BSCI 426/BIOL 622                         Fall '14                          Problem Set 8

assigned:     10/30/14
due:           11/06/14

1. Efficiency of Energy Transduction

Definition:      Efficiency = energy transduced/energy consumed

Consider the proton ATPase reconstituted into phospholipid vesicles with the F1 portion on the outer surface. Assume a stoichiometry of 3 protons transported per ATP hydrolyzed. Assume that the ratio of [ATP]/([ADP]*[Pi]) is such that the energy produced from the hydrolysis of ATP is 50 kJ/mole. What is the efficiency of energy transduction from ATP to a proton gradient under the following conditions:

                    pH (in)                         pH(out)                              voltage difference (usual convention)

a)                     7                                     8                                 + 140 mV
b)                     7                                     8                                 + 100 mV
c)                     7                                     8                                     0 mV
d)                     7                                     7                                     0 mV
e)                     7                                     7                                  - 100 mV
f)                     8                                     7                                        0 mV
g)                     7                                     8                                 + 200 mV
 

h) Find conditions that give 100% efficiency. How much energy is “actually” transduced under these conditions?
 

2.  Consider the motor in the Fo part of the ATPase.  Generate a mathematical model that predicts the probability of the motor rotating in a particular direction (clockwise or counterclockwise) as it is driven by a proton gradient.  Plot the probability of rotating clockwise and counterclockwise as a function of pH on one side of the membrane keeping the pH on the other side constant.  Choose pH values while thinking about the pK of the group being protonated on the c subunit.  How well does the model  work?
Hint: Assume that the probability of rotating one step to the right depends on the probability of the right carboxyl group to be protonated and the left one to be unprotonated.   What determines the probability of protonation? 

Optional, for a greater challenge:  Take the membrane potential into account by assuming that the potential effectively changes the pK of the groups.  How can this be done realistically without violation the law of conservation of energy?