Responses of recurrent nets of asymmetric ON and OFF cells

A neural field model of ON and OFF cells with all-to-all inhibitory feedback is investigated. External spatiotemporal stimuli drive the ON and OFF cells with, respectively, direct and inverted polarity. The dynamic differences between networks built of ON and OFF cells (“ON/OFF”) and those having only ON cells (“ON/ON”) are described for the general case where ON and OFF cells can have different spontaneous firing rates; this asymmetric case is generic. Neural responses to nonhomogeneous static and time-periodic inputs are analyzed in regimes close to and away from self-oscillation. Static stimuli can cause oscillatory behavior for certain asymmetry levels. Time-periodic stimuli expose dynamical differences between ON/OFF and ON/ON nets. Outside the stimulated region, we show that ON/OFF nets exhibit frequency doubling, while ON/ON nets cannot. On the other hand, ON/ON networks show antiphase responses between stimulated and unstimulated regions, an effect that does not rely on specific receptive field circuitry. An analysis of the resonance properties of both net types reveals that ON/OFF nets exhibit larger response amplitude. Numerical simulations of the neural field models agree with theoretical predictions for localized static and time-periodic forcing. This is also the case for simulations of a network of noisy integrate-and-fire neurons. We finally discuss the application of the model to the electrosensory system and to frequency-doubling effects in retina.