Single-molecule thermodynamics of rotary molecular motors in oxidative phosphorylation: Application to physical...

Classical thermodynamics has been enormously successful in quantitatively describing macroscopic processes by using its standard, well-known ensemble approach to analyze systems. Yet today, we know from a number of modern developments in physical chemistry, biochemistry, biophysics, and structural and molecular biology that several biochemical processes in enzymes, molecular motors, and other small systems take place in a single-molecule mode, one molecule/ion at a time. How can such single-molecule processes be described and reconciled using thermodynamics within a classical framework? The reader is brought up to date on recent attempts to answer this question (Section 1). The issues and challenges are addressed afresh by a modification of Gibbs' classical theory of irreversible processes, adapted to single molecules. After discussing the assumptions of the Gibbs framework and equation (Section 2), it is applied to local quantities, and a single molecule thermodynamics of physical processes is developed (Section 3). It is shown, by quantitative calculations, how to apply the results of the theory to membrane transport at a molecular level and to the prototype rotary molecular motor, F_OF₁-ATP synthase (Section 4). The results are interpreted based on Nath's two-ion theory of energy coupling and ATP synthesis. The multiple, variegated biological implications arising from the single-molecule thermodynamics are discussed in detail, and guidelines to achieve a true understanding of biochemical processes in vivo are offered (Section 5). The new molecular theory developed here shows that "thermodynamics of a single molecule" is not a contradiction in terms. A companion paper shall attempt a single-molecule thermodynamics description of chemical reactions, e.g. ATP hydrolysis-of overarching importance to living systems.