An isolated chloroplast thylakoid at develops a pH gradient of across its membrane…

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

An isolated chloroplast thylakoid at 298 K298\,\mathrm{K} develops a pH gradient of ΔpH=3\Delta\mathrm{pH}=3 across its membrane with negligible voltage (Δψ≈0\Delta\psi\approx0). Its ATP synthase ring has nc=14n_c=14 subunits, and making one ATP in the stroma costs ΔGATPstroma=45 kJ mol−1\Delta G_{\rm ATP}^{\rm stroma} = 45\,\mathrm{kJ\,mol^{-1}} (take kBT/e=25.7 mVk_BT/e=25.7\,\mathrm{mV} and 1kBT=2.48 kJ mol−11k_BT=2.48\,\mathrm{kJ\,mol^{-1}} at 298 K298\,\mathrm{K}). ((a)) Calculate the proton-motive force Δp\Delta p. ((b)) Test (nc/3)e∣Δp∣≥ΔGATPstroma(n_c/3)e|\Delta p| \ge \Delta G_{\rm ATP}^{\rm stroma} (no extra proton is charged for phosphate and nucleotide transport at this synthase), and give the margin in kJ mol−1\mathrm{kJ\,mol^{-1}} and in kBTk_BT per ATP.

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