A marine bacterium's ATP synthase has a rotor ring of 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 marine bacterium's ATP synthase has a rotor ring of nc=11 subunits. Its respiratory chain pumps ten protons out across the plasma membrane for every NADH oxidised, exactly as in mitochondria, and the ring turns three ATP per revolution. The synthase sits in that plasma membrane with its F1 head facing the cytoplasm, where the ATP is used. The bacterium maintains a proton-motive force of Δp=170mV, and making one ATP from ADP and phosphate in its cytoplasm costs 50kJmol−1. Take T=310K, at which kBT=4.28pNnm.
((a)) Decide, with a reason, whether the extra transport proton in the mitochondrial count applies to this bacterium, and derive the number of protons that must cross the membrane per ATP delivered to the cytoplasm, for this ring size.
((b)) Test whether the free-energy balance for that count is satisfied, quoting the margin (or shortfall) per ATP in kBT and in kJmol−1.
((c)) Estimate the P/O ratio for NADH oxidation in this bacterium, and compare it and the margin with a mammalian mitochondrion (nc=8, ∣Δp∣≈200mV, margin about 6kBT per ATP).