9 - ATP Synthase Energetics - BME 418 Quantitative Cell...

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BME 418, Quantitative Cell Biology Alan J. Hunt 9 - energetics of ATP-synthase ATP synthase structural points: - F 0 stoichiometry and arrangement determination. - What happens of b subunit cut? - Consists of two opposed reversible motors. Characteristics of ATP synthase (draw membrane and #s) : - G ATP = 67 kJ/mol = ~25 k b T/molecule = ~100 pN nm/molecule. - Reversible - Proton concentrations (pH). ~8.4 in matrix, 7.0 in intermembrane space - Size of structures ~ 20 nm for whole structure. How much energy is available per proton? - start with energy due to the concentration difference (from Boltzmann): 1 2 2 1 ln c c RT U U = - U1-U2=RT ln c2/c1 this works out to 8.31*300*ln(10e-7.0/10e-8.4) = 8.0 kJ/mol - however, there is also a charge separation, membrane behaves as a capacitor: C = Q/E 1.0 μ F/cm 2 for a typical cell membrane - potential across inner membrane = 0.15 V (how were V and pH determined?) - How much energy is released when one mole of protons is moved across a 0.15 V potential? Since 1 volt = 1 joule/coulomb And one Faraday: 1 4 10 65 . 9 electrons of per - × = = mol C mole coulombs F U E = 0.15 V x 9.64 x 10 4 = 14.5 kJ and the total energy per mole of protons = 14.5 kJ + 8.0 kJ = 22.5 kJ/mol Thus it will require at least 3 protons to synthesize one ATP molecule. In fact , three ATP per twelve protons
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