Gnaiger 2018 EBEC2018

From Bioblast
The protonmotive force under pressure: an isomorphic analysis.

Link: EBEC2018

Gnaiger E (2018)

Event: EBEC2018 Budapest HU

‘.. the sum of the electrical pressure difference and the osmotic pressure difference (i.e. the electrochemical potential difference) of protons’ [1] links to non-ohmic flux-force relationships between proton leak and protonmotive force pmF. This is experimentally established, has direct consequences on mitochondrial physiology, but is theoretically little understood [2,3]. Here I distinguish pressure from potential differences (diffusion: ΔμH+ or ΔdFH+; electric: ΔΨ or ΔelFp+), to explain non-ohmic flux-force relationships on the basis of four thermodynamic theorems. (1) Einstein’s diffusion equation [4] explains the concentration gradient (dc/dz) in Fick’s law as the product of chemical potential gradient (the vector force and resistance determine the velocity v of a particle) and local concentration c. This yields the chemical pressure gradient (van’t Hoff): ddΠ/dz = RT∙dc/dz. Flux [5] is the product of v and c; c varies with force. Therefore, flux-force relationships are non-linear. (2) The pmF is not a vector force; the gradient is replaced by a pressure difference, and local concentration by a distribution function or free activity α. Flux is a function of α and force, Jd = -udα∙ΔdFX = -ud∙ΔdΠX [6]. (3) At ΔelFp+ = -ΔdFH+, the diffusion pressure of protons, ΔdΠH+ = RT∙ΔcH+ [Pa=J∙m-3] is balanced by electric pressure, maintained by counterions of H+. Diffusional and electric pressures are isomorphic, additive, and yield protonmotive pressure pmp. (4) The dependence of proton leak on pmF varies with ΔelFp+ versus ΔdFH+, in agreement with experimental evidence. The flux-force relationship is concave at high mitochondrial volume fractions, but near-exponential at small mt-matrix volume ratios. Linear flux-pmp relationships imply a near-exponential dependence of the proton leak on the pmF ([7]; added 2022-07-04).

Bioblast editor: Gnaiger E O2k-Network Lab: AT Innsbruck Gnaiger E


  1. D. Swarovski Research Lab, Dept Visceral, Transplant Thoracic Surgery, Medical Univ Innsbruck
  2. Oroboros Instruments
Innsbruck, Austria. -


  1. Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Glynn Research, Bodmin. Biochim Biophys Acta Bioenergetics 1807:1507-38. - »Bioblast link«
  2. Garlid KD, Beavis AD, Ratkje SK (1989) On the nature of ion leaks in energy-transducing membranes. Biochim Biophys Acta 976:109-20. - »Bioblast link«
  3. Beard DA (2005) A biophysical model of the mitochondrial respiratory system and oxidative phosphorylation. PLOS Comput Biol 1(4):e36. - »Bioblast link«
  4. Einstein A (1905) Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann Physik 4, XVII:549-60. - »Bioblast link«
  5. Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - »Bioblast link«
  6. Gnaiger E (1989) Mitochondrial respiratory control: energetics, kinetics and efficiency. In: Energy transformations in cells and organisms. Wieser W, Gnaiger E (eds), Thieme, Stuttgart:6-17. - »Bioblast link«
  7. Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. - The symbols in the above abstract have been adjusted to those in the 5th ed.

Labels: MiParea: Respiration 

Regulation: Flux control, Ion;substrate transport, mt-Membrane potential  Coupling state: LEAK 

Event: Oral  MitoEAGLE 

Cookies help us deliver our services. By using our services, you agree to our use of cookies.