The text derives the potassium Nernst potential by pricing the free-energy cost of…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Molecular machines, transport and bioenergetics · Molecular machines, transport and bioenergetics

Life at Thermal Energy, Ch The membrane: barrier, capacitor and pump

Problem

The text derives the potassium Nernst potential by pricing the free-energy cost of moving one potassium ion from inside to outside the cell: a concentration term

k_BT\ln(c_{\rm out}/c_{\rm in})

and an electrical term

-eV_m

, set to zero at equilibrium. ((a)) Repeat this argument for an ion of general signed valence

z

(charge

q=ze

) to obtain a general formula for the Nernst potential

E_{\rm X}

. ((b)) Use your formula for calcium,

z=+2

, with

c_{\rm in} = 2.0\times10^{-4}\,\mathrm{mM}

inside and

c_{\rm out} = 1.8\,\mathrm{mM}

outside, at body temperature (

310\,\mathrm{K}

, where

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

), to find

E_{\rm Ca}

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