Theory of hydrogen bonded chains in bioenergetics

Abstract
Three thermodynamic cycles in which hydrogen bonded chains play a central role are presented as models for biological energy transduction. These include (i) a primitive, highly irreversible proton pump, (ii) a simple reversible chemical to electrical energy transducer and (iii) a reversible molecular engine which transduces pH differences to mechanical energy. A careful analysis is given to the free energy diagrams which reveal that the rate limiting step of the proton conduction is similar in the three cases. The limiting rate is essentially the inverse of the equilibration time for a localized proton to delocalize over a free energy barrier. Using basic hopping rates obtained from studies in ice, the kinetic equations are set up and solved by three methods for the simplest case of first passage of the proton. The agreement of the exact solution with a computerized difference equation approximation lends confidence to calculations using the latter method for more complicated cases where the exact method is intractable. For free energy barriers of 250–450 mV (6–10 kcal), equilibration times are rapid (μsec–msec) on a biological time scale. The kinetics of the complete cycles are also investigated and shown to be in agreement with the preceding calculation. For steady state linear transport and the special case when the transport of a single defect type is rate limiting, our kinetic results reduce to those obtained for single‐file transport.

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