BIOL Lecture9 Revisions

What is membrane potential (membrane voltage)?

Membrane potential is the difference in electric charges across a cell membrane. In most cells, it is negative inside relative to the outside. The negative sign means there are more negative charges on the inside of the cell.

What are the two basic rules governing the movement of ions across a membrane?

1. Ions move from higher to lower concentration (diffusion force, chemical gradient).
2. Ions move away from like charges and toward opposite charges (electrostatic force, electrical gradient).

What is the third factor that controls ion movement across a cell membrane, besides concentration and charge?

Permeability of the membrane to specific ions. Permeability is achieved by opening or closing ion channels, and it can change when the cell adopts a different physiological state.

In the two‑solution sodium chloride example, what happens if the membrane is equally permeable to both Na⁺ and Cl⁻?

Both ions diffuse from higher to lower concentration. The two solutions eventually have the same concentration, electric charges remain equal on both sides, and membrane potential is zero.

In the two‑solution sodium chloride example, what happens if the membrane is permeable only to Na⁺ (not Cl⁻)?

Na⁺ flows down its concentration gradient to the other side. One solution becomes increasingly positive (where Na⁺ went) and the other increasingly negative (where Na⁺ left). This creates a membrane potential.

When the membrane is permeable only to Na⁺, what two forces act on Na⁺?

1. Diffusion force – drives Na⁺ down its concentration gradient.
2. Electrostatic force – once a charge separation develops, the positive Na⁺ is attracted back to the negative side (opposite charges attract). These two forces oppose each other.

When do we reach equilibrium for an ion like Na⁺ across a membrane?

Equilibrium is reached when the diffusion force and the electrostatic force completely counteract each other. At that point, the net movement of the ion is zero, even though a concentration gradient still exists.

What is the equilibrium potential (equilibrium voltage) for an ion?

The equilibrium potential (also called equilibrium voltage) is the membrane voltage at which the electrical gradient exactly opposes the chemical (concentration) gradient, so that the net flux of that ion is zero. It is the voltage required to maintain a given concentration gradient.

For a typical resting neuron, what are the approximate equilibrium potentials (E_ion) for Na⁺, K⁺, and Cl⁻?

• E_Na⁺ ≈ +60 mV (positive)
• E_K⁺ ≈ ‑90 mV (negative)
• E_Cl⁻ ≈ ‑70 mV (negative, close to resting potential)

Why is the equilibrium potential for Na⁺ positive while the equilibrium potential for K⁺ is negative?

The sign of the equilibrium potential tells you the direction of the electrical force needed to balance the concentration gradient.

• Na⁺: concentration is higher outside, so the chemical gradient drives Na⁺ into the cell. To balance this, the inside must be positive (to repel Na⁺ inward? Wait careful: Positive inside repels positive Na⁺, so to push Na⁺ out you need positive inside. Actually, if inside is positive, Na⁺ is pushed out. That balances the inward chemical gradient. So E_Na⁺ is positive.)
• K⁺: concentration is higher inside, so chemical gradient drives K⁺ out of the cell. To balance this, the inside must be negative (to attract K⁺ back in). So E_K⁺ is negative.

For Cl⁻, the concentration gradient is inward (higher outside, lower inside) like Na⁺. Why is its equilibrium potential negative (‑70 mV) instead of positive?

Because Cl⁻ is negatively charged. To balance an inward chemical gradient (Cl⁻ wants to diffuse into the cell), the inside must be negative (negative repels Cl⁻, pushing it back out). So E_Cl⁻ is negative, unlike Na⁺ which is positive.

What is the typical resting membrane potential of a neuron?

‑70 mV (inside negative relative to outside).

At the resting membrane potential (‑70 mV), which ion(s) are at equilibrium?

Only Cl⁻ is near equilibrium (E_Cl⁻ ≈ ‑70 mV). Na⁺ and K⁺ are not at equilibrium – there is a net driving force on them.

At rest, is there a net driving force on Na⁺? If so, which direction?

Yes. E_Na⁺ is about +60 mV, but resting membrane potential is ‑70 mV. That means the inside is much more negative than the equilibrium potential for Na⁺. The electrical gradient strongly attracts Na⁺ inward (negative inside attracts positive Na⁺), and the chemical gradient also drives Na⁺ inward (higher outside). So Na⁺ has a large inward driving force at rest.

At rest, is there a net driving force on K⁺? If so, which direction?

Yes. E_K⁺ is about ‑90 mV, but resting membrane potential is ‑70 mV. That means the inside is not negative enough to fully balance K⁺'s outward chemical gradient. So K⁺ has a net outward driving force at rest (K⁺ tends to leave the cell).

What maintains the concentration gradients of Na⁺ and K⁺ across the cell membrane, keeping them away from equilibrium?

The Na⁺/K⁺ ATPase pump (sodium‑potassium pump). It actively transports 3 Na⁺ out and 2 K⁺ in for each ATP hydrolyzed, moving both ions against their electrochemical gradients. This maintains the high extracellular Na⁺ and high intracellular K⁺.

Why is the resting membrane potential closer to E_K⁺ (‑90 mV) than to E_Na⁺ (+60 mV)?

At rest, the membrane is much more permeable to K⁺ than to Na⁺. K⁺ leaks out through leaky K⁺ channels, pulling the membrane potential toward E_K⁺. The small resting Na⁺ permeability pulls it slightly away from E_K⁺ toward E_Na⁺, resulting in a resting potential of ‑70 mV (between E_K⁺ and E_Na⁺).

In a resting neuron, what are the approximate intracellular and extracellular concentrations of Na⁺ and K⁺?

• Na⁺: extracellular ~145 mM, intracellular ~15 mM (higher outside)
• K⁺: extracellular ~5 mM, intracellular ~150 mM (higher inside)
• Cl⁻: extracellular ~110 mM, intracellular ~10 mM (higher outside)

Draw a diagram of a cell with ion concentrations and membrane voltage. What six concentration numbers should you include?

You should include for Na⁺, K⁺, and Cl⁻:

• Inside concentration (e.g., Na⁺ 15 mM, K⁺ 150 mM, Cl⁻ 10 mM)
• Outside concentration (e.g., Na⁺ 145 mM, K⁺ 5 mM, Cl⁻ 110 mM)
  These numbers are approximate but typical for mammalian cells.

In your diagram, what membrane voltage should you write for a typical resting cell?

‑70 mV (inside negative relative to outside). Typical range is ‑30 to ‑70 mV, but resting neurons are around ‑70 mV.

For each ion (Na⁺, K⁺, Cl⁻), how do you draw the chemical gradient arrow?

The chemical gradient arrow points from high concentration to low concentration (direction of diffusion if no other forces).

• Na⁺: from outside (high) to inside (low) → arrow pointing inward.
• K⁺: from inside (high) to outside (low) → arrow pointing outward.
• Cl⁻: from outside (high) to inside (low) → arrow pointing inward.

For each ion, how do you draw the electrical gradient arrow at resting membrane potential (‑70 mV)?

The electrical gradient arrow points toward the opposite charge.

• Na⁺ (positive): inside is negative → electrical gradient arrow points inward (attracted to negative).
• K⁺ (positive): inside is negative → electrical gradient arrow also points inward (attracted to negative). Wait – but at rest, K⁺ has net outward driving force. That means the chemical gradient outward is stronger than the electrical gradient inward. So the electrical arrow is inward, chemical arrow outward. The combined arrow is outward.
• Cl⁻ (negative): inside is negative → negative repels negative → electrical gradient arrow points outward (away from negative inside).

For each ion, how do you draw the combined electro‑chemical gradient arrow?

The combined arrow is the net direction of ion movement if the membrane were permeable.

• Na⁺: both chemical and electrical arrows point inward → combined arrow inward (strong inward force).
• K⁺: chemical arrow outward, electrical arrow inward. At rest, outward chemical force is stronger → combined arrow outward.
• Cl⁻: chemical arrow inward, electrical arrow outward. At rest, they are nearly balanced (Cl⁻ is near equilibrium) → combined arrow near zero (or very small).

In your diagram of an axon at rest, what channels and pumps must you include?

• Leaky Na⁺ channels (few, small permeability)
• Leaky K⁺ channels (many, high permeability)
• Na⁺/K⁺ pump (Na⁺/K⁺ ATPase)

In the resting axon diagram, what should you label as the equilibrium voltages for Na⁺ and K⁺?

• E_Na⁺ ≈ +60 mV
• E_K⁺ ≈ ‑90 mV
• (E_Cl⁻ ≈ ‑70 mV, but not always required)

In the resting axon diagram, what is the typical membrane voltage?

‑70 mV

Draw arrows for the electro‑chemical gradient for Na⁺ at rest. Which direction?

Inward (both chemical and electrical forces drive Na⁺ into the cell).

Draw arrows for the electro‑chemical gradient for K⁺ at rest. Which direction?

Outward (chemical gradient outward is stronger than electrical gradient inward, so net outward).

What is the role of the Na⁺/K⁺ pump in maintaining the resting potential?

It actively transports 3 Na⁺ out and 2 K⁺ in per ATP, creating and maintaining the concentration gradients (low Na⁺ inside, high K⁺ inside). It also generates a small direct electrogenic effect (net export of one positive charge per cycle), contributing a few mV to the negative resting potential.

Why is the resting membrane potential essential for generating action potentials?

The resting potential (‑70 mV) provides a stored electrical energy that can be rapidly changed when voltage‑gated Na⁺ and K⁺ channels open. It sets the baseline from which depolarization (to threshold) and then the action potential occur.

True or False: At rest, the membrane is impermeable to Na⁺.

False. At rest, the membrane has a small permeability to Na⁺ through leaky Na⁺ channels. This small Na⁺ influx pulls the resting potential slightly away from E_K⁺ (‑90 mV) to about ‑70 mV.

If the membrane suddenly became perfectly permeable only to K⁺, what would the membrane potential become?

It would become E_K⁺ ≈ ‑90 mV (the equilibrium potential for K⁺), because K⁺ would diffuse down its gradient until the electrical force exactly balances the chemical force.

If the membrane suddenly became perfectly permeable only to Na⁺, what would the membrane potential become?

It would become E_Na⁺ ≈ +60 mV (the equilibrium potential for Na⁺).

What is the Nernst equation used for?

The Nernst equation calculates the equilibrium potential for a single ion given its concentrations inside and outside the cell. For a monovalent ion at 37°C: E_ion = (61.5 mV / z) × log([outside]/[inside]).

Using the Nernst equation, if [K⁺]outside = 5 mM and [K⁺]inside = 150 mM, what is E_K⁺?

E_K⁺ = 61.5 mV × log(5/150) = 61.5 × log(0.0333) = 61.5 × (‑1.48) ≈ ‑91 mV. (Matches typical ‑90 mV.)

Using the Nernst equation, if [Na⁺]outside = 145 mM and [Na⁺]inside = 15 mM, what is E_Na⁺?

E_Na⁺ = 61.5 mV × log(145/15) = 61.5 × log(9.67) = 61.5 × 0.985 ≈ +60.6 mV.

What is the Goldman‑Hodgkin‑Katz (GHK) equation used for?

The GHK equation calculates the resting membrane potential considering the relative permeabilities of multiple ions (usually Na⁺, K⁺, Cl⁻). It gives a weighted average of the equilibrium potentials based on permeability.

Why does the resting membrane potential (‑70 mV) sit between E_K⁺ (‑90 mV) and E_Na⁺ (+60 mV)?

Because at rest, P_K⁺ >> P_Na⁺ (much higher permeability to K⁺). The potential is pulled strongly toward E_K⁺, but the small Na⁺ permeability pulls it slightly in the positive direction, resulting in ‑70 mV.

If you added a drug that blocks all leaky K⁺ channels, what would happen to the resting membrane potential?

The membrane would become much less permeable to K⁺. The resting potential would depolarize (become less negative) because the influence of Na⁺ permeability would dominate, moving the potential toward E_Na⁺ (≈ +60 mV).

If you added a drug that blocks all leaky Na⁺ channels, what would happen to the resting membrane potential?

The resting potential would hyperpolarize (become more negative), moving closer to E_K⁺ (‑90 mV), because the small depolarizing influence of Na⁺ influx would be removed.

What is the difference between a chemical gradient and an electrical gradient?

• Chemical gradient (concentration gradient): difference in concentration of an ion across the membrane. Ions diffuse from high to low concentration.
• Electrical gradient: difference in charge (voltage) across the membrane. Ions move toward opposite charges and away from like charges.

What is the electro‑chemical gradient?

The combined effect of the chemical gradient and the electrical gradient on an ion. The net driving force determines the direction and magnitude of ion movement if the membrane is permeable to that ion.

At rest, is Cl⁻ at equilibrium? What does that mean?

Yes, Cl⁻ is approximately at equilibrium (E_Cl⁻ ≈ ‑70 mV). That means the net driving force on Cl⁻ is near zero – the chemical gradient (inward) is balanced by the electrical gradient (outward, because inside is negative repelling Cl⁻).

Why is the Na⁺/K⁺ pump considered an "active" transporter?

It moves ions against their electrochemical gradients using energy directly from ATP hydrolysis (primary active transport). It pumps 3 Na⁺ out (against both chemical and electrical gradients) and 2 K⁺ in (against its chemical gradient, but electrical gradient helps K⁺ in? Actually K⁺ inside is positive, but the inside is negative – the electrical gradient attracts K⁺ in, which helps. But the chemical gradient for K⁺ is outward, so the pump works against that.)

What would happen to the resting membrane potential if the Na⁺/K⁺ pump stopped working?

Over time, the concentration gradients would run down (Na⁺ would leak in, K⁺ would leak out). The resting potential would depolarize and eventually approach zero. The cell would lose its ability to generate action potentials.

In the two‑solution NaCl example, when the membrane is permeable only to Na⁺, why does the membrane potential stop changing at equilibrium?

At equilibrium, the diffusion force (driving Na⁺ down its concentration gradient) is exactly balanced by the electrostatic force (driving Na⁺ back up the electrical gradient). Net Na⁺ movement is zero, so the voltage stabilizes.

What is the definition of "equilibrium potential" in your own words?

The equilibrium potential is the membrane voltage at which an ion's chemical gradient is exactly balanced by the electrical gradient, so that there is no net movement of that ion across the membrane.

True or False: At the equilibrium potential for an ion, the concentration of that ion is equal on both sides of the membrane.

False. At equilibrium potential, there is still a concentration gradient – the electrical gradient is exactly opposing it, so no net flux occurs. Concentration differences are maintained by active transport.

Why does the resting membrane potential not equal the equilibrium potential of any single ion?

Because the membrane is permeable to multiple ions (primarily K⁺, but also slightly to Na⁺ and Cl⁻). The resting potential is a weighted average of the equilibrium potentials based on relative permeabilities.

What is the difference between a leak channel and a gated channel?

A leak channel (pore) is always open, allowing constant passive flux. A gated channel opens and closes in response to a signal (ligand, voltage, or mechanical stress), allowing regulated flux.

In the context of resting membrane potential, what are "leaky" channels?

"Leaky" channels are ion channels that are always open (not gated) at rest, allowing ions to move passively down their electrochemical gradients. Resting neurons have many leaky K⁺ channels and fewer leaky Na⁺ channels.

Why does increasing extracellular K⁺ concentration depolarize a neuron?

Increasing extracellular K⁺ reduces the K⁺ concentration gradient (less K⁺ wants to leave). The equilibrium potential for K⁺ becomes less negative (e.g., from ‑90 mV to ‑70 mV). Since resting potential is dominated by K⁺ permeability, the membrane depolarizes toward the new E_K⁺.

Why does decreasing extracellular Na⁺ concentration have a relatively small effect on resting potential?

Because resting permeability to Na⁺ is very low. Changing E_Na⁺ has little influence on the resting potential, which is dominated by K⁺. However, decreasing extracellular Na⁺ will reduce the driving force for Na⁺ entry during action potentials.

What is the difference between equilibrium potential and membrane potential?

• Equilibrium potential (E_ion) is the theoretical voltage that would exactly balance an ion's concentration gradient. It is calculated for a single ion.
• Membrane potential (Vm) is the actual voltage across the membrane at any given time, determined by the combined permeabilities and gradients of all ions.

If a cell's membrane potential equals the equilibrium potential for K⁺, what does that tell you about net K⁺ movement?

Net K⁺ movement is zero. However, there may still be K⁺ ions moving in both directions, but the fluxes are equal and opposite. The cell is at equilibrium for K⁺.

What is the sodium‑potassium pump's contribution (in mV) to the resting membrane potential?

The pump is electrogenic because it moves 3 positive charges out for every 2 positive charges in, net export of one positive charge per cycle. This directly contributes a small hyperpolarization of about ‑5 to ‑10 mV to the resting pot