Chapter 7
Fluctuations of the Proton Electromotive
Force Across Inner Mitochondrial
Membrane
The intermembrane mitochondrial space (I MMS) is delimited by the inner and
outer mitochondrial membranes and defines a region of molecular dimension where
fluctuations of the number of free protons and of trans-membrane voltage can
give rise to fluctuations in the proton-electromotive force (P MF ) across the inner
mitochondrial membrane (I MM).
We have applied the fluctuation-dissipation theorem (F DT ) to an electrical
equivalent circuit consisting of a resistor (R m ) in parallel with a capacitor (C m )
representing the passive electrical properties of the I MM, in series with another
capacitor (C b ) representing the proton buffering power of the I MMS fluid. An
access resistance, R a , was defined as a link between the capacitor C b and the
membrane.
Average P MF fluctuations across the I MM were calculated for different
assumptions concerning the inter-membrane space dimensions. The calculated
average P MF fluctuations were in the vicinity of 100 mV for relaxation times in
the few microseconds range. The corresponding fluctuational protonic free energy
is about 10 kJ/mole what compares with the binding energy for protons in different
transporters. This suggests that fluctuations in PMF can be of relevance in the
universe of forces influencing the molecular machinery embedded in the I MM. 1
7.1 Introduction
The synthesis of ATP in eukariotic cells occurs at the expense of proton flow driven
by the proton-motive force (P MF ) across ATP synthase molecules inserted in the
inner mitochondrial membrane (I MM). Proton gradients as high as 1 pH unit can
1 Reprinted from [1], Copyright DOI:https://doi.org/10.1103/PhysRevE.55.6285 by the American
Physical Society.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. A. Fornés, Principles of Brownian and Molecular Motors, Springer Series in
Biophysics 21, https://doi.org/10.1007/978-3-030-64957-9_7
111
Fluctuations of the Proton Electromotive
Force Across Inner Mitochondrial
Membrane
The intermembrane mitochondrial space (I MMS) is delimited by the inner and
outer mitochondrial membranes and defines a region of molecular dimension where
fluctuations of the number of free protons and of trans-membrane voltage can
give rise to fluctuations in the proton-electromotive force (P MF ) across the inner
mitochondrial membrane (I MM).
We have applied the fluctuation-dissipation theorem (F DT ) to an electrical
equivalent circuit consisting of a resistor (R m ) in parallel with a capacitor (C m )
representing the passive electrical properties of the I MM, in series with another
capacitor (C b ) representing the proton buffering power of the I MMS fluid. An
access resistance, R a , was defined as a link between the capacitor C b and the
membrane.
Average P MF fluctuations across the I MM were calculated for different
assumptions concerning the inter-membrane space dimensions. The calculated
average P MF fluctuations were in the vicinity of 100 mV for relaxation times in
the few microseconds range. The corresponding fluctuational protonic free energy
is about 10 kJ/mole what compares with the binding energy for protons in different
transporters. This suggests that fluctuations in PMF can be of relevance in the
universe of forces influencing the molecular machinery embedded in the I MM. 1
7.1 Introduction
The synthesis of ATP in eukariotic cells occurs at the expense of proton flow driven
by the proton-motive force (P MF ) across ATP synthase molecules inserted in the
inner mitochondrial membrane (I MM). Proton gradients as high as 1 pH unit can
1 Reprinted from [1], Copyright DOI:https://doi.org/10.1103/PhysRevE.55.6285 by the American
Physical Society.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. A. Fornés, Principles of Brownian and Molecular Motors, Springer Series in
Biophysics 21, https://doi.org/10.1007/978-3-030-64957-9_7
111