A cell at ( ) has

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Molecular machines, transport and bioenergetics · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch Channels, pumps and the resting potential

Problem

A cell at

310\,\mathrm{K}

(

k_BT/e = 26.7\,\mathrm{mV}

) has

[\mathrm{Na}]_i = 15\,\mathrm{mM}

[\mathrm{Na}]_o = 150\,\mathrm{mM}

and rests at

V_m = -70\,\mathrm{mV}

. Someone argues: "The net current across the resting membrane is zero, so the membrane must be sitting at thermodynamic equilibrium. If it is already at equilibrium, no energy input is needed to hold it there, so poisoning the sodium-potassium pump should not change the resting potential at all." ((a)) Compute the sodium Nernst potential

E_{\rm Na}

and compare it with

V_m

. ((b)) Say whether the argument is correct, and explain, using the comparison in part (a), why the resting state needs continuous metabolic input even though the total current is zero.

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