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How is membrane capacitance related to the increased speed of saltatory conduction?

How is membrane capacitance related to the increased speed of saltatory conduction?


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Here is the original question which inspired my question. As explained by the answers there, the reason saltatory conduction in myelinated neurons is faster than non-myelinated conduction is because the capacitance of the membrane is lowered by reducing the number of channels (Channel density) or equivalently, increasing the spacing between channels. I also did a preliminary study of membrane electrodynamic modelling here and here.

From what I gathered from the linked question, the decreased capacitance overcompensates the effect of absence of channels reinforcing the sodium current, and on the whole, increases the speed of conduction by allowing the depolarizing potential to travel to the adjacent node faster than in case of an unmyelinated fibre. In view of this, I have a question:-

Why does lower capacitance increase "the effectiveness of nearby nodes" or allow the depolarizing voltage to "travel not by ion diffusion, but as an electric field"? I am comfortable with capacitors and related physics, but why would lower capacitance allow propagation of the changing voltage as an electric field, is still unclear to me? (The links I have placed also help quantify the problem mathematically. This allows us to say that $lambda$, or the rate of spatial decay of potential, increases, decreasing the effective length of the neuron. Why should its decrease help faster conduction?)

And another question is, how would reduced density of sodium voltage gated channels cause a decreased capacitance?


Very nice question! I'll go through your three questions sequentially.

Q1: Why does lower capacitance increase "the effectiveness of nearby nodes" or allow the depolarizing voltage to "travel not by ion diffusion, but as an electric field"?

A: Capacitance basically results in sequestering of charge of opposite polarities along the cell membrane, which basically results in a neutralization of charge differences. The effect of this is explained on the website of Amrita and I quote:

[… ] a higher capacitance results in a lower potential difference. In a cellular sense, increased capacitance requires a greater ion concentration difference across the membrane.

What myelin does is insulating the neuron, thereby decreasing its capacitance. You could say that by increasing the thickness of the membrane, the negative insides of the cell do not attract positive charge outside the cell. It's a bit simplified, yet it effectively describes what myelin does (see cambridge web page on capacitance).

So in a myelinated axon, when Na+ enters the cell in a node of Ranvier, the positive charge entering the cell is not counterbalanced by outside negative charge and hence, the charge is not or at least less counterbalanced. This allows for the depolarizing potential to be transmitted by electric charge. If there were no myelin, the depolarizing potential would fade out pretty quickly along the axon by neutralizing charges outside the cell. Without myelin the opening of more sodium channels in the direct vicinity are necessary not only to transmit the action potential across the axon, but it is also necessary to amplify the signal to prevent it from dying out. In a myelinated axon, hence, the depolarizing potential reaches much farther and in answer to your next question:

Q2:This allows us to say that λ, or the rate of spatial decay of potential, increases, decreasing the effective length of the neuron. Why should its decrease help faster conduction?)

One could say that myelination effectively decreases the length of the axon (the lamba parameter) as the depolaring potential reaches further along the axon.

The fact that the depolarizing potential reaches further means that voltage-operated sodium channels can be activated at larger distances from a certain depolaring potential. Hence, adjacent nodes of Ranvier can be spaced by as much as 1.5 mm. Due to the fact that the next node is activated by passive spread of an electric field, which is pretty much instant, it skips the intervening distance with about light speed, greatly enhancing conduction velocity.

Q3: And another question is, how would reduced density of sodium voltage gated channels cause a decreased capacitance?

Basically there are no ion channels below a myelin sheath as they are totally useless there. It is the myelin that decreases capacitance and there happen to be no channels underneath.


The Hodgkin-Huxley model:

$$I=C_mfrac{dV}{dt} + g_k(V_m - V_k) + g_{Na}(V_m - V_{Na}) + g_l(V_m- V_l)$$

Where $C_m$ is membrane capacitance per unit area and $g_i$ are membrane conductances.

Reducing the number of channels does not affect capacitance; it basically reduces membrane conductance.

Myelination causes reduction of number of channels (concentrating them only at the nodes of Ranivier) and also increases the effective membrane thickness.

Capacitance decreases as an inverse function of "inter-plate distance" (of parallel plates) which is the membrane thickness. This reduces the capacitative current.It also prevents the build up charge and thereby allowing it to propagate forward (Longitudinal current). IMO, the effect of myelination of capacitance would be much less than that of its effect on conductance.


Why is Saltatory conduction faster?

Myelin greatly speeds up action potential conduction because of exactly that reason: myelin acts as an electrical insulator! Myelin sheath reduces membrane capacitance and increases membrane resistance in the inter-node intervals, thus allowing a fast, saltatory movement of action potentials from node to node.

Furthermore, how myelin causes faster conduction? By acting as an electrical insulator, myelin greatly speeds up action potential conduction (Figure 3.14). As it happens, an action potential generated at one node of Ranvier elicits current that flows passively within the myelinated segment until the next node is reached.

Besides, which is faster Saltatory vs continuous conduction?

Nerve signals transmit much faster than in continuous conduction because an action potential is generated only at the neurofibrils (segments of axon without myelination) of myelinated axon rather than along the entire length of unmyelinated axon.

Why are Unmyelinated axons slower?

This means that unmyelinated axons are slower in the conduction of electric signals, and therefore information, than myelinated axons. This is important because there is a disease whereupon the body's own immune system attacks the myelin sheath around the axons in the central nervous system.


Why is Saltatory conduction faster than continuous conduction?

Nerve signals transmit much faster than in continuous conduction because an action potential is generated only at the neurofibrils (segments of axon without myelination) of myelinated axon rather than along the entire length of unmyelinated axon. conduction occurs in unmyelinated axons.

is Saltatory conduction faster? Electrical signals travel faster in axons that are insulated with myelin. Action potentials traveling down the axon "jump" from node to node. This is called saltatory conduction which means "to leap." Saltatory conduction is a faster way to travel down an axon than traveling in an axon without myelin.

Subsequently, question is, how is Saltatory conduction different from continuous conduction?

Saltatory conduction is more efficient and action potentials only need to be generated from one node to the next, resulting in a much more rapid conduction when compared to continuous conduction.

Why is Saltatory conduction faster than an Unmyelinated Axon?

Myelin greatly speeds up action potential conduction because of exactly that reason: myelin acts as an electrical insulator! Myelin sheath reduces membrane capacitance and increases membrane resistance in the inter-node intervals, thus allowing a fast, saltatory movement of action potentials from node to node.


How does Saltatory conduction occur?

Saltatory Conduction. Saltatory conduction describes the way an electrical impulse skips from node to node down the full length of an axon, speeding the arrival of the impulse at the nerve terminal in comparison with the slower continuous progression of depolarization spreading down an unmyelinated axon.

One may also ask, how is Saltatory conduction different from continuous conduction? Saltatory conduction is more efficient and action potentials only need to be generated from one node to the next, resulting in a much more rapid conduction when compared to continuous conduction.

Also know, how does Saltatory conduction work quizlet?

In myelinated axons, action potentials jump from node to node, rather than traveling at a constant speed along the axon. Conduction in myelinated axons is called saltatory conduction. In large myelinated axons, action potentials are conducted along the axon at speeds up to 100 meters per second.

How does Saltatory conduction affect energy use in a neuron?

Sodium and potassium ions are more concentrated on opposite sides of the membrane. How does saltatory conduction affect energy use in a neuron? It reduces the work load for the sodium-potassium pump. Stimulus A depolarizes a neuron just barely above the threshold.


Intermediate Physics for Medicine and Biology

I have never liked the physical picture of an action potential jumping from one node to the next. The problem with this idea is that the action potential is distributed over many nodes simultaneously as it propagates along the axon. Consider an action potential with a rise time of about half a millisecond. Let the radius of the axon be 5 microns. Table 6.2 in Intermediate Physics for Medicine and Biology indicates that the speed of propagation for this axon is 85 m/s, which implies that the upstroke of the action potential is spread over (0.5 ms) × (85 mm/ms) = 42.5 mm. But the distance between nodes for this fiber (again, from Table 6.2) is 1.7 mm. Therefore, the action potential upstroke is distributed over 25 nodes! The action potential is not rising at one node and then jumping to the next, but it propagates in a nearly continuous way along the myelinated axon. I grant that in other cases, when the speed is slower or the rise time is briefer, you can observe behavior that begins to look saltatory (e.g., Huxley and Stampfli, Journal of Physiology, Volume 108, Pages 315�, 1949), but even then the action potential upstroke is distributed over many nodes (see their Fig. 13).

If saltatory conduction is not the best description of propagation along a myelinated axon, then what is responsible for the speedup compared to unmyelinated axons? Primarily, the action potential propagates faster because of a reduction of the membrane capacitance. Along the myelinated section of the membrane, the capacitance is low because of the many layers of myelin ( N capacitors C in series result in a total capacitance of C / N ). At a node of Ranvier, the capacitance per unit area of the membrane is normal, but the area of the nodal membrane is small. Adding these two contributions together leads to a very small average, or effective, capacitance, which allows the membrane potential to increase very quickly, resulting in fast propagation.

In summary, I don’t find the idea of an action potential jumping from node to node to be the most useful image of propagation along a myelinated axon. Instead, I prefer to think of propagation as being nearly continuous, with the reduced effective capacitance increasing the speed. This isn’t the typical explanation found in physiology books, but I believe it’s closer to the truth. Rather than using the term saltatory conduction, I suggest we use curretory conduction, for the Latin verb currere , “to run.”


How does myelination affect nerve impulse conduction velocity?

Nerve impulses are propagated in the form of action potentials, involving the rapid depolarisation of the nerve cell membrane from -70mV to +30mV, before repolarisation occurs returning the membrane potential to -70mV. This cycle of depolarisation and repolarisation is propagated along the nerve cell as an electrical signal. Myelinated axons are covered in a protective, lipid rich myelin sheath produced by Schwann cells. This insulates regions of the nerve cell, so they cannot depolarise. Regions that lack myelin are called “nodes of Ranvier” and these become the only areas where action potentials can form, resulting in “jumping” of the nerve impulse from node to node. This is called saltatory conduction. Saltatory conduction results in faster nerve impulse conduction velocity, as the action potentials can “jump” along the neuron.


How does myelination of neurones increase conduction velocity?

Myelination is the production of a myelin sheath - a fatty, electrically insulating layer formed by Schwann cells wrapping around the axons of neurons. This sheath is not continuous, there are gaps between Schwann cells which are called nodes of Ranvier. At these nodes, the axon membrane (containing sodium and potassium ion channels) is uncovered/exposed to ions in extracellular solution. Therefore depolarisation can only occur at the nodes of Ranvier. Since the action potential jumps from node to node (this is called saltatory conduction), the action potential travels a greater distance for a shorter period of time. In an unmyelinated axon, every single section of the membrane will have to be depolarised for the impulse to conduct along the axon, hence taking more time.


How does myelination affect time constant?

Rest of the in-depth answer is here. Likewise, people ask, does myelination increase time constant?

In textbooks, it says that myelination doesn't really affect the time constant as tau=RC where R is the membrane resistance and C is the membrane capacitance. Myelin increases membrane resistance while decreasing membrane capacitance so there isn't really an overall effect on the time constant.

Similarly, how does myelination speed up action potential? By acting as an electrical insulator, myelin greatly speeds up action potential conduction (Figure 3.14). Because current flows across the neuronal membrane only at the nodes (see Figure 3.13), this type of propagation is called saltatory, meaning that the action potential jumps from node to node.

Regarding this, what is the membrane time constant?

Membrane time constant is the time for the potential to fall from the resting to a fraction (1-l/e), or 63%, of its final value in the charging curve during the application of a small negative current pulse.

At what age is myelination complete?

With advancing age, a progressive increase in the grade of myelination was noted in these regions, and at about 40 months of age myelination was complete. However, in most of our patients aged 20 months, myelination in the peritrigonal areas appeared complete.


Physically modelling the Saltatory nerve impulse transmission?

The nerve impulse transmission is specifically a biophysical process. Under a resting stage, the membrane is already polarised (presence of charge on either side leading to a potential difference across it, due to its finite capacitance). Changes in this polarisations mediated by several agents, cause some part of this membrane to be depolarised (inversion of the charges in that localised area). This changes the potential difference across that region and starts ion flow from the depolarised region of the membrane to the adjacent polarised region, inducing the same depolarisation there. Myelinating a neuron is similar to lowering the capacitance of the neuron. Myelinating the neuron causes subsequent action potentials to be spatially separated, and the conduction of voltage between them occurs primarily through ion flow along the neuron. Here are some nerve conduction basics.

Now my actual question. Modelling a neuron as a simple one dimensional membrane/cable, how can a lowered capacitance lead to a faster conduction of the voltage perturbation i.e a change in voltage (depolarisation), which is initially limited to a small localised region? This conduction of the voltage change can occur through the ion flow along the inner side of the membrane and also due to long distance changes in potential due to the altered distribution of charges along the membrane. A very good physical modelling of the neuron is given here and here, but because of the quite complicated mathematical nature of the modified telegrapher's equation which appears as the final answer, I am unable to understand how lowered capacitance increases the speed of voltage conduction?

Tell me if this question is off-topic or too biological to be answered here.


Troubleshooting

This can sometimes be a difficult experiment, because the worm may not produce spikes depending on the amount and time of anesthetic used as well as the general health of the worm. If you stick to the 10% alcohol solution for about 3-6 minutes, the worm should produce spikes most of the time as soon as you start (don't forget to wash the worm in water after you anesthetize it).

You may also want to try touching the worm with more or less pressure. Sometimes a very small tap will work, other times a stronger press might be needed. Some worms respond better to a stimulus at the very end of their bodies, while other respond better to a stimulus a few centimeters inwards.

Finally, sometimes you will cause an artifact when you touch the worm. Looking closely on the artifact waveforms, the artifacts will appear at exactly the same on both channels. This is a fake spike and not physiological! Sometimes, drying your probe periodically helps also do not rehydrate the worm in water too much (though also be careful not to dry the worm out). It is a careful balance, and you will develop your own style and technique as you gain experience.

You can also use an air stimulus from an air can in lieu of a plastic, wooden, or glass tip if you are getting too many fake spikes. You may also want to flip the worm over so the ventral or bottom side is facing up. Doing this means when you touch the worm with your probe the touch will be closer to the nerve.