Write a complete, balanced equation for the couples reaction catalyzed by the no

Question

Write a complete, balanced equation for the couples reaction catalyzed by the normal Na+/K+ pump in the plasma membrane. Calculate the total exergonic free energy change deltaG for ATP hydrolysis under the conditions in the cell given below. Calculate the total endergonic free energy change deltaG for Na+ and K+ transport. Then calaculate the total free energy change deltaG for the complete coupled reaction of the Na+/K+ pump under cellular conditons. Discuss whether this reaction is favorable, and how efficiently the free energy of ATP hydrolysis is coupled to pumping

[ATP] = [Pi] = 20 mM, [ADP] = 0.5 mM, [Na+out] = 100 mM, [K+out] = 5 mM, [Na+in] = 10 mM, [K+in] = 200 mM. Vin-Vout = -70mV

Explanation / Answer

In animal cells, these gradients are established by the hydrolysis of ATP via the action of a membrane-spanning enzyme, Na+ /K+ ATPase, also called the "Na+ /K+ pump. " This enzyme catalyzes the reaction

3 Na+in + 2 K+ out + ATP 3 Na+ out + 2 K+ in + ADP + Pi

The free energy change for this reaction is the sum of the free energies of ATP hydrolysis and those for pumping Na+ and K+ against their concentration gradients.

GNa+ pump = GATP hydrolysis + GNa+ transport + GK+ transport

Physiological ionic conditions. In this case, Na+ ions are being pumped against the electrochemical gradient that normally exists in the cell. The work of pumping Na+ out of the cell consists of two terms, the chemical work of pumping the ion against its concentration gradient plus the electrical work of moving it against the electrical gradient across the membrane. Therefore the free energy of sodium transport is about 46 kJ/mol.

In vivo ,NMR of human skeletal muscle has established that G for ATP hydrolysis is 62 kJ/mol.

GNa = 3 RT In [Na+]o [Na+]i+ [ ZF] = 3 (5.7 kJ mol x log[ 100/ 10 ] (1) 96.5 mol.V/ kJ (0.070 V)) = 3 [5.7 + 6.755] kJ/mol = 37.365kJ/mol

The situation for K+ differs in that K+ ions are moving "downhill" with the electrical gradient but "uphill" against the K+ concentration gradient. Therefore, we need estimates of the two driving 'forces (Gchemical and Gelcctrical) to determine whether K+ transport is passive or active. = 2*( 5.7 log[200/5]+96.5(-0.070))=2*(5.7*1.602-6.755)=4.73kj/mol

Plugging the values for GNa and GK into equation shows that G for the Na+ /K+ ATPase reaction in resting muscle is about -16 kJ/mol. GNa pump = (62) +37.365+4.73= 19.90kJ/mol

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