explain the importance of the refractory period in determining the frequency of impulses

Control and Coordination in Mammals – The Refractory Period

Learning Objective (Cambridge AS & A‑Level Biology 9700)

Explain why the refractory period determines the maximum frequency at which a neuron or muscle fibre can fire an impulse, and use quantitative data to calculate that frequency.

1. Quick Review of Neuronal Structure & the Action Potential

• Key parts of a neuron (relevant to impulse generation)
  • Soma (cell body) – nucleus, metabolic centre.
  • Dendrites – receive graded (synaptic) potentials.
  • Axon hillock – high density of voltage‑gated Na⁺ channels; site of action‑potential initiation.
  • Myelinated axon – internodes speed conduction; Nodes of Ranvier contain Na⁺/K⁺ channels.
  • Axon terminal – releases neurotransmitter at the neuromuscular junction or synapse.
• Ionic basis of an action potential
  • Resting potential ≈ –70 mV (high K⁺ permeability, Na⁺/K⁺‑ATPase).
  • Depolarisation: voltage‑gated Na⁺ channels open → Na⁺ influx → membrane rises to ≈ +30 mV.
  • Repolarisation: Na⁺ channels inactivate; voltage‑gated K⁺ channels open → K⁺ efflux.
  • After‑hyperpolarisation (AHP): K⁺ channels stay open a few ms longer, membrane falls below –70 mV.
  • All‑or‑none principle – once threshold (≈ –55 mV) is reached, a full‑size action potential is produced.

2. The Refractory Period – Definition and Mechanisms

1. Absolute Refractory Period (ARP)
   • Na⁺ channels are either open or fully inactivated; a new action potential cannot be triggered, regardless of stimulus strength.
   • Duration is set by the time required for Na⁺‑channel inactivation gates to return to the resting (closed) state.
2. Relative Refractory Period (RRP)
   • Some Na⁺ channels have recovered, but the membrane is still hyper‑polarised because K⁺ channels remain open.
   • A second impulse can be generated only if the stimulus exceeds the normal threshold (i.e., a stronger depolarising current is needed).

Ionic basis of the RRP (150 words)

During the RRP, a proportion of voltage‑gated Na⁺ channels have returned to the closed (but activatable) state, while the delayed‑rectifier K⁺ channels are still open, producing an outward K⁺ current that drives the membrane potential below the resting level (after‑hyperpolarisation). The increased distance between the membrane potential and the Na⁺ equilibrium potential means a larger depolarising stimulus is required to reach the threshold for a new action potential. As K⁺ channels gradually close and Na⁺ channels fully recover, the threshold returns to its normal value and the RRP ends.

3. How the Refractory Period Limits Impulse Frequency

The shortest possible interval between two successive action potentials is the sum of the ARP and the RRP. This interval sets an upper ceiling on the firing rate.

Maximum possible frequency (f_max)

$$f_{\text{max}} = \frac{1}{\text{ARP} + \text{RRP}}$$

where ARP and RRP are expressed in seconds.

Example Calculation (2 sf)

Typical mammalian motor neuron:

• ARP = 0.8 ms = 8.0 × 10⁻⁴ s
• RRP = 0.4 ms = 4.0 × 10⁻⁴ s

$$f_{\text{max}} = \frac{1}{8.0\times10^{-4}+4.0\times10^{-4}} = \frac{1}{1.2\times10^{-3}} \approx 8.3\times10^{2}\ \text{Hz}$$

4. Factors that Influence the Refractory Period (and therefore f_max)

Factor	Effect on ARP / RRP	Resulting change in fmax
Ion‑channel kinetics (e.g., faster Na⁺ inactivation)	Shortens both ARP and RRP	Increases fmax
Temperature (higher)	Accelerates opening/closing of channels → shorter refractory periods	Higher firing rates (e.g., +2 °C ≈ 10 % rise in fmax)
Myelination	Clusters Na⁺ channels at nodes; reduces ARP	Higher fmax; demyelination lengthens ARP/RRP → lower fmax
Axon diameter	Larger diameter ↓ axial resistance → quicker repolarisation	Slight increase in fmax
Pharmacological agents (e.g., tetrodotoxin, K⁺‑channel blockers)	Block Na⁺ channels → lengthen ARP; prolong K⁺ opening → lengthen RRP	Reduced fmax, possible conduction failure

5. Physiological & Clinical Relevance

• Excitation‑contraction coupling – The firing frequency of a motor neuron determines the rate of Ca²⁺ release from the sarcoplasmic reticulum. Fast‑twitch fibres (short refractory periods) can fire at ≈ 1 kHz, producing rapid, powerful twitches; slow‑twitch fibres fire ≤ 600 Hz for sustained, fatigue‑resistant contractions.
• Sensory processing speed – Myelinated A‑δ fibres (short ARP/RRP) transmit sharp pain quickly, whereas unmyelinated C‑fibres (long refractory periods) convey dull, lingering pain.
• Clinical case‑studies
  • Multiple sclerosis (MS) – Demyelination increases ARP, reduces f_max, leading to slowed reflexes and muscle weakness.
  • Local anaesthetic (e.g., lidocaine) – Blocks Na⁺ channels, lengthening the ARP and preventing high‑frequency firing, producing reversible loss of sensation.
  • Anti‑arrhythmic class I drugs – Modify Na⁺‑channel recovery, altering refractory periods in cardiac tissue; analogous effects occur in neuronal firing.

6. Quantitative Summary – Typical Values

Neuron / Fibre Type	ARP (ms)	RRP (ms)	fmax (Hz, 2 sf)
Fast‑twitch motor neuron (myelinated)	0.7	0.3	1.2 × 10³
Slow‑twitch motor neuron (myelinated)	1.0	0.5	6.7 × 10²
Unmyelinated sensory fibre (C‑fibre)	2.5	1.0	2.9 × 10²

7. Practical Investigation – Measuring Refractory Periods (AO2)

Objective: Determine the absolute and relative refractory periods of a peripheral nerve and explore the effect of temperature.

1. Prepare a dissected frog sciatic nerve; attach stimulating electrodes at the proximal end and recording electrodes at the distal end.
2. Deliver a single suprathreshold stimulus (S₁) and record the action potential on an oscilloscope.
3. After a variable interval Δt, deliver a second stimulus (S₂) of identical intensity.
   • If no second response is seen, increase Δt until a response appears – the shortest Δt = ARP.
   • Continue increasing Δt; note when a second response appears with reduced amplitude (RRP start). Increase S₂ strength until a full‑size second action potential is obtained – the Δt at which this occurs marks the end of the RRP.
4. Repeat the protocol at 20 °C and 30 °C (maintain temperature with a water bath). Record ARP, RRP and calculate f_max for each temperature.
5. Data‑analysis task (AO2) – Plot Δt (ms) on the x‑axis against second‑response amplitude (mV) on the y‑axis. Use the graph to read ARP, RRP and to discuss the temperature effect quantitatively.

8. AO2 Practice Questions (Data Handling & Interpretation)

1. Given the table below, calculate f_max for a newly discovered fibre that has ARP = 0.9 ms and RRP = 0.6 ms. Show your work to 2 sf.
2. The recorded amplitudes for a nerve at 20 °C are: Δt = 0.5 ms → 0 mV; 0.9 ms → 2 mV; 1.3 ms → 8 mV; 1.7 ms → 12 mV (full size). Identify ARP and RRP from the data.
3. Explain, using the ionic mechanisms, why increasing the stimulus strength during the RRP restores a full‑size action potential.

9. Higher‑Order Thinking Questions (AO3)

• If a myelinated axon becomes demyelinated, predict how the ARP, RRP and f_max will change. Discuss the downstream impact on muscle control and reflex speed.
• During intense exercise body temperature rises by ≈ 2 °C. Using the temperature effect on channel kinetics, estimate the percentage change in f_max for fast‑twitch motor neurons.
• A toxin blocks 30 % of voltage‑gated Na⁺ channels. Discuss how this influences the absolute refractory period and the ability of the neuron to sustain high‑frequency firing.
• Compare a slow‑twitch fibre (ARP = 1.0 ms, RRP = 0.5 ms) with an unmyelinated C‑fibre (ARP = 2.5 ms, RRP = 1.0 ms). Which would be more affected by a 5 ms increase in the relative refractory period? Justify your answer.

10. Key Take‑aways (AO1)

• The refractory period guarantees unidirectional propagation and prevents overlap of successive action potentials.
• Its duration (ARP + RRP) directly determines the highest possible impulse frequency via the simple reciprocal relationship \(f_{\text{max}}=1/(ARP+RRP)\).
• Ion‑channel kinetics, temperature, myelination, axon diameter and pharmacological agents modify the refractory period, thereby influencing nerve‑signal speed, muscle contraction rates, and sensory perception.
• Understanding refractory periods underpins practical skills (measuring nerve impulses) and explains clinical conditions such as multiple sclerosis, the action of local anaesthetics, and anti‑arrhythmic drugs.