Electrophysiology III: The Hodgkin-Huxley Model

Question 1

What is the Hodgkin-Huxley model?

Answer 1

The Hodgkin-Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurones are initiated and propagated.

Question 2

What is the Ionic driving force (V)?

Answer 2

Ions have a driving force if the membrane potential is different from the equilibrium (reversal) potential for that ion.

Driving force is the difference between Vm and Eion

Driving Force (V) = Vm - Eion

Question 3

What changes the ionic driving force?

Answer 3

Seeing as the equilibrium potential of an ion is a constant and does not change (Eion), it is the changes in the membrane potential (Vm) which change the driving force.

Question 4

What is the Driving Force on Cl-?

Answer 4

The driving force on chloride at a membrane potential of -40mV is going to be:
· -40- -70= +30mV

The driving force on chloride at a membrane potential of -100mV is going to be:
· -100 - -70= -30mV

Question 5

If membrane potential is positive to the chloride reversal potential _-70mV), the sign of the driving force is going to be…

Answer 5

positive
-therefore, current is outward, meaning positive charge is leaving the cell, and the cell will hyperpolarise (as seen at a membrane potential of -40mV and -65mV)

• Positive current → positive charge leaving the cell
• Chloride moving opposite to the current (in this case, Cl- moving inward)

At -40mV membrane potential, the current is larger than at -65mV, because the difference between Vm and Eion is greater, meaning driving force is greater

Question 6

If membrane potential is negative to the chloride reversal potential _-70mV), the sign of the driving force is going to be…

Answer 6

negative
-therefore, the current is inward, meaning positive charge is going to be entering the cell, and the cell will depolarise (as seen at a membrane potential of -80mV and -100mV)

• Negative current → positive charge entering the cell
• Chloride moving opposite to the current (in this case, Cl- moving outward)

At -100mV membrane potential, the current is larger than at -80mV, because the difference between Vm and Eion is greater, meaning driving force is greater

*even though the chloride concentration gradient is inward, when Vm is more negative than chloride equilibrium potential, this provides a greater driving force to drive chloride outward

Question 7

How can we model Vm at steady state?

Answer 7

using an equivalent circuit model

Question 8

Solving for Vm

Answer 8

In steady state (resting Vm), there is no net inward or outward current (ions flowing in an out of the membrane, but the net inflow and outflow cancels out). Ignoring other ionic currents to simplify:
- IK + INa = 0

Substituting in the ionic currents:

• IK= gK (Vm - EK)
• INa = gNa (Vm - ENa)

We get:
- gK (Vm - EK) + gNa (Vm - ENa)

Then solve for Vm (picture)

• from this equation we can see that the influence over Vm is determined by the ionic equilibrium potentials scaled by the relative permeability to that ion
• the larger the conductance (g), the more dominant the ion will be in setting Vm
• e.g. if high K conductance and low Na conductance, Ek mainly determines membrane potential

Question 9

What is the ionic permeability hypothesis?

Answer 9

By the 1950s, it was established that:

• the action potential involved a transient reversal of Vm to a positive value
• and this was dependent on presence of extracellular sodium

Therefore, the hypothesis was that the permeability changes during the action potential consist of a rapid but transient increase in the permeability to sodium and a delayed increased in the permeability to potassium

Question 10

What causes the changes in membrane permeability?

Answer 10

Believed that the a change in permeability is triggered by a change in membrane voltage (Vm), in a graded but reversible manner:

• A change in Vm in the positive direction triggers molecular changes in the membrane that increase gNa (opening of voltage gated Na channels).
• The resulting increase in Na current moves Vm further in the direction of ENa (i.e. depolarises), resulting in still further increase in gNa (positive feedback).

Question 11

How can we test the permeability hypothesis?

Answer 11

To test this hypothesis, we need a way of measuring ionic permeability/conductance and showing that it varies as a function of Vm.

An ionic current is given by the conductance to the ion times the driving force on that ion:
· Iion= gion (Vm - Eion)

In principle, it would be simple to work out conductance (equation above), but for an action potential, Vm, Iion and gion are all changing simultaneously. To get around this, the voltage clamp technique was developed.

Question 12

How the membrane potential will change over time (no longer in steady state)

Answer 12

When the membrane is not in steady state:

• K+ flows out along the electrochemical gradient (therefore a portion of the current would be outward, and another portion would charge the membrane capacitor closer to the K+ equilibrium potential)
• Na+ flows in along the electrochemical gradient (therefore a portion of the current would be inward, and another portion would charge the membrane capacitor closer to the Na+ equilibrium potential)

However, because we have low gNa and high gK, the capacitive current is mainly dominated by K, charging it in the direction of the K+ equilibrium potential (negative inside, positive outside). The membrane changes to some level closer to the K+ equilibrium potential

Therefore, the inward Na and outward K current cancel out, and the membrane potential doesn’t change anymore and stays at this new value, which is determined by the charging of the membrane capacitor.

The important point is that to change the membrane potential, a portion of the current goes to charge the membrane capacitor.

Question 13

What is thr Voltage clamp?

Answer 13

An experimental technique used to measure the ionic currents through the membrane while holding (i.e. ‘clamping’) the membrane potential at a set level.

If you can hold/clamp Vm at a set value, you can hold the driving force constant (as Eion is already constant). Then, if you measure the current, you can calculate the conductance (gion)

Question 14

How is voltage clamping used to measure ionic currents of an action potential?

Answer 14

How is voltage clamping used to measure ionic currents of an action potential?
· Clamp Vm to some value that would normally be above threshold
· As membrane ‘tries’ to generate action potential, a feedback circuit (due to the clamp) rapidly detects deviations from the clamp value, and injects current to oppose/cancel this out
· This current injected is equal and opposite to the ionic currents flowing across the membrane

Question 15

Action potential recorded during current clamp recording vs voltage clamp recording

Answer 15

Current clamp (normal situation) is used to record membrane voltage.

Voltage clamp is used to record membrane current