The sarcoplasmic reticulum (SR) of a muscle fiber stores Ca2+ ions at a concentration of 21 mM, while the concentration of Ca2+ in the cytoplasm is 1 mM. Body temperature isT = 37 oC.
A.) What is the potential gradient across the SR membrane caused by Ca2+ ions?
B.) The calcium pumps of the SR membrane are called sarcoplasmic reticulum ATPases (SERCA). How much work is done by them while they pump 200 nmol of Ca2+ from the cytoplasm into the SR?
Definition of work:
G = H – TS = U + PV – TS
dG = δq + δw + PdV + VdP – SdT – TdS
If it’s possible to do more than expansion work, then: δw = δwother + δwexpansion
dG=TdS+δwother -PdV+PdV+VdP-SdT-TdS=δwother +VdP-SdT
Recall that μi = ∂G∂ni
Under constant temperature and pressure conditions: dG = δwother = nidμiδwother may be electrical work.
Note that below i and f indicate initial and final states respectively.
μi = μ◦i + RTln([i]) + zFφi
welectrical = nion(μf – μi) = nion(RTln[f] + zF(φf – φi))[i]