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Free Energy and Proton Movement

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I have attached a review sheet for my first exam in this class. We are going to have a problem similar to this on the exam. I have some idea about how to approach this problem but I want a clear understanding so I can relate it to similar problems. Please include a complete explanation with work. Thank you so much for your assistance.

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Solution Summary

The free energy in an enzyme cycle is calculated along with probability of states.

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See attachments for the math. I'm not very knowledgeable in the biology but as far as I know, archebacteria pump one proton per photon absorbed though in principle 9.5 protons can be pumped out per photon absorbed. ...

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