How slow K⁺ currents impact on spike generation mechanism?

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 (I_M) and the Ca²⁺-activated K⁺ current (I_AHP), and the conductance-based (Hodgkin−Huxley type) models including the slow K⁺ currents have succeeded to reproduce the electro-physiological properties of a neuron [1].

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 I_M facilitates the spike-timing coding, whereas I_AHP improves the spike rate-coding [2] and I_M increases the response to low-frequency input signals, whereas I_AHP decreases the response to low-frequency signals [3].

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 [4]. 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 I_M and I_AHP impact on spike generation mechanism differently and the parameters of I_M and I_AHP influence spike generation.