BIOSCI107 · Biology for Biomedical Science: Cellular Processes and Development
Neurons: Membrane Potential & Action Potentials
Topic 6 (exam Section C) is the course's one quantitative topic. It builds the resting membrane potential from the Nernst and Goldman equations and the Na⁺/K⁺ pump, then the action potential — voltage-gated Na⁺ channels with dual activation/inactivation gates, voltage-gated K⁺ channels, and the absolute and relative refractory periods — and finally conduction (myelination and saltatory conduction). Examined in the 40% final exam (paper Teleform MCQ) with genuine numeric calculation, so a calculator may be permitted here — confirm on Canvas.
What this chapter covers
- 01Resting membrane potential (−50 to −70 mV); only neurons and muscle are 'excitable'
- 02The ionic set-up: [K⁺]ᵢ high / [K⁺]ₒ low and [Na⁺]ᵢ low / [Na⁺]ₒ high, maintained by the Na⁺/K⁺ pump (3 out : 2 in); many leak K⁺ channels → resting P_K/P_Na ≈ 40:1
- 03Nernst equation E_ion = 61.5 mV × log₁₀([ion]ₒ/[ion]ᵢ): E_K ≈ −80 mV, E_Na ≈ +62 mV (permeable to one ion only)
- 04Goldman equation: Vm = 61.5 × log₁₀[(P_K[K]ₒ + P_Na[Na]ₒ)/(P_K[K]ᵢ + P_Na[Na]ᵢ)]; RMP sits near E_K because P_K ≫ P_Na
- 05Rule: raising permeability to an ion pulls Vm toward that ion's equilibrium potential
- 06Action potential stages: depolarisation (VG Na⁺ activate) → repolarisation (Na⁺ inactivate, VG K⁺ open) → after-hyperpolarisation
- 07VG Na⁺ channel's two gates (activation opens at threshold, inactivation closes after); all-or-none; absolute vs relative refractory periods
- 08Conduction: passive spread dissipates, so APs are regenerated; myelination (oligodendrocytes CNS, Schwann PNS) → fast saltatory conduction at nodes of Ranvier
Goldman equation — the effect of lowering extracellular Na⁺
- +1Set the permeabilities to the ratio: let P_K = 40 and P_Na = 1 (only the ratio matters). Numerator (outside) = P_K[K⁺]ₒ + P_Na[Na⁺]ₒ = 40×5 + 1×100 = 200 + 100 = 300. [+1]
- +1Denominator (inside) = P_K[K⁺]ᵢ + P_Na[Na⁺]ᵢ = 40×100 + 1×15 = 4000 + 15 = 4015. The ratio = 300/4015 ≈ 0.0747. [+1]
- +1Vm = 61.5 × log₁₀(0.0747) = 61.5 × (−1.127) ≈ −69.3 mV. Since −69.3 mV is more negative than the ~−65 mV baseline (computed the same way with [Na⁺]ₒ = 150 → ≈ −65 mV), lowering extracellular Na⁺ HYPERPOLARISES the cell by about 4 mV. [+1]
Key terms
- Resting membrane potential (RMP)
- The steady voltage across a resting cell membrane (inside negative, about −65 mV in a neuron). It arises from unequal Na⁺/K⁺ concentrations (set by the Na⁺/K⁺ pump) plus the membrane being far more permeable to K⁺ than Na⁺ (P_K/P_Na ≈ 40:1), so Vm sits close to E_K.
- Nernst equation
- E_ion = 61.5 mV × log₁₀([ion]ₒ/[ion]ᵢ) for a monovalent cation at body temperature — the equilibrium potential at which net flow of that single ion is zero. Valid only when the membrane is permeable to that one ion. Gives E_K ≈ −80 mV, E_Na ≈ +62 mV.
- Goldman equation
- Vm = 61.5 × log₁₀[(P_K[K⁺]ₒ + P_Na[Na⁺]ₒ)/(P_K[K⁺]ᵢ + P_Na[Na⁺]ᵢ)] — the resting potential when several ions contribute, weighted by their permeabilities. Only the permeability ratio matters; because P_K ≫ P_Na, resting Vm lies near E_K.
- Voltage-gated Na⁺ channel (two gates)
- The channel that drives the action potential's upstroke. It has an activation gate (closed at rest, opens at threshold) and an inactivation gate (open at rest, closes shortly after depolarisation). The two gates' timing creates the refractory period and the all-or-none spike.
- Absolute vs relative refractory period
- During the absolute refractory period (depolarisation + early repolarisation) no second action potential can fire because Na⁺ channels are inactivated. During the relative refractory period (after-hyperpolarisation, K⁺ channels still open) a stronger-than-normal stimulus can fire one. Together they enforce one-way, spaced-out signalling.
- Saltatory conduction
- Fast action-potential propagation along a myelinated axon, where the impulse is regenerated only at the nodes of Ranvier and spreads passively (and quickly) under the insulating myelin between nodes. Myelin is made by oligodendrocytes in the CNS and Schwann cells in the PNS.
Neurons: Membrane Potential & Action Potentials FAQ
When do I use the Nernst equation versus the Goldman equation?
Use the Nernst equation when only one ion's permeability matters — it gives that ion's equilibrium potential (the voltage at which its net flow is zero), e.g. E_K or E_Na. Use the Goldman equation when several ions contribute at once, as at the real resting potential, because it weights each ion by its permeability. At rest the membrane is far more permeable to K⁺ than Na⁺, so Goldman gives a Vm close to E_K but pulled slightly positive by the small Na⁺ leak.
Why does the resting potential sit near E_K and not E_Na?
Because permeability, not just concentration, sets where Vm lands. A resting neuron has many open leak K⁺ channels but few Na⁺ channels, so P_K/P_Na ≈ 40:1. The general rule is that Vm is pulled toward the equilibrium potential of whichever ion the membrane is most permeable to — here K⁺, whose E_K ≈ −80 mV. During an action potential Na⁺ permeability briefly dominates and Vm swings toward E_Na (≈ +62 mV).
How do the two gates on the Na⁺ channel explain the refractory period?
The voltage-gated Na⁺ channel has an activation gate (shut at rest, opens at threshold) and an inactivation gate (open at rest, swings shut soon after depolarisation). Right after a spike the inactivation gates are closed, so no stimulus can reopen the channels — the absolute refractory period. As the membrane repolarises the inactivation gates reset; during the after-hyperpolarisation a strong stimulus can fire a spike (relative refractory period). This is why action potentials are discrete and travel one way.
Can AI help me with membrane potentials in BIOSCI 107?
Yes, for study. Sia can re-run the Nernst and Goldman equations with any concentrations and show every step, and drill the depolarise/hyperpolarise interpretation and the AP stages. Use it to prepare for the final exam — it does not sit the exam for you, and the exam is an AI-free lane under the course's academic-integrity policy. Confirm permitted materials (including whether a calculator is allowed for Section C) on Canvas.
Exam move
This is the topic to over-practise, because it is the only one with real calculation and it carries Section C of the exam. Drill the Nernst equation until E_K and E_Na are reflexes (outside over inside; K⁺ negative, Na⁺ positive), then the Goldman equation using just the P_K/P_Na ratio, working the course's Study Questions until the arithmetic is automatic. Alongside the numbers, learn the one-line intuition — steepen the K⁺ gradient or raise P_K → hyperpolarise (toward E_K); raise external K⁺ or P_Na → depolarise — because many MCQ items ask for the direction, not the exact value. For the action potential, memorise the stage sequence with the channel behind each phase and the two-gate story that produces the refractory periods and the all-or-none spike. Finish with conduction (myelin, nodes of Ranvier, saltatory, oligodendrocytes vs Schwann cells). This is exam material (Topic 6, Section C); confirm the exam date, the Teleform format and whether a calculator is permitted on Canvas.
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