence of rebound activity in isolated cortical slabs. However, whereas thalamocortical neurons remained hyperpolarized after rebound excitation, because of the prolonged spike-bursts in inhibitory thalamic reticular neurons, the rebound depolarization in cortical neurons was prolonged, suggesting the role of intracortical excitatory circuits in this sustained activity. The role of intrathalamic events in triggering rebound cortical activity should be taken into consideration when analyzing information processes at the cortical level; at each step, corticothalamic volleys can set into action thalamic inhibitory neurons, leading to rebound spike-bursts that are transferred back to the cortex, thus modifying cortical activities.