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Gnaiger 2017 MiP2017

From Bioblast
Gnaiger E (2017) Protonmotive force and chemiosmotic pressure: a generalization of non-ohmic flux control of the proton leak. MiP2017.


Erich Gnaiger


Gnaiger Erich (2017)

Event: MiP2017


Chemiosmotic energy transformation is one of the unifying principles in bioenergetics and mitochondrial physiology [1]. However, despite of the emergence of sophisticated and specifically successful kinetic models [2,3], a general concept remains elusive on the control of proton flux by the protonmotive force. Modulation of the proton leak across the mitochondrial inner membrane, mtIM, is implicated in degenerative diseases related to life style, obesity and the metabolic syndrome, and impacts on the bioenergetic efficiency of ATP production. The present analysis refutes the concept of flux-force linearity on the basis of four molecular theorems without invoking any particular kinetic mechanisms. The theory is deeply rooted in the history of thermodynamics and is developed from first principles: (1) The product of an isomorphic force (e.g. electromotive force) and its conjugated steady-state flux yields power per volume, related to entropy production [4,5]. (2) A discontinuous two-compartmental system of constant volume is described consisting of dilute solutions in compartments 1 and 2 separated by a semipermeable membrane at constant temperature and barometric pressure. The mechanistic properties of the membrane, including its thickness, are incorporated in the conductivity and diffusion coefficient. This follows from Einstein’s diffusion equation [6] arranged for discontinuous diffusion. (3) At this stage, Fick’s law of diffusion is conceived as a linear flux-∆ pressure law. Isomorphic pressure is always expressed in units Pa=J∙m-3. (4) The linear flux-∆ pressure law of diffusion linked to ∆cH+ (not ∆pH) is generalized revealing proton flux as a linear and proportional function of chemiosmotic pressure. In a straight application of the concept of chemiosmotic pressure, an approximately semi-logarithmic dependence is predicted between proton leak flux and protonmotive force in the range from 0 to -20 kJ.mol-1 (0 to -0.2 V), under typical experimental conditions when the matrix volume is much smaller than the outer phase.

The misconception of Fick’s law as a linear relation between flux and force, combined with vague terminology [7], has caused and continues to cause heuristic confusion in physical chemistry and biology. A rigorously consistent nomenclature [7,8] provides a key to unlock the conceptual barrier of flux-force linearity and open the minds towards analysis of relationships between isomorphic pressure differences and fluxes. An alchemistic heritage of obscure terminology prevails when confusing pH differences and gradients, Gibbs energy and force or affinity [5,8], force and ∆ pressure. This is rooted in a remarkable tradition, as seen 150 years ago: “This force is called the pressure of the gas” (Maxwell 1867 [9]).

The flux-∆ pressure law provides the fundamental basis for the large range of linearity of the polarographic oxygen sensor (POS), which responds to oxygen flux as a linear function of the difference of partial O2 pressure, ∆pO2 [Pa], between the cathode and the stirred bulk medium separated by an oxygen-permeable membrane; nobody ever doubts that the POS responds non-linearly to the force or chemical potential difference, ∆μO2 [J∙mol-1] [10]. Yet the generalization of the flux-∆ pressure law yields a new perspective on the pattern and variability of the control of proton flux by the protonmotive force. The principle of chemiosmotic pressure does not contradict complex kinetic models that have been tuned to fit empirical results, but reveals non-linear flux-force relations as the rule, with linearly proportional flux-force dependence as possible although special cases. Chemiosmotic pressure and its isomorphic generalizations thus provide a solid bridge between thermodynamics and kinetics. Current research in bioenergetics and mitochondrial physiology is faced with challenges of applications in health (e.g. exercise and life style) and disease (e.g. metabolic syndrome). Unifying principles of flux control are, therefore, not only of academic importance, but help to improve the quality and efficiency of research, education, and impact on society.


  1. Daniel Swarovski Research Lab, Dept Visceral, Transplant Thoracic Surgery, Medical Univ Innsbruck, Austria
  2. Oroboros Instruments, Innsbruck, Austria – [email protected]


  1. Mitchell P, Moyle J (1967) Respiration-driven proton translocation in rat liver mitochondria. Biochem J 105:1147-62. - »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. Prigogine I (1967) Introduction to thermodynamics of irreversible processes. Interscience, New York, 3rd ed:147pp.
  5. Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - »Bioblast link«
  6. 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«
  7. 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«
  8. MitoEAGLE preprint 2017-11-01(14) The protonmotive force and respiratory control: Building blocks of mitochondrial physiology Part 1. - »Bioblast link«
  9. Maxwell JC (1867) On the dynamical theory of gases. Phil Trans Royal Soc London 157:49-88. - »Bioblast link«
  10. Hitchman ML, Gnaiger E (1983) A thermodynamic consideration of permeability coefficients of membranes. In: Polarographic oxygen sensors. Aquatic and physiological applications. Gnaiger E, Forstner H (eds), Springer, Berlin, Heidelberg, New York:31-6. - »Bioblast link«

Force or pressure? - The linear flux-pressure law

Gnaiger 2020 BEC MitoPathways
"For many decades the pressure-force confusion has blinded the most brilliant minds, reinforcing the expectation that Ohm’s linear flux-force law should apply to the hydrogen ion circuit and protonmotive force. .. Physicochemical principles explain the highly non-linear flux-force relation in the dependence of LEAK respiration on the pmF. The explanation is based on an extension of Fick’s law of diffusion and Einstein’s diffusion equation, representing protonmotive pressure ― isomorphic with mechanical pressure, hydrodynamic pressure, gas pressure, and osmotic pressure ― which collectively follow the generalized linear flux-pressure law."
Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2.
» pressure = force × free activity

Labels: MiParea: Respiration 

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

MitoEAGLE, Pressure, BEC 2020.2