How slow K+ currents impact on spike generation mechanism?
KeywordsFiring Rate Pyramidal Neuron Threshold Model Adaptive Threshold Spike Generation
Neuronal adaptation is the change in the responsiveness of a neuron over time, and may improve coding information from an environment. Adaptation originates from various factors, including single neurons, synapses, and network dynamics. Here we investigate adaptation in a responsiveness of a neuron. When a neuron received prolonged stimulation, it initially responds with a high firing rate, and the firing rate decrease. This is called spike-frequency adaptation, which is observed in most pyramidal neurons in various animals. Spike-frequency adaptation is usually accounted for by slow K+ currents, for example, the M-type K+ current (IM) and the Ca2+-activated K+ current (IAHP), and the conductance-based (Hodgkin−Huxley type) models including the slow K+ currents have succeeded to reproduce the electro-physiological properties of a neuron .
The detailed biophysical mechanism underlying spike-frequency adaptation may impact on the coding property of a neuron [2, 3]. For example, it was suggested that IM facilitates the spike-timing coding, whereas IAHP improves the spike rate-coding  and IM increases the response to low-frequency input signals, whereas IAHP decreases the response to low-frequency signals .
Due to the complexity of the conductance-based models, it is not clear how the slow K+ currents impact on spike generation mechanism, more specifically, how the parameters of the slow K+ currents regulate spike generation. For understanding the impact of slow K+ currents, we have developed a framework to reduce a detailed conductance-based model with slow K+ currents to an adaptive threshold model . We have deduced a formula that links the slow K+ parameters to the parameters of the reduced model. The formula was validated with the simulation of the detailed model. This formula clarifies how IM and IAHP impact on spike generation mechanism differently and the parameters of IM and IAHP influence spike generation.
This study was supported by JSPS KAKENHI Grant Number 24500372, 25870915, 25115728. We thank Shigeru Shinomoto and Romain Brette for stimulating discussions.
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