The extracellular concentrations of Na+ and K+ are 135mM and 6mM, respectively.
The intracellular concentrations of Na+ and K+ are 10mM and 105mM, respectively.
The membrane potential is 75mV. For Na+/K+ ATPase, 3Na+ are exported and 2K+ are imported. Calculate the total free energy in KJ/mole required to transport the ions.
To calculate the total free energy required to transport the ions using the Na+/K+ ATPase, we need to consider the concentration differences across the membrane and the membrane potential.
First, we need to calculate the electrochemical potential for Na+ and K+ separately. The electrochemical potential is the sum of the electrical potential and the concentration gradient potential.
For Na+:
Electrical potential (Ee) = membrane potential (Vm) - 0 (since there's no electrical gradient for Na+)
Concentration gradient potential (Ec) = RT * ln (outside concentration/inside concentration)
RT = 25.69348 mV at 298K (room temperature)
ln = natural logarithm
Using the given concentrations, we have:
Ec (Na+) = 25.69348 * ln (135/10) ≈ 192.7 mV
For K+:
Electrical potential (Ee) = membrane potential (Vm) - 0 (since there's no electrical gradient for K+)
Concentration gradient potential (Ec) = RT * ln (outside concentration/inside concentration)
Using the given concentrations, we have:
Ec (K+) = 25.69348 * ln (6/105) ≈ -177.9 mV (negative because there is an inward concentration gradient)
Next, we calculate the total free energy required to transport the ions using the Na+/K+ ATPase.
The change in free energy (ΔG) = -(n * F * E), where n is the number of ions transported, F is Faraday's constant (96.485 KJ/V.mol), and E is the electrochemical potential.
For Na+, since the ATPase exports 3 Na+ ions:
ΔG (Na+) = -(3 * 96.485 * 10^3 * 192.7 * 10^-3) ≈ -175.9 KJ/mol
For K+, since the ATPase imports 2 K+ ions:
ΔG (K+) = -(2 * 96.485 * 10^3 * -177.9 * 10^-3) ≈ 34.3 KJ/mol
Finally, we calculate the total free energy required by adding the individual free energies for Na+ and K+:
Total ΔG = ΔG (Na+) + ΔG (K+)
Total ΔG ≈ -175.9 + 34.3 ≈ -141.6 KJ/mol
Therefore, the total free energy in KJ/mol required to transport the ions is approximately -141.6 KJ/mol.