3. (60 pts) The Na/K ATPase maintains the electrochemical gradient required for

Question

3. (60 pts) The Na/K ATPase maintains the electrochemical gradient required for nerve impulses. Nerve cells expend about 70% of their ATP production on maintaining the Na' and K gradients that are responsible for the membrane potential. For nerve cells, the ion distribution is shown in the following table: Concentration (mM) Intracellular Extracellular Neuron Membrane Permeability (P Resting Active Ion Potassium (K) Sodium (Na) Chloride (Ch Proteins (A 4. 150 120 34 1.00 0.05 0.45 0.00 1.00 12.0 0.45 0.00 140 4 148 Reference: Molecular Cell Biology. 4th ed. Lodish et al., 2000 a. Calculate the Nernst membrane potential for potassium ions (K). b. Calculate the Nernst membrane potential for sodium ions Na Calculation of the membrane potential requires consideration of the permeability of each ion that contributes to the membrane potential using the Goldman equation: RT, [K"].PK+ + [Na*).PNa+ + [CI-?Pa In Note, subscripts e and i refer to extracellular and intracellular concentrations, respectively. Px is the relative membrane permeability for ion X. c. Calculate the membrane potential of a resting neuron at 310 K. d. Calculate the action potential of an active neuron at 310 K. neuron: The Na*/K ATPase pumps sodium ions out and potassium out of the ne e. Calculate the molar free energy required for transport of potassium ions (K). f. Calculate the molar free energy required for transport of sodium ions (Na) g. What is the total free energy required? Is the free energy of ATP hydrolysis sufficient to drive the Na*/K pump?

Explanation / Answer

The Nernst membrane potential for the K+ ion at 310 K is -94.97166 mV

The Nernst membrane potential for the Na+ ion at 310 K is 67.46812 mV

The Membrane potential of resting neuron at 310 K is -67.46811902494109mV

The Membrane potential of active neuron at 310 K is 48.88495978295115

Calculate molar free energy required for transport of potassium ion

For K C1=4, C2=140

?Gtransport = RTln(C2/C1) + ZF?V

RTln(C2/C1) = (2.479 kJ/mol) ln(140 mM/4 mM) = 2.479 kJ/mol ln(35) = 2.479 kJ/mol(3.55)

RTln(C2/C1) = 8.80 kJ/mol

ZF?V = (1)(96.5 kJ/(V•mol)(- 0.09V) = – 8.685 kJ/mol

?Gtransport = RTln(C2/C1) + ZF?V = +8.80kJ/mol – 8.685 kJ/mol = + 0.115 kJ/mol

Calculate molar free energy required for transport of Sodium ion

For Na C1=150, C2=12

?Gtransport = RTln(C2/C1) + ZF?V

RTln(C2/C1) = (2.479 kJ/mol) ln(12mM/150 mM) = 2.479 kJ/mol ln(0.08) = 2.479 kJ/mol(-2.526)

RTln(C2/C1) = -6.262 kJ/mol

ZF?V = (1)(96.5 kJ/(V•mol)(0.06V) = 5.79 kJ/mol

?Gtransport = RTln(C2/C1) + ZF?V = -6.262kJ/mol +5.8 kJ/mol = - 0.46 kJ/mol

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