A thylakoid membrane's light-harvesting antenna has chlorophylls spaced apart

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 thylakoid membrane's light-harvesting antenna has chlorophylls spaced r=1.3 nmr = 1.3\,\mathrm{nm} apart, with a Forster radius R0=5.0 nmR_0 = 5.0\,\mathrm{nm} between neighbours and an isolated excited-state (fluorescence) lifetime τ0=1.2 ns\tau_0 = 1.2\,\mathrm{ns}. ((a)) Using the Forster transfer rate kFRET=(1/τ0)(R0/r)6k_{\rm FRET} = (1/\tau_0)(R_0/r)^6, calculate the transfer rate between neighbouring chlorophylls and the corresponding hop time thop=1/kFRETt_{\rm hop} = 1/k_{\rm FRET}. ((b)) If the excitation must make about 2020 such hops to reach the reaction centre, estimate the total transit time and compare it with τ0\tau_0. ((c)) Once trapped, the reaction centre uses the absorbed photon's free energy to pump 44 protons across a small patch of membrane of area 2×10−12 cm22\times10^{-12}\,\mathrm{cm^2} and specific capacitance Cm=1 μF cm−2C_m = 1\,\mu\mathrm{F\,cm^{-2}}, starting from zero voltage. Estimate the voltage change Δψ\Delta\psi this produces. ((d)) Taking ΔpH=0\Delta\mathrm{pH} = 0 so that Δp=Δψ\Delta p = \Delta\psi, express this pmf in kBTk_BT per proton at 298 K298\,\mathrm{K} (where kBT/e=25.7 mVk_BT/e = 25.7\,\mathrm{mV}).

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