Gnaiger 2018 EBEC2018: Difference between revisions

Latest revision as of 22:17, 4 July 2022

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: Δμ_H⁺ or Δ_dF_H⁺; electric: ΔΨ or Δ_elF_p⁺), 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): d_dΠ/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, J_d = -u_d∙α∙Δ_dF_X = -u_d∙Δ_dΠ_X [6]. (3) At Δ_elF_p⁺ = -Δ_dF_H+, the diffusion pressure of protons, Δ_dΠ_H+ = RT∙Δc_H+ [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 Δ_elF_p⁺ versus Δ_dF_H+, 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

Affiliations

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

Innsbruck, Austria. - [email protected]

References

Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Glynn Research, Bodmin. Biochim Biophys Acta Bioenergetics 1807:1507-38. - »Bioblast link«
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«
Beard DA (2005) A biophysical model of the mitochondrial respiratory system and oxidative phosphorylation. PLOS Comput Biol 1(4):e36. - »Bioblast link«
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«
Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - »Bioblast link«
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«
Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5^th ed. https://doi.org/10.26124/bec:2020-0002 - The symbols in the above abstract have been adjusted to those in the 5^th ed.

Labels: MiParea: Respiration

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

Event: Oral MitoEAGLE

@@ Line 5: / Line 5: @@
 |year=2018
 |event=EBEC2018 Budapest HU
-|abstract=‘.. ''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. Here I distinguish pressure from potential differences (diffusion: Δ''μ<sub>H</sub>+'' or Δ<sub>d</sub>''F''<sub>H</sub>+; electric: Δ''Ψ'' or Δ<sub>el</sub>''F''), to explain non-ohmic flux-force relationships on the basis of four thermodynamic theorems. (1) Einstein’s diffusion equation explains the concentration gradient (d''c''/d''z'') 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 equation): d<sub>d</sub>Π/dz = RT∙d''c''/d''z''. Flux 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, ''J''<sub>d</sub> = ''b''∙''α''∙Δ<sub>d</sub>''F''<sub>B</sub> = -''b''∙Δ<sub>d</sub>Π<sub>B</sub>. (3) At Δ<sub>el</sub>''F'' = -Δ<sub>d</sub>''F''<sub>H</sub>+, the diffusion pressure of protons, Δ<sub>d</sub>Π<sub>H</sub>+ = ''RT''∙Δ<sub>c</sub><sub>H</sub>+ [Pa=J∙m<sup>-3</sup>] is balanced by electric pressure, maintained by counterions of H<sup>+</sup>. Diffusional and electric pressures are isomorphic, additive, and yield protonmotive pressure (pmp). (4) The dependence of proton leak on pmf varies with Δ<sub>el</sub>''F'' versus Δ<sub>d</sub>''F''<sub>H</sub>+, 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.
+|abstract=‘.. ''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: Δ''μ''<sub>H<sup>+</sup></sub> or Δ<sub>d</sub>''F''<sub>H<sup>+</sup></sub>; electric: Δ''Ψ'' or Δ<sub>el</sub>''F''<sub>p<sup>+</sup></sub>), to explain non-ohmic flux-'''[[force]]''' relationships on the basis of four thermodynamic theorems. (''1'') Einstein’s diffusion equation [4] explains the [[concentration]] gradient (d'''''c'''''/d'''''z''''') 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): d<sub>'''d'''</sub>'''''Π'''''/d'''''z''''' = ''RT''∙d'''''c'''''/'''d''z'''''. [[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, ''J''<sub>d</sub> = -''u''<sub>d</sub>∙''α''∙Δ<sub>d</sub>''F<sub>X</sub>'' = -''u''<sub>d</sub>∙Δ<sub>d</sub>''Π<sub>X</sub>'' [6]. (''3'') At Δ<sub>el</sub>''F''<sub>p<sup>+</sup></sub> = -Δ<sub>d</sub>''F''<sub>H</sub>+, the diffusion pressure of protons, Δ<sub>d</sub>''Π''<sub>H</sub>+ = ''RT''∙Δ''c''<sub>H</sub>+ [Pa=J∙m<sup>-3</sup>] is balanced by electric pressure, maintained by counterions of H<sup>+</sup>. Diffusional and electric pressures are isomorphic, additive, and yield protonmotive pressure ''pmp''. (''4'') The dependence of [[proton leak]] on ''pmF'' varies with Δ<sub>el</sub>''F''<sub>p<sup>+</sup></sub> versus Δ<sub>d</sub>''F''<sub>H</sub>+, 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).
-|editor=[[Kandolf G]], [[Gnaiger E]]
+|editor=[[Gnaiger E]]
+|mipnetlab=AT Innsbruck Gnaiger E
 }}
-{{Labeling}}
 == Affiliations ==
-::::#D. Swarovski Research Lab, Dept Visceral, Transplant Thoracic Surgery, Medical Univ Innsbruck
+::::# D. Swarovski Research Lab, Dept Visceral, Transplant Thoracic Surgery, Medical Univ Innsbruck
-::::#Oroboros Instruments
+::::# Oroboros Instruments
-::::::Innsbruck, Austria. - [email protected]
+:::::: Innsbruck, Austria. - [email protected]
-== Reference ==
+== References ==
-::::#Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Glynn Research, Bodmin, Biochim Biophys Acta Bioenergetics 1807:1507-38
+:::# Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Glynn Research, Bodmin. Biochim Biophys Acta Bioenergetics 1807:1507-38. - [[Mitchell 2011 Biochim Biophys Acta |»Bioblast link«]]
+:::# Garlid KD, Beavis AD, Ratkje SK (1989) On the nature of ion leaks in energy-transducing membranes. Biochim Biophys Acta 976:109-20. - [[Garlid 1989 Biochim Biophys Acta |»Bioblast link«]]
+:::# Beard DA (2005) A biophysical model of the mitochondrial respiratory system and oxidative phosphorylation. PLOS Comput Biol 1(4):e36. - [[Beard 2005 PLOS Comput Biol |»Bioblast link«]]
+:::# 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. - [[Einstein 1905 Ann Physik 549 |»Bioblast link«]]
+:::# Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - [[Gnaiger_1993_Pure_Appl_Chem |»Bioblast link«]]
+:::# 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. - [[Gnaiger_1989_Energy_Transformations |»Bioblast link«]]
+:::# Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5<sup>th</sup> ed. https://doi.org/10.26124/bec:2020-0002 - The symbols in the above abstract have been adjusted to those in the 5<sup>th</sup> ed.
+{{Labeling
+|area=Respiration
+|topics=Flux control, Ion;substrate transport, mt-Membrane potential
+|couplingstates=LEAK
+|event=Oral
+|additional=MitoEAGLE
+}}