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Bidirectional Modulation of Neuronal Responses by Depolarizing GABAergic Inputs

Kenji Morita ^*, Kunichika Tsumoto ^*  and Kazuyuki Aihara ^* 

^* Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan; and Exploratory Research for Advanced Technology (ERATO) Aihara Complexity Modelling Project, Japan Science and Technology Agency, Tokyo 151-0064, Japan

Correspondence: Address reprint requests to Kenji Morita, E-mail: morita{at}sat.t.u-tokyo.ac.jp.

The reversal potential of GABA_A receptor channels is known to be less negative than the resting membrane potential under some cases. Recent electrophysiological experiments revealed that a GABAergic unitary conductance with such a depolarized reversal potential could not only prevent but also facilitate action potential generation depending on the timing of its application relative to the excitatory unitary conductance. Using a two-dimensional point neuron model, we simulate the experiments regarding the integration of unitary conductances, and execute bifurcation analysis. Then we extend our analysis to the case in which the neuron receives two kinds of periodic input trains—an excitatory one and a GABAergic one. We show that the periodic depolarizing GABAergic input train can modulate the output time-averaged firing rate bidirectionally, namely as an increase or a decrease, in a devil's-staircase-like manner depending on the phase difference with the excitatory input train. Bifurcation analysis reveals the existence of a wide variety of phase-locked solutions underlying such a graded response of the neuron. We examine how the input time-width and the value of the GABA_A reversal potential affect the response. Moreover, considering a neuronal population, we show that depolarizing GABAergic inputs bidirectionally modulate the amplitude of the oscillatory population activity.