Single-molecule thermodynamics of reactive systems: Application to ATP hydrolysis

Classical thermodynamics describes macroscopic physical processes and chemical reactions by an ensemble approach, and the laws of thermodynamics have generally been regarded as laws of large numbers. However, enzymes, molecular motors, and many small systems in biology function by a single-molecule mode, one molecule at a time. A single-molecule thermodynamics of physical transport processes in rotary molecular motors in oxidative phosphorylation has been worked out recently (S. Nath, Biosystems 268 (2026) 105934). Here the single-molecular treatment is expanded to include chemically reactive systems, with specific focus on ATP hydrolysis. First the fundamental difference between the common usage of the free energy change, and the instantaneous change in Gibbs energy with the degree of advancement-or extent-of the chemical reaction, , is illustrated mathematically and graphically for both reversible and irreversible reactions, and some general misunderstandings are cleared up. It is shown that in the act-by-act, single-molecule mode of chemical reaction operating under nonequilibrium steady state conditions, the standard free energy change is the relevant thermodynamic property that is required to be considered. The results are applied to ATP hydrolysis-a chemical reaction of overarching importance to living systems-and interpreted based on Nath's torsional mechanism of energy transduction and ATP synthesis/hydrolysis. The variation of the standard Gibbs energy change of ATP hydrolysis, -or to be more precise-is calculated in aqueous solutions as a function of pH in the physiological range from 6 ‒ 9 and pMg between 1 ‒ 6 by use of the developed isotherm equations along with thermodynamic data on the ionization and stability constants of ATP, ADP, and Pi at 310 K, 1 atm, and an ionic strength of 0.2 M. Thermodynamic consequences and biological implications arising are discussed. An upper bound for the work done in an elementary cycle by a single molecule during ATP hydrolysis is derived. The results show that the quantitative role of the thermodynamic state function of (standard) Gibbs energy in reactions of biochemical processes can be retained, if correctly interpreted. The tabulated values of the standard free energies of ATP hydrolysis are shown to be useful for quantitative evaluations of reaction energetics as a function of the various system variables, , , , and .