Many types of cells are able to use membrane-spanning transport proteins and a source of energy to drive the active transport of glucose across the cell membrane. Let’s consider a specific protein that is able to transport (from outside the cell into the cytoplasm) one molecule of glucose for each molecule of ATP the protein hydrolyzes. The details of this process are not important for this problem except that you can treat it like equilibrium process. The overall reaction and the associated ΔG at 298 K for this process are given below. Glc(out) + ATP + H2O ⇌ Glc(in) + ADP + Pi @?=298 K, ΔG=−31.3 kJ mol-1 Additional Information: -Pi is “inorganic phosphate” (i.e. PO43– & related species). At equilibrium, [Pi] = 3 × 10-3 M. -The cell maintains a ratio of ATP to ADP of about 20 i.e. [ATP]/[ADP] = 20). -The maximum ratio of [Glc(in)] to [Glc(out)] occurs when the system is at equilibrium. a) Write an expression for the equilibrium constant for this process. b) Your expression for ?eq in part a) should not include [H2O]. Explain why, in no more than 2 sentences. c) Given all the information above, how large a ratio of [Glc(in)] to [Glc(out)] can the cell maintain? HINT: Use Δ? = −?? ln?eq+ and your equilibrium expression.
Many types of cells are able to use membrane-spanning transport proteins and a source of energy to drive the active transport of glucose across the cell membrane. Let’s consider a specific protein that is able to transport (from outside the cell into the cytoplasm) one molecule of glucose for each molecule of ATP the protein hydrolyzes.
The details of this process are not important for this problem except that you can treat it like equilibrium process. The overall reaction and the associated ΔG at 298 K for this process are given below.
Glc(out) + ATP + H2O ⇌ Glc(in) + ADP + Pi @?=298 K, ΔG=−31.3 kJ mol-1
Additional Information:
-Pi is “inorganic phosphate” (i.e. PO43– & related species). At equilibrium, [Pi] = 3 × 10-3 M.
-The cell maintains a ratio of ATP to ADP of about 20 i.e. [ATP]/[ADP] = 20).
-The maximum ratio of [Glc(in)] to [Glc(out)] occurs when the system is at equilibrium.
a) Write an expression for the equilibrium constant for this process.
b) Your expression for ?eq in part a) should not include [H2O]. Explain why, in no more than 2 sentences.
c) Given all the information above, how large a ratio of [Glc(in)] to [Glc(out)] can the cell maintain? HINT: Use Δ? = −?? ln?eq+ and your equilibrium expression.
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