Nonlinear mechanism for paradoxical facilitation of spike induced by inhibitory synapse in auditory nervous system for sound localization

A paradoxical nonlinear phenomenon called post-inhibitory facilitation (PIF) has been observed in the superior olive neuron for precise sound localization, which means that an inhibitory synaptic current appearing earlier than an excitatory one does not suppress but facilitates a spike for a short interval between the two currents. Although the PIF is reproduced for type III excitability/non-bifurcation and mediated by a fast low-threshold potassium current (I_KLT), contradictorily, explained with a negative threshold related to type II excitability/Hopf bifurcation, even if in the absence of the I_KLT. In the present paper, explanations to the seemingly contradictory nonlinear and ionic current mechanisms for the PIF are presented in a modified model containing the I_KLT. Firstly, the modified model exhibits Hopf bifurcation/type II for weak or zero I_KLT, in addition to non-bifurcation/type III for strong I_KLT which resembles the original models. Secondly, the PIF can be evoked for types III and II with a positive threshold, which presents novel conditions for the PIF. Thirdly, with the excitatory current considered, some traditional positive thresholds become novel negative thresholds, which presents successful explanations to the novel PIF modulated by the I_KLT and the inhibitory and excitatory synapses. The novel PIF appears for a strong and relatively slow inhibitory synaptic current which can induce membrane potential reduced to run across the negative threshold, while not for weak or fast inhibitory current or not for novel positive thresholds related to fast excitatory synapses. Finally, the PIF with short time interval appears for type III with fast dynamics, which is mainly mediated by the fast I_KLT, resembling the experiment. The PIF with wide interval appears for type II with slow dynamics, which is mediated by the weak I_KLT and/or the slow leak current (I_L), presenting a novel current to mediate the PIF. The bifurcation/excitability, novel threshold surface, I_KLT and I_L, and inhibitory and excitatory synapses present a comprehensive viewpoint on the PIF and the potential modulations to obtain the PIF with short interval for the precise sound localization.