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August  2012, 32(8): 2729-2757. doi: 10.3934/dcds.2012.32.2729

Type III excitability, slope sensitivity and coincidence detection

 1 Dynamics and Control, Beihang University, Beijing, China 2 Center for Neural Science, New York University, United States 3 Center for Neural Science, and Courant Institute of Mathematical Sciences, New York University, United States

Received  May 2011 Revised  July 2011 Published  March 2012

Some neurons in the nervous system do not show repetitive firing for steady currents. For time-varying inputs, they fire once if the input rise is fast enough. This property of phasic firing is known as Type III excitability. Type III excitability has been observed in neurons in the auditory brainstem (MSO), which show strong phase-locking and accurate coincidence detection. In this paper, we consider a Hodgkin-Huxley type model (RM03) that is widely-used for phasic MSO neurons and we compare it with a modification of it, showing tonic behavior. We provide insight into the temporal processing of these neuron models by means of developing and analyzing two reduced models that reproduce qualitatively the properties of the exemplar ones. The geometric and mathematical analysis of the reduced models allows us to detect and quantify relevant features for the temporal computation such as nearness to threshold and a temporal integration window. Our results underscore the importance of Type III excitability for precise coincidence detection.
Citation: Xiangying Meng, Gemma Huguet, John Rinzel. Type III excitability, slope sensitivity and coincidence detection. Discrete & Continuous Dynamical Systems - A, 2012, 32 (8) : 2729-2757. doi: 10.3934/dcds.2012.32.2729
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