Physiology: Excitable Membranes

Physiology: Excitable Membranes

The Nernst Equation

The equilibrium potential for any ion can be calculated using the Nernst equation: E = (RT/zF) × ln([ion]out/[ion]in). At 37°C this simplifies to E = (61/z) × log([ion]out/[ion]in) mV. This gives the membrane potential at which there is no net driving force on that ion.

Goldman-Hodgkin-Katz Equation

The resting membrane potential is more accurately described by the Goldman-Hodgkin-Katz (GHK) equation, which accounts for the relative permeabilities and concentrations of all permeant ions (primarily Na⁺, K⁺, and Cl⁻). Because the resting membrane is primarily permeable to K⁺ (PK >> PNa >> PCl), the RMP is close to, but more positive than, the K⁺ equilibrium potential.

Graded Potentials

Graded potentials are local changes in membrane potential produced by stimuli — they can be depolarising (e.g., EPSPs from excitatory synapses) or hyperpolarising (e.g., IPSPs from inhibitory synapses). Key features: (1) amplitude proportional to stimulus strength, (2) do not propagate actively — they decay with distance (electrotonically), (3) can be summed. Spatial summation: simultaneous inputs from multiple sites add together. Temporal summation: rapid sequential inputs from the same site add together. If the membrane potential reaches threshold (typically –55 mV) at the axon hillock, an action potential is generated.

Action Potential

Phase 1 — Rising phase (depolarisation): Threshold opening of voltage-gated Na⁺ channels → rapid Na⁺ influx → membrane depolarises to approximately +30–40 mV (approaches Na⁺ equilibrium potential). Phase 2 — Repolarisation: Inactivation of Na⁺ channels + delayed opening of voltage-gated K⁺ channels → K⁺ efflux drives membrane back toward K⁺ equilibrium potential. Phase 3 — Hyperpolarisation (afterhyperpolarisation): K⁺ channels remain open briefly, driving membrane below RMP (< –70 mV). Recovery: Na⁺/K⁺-ATPase restores ion gradients.

Refractory periods: Absolute refractory period (ARP): during the AP and immediately after, Na⁺ channels are inactivated — no stimulus can generate another AP. Relative refractory period (RRP): Na⁺ channels recovering but K⁺ channels still open — a suprathreshold stimulus can trigger another AP but frequency is limited. These periods determine maximum firing frequency.

Pharmacological Modulation

Tetrodotoxin (TTX) and saxitoxin block voltage-gated Na⁺ channels from outside — complete conduction block. Local anaesthetics (lidocaine, bupivacaine) block VG Na⁺ channels from inside — smaller fibres (pain) blocked first (differential block). Lithium prolongs action potentials (substitutes for Na⁺ inside channels but is pumped out more slowly).