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
Two order-of-magnitude estimates, one from the mitochondrion and one from the chloroplast.
((a)) A resting person has a basal metabolic rate of 100W, essentially all of it arising from oxidation of NADH (and similar carriers) through the electron-transport chain. For a synthase ring of nc=8, a typical measured P/O ratio is about 2.5, so a fraction of the 220kJmol−1 redox free energy of each NADH is dissipated directly as heat by the pumps, the synthase and its carriers, and proton leak, rather than being stored in ATP (taking 1ATP=55kJmol−1 in the cytosol). Estimate the power dissipated as this direct mitochondrial heat.
((b)) A light-harvesting antenna has about 250 chlorophylls per reaction centre. Assume, as an order-of-magnitude model, that an excitation must visit of order one chlorophyll per member of the antenna before it finds the reaction centre, and that each hop between neighbouring chlorophylls by Forster transfer takes about 1ps. Taking the isolated chlorophyll excited-state (fluorescence) lifetime as 1.0ns, estimate the total time for the excitation to reach the reaction centre, and the ratio of the fluorescence lifetime to this transit time. State whether most excitations are captured before they can fluoresce or internally decay.