Spike-frequency adaptation is modulated by interacting currents in an Hodgkin-Huxley-type model: Role of the Na,K-ATPase

Spike-frequency adaptation is a prominent feature of spiking neurons. Using a Hodgkin-Huxley-type model, we studied adaptation originating from the Na,K-ATPase electrogenic pump and its evolution in presence of a medium-duration calcium-dependent potassium channel. We found that the Na,K-ATPase induces spike-frequency adaptation with a time constant of up to a few seconds and interacts with the calcium-dependent potassium current through the output frequency, yielding a very typical pattern of instantaneous frequencies. Because channels responsible for spike-frequency adaptation can interact with each other, our results suggest that their meaningful time courses and parameters can be difficult to measure experimentally. To circumvent this problem, we developed a simple phenomenological model that captures the interaction between currents and allows the direct evaluation of the underlying biophysical parameters directly from the frequency vs. current curves. Finally, we found that for weak stimulations, the pump induces phasic spiking and linearly converts the stimulus amplitude in a finite number of spikes acting like an inhibitory spike-counter. Our results point to the importance of considering interacting currents involved in spike-frequency adaptation collectively rather than as isolated elements and underscore the importance of sodium as a messenger for long-term signal integration in neurons. Within this context, we propose that the Na,K-ATPase plays an important role and show how to recover relevant biological parameters from adapting channels using simple electrophysiological measurements.