Action Potentials & Ionic Excitability

General Features of the Action Potential (AP)

• Definition
  • A transient, all-or-none reversal of the membrane potential produced by a regenerative inward current in excitable membranes.
• Core functions
  • Rapid, long-distance information transfer in nerve & muscle fibres.
  • Command of effector responses (e.g. muscle contraction, neurotransmitter release).
• Coding concept
  • Spike transduction: graded-amplitude signals are converted to a spike-frequency code.
  • Spike frequency = \frac{1}{\text{inter-spike interval}}.
• Regenerative nature
  • Positive feedback → autocatalytic opening of voltage-gated channels → self-propagating impulse.

Spike Parameters & Refractory Periods

• Absolute Refractory Period (ARP)
  • Time after an AP when no stimulus can elicit another AP.
  • Sets the upper limit of firing rate.
• Relative Refractory Period (RRP)
  • Follows the ARP; threshold is elevated, but a stronger stimulus can evoke an AP.
  • Largely due to residual G_K increase & partial Na⁺ channel recovery.
• Consequences for signalling
  • Limits maximum spike frequency and shapes temporal coding.

Electrical Excitability Beyond Neurons

• Present in multiple tissues
  • Pancreatic β-cells: rhythmic burst firing at 11.1\,\text{mM} glucose.
  • Egg cells of sea urchin, tunicates, mice.
  • Plants, e.g. Venus flytrap generates APs to trigger leaf closure.
• Illustrates evolutionary conservation and versatility of AP mechanisms.

Historical Quest for the Ionic Basis

• Bernstein (1912)
  • "Membrane breakdown" hypothesis: all ionic gates open, E_m \rightarrow 0\,\text{mV}.
• Cole & Curtis (1939)
  • Wheatstone bridge with 20\,\text{kHz} carrier showed membrane impedance ↓ (conductance ↑) during an AP.
  • Supported Bernstein’s idea of a transient permeability increase but did not address overshoot.
• Hodgkin & Huxley (1939) / Cole & Curtis (1940)
  • First intracellular recordings in squid giant axon revealed an overshoot (membrane potential becomes positive), contradicting simple breakdown.

The Sodium Hypothesis (Hodgkin & Katz, 1949)

• Gradual replacement of extracellular Na^+ with impermeant choline proportionally reduced AP amplitude.
• Radio-isotope fluxes (Na^{24} in, K^{42} out) confirmed selective ion movements during an AP.
• Conclusion: AP rising phase = transient, selective P_{Na} increase.

Voltage-Gated Channels & The Voltage Clamp Revolution

• Need: separate voltage (command) from resulting current.
• Kenneth S. Cole (1949) invented the feedback voltage clamp.
  • Amplifier injects current I{clamp} such that Vm = preset V_{command}.
  • Capacitive current (I_{cap} = C \frac{dV}{dt}) is brief; remaining current reflects ionic flow.
• Squid giant axon observations (Hodgkin & Huxley, 1952)
  • Early inward current (fast, transient) → carried by Na^+.
  • Late outward current (delayed, sustained) → carried by K^+.

Why Current–Voltage (I–V) Relations Matter

• Early inward I_{Na} increases then decreases with stronger depolarization because
  • G_{Na} ↑ (more channels open).
  • Driving force (Vm - E{Na}) ↓ (approaches equilibrium).
• IK grows monotonically: both GK and driving force (Vm - EK) increase.

Identifying Ionic Species

1. I–V curve construction across voltages (Hodgkin, Huxley & Katz, 1952).
2. Ion substitution
   • Replace 90 % extracellular Na^+ → E_{Na} shifts from +55\,\text{mV} to -9\,\text{mV}; inward current disappears.
3. Pharmacology
   • Tetrodotoxin (TTX) blocks Na^+ channels → abolishes early inward current.
   • Tetraethyl-ammonium (TEA) blocks K^+ channels (internally in squid) → abolishes late outward current.

Na⁺ Channel Inactivation & K⁺ Channel Dynamics

• Na⁺ channels
  • Activate rapidly on depolarization, then inactivate (close) even while V_m remains positive.
  • Pronase injection removes inactivation → persistent I_{Na} despite depolarization (Armstrong, Bezanilla & Rojas, 1973).
  • "Ball-and-chain" model: cytoplasmic inactivation gate occludes pore after activation (Armstrong & Bezanilla, 1977).
• K⁺ channels (squid axon type)
  • Activate slowly, do not inactivate during maintained depolarization.
  • Other K⁺ subtypes (e.g., A-type) do inactivate; diversity underlies varied firing patterns.

Determinants of Threshold Potential

• Typical threshold: -55\,\text{mV} \pm 5\,\text{mV}.
• Dual feedback loops (Carpenter & Reddi, 2012)
  • Positive: depolarization → P_{Na} ↑ → further depolarization.
  • Negative: depolarization → P_{K} ↑ → repolarizing influence.
• Factors elevating threshold
  • Enhanced G_K (e.g., during RRP).
  • Residual Na⁺ channel inactivation (accommodation).

Quantifying Conductances: Ohm’s Law

• V = I R \;\Rightarrow\; G = \frac{1}{R} = \frac{I}{V}.
• Ionic conductances
  • G{Na} = \frac{I{Na}}{(Vm - E{Na})}
  • G{K} = \frac{I{K}}{(Vm - E{K})}
• Hodgkin & Huxley (1952d) introduced gating variables
  • m (Na⁺ activation), h (Na⁺ inactivation), n (K⁺ activation).
  • AP reconstructed in 10-µs steps; 5-ms AP computed in 8 h on a mechanical calculator.

Calcium & Membrane Excitability

• Extracellular [Ca^{2+}] modulates surface charge & threshold (Frankenhaeuser–Hodgkin, 1957).
  • Hypocalcaemia (↓[Ca^{2+}]_o) → threshold shifts ~10$–15\,\text{mV} more negative → hyper-excitability.
  • Clinical: tingling, cramps, laryngospasm, seizures.
  • Hypercalcaemia (↑[Ca^{2+}]_o) → threshold more positive → hypo-excitability.
  • Clinical: fatigue, depression, arrhythmias, coma.
• Hormonal control
  • Parathyroid hormone (PTH) ↑ [Ca^{2+}]o; Calcitonin ↓ [Ca^{2+}]o.
• Mechanistic view: Ca²⁺ ions bind to outer membrane sites, creating an additional electric field that offsets depolarizing stimuli (“surface potential theory”).

Propagation of the Action Potential

Unmyelinated Axons

• Continuous conduction; each segment depolarizes the next by local current spread.
• ARP (due to Na⁺ inactivation) prevents back-propagation → unidirectional travel.
• RRP (elevated G_K) demands stronger stimulus for premature firing.

Myelinated Axons & Saltatory Conduction

• Insulating myelin ↑ membrane resistance, ↓ capacitance → faster, energy-efficient propagation.
• APs regenerate only at nodes of Ranvier (rich in Na⁺ channels clustered ≤ 21\,\mu\text{m} apart).
  • Passive spread between nodes described by \Delta Vm(x) = \Delta V0 e^{-x/\lambda}.
  • Example: \Delta V0 = 100\,\text{mV}, \; x = 22\,\mu\text{m}, \; \lambda \approx 37\,\mu\text{m} \rightarrow \Delta Vm \approx 13.7\,\text{mV} (still above threshold).
• Channel distribution (Debanne et al., 2011)
  • Na⁺ channels densely at nodes; K⁺ (various subtypes) at juxtaparanodes; Ca²⁺ channels in terminals.

Summary of Key Pharmacological & Experimental Tools

• Voltage clamp & feedback amplifiers.
• Selective toxins: TTX (puffer fish), TEA, Pronase.
• Ion substitution (choline, Li⁺) & radioactive tracers (Na^{24}, K^{42}$$).

Ethical & Practical Implications

• Toxins (TTX) pose risks but serve as critical research & clinical tools (analgesia trials).
• Understanding excitability informs treatment of arrhythmias, epilepsy, hypo/hyper-calcaemia.
• Plant and invertebrate APs inspire bio-engineering (e.g., Venus flytrap sensors).

Historical Acknowledgement

• Alan Hodgkin & Andrew Huxley: 1963 Nobel Prize for elucidating ionic mechanism of the AP.
• Their quantitative approach set the paradigm for modern electrophysiology and computational neuroscience.