BIOC 460, sample problems for calculation of free energy of ion transport p. 1 BIOC 460, two sample problems for calculation of free energy of transport of charged solutes 1. A eukaryotic chloride channel, when open, permits Cl– ions to flow spontaneously across the membrane in the direction required to go toward equilibrium, as dictated by the sign of ∆Gtransport. Show your work for calculations. (Hint: draw a sketch of cell with C1 and C2 and charge gradient.) A. The transport of Cl– ions by this channel would best be described as an example of 1) simple diffusion 3) primary active transport 2) facilitated diffusion 4) secondary active transport B. The equation for the free energy of transport is : ∆Gt = RTln C2/C1 + ZF∆V. Suppose that the extracellular concentration of Cl– is 123 mM and the intracellular concentration is 4 mM. The membrane electrical potential (∆V) is 0.06 V, inside negative relative to outside. At 298 K, for transport of Cl– ions from the outside into the cell: 1) Calculate the chemical potential term of ∆Gtransport for transport of Cl– ions into the cell (the term reflecting the concentration gradient for Cl– ions). Does this term favor the flow of Cl– ions into the cell, or out of the cell? 2) Calculate the electrical potential term of ∆Gtransport for transport of Cl– ions into the cell, the term reflecting the electrical gradient across the membrane. Does this term favor flow of Cl– ions into the cell, or out of the cell? 3) Calculate the overall ∆Gtransport for flow of Cl– ions from outside into the cell. Would Cl– ions flow into the cell, or out of the cell, under conditions described in question above? 2. Show your work for calculations. (Hint: draw a sketch of cell with C1 and C2 and charge gradient.) Suppose that a protein transports K+ ions across the membrane. Intracellular [K+] = 157 mM and extracellular [K+] = 4 mM, and plasma membrane ∆V = 0.06 V, inside negative relative to outside. At 298K, consider transport of K+ ions into the cell. A. Is the chemical potential term (concentration gradient) favorable or unfavorable for transporting K+ ions into the cell? What is the sign on that term? Calculate the chemical potential term. B. Is the electrical potential term (charge gradient) favorable or unfavorable for transporting K+ ions into the cell? What is the sign on that term? Calculate the electrical potential term. C. Calculate the overall ∆Gtransport for flow of K+ ions from outside into the cell. Would K+ ions flow into the cell spontaneously under conditions described in question above (by facilitated diffusion), or would an active transport process be required?BIOC 460, sample problems for calculation of free energy of ion transport p. 2 ANSWERS, with notes: 1. A eukaryotic chloride channel, when open, permits Cl– ions to flow spontaneously across the membrane in the direction required to go toward equilibrium, as dictated by the sign of ∆Gtransport. Show your work for calculations. (Hint: draw a sketch of cell with C1 and C2 and charge gradient.) A. The transport of Cl– ions by this channel would best be described as an example of 1) simple diffusion 3) primary active transport *2) facilitated diffusion 4) secondary active transport “flow spontaneously across the membrane in the direction required to go toward equilibrium” means “downhill” flow of ions, no free energy input required, so passive transport, not active; protein involved, so it’s facilitated diffusion, not simple diffusion. B. The equation for the free energy of transport is: ∆Gt = RTln C2/C1 + ZF∆V Suppose that the extracellular concentration of Cl– is 123 mM and the intracellular concentration is 4 mM. The membrane electrical potential (∆V) is -0.06 V, inside negative relative to outside. At 298 K, for transport of Cl– ions from the outside into the cell: 1) Calculate the chemical potential term of ∆Gtransport for transport of Cl– ions into the cell (the term reflecting the concentration gradient for Cl– ions). Does this term favor the flow of Cl– ions into the cell, or out of the cell? Draw diagram as shown below, reflecting the Cl– concentrations inside and outside the cell, as given. Question concerns direction of transport from outside INTO cell, so draw arrow on diagram reflecting transport direction stated in question. C1 = 123 mM; C2 = 4 mM. RTln(C2/C1) = (2.479 kJ/mol) ln(4 mM/123 mM) = 2.479 kJ/mol ln(0.0325) = 2.479 kJ/mol(–3.42) Chemical potential term = –8.5 kJ/mol (favorable to transport Cl– ions into cell) (That was clear from the fact that concentration outside cell was greater than concentration inside cell, so Cl– ions would have to flow in to try to equalize the concentration of Cl–.) 2) Calculate the electrical potential term of ∆Gtransport for transport of Cl– ions into the cell, the term reflecting the electrical gradient across the membrane. Does this term favor flow of Cl– ions into the cell, or out of the cell? On diagram add symbols for negative and positive charges to reflect the information given in question (“inside negative relative to outside”, which is typical for plasma membrane electrical gradients). That means there are more negative charges inside, or more positive charges outside the cell. Charge gradient makes this term unfavorable for transport of Cl– ions into cell (this term > 0 for transport into cell; term has + sign) ZF∆V = (-1)(96.5 kJ/(V•mol)(-0.06 V) = + 5.79 kJ/mol 3) Calculate the overall ∆Gtransport for flow of Cl– ions from outside into the cell. Would Cl– ions flow into the cell, or out of the cell, under conditions described in question above? ∆Gtransport = RTln(C2/C1) + ZF∆V = –8.5 kJ/mol + 5.8 kJ/mol = – 2.7 kJ/mol Overall ∆Gtransport is negative, so movement of Cl– ions into cell is favored, in spite of unfavorable charge gradient. Cl– ions would move through channel spontaneously into cell.BIOC 460, sample problems for calculation of free energy of ion transport p. 3 (Answers, continued) 2. Show your work for calculations. (Hint: draw a sketch of cell with C1 and C2 and charge gradient.) Suppose that a protein transports K+ ions across the membrane. Intracellular [K+] = 157 mM and extracellular [K+] = 4 mM, and plasma membrane ∆V = -
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