Oscillatorylike behavior in feedforward neuronal networks.
We demonstrate how rhythmic activity can arise in neural networks from feedforward rather than recurrent circuitry and, in so doing, we provide a mechanism capable of explaining the temporal decorrelation of γ-band oscillations. We compare the spiking activity of a delayed recurrent network of inhibitory neurons with that of a feedforward network with the same neural properties and axonal delays. Paradoxically, these very different connectivities can yield very similar spike-train statistics in response to correlated input. This happens when neurons are noisy and axonal delays are short. A Taylor expansion of the feedback network's susceptibility-or frequency-dependent gain function-can then be stopped at first order to a good approximation, thus matching the feedforward net's susceptibility. The feedback network is known to display oscillations; these oscillations imply that the spiking activity of the population is felt by all neurons within the network, leading to direct spike correlations in a given neuron. On the other hand, in the output layer of the feedforward net, the interaction between the external drive and the delayed feedforward projection of this drive by the input layer causes indirect spike correlations: spikes fired by a given output layer neuron are correlated only through the activity of the input layer neurons. High noise and short delays partially bridge the gap between these two types of correlation, yielding similar spike-train statistics for both networks. This similarity is even stronger when the delay is distributed, as confirmed by linear response theory.
Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Canada K1N 6N5.
Alexandre
A
Payeur
Department of Cell and Molecular Medicine, University of Ottawa, 451 Smyth Road, Ottawa, Canada K1H 8M5.
Leonard
L
Maler
Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Canada K1N 6N5 and Department of Cell and Molecular Medicine, University of Ottawa, 451 Smyth Road, Ottawa, Canada K1H 8M5.
André
A
Longtin
D000200:Action Potentials / Q000502:physiology; D005246:Feedback; D065818:Gamma Rhythm / Q000502:physiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D010507:Periodicity