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.

Integration of circadian and phototransduction pathways in the network controlling CAB gene transcription in Arabidopsis

The transcription of CAB genes, encoding the chlorophyll a/b-binding proteins, is rapidly induced in dark-grown Arabidopsis seedlings following a light pulse. The transient induction is followed by several cycles of a circadian rhythm. Seedlings transferred to continuous light are known to exhibit a robust circadian rhythm of CAB expression. The precise waveform of CAB expression in light–dark cycles, however, reflects a regulatory network that integrates information from photoreceptors, from the circadian clock and possibly from a developmental program. We have used the luciferase reporter system to investigate CAB expression with high time resolution. We demonstrate that CAB expression in light-grown plants exhibits a transient induction following light onset, similar to the response in dark-grown seedlings. The circadian rhythm modulates the magnitude and the kinetics of the response to light, such that the CAB promoter is not light responsive during the subjective night. A signaling pathway from the circadian oscillator must therefore antagonize the phototransduction pathways controlling the CAB promoter. We have further demonstrated that the phase of maximal CAB expression is delayed in light–dark cycles with long photoperiods, due to the entrainment of the circadian oscillator. Under short photoperiods, this pattern of entrainment ensures that dawn coincides with a phase of high light responsiveness, whereas under long photoperiods, the light response at dawn is reduced.