describe and explain changes to the membrane potential of neurones, including: how the resting potential is maintained, the events that occur during an action potential, how the resting potential is restored during the refractory period

Control and Coordination in Mammals – Neuronal Membrane Potential

Learning Objective

Describe and explain the changes to the membrane potential of neurones, including:

• How the resting membrane potential (RMP) is maintained
• The events that occur during an action potential (AP)
• How the RMP is restored during the refractory period
• How the impulse propagates along an axon
• The basic mechanisms of synaptic transmission (electrical and chemical)

1. Resting Membrane Potential (RMP)

1.1 Ion Concentration Gradients

1.2 Key Processes that Maintain the RMP

• Leak (non‑gated) channels – mainly K⁺ leak channels allow K⁺ to diffuse out, making the interior negative.
• Na⁺/K⁺‑ATPase (sodium‑potassium pump) – uses 1 ATP to move 3 Na⁺ out and 2 K⁺ in, reinforcing the concentration gradients and contributing ≈ ‑10 mV to the RMP.
• Selective permeability – at rest the membrane is ≈ 90 % permeable to K⁺, ≈ 5 % to Na⁺ and ≈ 5 % to Cl⁻.
• Electro‑chemical equilibrium – each ion has an equilibrium (Nernst) potential; the RMP is closest to the K⁺ equilibrium potential because of the high K⁺ permeability.

1.3 Nernst Equation (Equilibrium Potential of a Single Ion)

1.4 Goldman‑Hodgkin‑Katz (GHK) Equation – Calculating the RMP from Multiple Ions

Numerator   = 1·(5) + 0.04·(145) + 0.45·(4)   = 5 + 5.8 + 1.8 = 12.6
Denominator = 1·(140) + 0.04·(15) + 0.45·(120) = 140 + 0.6 + 54 = 194.6
V_m = 26.7 ln(12.6 / 194.6) ≈ 26.7 ln(0.0648) ≈ 26.7·(‑2.74) ≈ -73 mV

1.5 Summary of Factors that Set the RMP

• K⁺ leak channels → major contributor
• Na⁺/K⁺‑ATPase → maintains concentration gradients and adds a small hyperpolarising component
• Relative permeabilities (P_K ≫ P_Na, P_Cl) → RMP lies near E_K
• Cl⁻ is largely at its equilibrium potential, so it does not drive the RMP away from E_K

2. Action Potential (AP)

2.1 Overview

An action potential is a rapid, self‑propagating depolarisation of the neuronal membrane. Once the threshold (≈ ‑55 mV) is reached, voltage‑gated Na⁺ channels open in an all‑or‑none fashion, producing a stereotyped voltage‑time curve.

2.2 Voltage‑Time Diagram (Key Concept)

2.3 Phases of a Single Action Potential

1. Depolarisation (0–1 ms)

   • Threshold reached → voltage‑gated Na⁺ channels open (fast activation).
   • Na⁺ rushes inward (electro‑chemical driving force ≈ +120 mV).
   • Membrane potential rises rapidly to a peak of ≈ +30 mV.

2. Repolarisation (1–2 ms)

   • Na⁺ channels enter an inactivated state (cannot reopen until repolarised).
   • Voltage‑gated K⁺ channels open (delayed activation, slower kinetics).
   • K⁺ exits the cell, driving the membrane potential back toward the negative RMP.

3. Hyper‑polarisation (after‑potential, 2–4 ms)

   • K⁺ channels close slowly, so K⁺ continues to leave.
   • Membrane potential briefly becomes more negative than the resting level (≈ ‑80 mV).

2.4 Ion‑Channel Kinetics (Voltage‑Gated Channels)

• Na⁺ channels – rapid activation (≈ 0.1 ms), fast inactivation (≈ 1 ms).
• K⁺ channels (delayed rectifiers) – slower activation (≈ 0.5 ms), no fast inactivation; close over several milliseconds.
• Ca²⁺ channels (at the presynaptic terminal) – high‑threshold, slower opening; essential for neurotransmitter release.

2.5 Propagation of the Impulse

• Local current – depolarisation of one segment creates an electric field that depolarises the adjacent segment, opening its Na⁺ channels.
• Unmyelinated axon (continuous conduction) – the AP is regenerated at every point along the membrane. Speed ≈ 0.5–2 m s⁻¹.
• Myelinated axon (saltatory conduction)

  • Myelin (Schwann cells in PNS, oligodendrocytes in CNS) insulates the membrane, leaving gaps called nodes of Ranvier.
  • AP “jumps” from node to node, increasing speed 10‑fold (≈ 10–120 m s⁻¹) and reducing ATP demand because fewer Na⁺/K⁺ pumps are required.

3. Refractory Period & Restoration of the Resting Potential

3.1 Absolute Refractory Period (ARP)

• All voltage‑gated Na⁺ channels are in the inactivated state.
• No further AP can be generated, regardless of stimulus strength.
• Duration ≈ 1 ms (covers depolarisation and early repolarisation).

3.2 Relative Refractory Period (RRP)

• Some Na⁺ channels have recovered to the closed (activatable) state, but many K⁺ channels remain open.
• A stronger than normal stimulus can elicit an AP, but the peak is reduced and the threshold is higher.
• Duration ≈ 2–4 ms (covers late repolarisation and hyper‑polarisation).

3.3 Membrane Time Constant (τ) and Capacitance

The rate at which the membrane potential returns toward the RMP is described by the RC time constant:

\$\tau = Rm \times Cm\$

• R_m – membrane resistance (Ω·cm²); higher resistance → slower voltage change.
• C_m – membrane capacitance (≈ 1 µF cm⁻² for typical neurones).
• During the RRP the membrane behaves like an RC circuit; voltage decays exponentially: V(t)=V_0 e^{-t/τ}.

3.4 Mechanisms that Restore the RMP

1. Na⁺/K⁺‑ATPase – actively restores the original Na⁺ and K⁺ gradients (3 Na⁺ out / 2 K⁺ in per ATP).
2. Closure of voltage‑gated K⁺ channels – stops the outward K⁺ current, allowing leak channels to dominate again.
3. Leak (non‑gated) channels – maintain the baseline permeability that defines the RMP.

3.5 Practical Activity (AO2 – Measuring Refractory Period)

1. Clamp the membrane at –70 mV.
2. Apply a brief depolarising pulse to trigger an AP.
3. Immediately apply a second pulse at varying intervals (0.5 ms, 1 ms, 2 ms, …).
4. Record whether a second AP is produced. The shortest interval that yields a full‑amplitude AP marks the end of the absolute refractory period; intervals that give a reduced‑amplitude AP indicate the relative refractory period.

4. Synaptic Transmission

4.1 Electrical Synapses (Gap Junctions)

• Direct cytoplasmic connections between adjacent neurones.
• Allow ions and small molecules (< 1 kDa) to pass, producing an almost instantaneous postsynaptic response.
• Found in escape‑response circuits of invertebrates and in specialised mammalian regions (e.g., retinal interneurons).

4.2 Chemical Synapses – Main Mode in the Human Nervous System

1. Arrival of the AP at the presynaptic terminal

   • Depolarisation opens voltage‑gated Ca²⁺ channels.
   • Ca²⁺ influx (driven by its steep electro‑chemical gradient) triggers vesicle fusion.

2. Neurotransmitter release

   • Synaptic vesicles containing neurotransmitter (e.g., acetylcholine, glutamate, GABA) fuse with the presynaptic membrane via the SNARE complex.
   • Neurotransmitter diffuses across the ~20 nm synaptic cleft.

3. Postsynaptic response

   • Ionotropic receptors* – ligand‑gated ion channels (e.g., nicotinic AChR, AMPA) produce fast EPSPs or IPSPs.
   • Metabotropic receptors* – G‑protein‑coupled receptors that activate second‑messenger cascades, giving slower, longer‑lasting effects.

   The resulting change in membrane potential is termed an EPSP (excitatory) or IPSP (inhibitory).

4. Termination of the signal

   • Enzymatic degradation (e.g., acetylcholinesterase breaks down ACh).
   • Re‑uptake into the presynaptic terminal via specific transporters.
   • Diffusion away from the cleft.

4.3 Integration of Synaptic Signals

• Neurones receive many EPSPs and IPSPs simultaneously.
• Temporal summation – closely spaced inputs add together.
• Spatial summation – inputs arriving at different dendritic locations sum at the axon hillock.
• If the combined depolarisation reaches the threshold (≈ ‑55 mV), an AP is generated; otherwise the cell remains at RMP.

5. Key Points to Remember

• The RMP (~‑70 mV) is set mainly by K⁺ leak channels and the Na⁺/K⁺‑ATPase; individual ion equilibrium potentials are calculated with the Nernst equation, while the GHK equation combines them.
• An AP is an all‑or‑none event that requires a threshold of ≈‑55 mV, rapid opening of voltage‑gated Na⁺ channels, and subsequent delayed opening of voltage‑gated K⁺ channels.
• Propagation:

  • Continuous conduction in unmyelinated axons.
  • Saltatory conduction in myelinated axons – faster and more energy‑efficient.

• The absolute refractory period (≈ 1 ms) prevents a second AP during Na⁺ channel inactivation; the relative refractory period (≈ 2–4 ms) raises the threshold because of lingering K⁺ conductance.
• Restoration of the RMP after an AP relies on the Na⁺/K⁺‑ATPase, closure of K⁺ channels, and the constant activity of leak channels.
• Synaptic transmission:

  • Electrical synapses give instantaneous transmission via gap junctions.
  • Chemical synapses use Ca²⁺‑triggered neurotransmitter release, with ionotropic or metabotropic receptors producing EPSPs or IPSPs.
  • Temporal and spatial summation at the axon hillock determines whether the threshold for a new AP is reached.