Axel Brünger, Zan Schulten, and Klaus Schulten.
A network thermodynamic investigation of stationary and
non-stationary proton transport through proteins.
Zeitschrift für Physikalische Chemie, NF136:1-63, 1983.
BRUN83
A model for the biological transport of protons in linear hydrogen-bonded chains formed from the amino acid side groups of membrane proteins has been investigated in detail. The description assumes first-order kinetics for transitions between all possible proton distributions in the hydrogen-bridged chain. The corresponding master equation is solved numerically and in some representative cases also analytically. The following time-dependent observables have been evaluated: 1) proton current at the conductor ends, 2) charge displacement within the conductor, 3) free energy decrement, and 4) state of protonation of the conductor groups. It is shown which observable conduction properties reveal features of the internal dynamics and structure of proton conductors. In particular, the following observations are considered: titration of the stationary, applied voltage-induced proton currents; coupling of the proton transport to alternating electric fields or to electric field jumps; measurement of the relaxation of the above four observables following injection or ejection of a proton. We also demonstrate the possibility of constructing heterogeneous conductors with a diodic voltage-current characteristic. Allowing the interaction between the proton conductors and injecting or ejecting group to be time-dependent, we investigated the refractory phase that exists after an initial proton current pulse and demonstrated the buffering capacity of the conductors, a function that we associate with the "blue light effect" of bacteriorhodopsin. Among the theoretical developments are an algorithm to obtain the graph of the main kinetic pathways from the solution of a high-dimensional master equation, an expression for the proton resistance of a conductor derived in the framework of linear irreversible thermodynamics, a reduction of the kinetic pathways by condensing fast processes to yield analytical expressions for the observables, and finally the analytical evaluation of relaxation times by the theory of first-passage times.
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