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

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Title: Single-molecule thermodynamics of rotary molecular motors in oxidative phosphorylation: Application to physical transport processes.
Authors: Nath S; Department of Biochemical Engineering and Biotechnology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India. Electronic address: sunath@iitd.ac.in.
Source: Bio Systems [Biosystems] 2026 Oct; Vol. 268, pp. 105934. Date of Electronic Publication: 2026 Aug 28.
Publication Type: Journal Article
Language: English
Journal Info: Publisher: Elsevier Science Ireland Country of Publication: Ireland NLM ID: 0430773 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1872-8324 (Electronic) Linking ISSN: 03032647 NLM ISO Abbreviation: Biosystems Subsets: MEDLINE
Imprint Name(s): Publication: Limerick : Elsevier Science Ireland
Original Publication: Amsterdam, North-Holland Pub. Co.
MeSH Terms: Molecular Motor Proteins*/metabolism , Molecular Motor Proteins*/chemistry , Proton-Translocating ATPases*/metabolism , Proton-Translocating ATPases*/chemistry , Oxidative Phosphorylation* , Thermodynamics*, Adenosine Triphosphate/metabolism ; Biological Transport/physiology
Abstract: 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, FOF1-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.
(Copyright © 2026 Elsevier B.V. All rights reserved.)
Competing Interests: Declaration of competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Contributed Indexing: Keywords: Biological energy transduction; Biological thermodynamics or biothermodynamics; F(O)F(1)-ATP synthase and ATP synthesis/hydrolysis; Intramembrane binding sites; Ion transport across membranes; Irreversible thermodynamics and nonequilibrium thermodynamics; Local fields; Mitchell's chemiosmotic theory; Molecular motors and nanosystems; Molecular theory; Nath's two-ion theory of energy coupling and ATP synthesis; Non-ergodic processes; Oxidative phosphorylation and photophosphorylation; Proton and anion in condensed media; Single molecules; Succinate
Substance Nomenclature: 8L70Q75FXE (Adenosine Triphosphate)
0 (Molecular Motor Proteins)
EC 3.6.3.14 (Proton-Translocating ATPases)
Entry Date(s): Date Created: 20260828 Date Completed: 20260906 Latest Revision: 20260914
Update Code: 20260914
DOI: 10.1016/j.biosystems.2026.105934
PMID: 42665224
Database: MEDLINE
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  Data: Single-molecule thermodynamics of rotary molecular motors in oxidative phosphorylation: Application to physical transport processes.
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  Data: <searchLink fieldCode="AU" term="%22Nath+S%22">Nath S</searchLink>; Department of Biochemical Engineering and Biotechnology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India. Electronic address: sunath@iitd.ac.in.
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  Data: <searchLink fieldCode="MM" term="%22Molecular+Motor+Proteins%22">Molecular Motor Proteins*</searchLink>/<searchLink fieldCode="MM" term="%22Molecular+Motor+Proteins+metabolism%22">metabolism</searchLink> <br /><searchLink fieldCode="MM" term="%22Molecular+Motor+Proteins%22">Molecular Motor Proteins*</searchLink>/<searchLink fieldCode="MM" term="%22Molecular+Motor+Proteins+chemistry%22">chemistry</searchLink> <br /><searchLink fieldCode="MM" term="%22Proton-Translocating+ATPases%22">Proton-Translocating ATPases*</searchLink>/<searchLink fieldCode="MM" term="%22Proton-Translocating+ATPases+metabolism%22">metabolism</searchLink> <br /><searchLink fieldCode="MM" term="%22Proton-Translocating+ATPases%22">Proton-Translocating ATPases*</searchLink>/<searchLink fieldCode="MM" term="%22Proton-Translocating+ATPases+chemistry%22">chemistry</searchLink> <br /><searchLink fieldCode="MM" term="%22Oxidative+Phosphorylation%22">Oxidative Phosphorylation*</searchLink> <br /><searchLink fieldCode="MM" term="%22Thermodynamics%22">Thermodynamics*</searchLink><br /><searchLink fieldCode="MH" term="%22Adenosine+Triphosphate%22">Adenosine Triphosphate</searchLink>/<searchLink fieldCode="MH" term="%22Adenosine+Triphosphate+metabolism%22">metabolism</searchLink> ; <searchLink fieldCode="MH" term="%22Biological+Transport%22">Biological Transport</searchLink>/<searchLink fieldCode="MH" term="%22Biological+Transport+physiology%22">physiology</searchLink>
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  Data: 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<subscript>O</subscript>F<subscript>1</subscript>-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.<br /> (Copyright © 2026 Elsevier B.V. All rights reserved.)
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  Data: Declaration of competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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  Data: <i>Keywords: </i>Biological energy transduction; Biological thermodynamics or biothermodynamics; F(O)F(1)-ATP synthase and ATP synthesis/hydrolysis; Intramembrane binding sites; Ion transport across membranes; Irreversible thermodynamics and nonequilibrium thermodynamics; Local fields; Mitchell's chemiosmotic theory; Molecular motors and nanosystems; Molecular theory; Nath's two-ion theory of energy coupling and ATP synthesis; Non-ergodic processes; Oxidative phosphorylation and photophosphorylation; Proton and anion in condensed media; Single molecules; Succinate
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        Value: 10.1016/j.biosystems.2026.105934
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      – Code: eng
        Text: English
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      Pagination:
        StartPage: 105934
    Subjects:
      – SubjectFull: Adenosine Triphosphate metabolism
        Type: general
      – SubjectFull: Biological Transport physiology
        Type: general
      – SubjectFull: Molecular Motor Proteins metabolism
        Type: general
      – SubjectFull: Molecular Motor Proteins chemistry
        Type: general
      – SubjectFull: Proton-Translocating ATPases metabolism
        Type: general
      – SubjectFull: Proton-Translocating ATPases chemistry
        Type: general
      – SubjectFull: Oxidative Phosphorylation
        Type: general
      – SubjectFull: Thermodynamics
        Type: general
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      – TitleFull: Single-molecule thermodynamics of rotary molecular motors in oxidative phosphorylation: Application to physical transport processes.
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              Text: 2026 Oct
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