## action potectial amplitude

thats_karlo
Posts: 108
Joined: Thu Sep 08, 2005 11:49 am

### action potectial amplitude

Hi,

Consider a simple single compartment model with inserted "hh" mechanism. Then, for a given amplitude of current clamp model generates several action potential for a specific set of geometry, passive and active property. (assume model generate 4 spikes and action potential amplitude is around +40 mV).However, when some parameters in the model are changed, still model generates a firing pattern but maximum amplitude of AP changes dramatically and for example it finds a value equal to 0 mV.

I thought when model fires an action potential its amplitude has to be constant during firing pattern and even for different set of model parameters.

Code: Select all

``````create A
A {L=10 diam=10 insert hh }
// insert a current clamp  (del= 200 dur =100 amp=0.02 )``````
run the code . you will get 6 spike: maximum amplitude of first spike is ~39mV and other ~28mV, why difference between first and other spikes amplitude?
and if for example you changed the A.diam=1 you will get more spike (cause of higher input resistance ) but maximum amplitude of first spike is ~42mV and other ~0 mV. Why such a big difference amplitude between these two case?
ted
Posts: 5784
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
Contact:

### Re: action potectial amplitude

thats_karlo wrote:I thought when model fires an action potential its amplitude has to be constant during firing pattern and even for different set of model parameters.
In a model, and also in a real cell, the total membrane ionic current must be equal and opposite to the total membrane capacitive current (because of conservation of charge). For a single compartment model, or an electrically compact cell, this fact can be expressed by the equation

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``````c*dv/dt = SUMMA i_x
x``````
where the i_x are the currents attributable to each of the ionic species x.

At any point where v reaches a maximum or minimum, dv/dt is 0. Therefore at any maximum or minimum of membrane potential, the sum of all ionic currents must be 0.

Imagine a single compartment model with three ionic currents: sodium, potassium, and leak. Then at the spike peak, 0 = gNa * (v - eNa) + gK * (v - eK) + gL * (v - eL) where gx and ex are the membrane conductance and equilibrium potential for ionic species x. Solving for v gives v = (gNa*eNa + gK * eK + gL * eL)/(gNa + gK + gL).

Notice that
1. the denominator is the total membrane conductance gm
2. gNa/gm, gK/gm, and gL/gm are the fractions of membrane conductance that are attributable to sodium, potassium, and leak.
3. membrane potential at the peak of the spike is the average of the ionic equilibrum potentials, weighed by their fractional contribution to total membrane conductance. In other words, the peak membrane potential is the weighted sum of the ionic equilibrium potentials at the time of the spike peak.

At the peak of the spike, membrane potential will be closest to the equilibrium potential of whichever ionic species makes the biggest contribution to total membrane conductance. Anything that makes gK larger, or gNa smaller, at the peak of the spike, will reduce the peak amplitude of the spike.

What do you think happens to gK activation during injection of a sustained depolarizing current? And what do you think happens to gNa inactivation during injection of a sustained depolarizing current? Can you use a model to test your predictions? e.g. by demonstrating the time course of gK and gNa during repetitive spiking?

This really belongs under General Questions and Discussions about Computational Neuroscience; I will move this thread to that area, and leave a "shadow topic" in its original location.
thats_karlo
Posts: 108
Joined: Thu Sep 08, 2005 11:49 am

### Re: action potectial amplitude

Thanks for all your points on my question. As an example, I run the code in Neuron Tutorial , sthA.hoc. and as a simple case i compared results for two situations, when (1) soma.diam=18.8, (2) soma.diam=1.88. For the second case the total ionic current is much smaller than (1) and therefore the action potential amplitude changes from ~38mV to ~-10mV ( Vinit=-65 mV). Let me ask my question with other words:
If we want to have the same amplitude of AP in the (2) model, which parameters have to changed, or even is it possible ? (i increased (decreased) capacitance/ gnabar_hh/gkabar_hh/ gl_hh and never got an action potentials with amplitude around 38mV ). What strategy small or big cell - with the same electrophysiological responses- dose follow to generate the same amplitude of AP?
ted
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Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
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### Re: action potectial amplitude

thats_karlo wrote:If we want to have the same amplitude of AP in the (2) model, which parameters have to changed, or even is it possible ? (i increased (decreased) capacitance/ gnabar_hh/gkabar_hh/ gl_hh and never got an action potentials with amplitude around 38mV ). What strategy small or big cell - with the same electrophysiological responses- dose follow to generate the same amplitude of AP?
Real cells know how to do this without any outside help, by adjusting expression of ion channels. The modeler's equivalent is channel densities. Leak probably won't have much effect.
thats_karlo
Posts: 108
Joined: Thu Sep 08, 2005 11:49 am

### Re: action potectial amplitude

The modeler's equivalent is channel densities. Leak probably won't have much effect.
I'm using sthA.hoc in Tutorial section of NEURON. in this model except leak current we only have gnabar_hh and gkbar_hh.
increasing gnabar to 0.2 (default is 0.12). makes cell more excitable. and it generates AP even without any injected current for vint=-65. and AP amplitude is close to 38mV. To keep membrane potential constant and equal to -65 mV before injected current depolarized current, i used another hyperpolarized current (-0.001nA). in this situation again AP amplitude backs to -10 mV. I checked for other possible value of model parameters and never got AP with amplitude close to 38 mV (as default). Any advices?!
ted