Suppose a biological membrane with a specific capacitance of 1 μF/cm^2 has a resting surface charge density of 0.1 μC/cm^2. Also suppose there are 50 sodium channels per μm^2 and thatwhen each opens for 1 ms, 1000 Na+ ions flow through the channel, resulting in a reduction of the potential difference (the membrane voltage). Compare this membrane’s resting potentialvoltage to the membrane voltage 1 ms after 10% of these channels open, assuming no other changes occur during this time.

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Asked Nov 19, 2019
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Suppose a biological membrane with a specific capacitance of 1 μF/cm^2 has a resting surface charge density of 0.1 μC/cm^2. Also suppose there are 50 sodium channels per μm^2 and that
when each opens for 1 ms, 1000 Na+ ions flow through the channel, resulting in a reduction of the potential difference (the membrane voltage). Compare this membrane’s resting potential
voltage to the membrane voltage 1 ms after 10% of these channels open, assuming no other changes occur during this time.

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Step 1

The total charge associated per unit (µm2) area of membrane is

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10%ne um natof Na nane -10% atoms channel Na* um

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Step 2

Substituting the values gives

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50 channel 1000 Na* 1.6x101c] O 10% Na channel um = 8x101 C/um

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Step 3

Total charge associated per unit (µm2) are...

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um A- 10 m2 10-m =10 m

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Electrostatic Potential and Capacitance

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