Previous work has shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons can reveal oscillatory activity. For example, Börgers and Kopell (2003) have shown that oscillations occur when the excitatory neurons receive a sufficiently large input. A constant drive to the excitatory neurons is sufficient for oscillatory activity. Other studies (Doiron, Chacron, Maler, Longtin, & Bastian, 2003; Doiron, Lindner, Longtin, Maler, & Bastian, 2004) have shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons reveal oscillatory activity only if the excitatory neurons receive correlated input, regardless of the amount of excitatory input. In this study, we show that these apparently contradictory results can be explained by the behavior of a single model operating in different regimes of parameter space. Moreover, we show that adding dynamic synapses in the inhibitory feedback loop provides a robust network behavior over a broad range of stimulus intensities, contrary to that of previous models. A remarkable property of the introduction of dynamic synapses is that the activity of the network reveals synchronized oscillatory components in the case of correlated input, but also reflects the temporal behavior of the input signal to the excitatory neurons. This allows the network to encode both the temporal characteristics of the input and the presence of spatial correlations in the input simultaneously.

A minimal model is presented to explain changes in frequency, shape, and amplitude of Ca 2+ oscillations in the neuroendocrine melanotrope cell of Xenopus Laevis . It describes the cell as a plasma membrane oscillator with influx of extracellular Ca 2+ via voltage-gated Ca 2+ channels in the plasma membrane. The Ca 2+ oscillations in the Xenopus melanotrope show specific features that cannot be explained by previous models for electrically bursting cells using one set of parameters. The model assumes a K Ca -channel with slow Ca 2+ -dependent gating kinetics that initiates and terminates the bursts. The slow kinetics of this channel cause an activation of the K Ca -channel with a phase shift relative to the intracellular Ca 2+ concentration. The phase shift, together with the presence of a Na + channel that has a lower threshold than the Ca 2+ channel, generate the characteristic features of the Ca 2+ oscillations in the Xenopus melanotrope cell.