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Gibbs Free Energy (GFE) is the amount of change of energy during a reaction, either energy consumed or generated. The movement of any molecule (non-charged) down, or up a concentration gradient involves a change in free energy, Δ G ("Delta G") Moving down the concentration gradient releases energy so Δ G is negative Moving up the concentration gradient consumes energy so Δ G is positive The amount of free energy released or consumed can be calculated from the equation Δ Gin means the energy either released, or must be put in to the system, for the molecule to move from the ECF into the ICF, in other words, molecule moving into the cell. That’s what the “in” means with the term Δ Gin. What this means is that: when [X]in is less than [X]out, then Δ G will be negative. When [X]in is more than [X]out, then Δ G will be positive.
Active Transport of Glucose Filtration of the blood in the glomeruli of the kidneys produces “filtrate” with a concentration of glucose about the same as that of the blood (~ 5 mM/L ). All of this glucose is normally reclaimed by transport
- from the filtrate within the proximal tubule
- across the plasma membrane at the apical surface of the epithelial cells lining the tubule and
- across the plasma membrane at the basolateral surface of the cell into the interstitial fluid and
- back into the blood. As the process continues and more and more glucose is removed from the filtrate, the concentration gradient against which the glucose must be pumped by active transport, increases. This means that GFE for glucose in this scenario must be positive.
Problem: What is the free energy needed to move glucose from the filtrate into the proximal tubule cells when the concentration in the filtrate has dropped to 0.00 6 mM/L? The problem is to pump glucose into the cell where it is about 6.0 mM/L. So, the total gradient through which the glucose must be pumped is 0 .00 6 mM/L → 6.0 mM/L. Δ Gin = (2)(310) x ln (6.0/.00 6 ) = 620 ln ( 1000 ) = (620)(6. 9 ) = + 4,278 cal/mole = + 4.3 kcal/mole What this means is that more than 4.3 kcal/mole is needed to move glucose against is gradient. Where is the needed energy to come from? The Na+/glucose transporter The active transport of glucose is mediated by the Na+/glucose transporter. This is a symporter because both the sodium ion and the glucose molecule are passing through the membrane in the same direction :
- sodium DOWN its gradient of about o 140 mM/L outside to o 10 mM/L inside
- while glucose is going against its gradient ( 0.00 6 mM/L → 6 mM/L ). A mole of sodium ions (Na+) moving down this concentration gradient releases −1.6 kcal/mole of free energy. Δ Gin = (2)(310) ln (10/140) = (620) ln (0.07) = (620)(− 2.64) = − 1 ,637 cal/mole = −1.6 kcal/mole
Many cellular processes depend on a strong Na+^ concentration gradient. Maintaining this gradient is the job of the Na+/K+^ ATPase pump, moving 3 Na+’s out of the cell and moving 2 K+’s into the cell, both against their concentration gradients. The energy for this comes from ATP. The Na+/K+^ ATPase pump is the greatest single user of energy in our body. GFE and Na+/K+^ ATPase pump Suppose you had the following concentrations of Na+^ and K+: ICF - Na+: 15 mM/L, K+: 140 mM/L ECF - Na+: 145 mM/L, K+: 5 mM/L and suppose the resting membrane potential is - 70mV. How much energy needs to be supplied to the Na+/K+^ ATPase pump in order for it to move the Na+/K+? Concentration calculation For Na+: Δ Gin = (2)(310) x ln ( 15 / 140 ) (620)(-2.2) = - 1,364 cal/mole or - 1.4 kcal/mole For K+: Δ Gin = (2)(310) x ln ( 140 / 5 ) (620)(3.3) = 2,046 cal/mole or 2.1 kcal/mole Electrical force calculation For Na+: Δ G = (+1)(23,062)(- 0.07) = −1,614 cal/mole ( −1.6 kcal/mole ) For K+: Δ G = (+1)(23,062)(- 0.07) = −1,614 cal/mole ( −1.6 kcal/mole ) Total Δ Gin for Na+: - 1.4 kcal/mole + - 1.6 kcal/mole = - 3.0 kcal/mole x 3 = - 9.0 kcal/mole Total Δ Gin for K+: 2. 1 kcal/mole + - 1.6 kcal/mole = 0.5 kcal/mole x 2 = 1 .0 kcal/mole 9.0 + 1.0 = 10 kcal/mole to move 3 Na+’s out of the cell and 2 K+’s into the cell. Therefore, hydrolysis of ATP must yield greater than 10 kcal/mole to supply the Na+/K+^ ATPase pump.
