Phenomenological models of NaV1.5: Hodgkin-Huxley and kinetic formalisms (Andreozzi et al 2019)

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"Computational models of ion channels represent the building blocks of conductance-based, biologically inspired models of neurons and neural networks. Ion channels are still widely modelled by means of the formalism developed by the seminal work of Hodgkin and Huxley (HH), although the electrophysiological features of the channels are currently known to be better fitted by means of kinetic Markov-type models. The present study is aimed at showing why simplified Markov-type kinetic models are more suitable for ion channels modelling as compared to HH ones, and how a manual optimization process can be rationally carried out for both. ..."
1 . Andreozzi E, Carannante I, D'Addio G, Cesarelli M, Balbi P (2019) Phenomenological models of NaV1.5. A side by side, procedural, hands-on comparison between Hodgkin-Huxley and kinetic formalisms Scientific Reports 9:17493 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Channel/Receptor;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Sodium;
Gap Junctions:
Gene(s): Nav1.5 SCN5A;
Simulation Environment: NEURON; Python;
Model Concept(s): Markov-type model;
Implementer(s): Carannante, Ilaria [ilariac at]; Balbi, Pietro [piero.balbi at]; Andreozzi, Emilio [emilio.andreozzi at];
Search NeuronDB for information about:  I Sodium;
Voltage clamp with "five" levels. Clamp is on at time 0, and off at time
dur[0]+dur[1]+dur[2]. When clamp is off the injected current is 0.
Do not insert several instances of this model at the same location in order to
make level changes. That is equivalent to independent clamps and they will
have incompatible internal state values.

The control amplifier has the indicated gain and time constant.  The
input amplifier is ideal.  

                +-|\____rstim____>to cell
-amp --'\/`-------|/
	        |___    __|-----/|___from cell
		    `'`'        \|

The clamp has a three states which are the voltage input of the gain amplifier,
the voltage output of the gain amplfier, and the voltage output of the
measuring amplifier.
A good initial condition for these voltages are 0, 0, and v respectively.

This model is quite stiff.  For this reason the current is updated
within the solve block before updating the state of the clamp. This
gives the correct value of the current on exit from fadvance(). If we
didn't do this and
instead used the values computed in the breakpoint block, it 
would look like the clamp current is much larger than it actually is since it
doesn't take into account the change in voltage within the timestep, ie
equivalent to an almost infinite capacitance.
Also, because of stiffness, do not use this model except with secondorder=0.

This model makes use of implementation details of how models are interfaced
to neuron. At some point I will make the translation such that these kinds
of models can be handled straightforwardly.

Note that since this is an electrode current model v refers to the
internal potential which is equivalent to the membrane potential v when
there is no extracellular membrane mechanism present but is v+vext when
one is present.
Also since i is an electrode current,
positive values of i depolarize the cell. (Normally, positive membrane currents
are outward and thus hyperpolarize the cell)


	RANGE e0,vo0,vi0,dur,amp,gain,rstim,tau1,tau2,fac,i

	(nA) = (nanoamp)
	(mV) = (millivolt)
	(uS) = (microsiemens)

	dur[NSTEP] (ms)		<0, 1e9>
	amp[NSTEP] (mV)
	gain = 1e5		<0,1e9>
	rstim = 1 (megohm)	<1e-9,1e9>
	tau1 = .001 (ms)	<0,1e9>
	tau2 = 0   (ms)		<0,1e9>
	e0 (mV) vo0 (mV) vi0(mV)
	fac=0			<1,10>

	v (mV)	: automatically v + vext when extracellular is present
	dt (ms)
	i (nA)
	stim (mV)
	tc (ms)

	e (mV)
	vo (mV)
	vi (mV)

	e0 = 0
	vo = v
	vo0 = v
	vi = v
	vi0 = v
	e = 0
	FROM j=0 TO NSTEP-1 { if (dur[j] > 0 && amp[j] != 0) {
		: nrn/lib/hoc/electrod.hoc always installs a VClamp
		: stopping cvode here if the clamp is on still allows
		: that tool to control a IClamp under cvode
		{extern int cvode_active_;
		if (cvode_active_) {
			hoc_execerror("VClamp", " does not work with CVODE");

	SOLVE update METHOD after_cvode : but not really (see above)
	i = icur()

PROCEDURE vstim() { : can't be called from update since vinput must
			: remain constant throughout dt interval and
			: update is called at t+dt
	tc = 0 (ms)
	FROM j=0 TO NSTEP-1 {
		stim = amp[j]
		tc = tc + dur[j]
		if (t < tc) {
			tc = tc + 100	: clamp is definitely not off

FUNCTION icur()(nA) {  : since this function uses range variables, it
			: should not be called from hoc. If you want to
			: know the current, look in i_vc
	LOCAL vout
	if (t > tc) {
		e0 = 0
		vo0 = 0
		icur = 0
		SOLVE clamp
		icur = (vo - v)/rstim

LINEAR clamp {
	LOCAL t1, t2
	t1 = tau1/dt
	t2 = tau2/dt
	~ vi = v + fac*vo - fac*v
	~ t2*vo - t2*vo0 + vo = -gain * e
	~ -stim - e  +  vi - e  +  t1*vi - t1*e - t1*(vi0 - e0)
	  = 0

PROCEDURE update() {
	i = icur()
	e0 = e
	vo0 = vo
	vi0 = vi
	return 0;

This implementation is not very high level since the clamp uses a state which
must be computed at the same time as the membrane potential and doesn't fit
into the paradigm normally used for channel states.
The state, vinput0, at t is integrated from its old value saved in vinput.
The value of vinput (as well as the initial values of v and the output
of the control amplifier) is updated when the SOLVE
is executed.  Notice that the icur function is very stiff with respect to
v. For this reason i is only good for the user after the SOLVE is