237_DE_S09_PS4_ANSWERS - Assignment#4 Lipids and Membranes...

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Assignment #4 Lipids and Membranes CHEM 237 DE Spring 2009 1. For this problem, any constants needed are found in the table on p. 13 of your textbook; assume 37 o C for the temperature. Using the equation for the free energy of transport (inside, C I , to outside, C O ), Δ G = RT ln (C O /C I ) calculate the Δ G of transport for Ca 2+ , from the inside to the outside, with an inside concentration of [Ca 2+ ] of 0.1 2+ ] of 1 mM, assuming there is no membrane potential. Now, taking into consideration the membrane potential, Δ &, of 50 mV (inside negative), and the equation Δ G = RT ln (C I /C O ) + Z F Δ & How does the Δ G change when the membrane potential is considered? Explain the difference. Could a Ca 2+ ATPase active transporter be used to transport Ca 2+ in this instance? ANSWER: (5 marks for each calculation) The Ca 2+ is going from inside to outside, so we use the equation as indicated above (corrected from the original version of the assignment). Using the value of R of 8.3145 J K -1 mol -1 and 37 o C, or 310 o K: Δ G = RT ln (C O /C I ) Δ G = (8.3145 J K -1 mol -1 ) (310 o K) ln (10 -3 M/10 -7 M) Δ G = 2577 J mol -1 (9.21) Δ G = 23,734 J/mol = 23.7 kJ/mol If we take the membrane potential into consideration, Δ G = RT ln (C O /C I ) + Z f Δ & Δ G = (8.3145 J K -1 mol -1 ) (310 o K) ln (10 -3 M/10 -7 M) + (2) 96,485 J V -1 mol -1 (0.05 V) Δ G = 23,734 J/mol + 9,648 J/mol Δ G = 33,382 J/mol = 33.4 kJ/mol (4 marks) Now, why should the Δ G change? Think about the environment that the Ca 2+ is in. Inside the cell, the Ca 2+ is in a more negative environment (more negative charges than positive charges), and the transport process takes the positive Ca 2+ from the nice, cozy (-) environment into the less accommodating (+) environment outside the cell. No wonder the Δ G becomes more unfavorable! (3 marks) What about ATP? Clearly, this transport process is unfavorable, and coupling to ATP hydrolysis is required to transport the Ca 2+ . But is one ATP enough? When we consider the membrane potential, the Δ G is 33.4 kJ/mol, and ATP only yields -30.5 kJ/mol, which is not enough. Granted, we are only considering Δ G o’ values, and these values can change if we were to consider Δ G values. 2. Assume that you are investigating this Ca 2+ ATPase that transports Ca 2+ out of the cell as discussed in problem 1.
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a. Draw a figure showing the Ca 2+ transport process in a figure like the one about the Na K ATPase in the lecture notes. Be sure to label the inside and outside of the cell. ANSWER:
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237_DE_S09_PS4_ANSWERS - Assignment#4 Lipids and Membranes...

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