L08 MSK Physiology 2 Excitable Membranes

Overview

The lecture works through electrical signalling in nerve and muscle in three colour-coded parts. First, what sets the membrane potential: the electrochemical gradient, equilibrium potentials for single ions via the Nernst equation, and the resting membrane potential for the whole cell via the Goldman-Hodgkin-Katz equation. Second, passive (local, graded) potentials, which are how information enters an excitable cell and how it is integrated by summation. Third, the action potential, which is how the integrated signal is transmitted over distance, including its ionic mechanism, the channel states that generate threshold, repolarisation and afterhyperpolarisation, the refractory periods, and clinical and research examples of channel block.

Electrochemical gradient

Ion movement across the membrane is driven by two components:

• Chemical potential: concentration dependent; ions move from high concentration to low concentration.
• Electrical potential: charge (valence) dependent.

Two further conditions determine whether the gradient produces any current:

• Concentration difference is set up by the ionic distribution across the membrane and is maintained by the K+-ATPase, which uses ATP to pump 3 Na+ out and 2 K+ in.
• Permeability: the gradient only works if specific ion channels are open and ions can flow.

Ionic distribution used in the lecture:

Ion	Outside	Inside
Na+	145 mM	10 mM
K+	4 mM	150 mM

The inside of the cell sits at -70 mV. Na+ moves into the cell and K+ moves out of the cell down their concentration gradients, with the electrical component acting in the opposing direction.

Equilibrium potentials and the Nernst equation

The Nernst equation gives the equilibrium potential for a given ion. It is:

• the potential difference between the inside and outside of the cell for that ion,
• the point at which that ion is at equilibrium,
• the point at which there is no net movement of that ion across the membrane.

$E_X=\frac{RT}{zF}\ln \frac{[X^{+}{]}_o}{[X^{+}{]}_i}$

Where $E_X$ is the equilibrium potential for ion X, $R$ the gas constant, $T$ the temperature in K, $z$ the valency, $F$ Faraday’s constant, $[X{]}_o$ the concentration outside and $[X{]}_i$ the concentration inside.

Simplified at 37 degrees C:

$E_{ion}=\frac{61}{z}\log \frac{C_{out}}{C_{in}}$

Values given: $E_{Na}=+61$ mV, $E_K=-97$ mV.

Key points:

• This is for a single ion only. It is not the RMP.
• The bigger the concentration difference ($C_{out}/C_{in}$), the bigger the voltage.
• The concentration difference provides the driving force.
• Ions do not contribute to the RMP unless they can cross the membrane, and non-penetrating solutes do not contribute to the membrane potential at all.
• The driving force cannot move ions if there is no mechanism for them to cross, so open channels are required.

Membrane potential follows the dominant permeability

Reference values used in the worked graph: $V_{Na}=+61$ mV, $V_{Cl}=-64$ mV, $V_{rest}=-68$ mV, $V_K=-97$ mV. Three permeability states were compared:

State	pK	pNa	pCl	Membrane potential
Rest	1	0.05	0.45	$V_{rest}$, -68 mV
K+ only	1	0	0	$V_K$, -97 mV
Na+ only	0	1	0	$V_{Na}$, +61 mV

The membrane potential moves to the equilibrium potential of whichever ion the membrane is exclusively permeable to. At rest the permeabilities are mixed but dominated by K+, so the potential lies near to, but not at, $E_K$.

Resting membrane potential: the Goldman-Hodgkin-Katz equation

The Goldman-Hodgkin-Katz equation calculates the resting membrane potential, taking into account the concentration difference of the main ions involved and their experimentally determined permeability.

$\Delta \psi =\frac{RT}{F}\ln \frac{P_K[K{]}_o+P_{Na}[Na{]}_o+P_{Cl}[Cl{]}_i}{P_K[K{]}_i+P_{Na}[Na{]}_i+P_{Cl}[Cl{]}_o}$

• $P$ is permeability, expressed as a ratio: how many ion channels there are and whether they are open.
• If the $[out]/[in]$ concentration ratio changes, the RMP changes too.
• The formula allows the RMP to be calculated if the ionic composition of the ECF or ICF changes.

Important

Changes in extracellular K+ can change the RMP, which changes excitability, leading to paralysis, cardiac arrhythmia and death.

Passive (local, graded) potentials

What they are:

• Local changes in membrane potential.
• Caused by opening or closing of ion channels.
• Occurring in response to events external to the membrane.
• Either excitatory (leading to active, regenerative responses in the membrane) or inhibitory (leading to reduced responses or decreased neuronal activity).
• Graded: local amplitude reflects the amount of input and the distance from the site of input.

Where they occur: at sensory receptors in the peripheral nervous system and at synapses on dendrites and soma in the CNS, that is, wherever information is moving into an excitable cell.

Why they matter: all information processing in the nervous system is based on graded potentials.

Stimuli that generate them include touch on a skin pressure receptor, synaptic transmission (neurotransmitter binding its receptor to give an EPSP or IPSP), and light hitting a photoreceptor.

Mechanism: ions flow according to the forces described above, causing a local change in membrane potential. If Na+ channels open, Na+ flows into the cell, and that local region depolarises (less negative inside, locally), producing a local excess of positive charge that spreads sideways from the channel.

Grading and decay

At the dendrites and cell body:

• The larger the stimulus, the more channels open.
• More channels means more flow of ions.
• More ions means more depolarisation.
• So the size of the potential is proportional to the stimulus, that is, it is graded in size.
• But the potential decays with distance from the stimulus site, due to outward leak of positive charges.

Positive ions enter at one point, flow along the inside of the axon, and leak outward through the membrane along its length, so neighbouring regions are depolarised progressively less with time and distance from the origin. Plotted against distance, a large stimulus peaks higher than a small stimulus, but both decay symmetrically in both directions back towards RMP.

Three properties of graded potentials:

1. They outlast the stimulus (delayed rise and delayed fall relative to a brief square stimulus pulse).
2. Their size reflects stimulus size.
3. They spread decrementally.

These properties make them good for information processing because:

• They spread, and their electrotonic spread is passive.
• They outlast the stimulus, with amplitude decreasing over time.
• Their size reflects the size and locality of the stimulus.
• Therefore they can add together over time: temporal and spatial summation allows input integration.

They are not good for carrying information long distances, because they get smaller as they spread, cannot regenerate, and will have faded completely some distance away.

Spatial and temporal summation

Ion pumps maintain electrochemical gradients and ion channels determine the resting potential. Inputs are processed as graded potentials, and signals are transmitted as action potentials. Four cases, each measured against the threshold of the postsynaptic axon with rest at -70 mV:

1. Subthreshold, no summation: two well-spaced stimuli at the same excitatory synapse (E1, E1) each produce a small depolarisation that decays before the next arrives; neither reaches threshold.
2. Temporal summation: two stimuli at the same synapse (E1, E1) in rapid succession sum to reach threshold and trigger an action potential.
3. Spatial summation: simultaneous stimuli at two different excitatory synapses (E1 + E2) sum to reach threshold and trigger an action potential.
4. Spatial summation of EPSP and IPSP: an inhibitory input combined with an excitatory input (E1 + I1) leaves the membrane potential essentially unchanged at rest, and no action potential is produced.

The action potential: general features

The action potential is:

• Generated at the axon hillock (initial segment).
• Triggered at threshold, the “magic membrane potential”.
• Self-regenerating.
• All-or-nothing.

It is due to changes in permeability, the ratios of inside to outside ion concentrations, voltage gated Na+ channels and K+ channels.

The neuron diagram places the axon hillock between the cell body (with apical and basal dendrites, excitatory and inhibitory input terminals, nucleus and cytoplasm) and the myelinated axon with its nodes of Ranvier, identifying it as the site of generation.

The trace starts at RMP (-70 mV), depolarises to an overshoot peak of about +30 mV, repolarises, and then undergoes afterhyperpolarisation below RMP with a slow return. The absolute refractory period spans the spike (roughly 0 to 1 msec) and is followed by the relative refractory period (roughly 1 to 8 msec).

The seven stages

1. RMP.
2. Depolarisation to threshold (the pre-potential).
3. Opening of voltage gated Na+ channels, giving rapid depolarisation.
4. Peak of the action potential, approximately $E_{Na}$; Na+ channels inactivate.
5. Opening of voltage gated K+ channels, giving repolarisation.
6. K+ channels still open, so $P_K$ is higher and the potential is closer to $E_K$: hyperpolarisation. Inactivation of Na+ channels ends.
7. RMP.

From stage 4 to stage 6 it is impossible to have another action potential: the absolute refractory period. From stage 6 to stage 7 it is harder to trigger an action potential: the relative refractory period.

On the permeability plot, the Na+ permeability curve rises and falls early and sharply, while the K+ permeability curve rises later, peaks after the Na+ curve has fallen, and decays slowly. The channel cartoons show both channels closed at stages 1 and 7, Na+ open with inward current during the upstroke, and K+ open during repolarisation and hyperpolarisation.

Threshold and regeneration

Voltage gated Na+ channels go from closed to open on depolarisation, and their open probability increases with depolarisation, which produces the action potential.

The action potential is regenerative: Na+ channels open, current flows, the membrane depolarises, more channels open, more current flows, and so on.

Repolarisation and the absolute refractory period

The full voltage gated Na+ channel cycle is: closed, then open on depolarisation, then inactivated, then closed again on repolarisation.

After opening, the channels inactivate into a non-permeable state, so an action potential cannot be added on top of another. This is the absolute refractory period, during which it is impossible to evoke another action potential no matter how strong the stimulus. Meanwhile the K+ channels are opening and the membrane potential is repolarising.

Afterhyperpolarisation and the relative refractory period

• Voltage gated K+ channels remain open longer, and other K+ channels are activated by Ca2+ and Na+.
• The K+ to Na+ permeability ratio is even higher than normal.
• The membrane potential therefore gets closer to $E_K$ than normal.

During the afterhyperpolarisation it is harder to evoke an action potential, but it is possible if a bigger stimulus is used: this is the relative refractory period. It is possible because the Na+ channels are again ready to be opened, and it is harder because the increased K+ permeability puts the resting potential further from threshold.

Clinical note: blockers of voltage gated Na+ channels

• Tetrodotoxin (TTX) is found in puffer fish, the blue ringed octopus, and several other species that accumulate TTX-producing bacteria. TTX selectively enters voltage gated Na+ channels, binds there, blocks the pore and prevents the upstroke, so no action potential is possible. It is slowly reversible but deadly.
• Saxitoxin is a similar toxin found in shellfish following algal blooms (“red tide”). It is among the most potent of all biological toxins, 10,000 times deadlier than cyanide, and causes paralytic shellfish poisoning.
• Local anaesthetics such as Lidocaine also block voltage gated Na+ channels but are short acting. They show use-dependent block, especially of TTX-resistant Na+ channels in small diameter pain fibres. The local anaesthetic molecule reaches the channel by the intracellular route, entering the open channel pore rather than crossing via the external or membrane route.

Research note: lithium

Lithium blocks a K+ channel, influencing action potential frequency, duration and the relative refractory period. In addition to voltage gated K+ channels, some K+ channels are opened by Na+ entry, accounting for around 60 % of the total K+ current in some brain neurons. Li+ enters through Na+ channels but does not open these K+ channels, so action potential duration, afterhyperpolarisation and refractory period are all affected. The lecture poses this as an open question: is this relevant to how Li+ stabilises brain networks in bipolar disorder?

Experimentally, normal brain neurons fire regularly spaced single spikes, whereas in 5 mM lithium the spikes are replaced by clusters of multiple spikes riding on broadened depolarisations, that is, lithium lengthens the action potential and permits repetitive firing.

Transcript flags (2)

Slide 3: the last line of slide text (“…ions can flow”) is cut off at the bottom edge of the slide; the wording was confirmed from the extracted text layer.
Slide 17: the bullet “K+:Na+ permeability ratio even higher than normal” is clipped at the right-hand slide edge; the wording was confirmed from the extracted text layer.

Self-test

1. Name the two components of the electrochemical gradient and state what each depends on.
2. State the intracellular and extracellular concentrations of Na+ and K+ given in the lecture, and the resting intracellular voltage.
3. Describe what the Na+/K+-ATPase does and its stoichiometry.
4. Define the equilibrium potential for an ion in three ways.
5. Write the Nernst equation and define each of its terms.
6. Write the simplified Nernst equation at 37 degrees C and give the values quoted for $E_{Na}$ and $E_K$.
7. Explain why a non-penetrating solute makes no contribution to the membrane potential.
8. Predict the membrane potential of a cell whose membrane is made exclusively permeable to K+, then exclusively permeable to Na+, and explain why the resting potential lies near but not at $E_K$.
9. Write the Goldman-Hodgkin-Katz equation and explain what $P$ represents.
10. Explain how a change in extracellular K+ produces paralysis or cardiac arrhythmia.
11. Define a graded potential and list where in the nervous system graded potentials occur.
12. Explain why a graded potential decays with distance from the stimulus site.
13. List the three properties of graded potentials and explain why these properties make them suited to information processing but unsuited to long-distance transmission.
14. Distinguish temporal from spatial summation, and predict the outcome when an EPSP and an IPSP arrive together.
15. State where the action potential is generated and list the four features that characterise it.
16. Describe the seven stages of the action potential, naming the channel events at each.
17. Explain why the action potential is described as regenerative.
18. Describe the three-state cycle of the voltage gated Na+ channel and relate it to the absolute refractory period.
19. Explain why the relative refractory period is a period in which an action potential is harder but not impossible to evoke.
20. Explain the mechanism by which tetrodotoxin abolishes the action potential, and name the species that carry it.
21. Distinguish tetrodotoxin from lidocaine in terms of duration of action and route of access to the channel.
22. Explain how lithium alters action potential duration and firing pattern in brain neurons.
23. A diner develops paralysis after eating shellfish harvested during a red tide. Name the likely toxin and explain the mechanism of the paralysis.
24. Integrative: a weak touch stimulus on a skin receptor produces no sensation, while a stronger one does. Trace the sequence from stimulus to action potential, naming the potentials and the integrative processes involved.

Answers

Reveal answers

1. Chemical potential, which is concentration dependent (ions move from high to low concentration), and electrical potential, which is charge (valence) dependent.
2. Na+ 145 mM outside and 10 mM inside; K+ 4 mM outside and 150 mM inside; the inside of the cell is at -70 mV.
3. It uses ATP to pump 3 Na+ out of the cell and 2 K+ in, maintaining the concentration difference across the membrane.
4. The potential difference between inside and outside the cell for that ion; the point at which that ion is at equilibrium; the point at which there is no net movement of that ion across the membrane.
5. $E_X=\frac{RT}{zF}\ln \frac{[X^{+}{]}_o}{[X^{+}{]}_i}$, where $E_X$ is the equilibrium potential for ion X, $R$ the gas constant, $T$ temperature in K, $z$ valency, $F$ Faraday’s constant, $[X{]}_o$ the outside concentration and $[X{]}_i$ the inside concentration.
6. $E_{ion}=\frac{61}{z}\log \frac{C_{out}}{C_{in}}$; $E_{Na}=+61$ mV and $E_K=-97$ mV.
7. Ions do not contribute to the RMP unless they can cross the membrane. A driving force cannot move ions without a mechanism for crossing, so a non-penetrating solute contributes nothing.
8. With K+ only (pK = 1, pNa = 0, pCl = 0) the potential falls to $V_K$, -97 mV; with Na+ only (pNa = 1) it rises to $V_{Na}$, +61 mV. At rest the permeabilities are mixed (pK = 1, pNa = 0.05, pCl = 0.45) and dominated by K+, so the potential sits near $E_K$ but not at it, at $V_{rest}$ of -68 mV.
9. $\Delta \psi =\frac{RT}{F}\ln \frac{P_K[K{]}_o+P_{Na}[Na{]}_o+P_{Cl}[Cl{]}_i}{P_K[K{]}_i+P_{Na}[Na{]}_i+P_{Cl}[Cl{]}_o}$. $P$ is permeability expressed as a ratio: how many ion channels there are and whether they are open.
10. Changing extracellular K+ changes the $[out]/[in]$ ratio for K+, which changes the RMP calculated by the GHK equation. A changed RMP changes excitability, which can cause paralysis, cardiac arrhythmia and death.
11. A local change in membrane potential caused by opening or closing of ion channels in response to events external to the membrane, graded in that its local amplitude reflects the amount of input and the distance from the input site. They occur at sensory receptors in the peripheral nervous system and at synapses on dendrites and soma in the CNS, that is, wherever information moves into an excitable cell.
12. Positive charge entering at one point flows along the inside of the cell but leaks outward through the membrane along its length, so the depolarisation of neighbouring regions falls off with distance and time from the origin.
13. They outlast the stimulus, their size reflects stimulus size, and they spread decrementally. Because they spread passively, outlast the stimulus and are graded, they can add together over time and space, allowing input integration. Because they get smaller as they spread and cannot regenerate, they fade completely some distance away and are not suited to carrying information long distances.
14. Temporal summation is two stimuli at the same synapse in rapid succession summing to reach threshold; spatial summation is simultaneous stimuli at two different excitatory synapses summing to reach threshold. An EPSP arriving with an IPSP leaves the membrane potential essentially unchanged at rest, and no action potential is produced.
15. It is generated at the axon hillock (initial segment). It has a threshold, is self-regenerating, is all-or-nothing, and arises from changes in permeability and ion ratios via voltage gated Na+ channels and K+ channels.
16. (1) RMP. (2) Depolarisation to threshold, the pre-potential. (3) Voltage gated Na+ channels open, giving rapid depolarisation. (4) Peak at approximately $E_{Na}$, with Na+ channel inactivation. (5) Voltage gated K+ channels open, giving repolarisation. (6) K+ channels still open, higher $P_K$, potential closer to $E_K$, so hyperpolarisation; Na+ channel inactivation ends. (7) Return to RMP.
17. Because Na+ channel open probability increases with depolarisation: Na+ channels open, current flows, the membrane depolarises further, which opens more channels and drives more current, in a self-sustaining cycle.
18. Closed goes to open on depolarisation, open goes to inactivated (a non-permeable state), and inactivated returns to closed on repolarisation. While the channels are inactivated no action potential can be evoked no matter how strong the stimulus, which is the absolute refractory period, spanning stages 4 to 6.
19. It is possible because the Na+ channels are again ready to be opened, and harder because the increased K+ permeability during the afterhyperpolarisation holds the membrane potential further from threshold.
20. TTX selectively enters voltage gated Na+ channels, binds there and blocks the pore, preventing the upstroke so that no action potential is possible; the block is slowly reversible but deadly. It is found in puffer fish, the blue ringed octopus and other species that accumulate TTX-producing bacteria.
21. TTX binds the channel and is slowly reversible and deadly. Lidocaine also blocks voltage gated Na+ channels but is short acting, shows use-dependent block especially of TTX-resistant channels in small diameter pain fibres, and reaches the pore from the intracellular side of the open channel rather than via the external or membrane route.
22. Lithium blocks a K+ channel, including K+ channels opened by Na+ entry (around 60 % of total K+ current in some brain neurons); Li+ enters through Na+ channels but does not open them. Action potential duration, afterhyperpolarisation and refractory period are all affected: in 5 mM lithium, regular single spikes are replaced by clusters of multiple spikes on broadened depolarisations.
23. Saxitoxin, causing paralytic shellfish poisoning. Like TTX it blocks voltage gated Na+ channels, so the upstroke and therefore the action potential cannot occur and excitable tissue cannot fire; it is among the most potent biological toxins, 10,000 times deadlier than cyanide.
24. The stimulus opens channels in the receptor membrane; Na+ flows in and produces a local graded (passive) potential whose size is proportional to the stimulus. The potential spreads passively and decays with distance. A weak stimulus opens few channels, giving a small potential that decays before reaching threshold at the axon hillock. A stronger stimulus opens more channels, giving a larger potential, and repeated or simultaneous inputs sum temporally and spatially so that threshold is reached at the axon hillock, where voltage gated Na+ channels open regeneratively and an all-or-nothing action potential is generated and transmitted.