knadapt

Package knadapt provides code for sodium (Na) gated potassium (K) currents that drive adaptation (accommodation) in neural firing. As neurons spike, driving an influx of Na, this activates the K channels, which, like leak channels, pull the membrane potential back down toward rest (or even below). Multiple different time constants have been identified and this implementation supports 3: M-type (fast), Slick (medium), and Slack (slow)

Here's a good reference:

Kaczmarek, L. K. (2013). Slack, Slick, and Sodium-Activated Potassium Channels. ISRN Neuroscience, 2013. https://doi.org/10.1155/2013/354262

This package supports both spiking and rate-coded activations.

Spiking

The logic is simplest for the spiking case:

	if spike {
		gKNa += Rise * (Max - gKNa)
	} else {
		gKNa -= 1/Tau * gKNa
	}

The KNa conductance ($g_{kna}$ in mathematical terminology, gKNa in the program) rises to a Max value with a Rise rate constant, when the neuron spikes, and otherwise it decays back down to zero with another time constant Tau.

Rate code

The equivalent rate-code equation just substitutes the rate-coded activation variable in as a multiplier on the rise term:

	gKNa += act * Rise * (Max - gKNa) - (1/Tau * gKNa)

Defaults

The default parameters, which were fit to various empirical firing patterns and also have proven useful in simulations, are:

Channel Type	Tau (ms)	Rise	Max
Fast (M-type)	50	0.05	0.1
Medium (Slick)	200	0.02	0.1
Slow (Slack)	1000	0.001	1.0