Small conductance potassium channels cause an activity-dependent spike frequency adaptation and make the transfer function of neurons logarithmic

We made a computational model of a single neuron to study the effect of the small conductance (SK) Ca2+-dependent K+ channel on spike frequency adaptation. The model neuron comprised a Na+ conductance, a Ca2+ conductance, and two Ca2+-independent K+ conductances, as well as a small and a large (BK) Ca2+-activated K+ conductance, a Ca2+ pump, and mechanisms for Ca2+ buffering and diffusion. Sustained current injection that simulated synaptic input resulted in a train of action potentials (APs) which in the absence of the SK conductance showed very little adaptation with time. The transfer function of the neuron was nearly linear, i.e., both asymptotic spike rate as well as the intracellular free Ca2+ concentration ([Ca2+](i)) were approximately linear functions of the input current. Adding an SK conductance with a steep nonlinear dependence on [Ca2+], (Leinders and Vijverberg, 1992. Pflugers Arch. 422:223-232; Kohler, Hirschberg, Bond, Kinzie, Marrion, Maylie, and Adelman. 1996. Science. 273:1709-1714) caused a marked time-dependent spike frequency adaptation and changed the transfer function of the neuron from linear to logarithmic. Moreover, the input range the neuron responded to with regular spiking increased by a factor of 2.2. These results can be explained by a shunt of the cell resistance caused by the activation of the SK conductance. It might turn out that the logarithmic relationships between the stimuli of some modalities (e.g., sound or light) and the perception of the stimulus intensity (Fechner's law) have a cellular basis in the involvement of SK conductances in the processing of these stimuli.