Biophysical Journal 8: 1434-1457 (1968)
© 1968 the Biophysical Society

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Energetics of Active Transport Processes

ABSTRACT

Discussions of active transport usually assume stoichiometry between the rate of transport J₊ and the metabolic rate J_r. However, the observation of a linear relationship between J₊ and J_r does not imply a stoichiometric relationship, i.e., complete coupling. Since coupling may possibly be incomplete, we examine systems of an arbitrary degree of coupling q, regarding stoichiometry as a limiting case. We consider a sodium pump, with J₊ and J_r linear functions of the electrochemical potential difference, -X₊, and the chemical affinity of the metabolic driving reaction, A. The affinity is well defined even for various complex reaction pathways. Incorporation of a series barrier and a parallel leak does not affect the linearity of the composite observable system. The affinity of some region of the metabolic chain may be maintained constant, either by large pools of reactants or by regulation. If so, this affinity can be evaluated by two independent methods. Sodium transport is conveniently characterized by the open-circuit potential ()_I=0 and the natural limits, level flow (J₊)_X+=0, and static head X⁰₊ = (X₊)_J+=0. With high degrees of coupling -X⁰₊/F approaches the electromotive force E_Na (Ussing); -X⁰₊/F cannot be identified with ((RT/F) ln f)_X+=0, where f is the flux ratio. The efficiency = -J₊X₊/J_rA is of significance only when appreciable energy is being converted from one form to another. When either J₊ or -X₊ is small is low; the significant parameters are then the efficacies _J+ = J₊/J_rA and _X+ = -X₊/J_rA, respectively maximal at level flow and static head. Leak increases both J₊ and _J+ for isotonic saline reabsorption, but diminishes -X⁰₊ and _X. Electrical resistance reflects both passive parameters and metabolism. Various fundamental relations are preserved despite coupling of passive ion and water flows.