A yeast mitochondrion has an ATP synthase rotor ring with subunits

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Molecular machines, transport and bioenergetics · Molecular machines, transport and bioenergetics

Forces, Machines and Signals, Ch Proton gradients, ATP synthesis and photosynthesis

Problem

A yeast mitochondrion has an ATP synthase rotor ring with nc=10n_c=10 subunits. The proton-motive force has magnitude ∣Δp∣=190 mV|\Delta p| = 190\,\mathrm{mV}, and delivering one ATP to the cytosol costs ΔGATPcyt=52 kJ mol−1\Delta G_{\rm ATP}^{\rm cyt} = 52\,\mathrm{kJ\,mol^{-1}} at 310 K310\,\mathrm{K} (1kBT=2.58 kJ mol−11k_BT = 2.58\,\mathrm{kJ\,mol^{-1}} at this temperature). ((a)) Find the number of protons used per ATP, including the one that pays for phosphate and nucleotide transport. ((b)) Test whether (nc/3+1)e∣Δp∣≥ΔGATPcyt(n_c/3+1)e|\Delta p| \ge \Delta G_{\rm ATP}^{\rm cyt}, and state the margin per ATP in kJ mol−1\mathrm{kJ\,mol^{-1}} and in kBTk_BT.

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