Anomalous Spike in A-conductance

[lb5999]

Hi NEURON Forum,

I am using a .mod file called borgka.mod, which is a model of the A-current membrane mechanism. This transient outward potassium current activates during the rising phase of an afterhyperpolarisation, and consequently prolonges the AHP.. delaying the return to resting potential/increasing the interspike interval.

borgka.mod:

http://senselab.med.yale.edu/ModelDb/sh ... borgka.mod

The trouble with this .mod file is that the nature of the timeconstants means that the A-current also activates on the falling phase of the AHP, and indeed the action potential; during this period, the membrane potential is both strongly activated and deinactivating. This, combined, with the relative response speeds of the gates (as specified by the time-constants), results in an anomalous spike in A-conductance. This results in counterintuitive results; the spike in A-conductance happens way before it biologically occurs, and consequently the AHP tends to shorten as, for example, the maximal conductance density of the channel is increased.

I was wondering whether there was a way of specifying in this .mod file that A-conductance could only flow on the upstroke of an AHP? I am not familiar with how to modify NMODL files, so it would be difficult for me to implement this. I thought that perhaps constraining A-current to flow when the derivative of the membrane potential is positive would mean that it would only flow during the upstroke of the afterhyperpolarisation (assuming that the parameter values didn't mean that it could potential activate during the upstroke of an action potential, too)... how would I implement this? Is there a more robust way to insure A-current only flows from an inactivated state?

Thanks,

lb

[ted]

Interesting. Can be examined in a single compartment model with hh and borgka, with gkabar_borgka = 0, and plotting n_borgka*l_borgka during a spike. The activation state n increases rapidly upon depolarization but decays only very slowly thereafter. The inactivation state l (lower case L) falls slowly and slightly while v rises above resting membrane potential, but rises _above_ its resting level during the post-spike hyperpolarization. It is this increase of l that makes the product l*n, hence the conductance of the borgka mechanism, show a prolonged increase--slightly above the maximum that it attains during the rising phase of the spike!--that persists for tens of seconds after the spike.

I was wondering whether there was a way of specifying in this .mod file that A-conductance could only flow on the upstroke of an AHP? . . . I thought that perhaps constraining A-current to flow when the derivative of the membrane potential is positive would mean that it would only flow during the upstroke of the afterhyperpolarisation . . . how would I implement this?

That would be a crude hack.

Is there a more robust way to insure A-current only flows from an inactivated state?

The question is how to get the current time course that you want without having to use ad hoc tricks. To me it looks like the problem is with the time course of n, which takes far too long to collapse after v repolarizes. That brings the voltage dependence of its time constant into question. You might check whatever source(s) served as the empirical basis for this mechanism, to see if the implementation has strayed from what the original data showed.

Another alternative is to look for a different A current mechanism. ModelDB contains lots of models implemented with NEURON that involve A currents, and only a few of them use borgka.mod (or bgka.mod which in at least one case seems on first glance to be identical to the problematic borgka.mod).

[lb5999]

Thanks Ted, thats brilliant. I'll let you know how I get on.

lb

[ted]

The A current specified by borgka.mod behaves more like a D current.