Can action potential propagation be modeled by joining several RC circuits?

In summary, small fibres have low speed and larger ones have a higher one but, in my opinion, since membrane thickness doesn't really vary in unmyelinated axons, capacity is enlarged!" The capacity (amount of charge that can be stored) of a capacitor is increased as the cross-sectional area (the size of the individual plates) decreases. This is because the smaller the area, the more space there is for the charge to be distributed evenly across the plates.
  • #1
somasimple
Gold Member
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Hi All,

I took the following from this page. http://en.wikipedia.org/wiki/Action_potential

The action potential

When a stimulus arrives at a receptor or nerve ending, its energy causes a temporary reversal of the charges on the neuron cell surface membrane. As a result, the negative charge of 70 mV inside the membrane becomes a positive charge of around +40mV. This is known as the action potential, and in this condition the membrane is said to be depolarised. (See depolarization) This depolarization occurs because channels in the axon membrane change shape, and hence open or close, depending on the voltage across the membrane. They are therefore called voltage-gated ion channels. The sequence of events is described below.

1. At resting potential some potassium leak channels are open but the voltage-gated sodium channels are closed. Potassium diffusing down the potassium concentration gradient creates a negative-inside membrane potential.
2. A local membrane depolarization caused by an excitatory stimulus causes some voltage-gated sodium channels in the neuron cell surface membrane to open and therefore sodium ions diffuse in through the channels along their electrochemical gradient. Being positively charged, they begin a reversal in the potential difference across the membrane from negaitve-inside to positive-inside. Initially, the inward movement of sodium ions is also favored by the negative-inside membrane potential.
3. As sodium ions enter and the membrane potential becomes less negative, more sodium channels open, causing an even greater influx of sodium ions. This is an example of positive feedback. As more sodium channels open, the sodium current dominates over the potassium leak current and the membrane potential becomes positive inside.
4. Once a membrane potential of around +40 mV has been established, voltage-sensitive inactivation gates of the sodium channels, sensitive to the now positive membrane potential gradient, close (so further influx of sodium is prevented). While this occurs, the voltage-sensitive activation gates on the voltage-gated potassium channels begin to open.
5. As voltage-gated potassium channels open and there is a large outward movement of potassium ions driven by the potassium concentration gradient and initially favored by the positive-inside electrical gradient. As potassium ions diffuse out, this movement of positive charge causes a reversal of the membrane potential to negative-inside and repolarisation of the neuron back towards the large negative-inside resting potential.
6. The large outward current of potassium ions through the voltage-gated potssium channels causes the temporary overshoot of the electrical gradient, with the inside of the neuron being even more negative (relative to the outside) than the usual resting potential. This is called hyperpolarisation (hyperpolarization). The voltage-sensitive inactivation gates on the potassium channels now close and the continual movement of potassium through potassium leak channels again dominates the membrane potential. Sodium-potassium pumps continue to pump sodium ions out and potassium ions in, preventing any long-term loss of the ion gradients. The resting potential of -70 mV is re-established and the neuron is said to be repolarised.

Propagation
Propagating action potentials can be modeled by joining several RC circuits, each one representing a patch of membrane.
Enlarge
Propagating action potentials can be modeled by joining several RC circuits, each one representing a patch of membrane.

In unmyelinated axons, action potentials propagate as an interaction between passively spreading membrane depolarization and voltage-gated sodium channels. When one patch of cell membrane is depolarized enough to open its voltage-gated sodium channels, sodium ions enter the cell by facilitated diffusion. Once inside, positively-charged sodium ions "nudge" adjacent ions down the axon by electrostatic repulsion (analogous to the principle behind Newton's cradle) and attract negative ions away from the adjacent membrane. As a result, a wave of positivity moves down the axon without any individual ion moving very far. Once the adjacent patch of membrane is depolarized, the voltage-gated sodium channels in that patch open, regenerating the cycle. The process repeats itself down the length of the axon, with an action potential regenerated at each segment of membrane.

The main impediment to conduction speed in unmyelinated axons is membrane capacitance. In an electric circuit, the capacity of a capacitor can be decreased by decreasing the cross-sectional area of its plates, or by increasing the distance between plates.

I'm lost with these comments because I learned that small fibres have low speed and larger ones have a higher one but, in my opinion, since membrane thickness doesn't really vary in unmyelinated axons, capacity is enlarged!

That seems to contradict the wiki?
 
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  • #2
The smaller the cross-sectional area of the fiber the more resistance to current and thus the slower the conduction velocity. This is derived from the assumption that an axon is equivalent to a cylinderical wire or cable. Just think of the equation for resistance of a wire Resistance is proportional to (Resistivity Constant) * (Characteristic Length)*1/(Cross-sectional Area).

I'm not really sure what you mean when you say the capacitance is enlarged. Can you re-word it for me please.
 
  • #3
Hi,

Thanks for your reply.
If membrane is taken as the insulator of your cable, it is assumed that the thickness of this insulator change the capacitance property of the cable.

With small fibres, the ratio axon diameter/membrane involves a low capacitance and thus a high speed of propagation (see text above).

In large fibres, axon diameter is larger but membrane is quite constant then capacitance is increased and normally as they stated, the speed may be lowered? It is a fact that large fibres are faster than small ones.
 
  • #4
I'm not a neuroscience expert, but I can tell you somethings from what I've learned.

The resting potential that is negative inside with the outside as reference is only true for places very close to the membrane. By this I mean that if you count all the ions inside the cell (includes axon) and divided by the volume of the cell to get the concentration, you would find that if this is done for the same volume outside the cell you would get the same concentrations. The only places the concentrations are different are very close to the membrane due to the myriad of protein channels and pumps.
Using this information I would say that the capacitance shouldn't depend on the diameter of the axon, since the thickness of it is all that the ions in close proximity "care" about. Maybe someone else can help, but this is my take.
 
  • #5
Hi,
Thanks again, but the small citations are made by neuroscientists and biologists.

Using this information I would say that the capacitance shouldn't depend on the diameter of the axon, since the thickness of it is all that the ions in close proximity "care" about. Maybe someone else can help, but this is my take.

Hmm, Could we reverse the statement like that?
Since the close proximity of ions in the axon, and its membrane thickness, I would say that diameter of the axon and capacitance are not linked to the speed of propagation?
 
  • #6
somasimple said:
If membrane is taken as the insulator of your cable, it is assumed that the thickness of this insulator change the capacitance property of the cable.

This may be the wrong way to think about an axon. The membrane of the axon contains ion channels that actively pump ions inwards and outwards across the membrane to change (or restore, or maintain) the potential. So it's not accurate to say that the membrane is an insulator since the "resting" membrane works pretty hard to shepherd ions around.

Although I don't know how cross-section affects speed of conduction, my guess would be that more cross-section means more surface area, which means more ion channels.
 
  • #7
Solitons

somasimple wrote:

< I'm lost with these comments because I learned that small fibres have low speed and larger ones have a higher one but, in my opinion, since membrane thickness doesn't really vary in unmyelinated axons, capacity is enlarged! >

Hopefully, this webpage may be of help.

Solitons- Solitary wave packets
http://www.diamondhead.net/p2-4.htm


With regards
Lew
 
  • #8
Hi All,

Action potential propagation is not solitonic at all. It can't. I thought it was but I'm convinced that the solution goes with a similar but complex solution.
http://www.somasimple.com/forums/showthread.php?t=867
BTW, I agree with many points of the page you posted.

It has been tested. when two APs coming from opposite direction, "collide", they vanish. It seems to me very understandable.

BTW, I elaborated a theory based upon facts.
Perhaps are you able to bring your criticisms?

http://www.somasimple.com/forums/showthread.php?t=2536
http://www.somasimple.com/forums/showthread.php?t=1191
http://www.somasimple.com/forums/showthread.php?t=958
 
Last edited:

1. What is an action potential?

An action potential is an electrical signal that travels along the membrane of a neuron. It is responsible for carrying information between neurons and is essential for communication within the nervous system.

2. How does an action potential occur?

An action potential occurs when the membrane potential of a neuron reaches a certain threshold, causing a rapid depolarization of the membrane. This depolarization then triggers the opening of voltage-gated ion channels, allowing an influx of positively charged ions into the cell. This influx of ions creates an electrical current that travels down the length of the neuron.

3. What is the importance of the action potential?

The action potential is important because it allows for rapid and efficient communication within the nervous system. It allows for the transmission of signals between neurons, which is essential for processes such as movement, sensation, and cognitive function.

4. Can an action potential be inhibited?

Yes, an action potential can be inhibited. This can occur through a process called hyperpolarization, where the membrane potential becomes more negative, making it more difficult for an action potential to occur. Additionally, certain drugs and medications can also inhibit action potentials by blocking the opening of ion channels.

5. How does the action potential end?

The action potential ends when the membrane potential returns to its resting state. This is achieved through the closing of voltage-gated ion channels and the opening of potassium channels, allowing for the outflow of positively charged ions, which restores the membrane potential to its negative resting state.

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