Gnaiger 2018 EBEC2018: Difference between revisions

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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. Here I distinguish pressure from potential differences (diffusion: Δμ_H+ or Δ_dF_H+; electric: ΔΨ or Δ_elF), to explain non-ohmic flux-force relationships on the basis of four thermodynamic theorems. (1) Einstein’s diffusion equation 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 equation): d_dΠ/dz = RT∙dc/dz. 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_d = b∙α∙Δ_dF_B = -b∙Δ_dΠ_B. (3) At Δ_elF = -Δ_dF_H+, the diffusion pressure of protons, Δ_dΠ_H+ = RT∙Δ_c_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 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.

• Bioblast editor: Kandolf G, Gnaiger E

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Affiliations

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

Innsbruck, Austria. - [email protected]

Reference

Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Glynn Research, Bodmin, Biochim Biophys Acta Bioenergetics 1807:1507-38

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 |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/d''z'' = 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. 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.
 |editor=[[Kandolf G]], [[Gnaiger E]]
 }}
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 ::::#Oroboros Instruments
 ::::::Innsbruck, Austria. - [email protected]
+== Reference ==
+::::#Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Glynn Research, Bodmin, Biochim Biophys Acta Bioenergetics 1807:1507-38