Neurons transmit and process information by generating action potentials (spikes). Spike generation process follows all-or-none law, that is, if the membrane potential of a neuron exceeds a threshold value that is called spike threshold, the neuron generates a stereotyped spike. The spike threshold is assumed to be constant in the conventional view.
Intracellular recordings in vivo have shown that the spike threshold of neurons is highly variable. Spike threshold variation is functionally important for several reasons. For example, the threshold variation promotes the coincidence detection of synaptic inputs, improves signal transmission of a neuron, and sharpens the feature selectivity of a sensory neuron.
Among cellular mechanisms underlying the spike threshold variation, the ion channel kinetics may be considered to be essential. To understand the biophysical mechanism underlying the threshold variation, we examined the spike threshold of an extended Hodgkin-Huxley model that contains sodium, potassium, muscarinic potassium (IM), calcium and calcium-dependent potassium current (IAHP) (Pospischil et. al., Biol Cybern, 2008; Tsubo et. al., Neural Netw, 2004). It is shown that the ionic currents after a spike are approximated by the sum of exponential functions and an extended multi-timescale adaptive threshold model (Kobayashi et. al., Front Comput Neurosci, 2009) can approximate the detailed Hodgkin-Huxley model accurately. The result suggests that the spike threshold is mainly modulated by the slow K+ currents, i.e., IM and IAHP. The analysis shows that the slow K+ currents contribute to the spike-frequency adaptation, however, they modulate the threshold differently. Specifically, IM increases the threshold immediately after a spike, whereas IAHP increases it with a delay (~50 [ms]).