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Spike-frequency adaptation is a very prominent feature of spiking neurons. Using a Hodgkin-Huxley-type model, we study adaptation originating from the Na,K-ATPase electrogenic pump and its evolution in presence of a medium-duration calcium-dependent potassium channel. We find 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 interact with each other, our results suggest that their meaningful time courses and parameters cannot be directly measured by isolation through pharmacological blocking. To circumvent this limitation, we develop a simple abstract model that captures the interaction between currents and allows the direct evaluation of underlying biophysical parameters from the frequency vs. current curves. Finally, we find 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. |
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