Action Potential: Generation, Propagation, and Conduction Velocity

Action Potential (AP) Topics

• Anatomy of a Neuron: Discussion of basic neuronal structure.

• Axon Hillock: The site where action potentials are typically initiated.

• Voltage-gated ion channels: Crucial for determining the shape of the action potential.

• Absolute and relative refractory periods: Mechanisms ensuring one-way propagation and limiting firing rate.

• Action potential conduction: How the signal propagates along the axon.

• Conduction velocity: Affected by axon diameter and myelination.

• Saltatory conduction: The 'jumping' conduction in myelinated axons.

• Recommended Reading: Chapter 12: pages 330-336.

Important Channels for Action Potential Generation

Voltage-gated Na+ Channel

• Structure: Contains a voltage sensor that activates at the threshold voltage, physically opening a gate.

• Inactivation Ball: A unique feature that seals the pore and prevents further Na+ entry into the cell, leading to inactivation.

• States: Can exist in three states:

  1. Open: Gate is open, Na+ rushes into the cell (inward current) based on its electrochemical gradient.

  2. Inactive: Inactivation ball blocks the pore, even if the main gate is technically open or closing. Cannot respond to further depolarization.

  3. Closed: Gate is closed, inactivation ball is dissociated. Can respond to depolarization.

• Function: Opening dramatically increases membrane permeability to Na+, moving the membrane potential towards the Nernst potential for Na+ ($E_{Na+}$).

Voltage-gated K+ Channel

• Structure: Contains a gate that opens and closes in response to membrane potential ($V_m$).

• No Inactivation Ball: Unlike Na+ channels, K+ channels do not have an inactivation ball.

• States: Can exist in two states:

  1. Open: Gate is open, K+ rushes out of the cell (outward current) based on its electrochemical gradient.

  2. Closed: Gate is closed.

• Function: Opening increases membrane permeability to K+, moving the membrane potential towards the Nernst potential for K+ ($E_{K+}$).

Phases of an Action Potential

1) Resting Membrane Potential

• State: Neuron is at its baseline membrane potential (e.g., $-70 ext{ mV}$).

• Ion Movement: Na+ and K+ movement is governed by passive membrane properties, primarily leak channels and the Na+/K+ ATPase pump.

• Channel States:

  • Voltage-gated Na+ channels: Closed.

  • Voltage-gated K+ channels: Closed.

• Permeability: Permeability to K+ is greater than Na+ (e.g., PK > P{Na}) due to more K+ leak channels.

2) Rising Phase (Depolarization)

• Trigger: Membrane depolarizes to threshold (typically around $-55 ext{ mV}$).

• Channel Activation: Voltage-gated Na+ channels rapidly open in response to reaching threshold.

• Ion Movement: Positively charged Na+ ions rush into the cell.

• Permeability Change: Membrane permeability to Na+ massively increases (e.g., $600 ext{x}$), becoming much greater than K+ (P{Na} eta eta PK).

• Membrane Potential: $V_m$ rapidly moves towards the Nernst Potential for Na+ (e.g., $+60 ext{ mV}$).

• K+ Channels: Voltage-gated K+ channels are activated by depolarization but open slowly and with a delay, so they remain effectively closed during the initial rising phase.

3) Falling Phase (Repolarization)

• Na+ Channel Inactivation: Voltage-gated Na+ channels become inactivated by the inactivation ball physically blocking the pore, despite the voltage gate still being open due to depolarization.

• Na+ Permeability: Na+ permeability massively decreases.

• K+ Channel Opening: Voltage-gated K+ channels, which were slowly activated, are now fully open.

• K+ Permeability: Membrane permeability to K+ massively increases (e.g., $300 ext{x}$), becoming much greater than Na+ (PK eta eta P{Na}).

• Ion Movement: K+ ions rush out of the cell.

• Membrane Potential: $V_m$ rapidly moves back towards the Nernst Potential for K+ (e.g., $-90 ext{ mV}$), causing repolarization.

4) Undershoot Phase (Hyperpolarization)

• K+ Channel Closing: Voltage-gated K+ channels begin to slowly close.

• Na+ Channel Recovery: The inactivation ball dissociates from the pore of voltage-gated Na+ channels, allowing them to return to the closed (but active) state, ready to respond to a new depolarization.

• Permeability: K+ permeability remains higher than the resting state for a brief period due to the slow closing of K+ channels, while Na+ permeability is low.

• Membrane Potential: $V<em>m$ undershoots the resting membrane potential, briefly hyperpolarizing further towards $E</em>{K+}$ before returning to rest.

Applying the Goldman-Hodgkin-Katz (GHK) Equation

• The GHK equation explains how membrane potential ($V_m$) changes as membrane permeability ($P$) to different ions changes, specifically in response to the opening and closing of voltage-gated ion channels.

• $V_m$ moves towards the Nernst potential of the ion with the highest permeability.

• The general GHK equation is given by:
  $V<em>m = rac{RT}{F} ext{ln} imes rac{P</em>K [K^+]<em>o + P</em>{Na} [Na^+]<em>o + P</em>{Cl} [Cl^-]<em>i}{P</em>K [K^+]<em>i + P</em>{Na} [Na^+]<em>i + P</em>{Cl} [Cl^-]_o}$
  Note: The slide simplifies by only showing cations, and the $[Cl^-]$ terms are inverted for convenience. For the provided example calculations, a simplified form without chloride is implicitly used given the inputs.

Constants Used:

• Gas Constant ($R$): $8.314 ext{ j/mol} ext{K}$

• Temperature ($T$): $310 ext{ K}$ ($37^ ext{C}$)

• Faraday Constant ($F$): $96500 ext{ C/mol}$

• Combined term $rac{RT}{F}$ is approximately $0.026 ext{ V}$ at $310 ext{ K}$.

Ion Concentrations (mM):

• $[K^+]_o = 4$ (Outside)

• $[K^+]_i = 155$ (Inside)

• $[Na^+]_o = 145$ (Outside)

• $[Na^+]_i = 15$ (Inside)

GHK Application to Depolarization Phase (Near Peak)

• Relative Permeability: $P<em>K = 30$, $P</em>{Na} = 600$ (reflects high Na+ permeability).

• Calculation:
  $V<em>m = 0.026 ext{ V} ext{ln} imes rac{30[4]</em>o + 600[145]<em>o}{30[155]</em>i + 600[15]<em>i}$ $V</em>m = 0.026 ext{ V} ext{ln} imes rac{120 + 87000}{4650 + 900}$
  $V<em>m = 0.026 ext{ V} ext{ln} imes rac{87120}{5550}$ $V</em>m = 0.026 ext{ V} imes (+1.85)$
  $V_m = +0.049 ext{ V}$ or $+49 ext{ mV}$

• Note: This value is near the peak of depolarization, demonstrating how $V<em>m$ approaches $E</em>{Na+}$ during the rising phase.

GHK Application to Repolarization Phase (Near Middle)

• Relative Permeability: $P<em>K = 300$, $P</em>{Na} = 100$ (reflects high K+ permeability).

• Calculation:
  $V<em>m = 0.026 ext{ V} ext{ln} imes rac{300[4]</em>o + 100[145]<em>o}{300[155]</em>i + 100[15]<em>i}$ $V</em>m = 0.026 ext{ V} ext{ln} imes rac{1200 + 14500}{46500 + 1500}$
  $V<em>m = 0.026 ext{ V} ext{ln} imes rac{15700}{48000}$ $V</em>m = 0.026 ext{ V} imes (-1.11)$
  $V_m = -0.029 ext{ V}$ or $-29 ext{ mV}$

• Note: This value is near the middle of repolarization, showing how $V<em>m$ approaches $E</em>{K+}$ during the falling phase.

Action Potential Propagation (Conduction)

• Mechanism: Once initiated, an action potential propagates along the entire length of the axon through a chain reaction.

• Local Current Flow:

  • During the rising phase (active area), Na+ influx causes depolarization.

  • This depolarization spreads through local current flow to adjacent, inactive areas of the membrane.

  • This local current flow depolarizes the adjacent inactive area from resting potential to threshold.

  • This triggers new voltage-gated Na+ channels to open in the adjacent area, regenerating the action potential.

• Contiguous Conduction: Action potentials are regenerated successively along the entire axon membrane (in unmyelinated axons).

Refractory Periods: Ensuring One-Way Propagation

• Refractory periods ensure that an action potential propagates in one direction (from the axon hillock to the terminal ends) and prevents reverse (antidromic) propagation.

1) Absolute Refractory Period (ARP)

• Definition: The period during which a particular patch of axonal membrane, having just undergone an action potential, is absolutely incapable of initiating another action potential, regardless of the strength of the stimulus.

• Mechanism: This occurs because voltage-gated Na+ channels are either already open or in their inactivated state and cannot be reopened immediately.

• Timing: Coincides with the rising and most of the falling phases of the action potential.

2) Relative Refractory Period (RRP)

• Definition: The period immediately following the absolute refractory period, during which an action potential can be initiated, but only if the stimulus is significantly stronger than the initial (threshold) stimulus.

• Mechanism:

  • Some voltage-gated Na+ channels have recovered from inactivation to the closed state.

  • However, many voltage-gated K+ channels are still open, causing hyperpolarization (undershoot).

  • A stronger stimulus is needed to overcome this increased K+ efflux and reach threshold.

• Timing: Coincides with the later part of the falling phase and the undershoot (hyperpolarization) phase.

Factors Affecting Conduction Velocity

Conduction velocity (the speed at which an action potential propagates) is dependent upon the passive electrical properties of the axon.

1. Axon Diameter

• Internal Resistance ($R_i$): Inversely correlated with axon diameter. Larger diameter means lower internal resistance.

• Effect: Smaller neurons conduct action potentials slower than larger neurons.

• Reasoning: A larger diameter reduces axial resistance, allowing local currents to spread further and faster, thus depolarizing adjacent membrane patches to threshold more quickly.

• Relationship: Conduction velocity (V) is proportional to the square root of the diameter ($V imes D^{0.5}$) for unmyelinated axons and proportional to the first power ($V imes D^1$) for myelinated axons according to some models.

2. Myelination

• Myelin Sheath: Formed by glial cells (Schwann cells in the PNS, Oligodendrocytes in the CNS) wrapping around the axon up to $200$ times with their plasma membrane.

• Nodes of Ranvier: Gaps in the myelin sheath where voltage-gated ion channels are concentrated.

• Effect on Membrane Resistance ($R_m$): Myelin acts as an insulator, dramatically increasing membrane resistance by preventing charge flow across the membrane under the myelin.

• Effect on Membrane Capacitance ($C_m$): Myelin decreases membrane capacitance by increasing the distance between intracellular and extracellular fluid, reducing the ability of the membrane to store charge.

• Time Constant ($au$): Largely unaffected because the increase in $R<em>m$ is offset by a decrease in $C</em>m$ ($au = R<em>m C</em>m$).

• Length Constant ($au$): Dramatically increased due to the significant increase in $R<em>m$ ($au = rac{R</em>m}{R<em>o + R</em>i}$). A larger length constant means local current can spread farther down the axon before decaying.

• Saltatory Conduction ("Jumping Conduction"):

  • Instead of continuous regeneration, action potentials effectively "jump" from one Node of Ranvier to the next.

  • Electrostatic current flow, which is very fast, spreads passively underneath the myelinated segments.

  • The signal is renewed vigorously only at the Nodes of Ranvier where voltage-gated channels are present.

  • This significantly speeds up conduction compared to unmyelinated axons of similar diameter.

Summary of Conduction Velocity Factors

• Larger Axon Diameter: Decreases internal resistance ($R_i$), increases length constant ($au$), leading to faster conduction.

• Myelination: Increases membrane resistance ($R<em>m$) and dramatically increases the length constant ($au$), enabling saltatory conduction and much faster propagation. The equation for length constant is $au = rac{R</em>m}{R<em>o+R</em>i}$.

These two factors allow for efficient and rapid transmission of nerve impulses over long distances.