Describe the action potential

Overview

An action potential is a rapid, transient reversal of the membrane potential in excitable cells (neurons and muscle cells), serving as the fundamental unit of electrical signaling in the nervous system. It's an all-or-none event that propagates along the axon without decreasing in amplitude.

The Resting State: Setting the Stage

Before understanding the action potential, we must understand what resting membrane potential is and why it exists.

Derivation: Why -70 mV?

Starting from first principles:

1. Ion distributions (typical mamalian neuron):

   • K⁺: 140 mM inside, 5 mM outside
   • Na⁺: 15 mM inside, 150 mM outside
   • Cl⁻: 10 mM inside, 110 mM outside
   • Large anions (A⁻): 100 mM inside, 0 mM outside

2. The Nernst equation tells us the equilibrium potential for each ion:

$E_{ion} = \frac{RT}{zF} \ln\frac{[ion]_{out}}{[ion]_{in}}$

Where:

• R = gas constant (8.314 J/(mol·K))
• T = absolute temperature (310 K for body temp)
• z = ionic charge
• F = Faraday constant (96,485 C/mol)

At body temperature, this simplifies to:

$E_{ion} = \frac{61.5 \text{ mV}}{z} \log_{10}\frac{[ion]_{out}}{[ion]_{in}}$

Why this form? Natural log converts to log₁₀ (ln x = 2.303 log₁₀ x), and RT/F at 310 K = 26.7 mV × 2.303 ≈ 61.5 mV.

3. Calculate equilibrium potentials:

For K⁺ (z = +1): $E_K = 61.5 \log_{10}\frac{5}{140} = 61.5 \times (-1.45) = -89 \text{ mV}$

For Na⁺ (z = +1): $E_{Na} = 61.5 \log_{10}\frac{150}{15} = 61.5 \times 1 = +61.5 \text{ mV}$

4. Goldman-Hodgkin-Katz equation accounts for membrane permeability:

$V_m = 61.5 \log_{10}\frac{P_K[K^+]_{out} + P_{Na}[Na^+]_{out} + P_{Cl}[Cl^-]_{in}}{P_K[K^+]_{in} + P_{Na}[Na^+]_{in} + P_{Cl}[Cl^-]_{out}}$

Why this matters: At rest, P_K : P_Na : P_Cl ≈ 1 : 0.04 : 0.45. The membrane is most permeable to K⁺, so resting potential is closer to E_K than E_Na.

Pluging in values: V_m ≈ -70 mV

5. The Na⁺/K⁺-ATPase pump maintains these gradients by actively transporting 3 Na⁺ out and 2 K⁺ in per ATP hydrolyzed, working against their concentration gradients.

Answer: Because the membrane isn't only permeable to K⁺. Na⁺ is constantly leaking in (even at rest), pulling the potential toward +61.5 mV. The actual potential is a weighted average based on permeabilities. GHK accounts for multiple ions; Nernst assumes only one ion can cross.

The Action Potential: Phase by Phase

Phase 1: Resting State

• Membrane at -70 mV
• Most voltage-gated Na⁺ channels are closed (but capable of opening)
• Most voltage-gated K⁺ channels are closed
• Leak channels (especially K⁺) maintain the resting potential

Phase 2: Depolarization to Threshold

What happens: A stimulus (synaptic input, sensory receptor) causes local depolarization.

Why it matters: Voltage-gated Na⁺ channels have a voltage sensor (S4 segment with positive charges). At rest, the negative inside voltage holds them closed.

The critical moment: When depolarization reaches threshold (typically -55 mV), enough Na⁺ channels open to trigger positive feedback:

$\text{Depolarization} \rightarrow \text{Na}^+ \text{ channels open} \rightarrow \text{Na}^+ \text{ influx} \rightarrow \text{More depolarization}$

Derivation of Na⁺ current:

The driving force for Na⁺ is the difference between membrane potential and Na⁺ equilibrium potential:

$I_{Na} = g_{Na}(V_m - E_{Na})$

Where g_Na is Na⁺ conductance (proportional to open channels).

At threshold (-55 mV):

• Driving force = -55 - (+61.5) = -116.5 mV
• This large negative value means strong inward current (positive charges moving in)

Why this step? This inward current (negative = inward for positive ions) brings in ~14.5 × 10⁹ Na⁺ ions per millisecond, rapidly depolarizing the membrane.

Phase 3: Rising Phase (Rapid Depolarization)

What happens: Explosive opening of voltage-gated Na⁺ channels. The membrane potential races toward E_Na (+61.5 mV).

Why it stops at +40 mV (not +61.5 mV):

1. Na⁺ channel inactivation: After ~1 ms, an inactivation gate (ball-and-chain structure) physically blocks the channel pore. The channel is now inactivated (closed and unresponsive).

2. K⁺ channels begin opening: Voltage-gated K⁺ channels are slower to respond but start opening as membrane becomes positive.

Mathematical insight: The rate of potential change follows:

$\frac{dV}{dt} = \frac{I_{Na} + I_K + I_{leak}}{C_m}$

Where C_m is membrane capacitance (~1 μF/cm²).

During the rising phase, I_Na >> I_K, so dV/dt is large and positive (rapid rise).

Inactivation enforces a refractory period and allows the neuron to reset.

Phase 4: Repolarization

What happens: The membrane potential rapidly returns toward resting.

Mechanism:

1. Na⁺ channels are inactivated (no more inward current)
2. Voltage-gated K⁺ channels are now fully open (delayed rectifier channels)
3. K⁺ flows out down its electrochemical gradient

Driving force for K⁺ at +40 mV:

$I_K = g_K(V_m - E_K) = g_K(40 - (-89)) = g_K(129 \text{ mV})$

This is a large outward current (positive = outward for positive ions), removing positive charge and returning the membrane toward negative.

Why it works: K⁺ conductance (g_K) is now HIGH because many voltage-gated K⁺ channels are open. From our equation above:

$\frac{dV}{dt} = \frac{I_K + I_{leak}}{C_m}$

Since I_K is large and negative (outward), dV/dt is large and negative (rapid fall).

Why this step? This explains why repolarization is fast (1-2 ms)—the outward current is strong.

Phase 5: Hyperpolarization (Undershoot)

What happens: The membrane briefly becomes MORE negative than resting (-80 to -90 mV).

Why: Voltage-gated K⁺ channels are slow to close. Even after the membrane reaches -70 mV, many K⁺ channels remain open for a few milliseconds, continuing to drive the potential toward E_K (-89 mV).

Biological significance: This undershoot contributes to the absolute refractory period (see below).

Return to resting: K⁺ channels eventually close, and leak channels + the Na⁺/K⁺ pump restore -70 mV.

The Refractory Periods

Absolute Refractory Period (~1-2 ms)

Cause: Na⁺ channels are inactivated. No matter how strong the stimulus, they CANNOT open.

Why it matters:

• Ensures action potentials travel in one direction (can't go backward because channels behind are inactivated)
• Limits maximum firing frequency (~500-1000 Hz)

Molecular detail: Inactivation requires the membrane to repolarize below ~-50 mV before the inactivation gate releases and channels can return to the closed (but ready) state.

Relative Refractory Period (~3-5 ms)

Cause:

1. Some Na⁺ channels still inactivated
2. Voltage-gated K⁺ channels still open (hyperpolarization)

Effect: A larger-than-normal stimulus is needed to reach threshold because:

• Fewer Na⁺ channels are available
• More K⁺ channels are open (opposing depolarization)

Formula insight: Threshold is dynamic. If extra K⁺ channels are open:

$\text{Effective threshold} = V_{threshold} + \Delta V_{K-leak}$

You need to overcome additional K⁺ eflux.

If you artificially stimulated during the absolute refractory period, nothing would happen—the Na⁺ channels are physically blocked by their inactivation gates.

All-or-None Principle

Why this works:

1. The positive feedback loop of Na⁺ entry is self-amplifying
2. The number of available Na⁺ channels and driving force determine amplitude
3. These factors are properties of the membrane, not the stimulus

How information is encoded: Via frequency coding (rate of action potentials), not amplitude.

The amplitude of each spike is identical (~110 mV). The brain interprets more spikes/second as stronger stimulus intensity.

Propagation Along the Axon

How does the action potential move?

1. Local current flow: When one segment depolarizes to +40 mV, positive charges spread passively to adjacent segments (inside the axon).

2. Threshold reached in next segment: This depolarizes the next segment to threshold, opening its Na⁺ channels.

3. Regeneration: Each segment generates its own full-amplitude action potential.

Why unidirectional? The segment behind is in its absolute refractory period (Na⁺ channels inactivated).

Conduction Velocity

Factors affecting speed:

1. Axon diameter: Larger diameter = lower internal resistance = faster spread of local currents $v \propto \sqrt{d}$

2. Myelination: Myelin (insulating sheath) forces the action potential to "jump" between Nodes of Ranvier (gaps in myelin). This saltatory conduction is much faster (up to 120 m/s) than continuous conduction (0.5-2 m/s in unmyelinated axons).

Why saltatory is faster: The capacitive current (charging the membrane) only occurs at nodes, not along the entire myelinated segments. Less membrane to charge = faster.

$\lambda = \sqrt{\frac{r_m}{r_i}}$

Where r_m = membrane resistance, r_i = internal axial resistance.

Larger λ → current spreads farther → faster conduction between nodes.

Common Misconceptions

Steel-man: This intuition captures that charge is moving, which is true. The error is thinking it's passive conduction (like a wire).

The fix: Action potentials are actively regenerated at each point. The axon membrane is more like a chain of amplifiers than a passive conductor. Each segment uses metabolic energy (stored in ion gradients) to boost the signal.

Evidence: Cut a neuron's axon in half. If it were passive conduction, the signal would weaken dramatically. Instead, each segment actively fires, so the signal travels full length without decay.

Steel-man: The pump DOES establish the gradients that store potential energy. Without it, neurons couldn't fire repeatedly.

The fix: The pump is too slow (milliseconds) to generate the action potential itself (which happens in 1-2 ms). Think of the pump as charging a battery; the action potential is the discharge. Voltage-gated channels (passive conduits) allow rapid discharge; the pump slowly recharges.

Analogy: A dam stores water (pump maintains gradients). Opening the floodgates releases water rapidly (channels open, action potential). The dam doesn't push water through during the flood.

Steel-man: During hyperpolarization, you DO need to depolarize MORE to reach -55 mV from -80 mV than from -70 mV. The math checks out.

The fix: But many voltage-gated K⁺ channels are still open. Any depolarizing current is opposed by this high K⁺ conductance. It's not just about the voltage distance—it's about the conductance state. The cell is less excitable because of the high g_K, not just the negative voltage.

Think of it as a bucket with a bigger drain hole (high g_K)—you can pour water in (depolarizing current), but it drains out faster, making it hard to fill.

Memory Aids

Na⁺ channels cycle through all four. K⁺ channels typically lack inactivation (just closed↔ open).

The "springs" are actually chemicals (sodium and potassium ions) that are stored on different sides of the cell's wall, like water behind a dam. The "mousetraps" are special doors in the wall that pop open when the voltage changes.

Here's the cool part: when the first door opens, sodium rushes in (like water through a gate), making that spot positively charged. This positive charge opens the NEXT door down the line, and sodium rushes in there too. It's a chain reaction!

But why doesn't it go on forever? Each door has a self-closing mechanism. After it opens, it slams shut and locks for a tiny moment (that's the "refractory period"). So the signal can only go forward, not backward. Then potassium doors open to let the positive charge back out, resetting everything.

The neuron is constantly using energy (like a little battery) to pump the sodium back out and potassium back in, getting ready for the next signal. It's like resetting all those mousetraps so you can trigger them again!

Connections

• Resting Membrane Potential - the starting point
• Voltage-Gated Ion Channels - the molecular machinery
• Synaptic Transmission - what happens when the action potential reaches the axon terminal
• Myelination and Saltatory Conduction - how speed is optimized
• Nernst Equation - equilibrium potential for each ion
• Goldman-Hodgkin-Katz Equation - multi-ion membrane potential
• Patch Clamp Techniques - how we measure these events
• Hodgkin-Huxley Model - mathematical model of action potentials
• Multiple Sclerosis - demyelinating disease that disrupts propagation
• Local Anesthetics - drugs that block Na⁺ channels
• Cardiac Action Potential - similar principles, different ion channel subtypes

#flashcards/biology

What is an action potential? :: A rapid, transient reversal of membrane potential in excitable cells, serving as the fundamental unit of electrical signaling. It's an all-or-none event that propagates without decreasing in amplitude.

Why is resting potential closer to E_K (-89 mV) than E_Na (+61.5 mV)? :: Because at rest, the membrane is much more permeable to K⁺ than Na⁺ (P_K : P_Na ≈ 25:1), so K⁺ has greater influence on the membrane potential.

Concept Map

Hinglish (regional understanding)