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Q3(b):
Explain the following processes: (b) Depolarisation of the membrane of a nerve fibre

Solution :

Theoretical Foundation: The Resting Membrane Potential

Before the initiation of an action potential, the axonal membrane exists in a state of polarized equilibrium. At rest, the axoplasm contains a high concentration of $K^+$ and negatively charged proteins, while the extracellular fluid contains a high concentration of $Na^+$. Due to the selective permeability of the membrane—maintained largely by the $Na^+/K^+$ ATPase pump—the resting membrane potential is approximately $-70\,mV$ [Per the Goldman-Hodgkin-Katz equation].

Step 1: Application of Stimulus and Permeability Shift

When a stimulus of threshold intensity is applied to the nerve fibre, the voltage-gated $Na^+$ channels undergo a conformational change. This leads to a rapid increase in the permeability of the membrane to sodium ions ($Na^+$). [Justification: Ion channels operate via electrochemical gradients, where $Na^+$ ions flow from a region of high concentration to low concentration].

Extracellular (High Na+) Axoplasm (High K+) Na+ Influx

Step 2: The Influx of Sodium Ions ($Na^+$)

As the $Na^+$ channels open, sodium ions rush into the neuron down their concentration gradient. This influx of positively charged ions neutralizes the negative charge on the inner surface of the membrane. The membrane potential shifts from its resting state ($-70\,mV$) toward zero and eventually becomes positive. This transition to a positive internal charge is defined as Depolarisation.

Step 3: Analytical Data of the Action Potential

Phase Membrane Potential ($mV$) Ion Movement
Resting Potential $-70\,mV$ $Na^+/K^+$ Pump Active
Depolarisation $-70\,mV \rightarrow +30\,mV$ Rapid $Na^+$ Influx
Repolarisation $+30\,mV \rightarrow -70\,mV$ $K^+$ Efflux

Step 4: The All-or-None Principle

Depolarisation only proceeds to completion if the stimulus reaches a critical "threshold" level (typically $-55\,mV$). If the stimulus is sub-threshold, the membrane remains at its resting potential. Once the threshold is breached, the massive influx of $Na^+$ triggers an Action Potential, which propagates along the axon via local current circuits [Per the Hodgkin-Huxley model of membrane excitability].

Final Solution: Depolarisation is the process wherein the sudden increase in the permeability of the axonal membrane to $Na^+$ ions results in a rapid influx of $Na^+$ into the axoplasm, causing the membrane potential to change from negative to positive, effectively triggering an action potential across the nerve fibre.


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