Questions: The Hodgkin-Huxley Model

Question 1

A drug selectively blocks the sodium inactivation gate (the 'h' gating variable) without affecting sodium activation (m) or potassium activation (n). What would happen to action potential firing?

• A. Action potentials would be smaller in amplitude because sodium conductance would be reduced
• B. The neuron would fail to fire because both m and h are required for any sodium current to flow
• C. The membrane would become persistently depolarized and the neuron would lose the ability to fire repeated action potentials, because sodium channels could open but never inactivate
• D. Action potentials would be prolonged but normal in all other respects, because h only controls the duration of the sodium current

Answer: (C)

The h gate is the sodium inactivation gate — it closes slowly during depolarization, terminating the sodium current and allowing repolarization. Without h inactivation, sodium channels that open during depolarization would remain open indefinitely, producing a sustained inward current that holds the membrane depolarized. The neuron would be locked in a depolarized state, unable to repolarize and thus unable to fire another action potential. This is also why scorpion toxins and certain local anesthetic side effects that block sodium inactivation cause sustained depolarization and repetitive firing or paralysis.

Question 2

What produces the action potential threshold — the critical membrane voltage above which regenerative firing occurs in the Hodgkin-Huxley model?

• A. A fixed voltage sensor in the sodium channel that triggers simultaneously in all channels when reached
• B. The point at which sodium influx through activated channels exceeds the repolarizing outward potassium current, creating a self-amplifying positive feedback loop
• C. A voltage-gated calcium channel that opens at threshold and triggers sodium channel opening
• D. The equilibrium potential for sodium, which the membrane must approach before further depolarization can occur

Answer: (B)

Threshold is an emergent property of competing currents, not a fixed property of any single channel. As voltage increases, sodium channels begin to open (m increases), producing inward sodium current that further depolarizes the membrane, opening more channels. Below threshold, outward leak and potassium currents are sufficient to counteract this inward current and return the membrane to rest. Above threshold, the inward sodium current wins — the feedback becomes regenerative ('all-or-none'). Threshold is the tipping point of this competition, which is why it is not a sharp fixed value but can vary with recent activity, temperature, and channel availability.

Question 3

In the Hodgkin-Huxley model, the refractory period emerges from the combination of slow sodium inactivation recovery (h gate) and sustained potassium activation (n gate), rather than from any single channel property.

• T. True
• F. False

Answer: True

The absolute refractory period occurs when h (sodium inactivation) is near zero and n (potassium activation) is still elevated — sodium channels cannot reopen, and potassium channels are actively hyperpolarizing the membrane. The relative refractory period follows as h slowly recovers but n is still partially activated, requiring a stronger-than-normal stimulus to trigger threshold. No single channel produces this behavior; it is the combined dynamics of m, h, and n with their different time constants. This is a central example of how complex neural behavior is emergent from interacting conductances.

Question 4

The Hodgkin-Huxley model can predict action potential firing in any neuron using the same fixed parameters that Hodgkin and Huxley measured from the squid giant axon.

• T. True
• F. False

Answer: False

The HH model framework is general, but the specific parameters — the voltage-dependent rate constants (α and β) for m, h, and n, the maximum conductances, and the reversal potentials — were measured empirically from the squid giant axon and apply precisely only to that preparation. Different neuron types (cerebellar Purkinje cells, dopamine neurons, cardiac cells) have different channel complements, different kinetics, and sometimes entirely different channel types (calcium channels, HCN channels, persistent sodium currents). The HH architecture has been extended to model these neurons by adding conductances and modifying parameters, but the original squid parameters cannot be transplanted directly.

Question 5

Why is the action potential threshold not simply a property of sodium channels alone? Explain what makes it an emergent property of the interaction between sodium and potassium conductances.

Model answer: Threshold depends on the balance between the inward sodium current (depolarizing) and the combined outward currents — potassium, leak, and any inactivation. At membrane voltages below threshold, a small depolarization opens a few sodium channels (m increases slightly), but the resulting inward sodium current is too small to overcome the outward currents pulling the membrane back to rest. The system is stable. Above threshold, sodium activation becomes self-reinforcing: enough channels open that the inward current outpaces the restorative outward currents, causing further depolarization that opens still more channels. Threshold is the unstable equilibrium point where these competing dynamics are exactly balanced — tip one way and the membrane returns to rest; tip the other and regenerative firing occurs.

This emergent quality is why HH is more than an empirical fit — it provides a mechanistic explanation for why neurons fire in an all-or-none fashion. No single channel has a 'threshold voltage' built in; threshold emerges from the dynamics of a system of coupled differential equations. This insight generalizes: many threshold phenomena in biology (gene expression switches, cell fate decisions) involve the same architecture of competing positive and negative feedback with a tipping point.