Membrane Potential, ubiquinone and pH gradient



Introduction



The
bc1 operates via the modified Q-cycle in which ubiquinol (UQH2) is oxidized at the Qo centre on the cytosolic side of the membrane. The two protons are released into the intermembrane space and the first electron is passed to the high potential chain consisting of an iron-sulphur centre (FeS) in the iron sulphur protein and heme c1, and then passed to cytochrome c (Cytc). The second electron is passed to the low potential chain consisting of heme bL and bH and then used to reduce ubiquinone at the Qi centre using protons from the matrix.

The two b-hemes straddle the membrane and their oxidation state is sensitive to the membrane potential so that they are an intrinsic sensor of the membrane potential.

While the algorithm to calculate the membrane potential from the oxidation state of the hemes is complex and based on a sophisticated thermodynamic analysis, the Iberius makes measuring the membrane potential very simple.

First the Iberius cell spectroscopy system measures the oxidation state of
bH, bL and Cytc as well as the turnover number of the bc1 complex. Then the Iberius software implements the algorithms to calculate the membrane potential, pH gradient and redox potential of the ubiquinone pool in millivolts. The methodology and algorithms have been published [1, 2]

To achieve millivolt precision, the calculation is based on the average data over a 30 second epoch.

Figure 1 Cartoon of the bc1 complex showing electron bifurcation (red arrows) at the Qo centre and location of the b-hemes with respect to the membrane.

Redox Plots



We use redox plots as a graphical illustration between the oxidation state of a heme and the redox potential. The Iberius measures the oxidation state and then the redox potential is calculated.
The redox plot has a shape so that the area under the curve is the fraction of redox centres oxidize or reduced. The redox plot is symmetric about the midpoint potential, which is the redox potential at which the redox centre is 50% oxidized or reduced. The area above the redox potential is the reduced fraction and the area below the redox potential is the oxidized fraction.

The redox plot shown is for an n=1 simple redox centre such as Cytc. An n=2 redox centre has a redox plot which is half the width. The relationship between redox potential (Eh) and oxidation state for simple Nernst redox centres is given by:



where O is the oxidized fraction, R is the reduced fraction and n is the number of electrons the centre can carry.

Figure 2. Graphical representation of the relationship between oxidation state and redox potential for a simple n=1 redox couple with a midpoint potential of 40mV.

Redox Equilibrium



In the absence of a membrane potential, the free energy change for moving an electron from bL to bH is given by



where EhbL and EhbH are the redox potentials of
bL and bH, respectively.

The hemes are close together and the intra-electron transfer between them is much faster than the net flux so that the hemes will be in equilibrium and the ΔG will be zero. In this case, the redox potentials of
bL and bH will be equal. However, the oxidation states will be different because the midpoint potentials of bH and bL are different (see figure 3).

Figure 3 Redox poise of the bL and bH hemes in the bc1 complex in the absence of a membrane potential. bH and bL are shown as an n=1 Nernst redox plots with a midpoint potential of +40mV and -90mV, respectively.

ΔG of Charge Movement in an Electric Field



In the presence of a membrane potential, the electron that moves from bL to bH has to move against the electric field generated by the membrane potential. The free energy change for a movement in a homogeneous electric field is given by

ΔG=dE

where d is the distance moved perpendicular to the plane of the membrane and E is the electric field. The membrane potential is the free energy change to move a charge across the whole membrane e.g.

ΔΨ=DE

where Δψ is the membrane potential and D is the thickness of the membrane. This means that the free energy change to move a charge a distance d is given by:

ΔG=d/D ΔΨ

The fraction d/D is called the dielectric distance. The dielectric distance is just the fraction of the thickness that the electron moves when the electric field is homogeneous. For an inhomogeneous electric field, the free energy is still the product of dielectric distance and membrane potential, but the dielectric distance is only approximated by the fractional distance.



Figure 4 Charge separation due to the proton pumps, and ion and metabolite uniporters and exchangers, lead to net positive charge on the cytosolic side and negative charge on the matrix side of the inner membrane, respectively. This charge separation generates an electric field in the membrane which integrates across the membrane to give the membrane potential.

Calculation of Membrane Potential



The change in free energy for moving an electron from
bL to bH in the presence of an electric field is the sum of the change in free energy due to the difference in redox potentials and the free energy required to move the electron against the electric field. The equation becomes:



where Δψ is the membrane potential and β is the dielectric distance between the two b-hemes. The dielectric distance has been approximated as 0.5 [3] and is consistent with their location in the crystal structure.

The two hemes remain in close equilibrium so that the ΔG is still zero. The membrane potential is then given by twice the difference in redox potentials of the
bH and bL hemes (twice the length of the red bar in Figure 5).

The oxidation states of the hemes can be measured with the Iberius, their redox potentials calculated from their oxidation state, and then the membrane potential calculated in millivolts.



Figure 5 Redox poise of the bL and bH hemes in the bc1 complex in the presence of a membrane potential of 150mV.

Redox Potential of the UQ/UQH2 pool



The bH heme reduces UQ at the Qi centre. This requires the electron to move from bH to Qi and a proton to move from the matrix to the Qi centre, both against the membrane potential. This is equivalent to the movement of a positive charge from the matrix to bH. The ΔG for this reaction is:



Where α is the dielectric depth of
bH and estimated to be 0.25 from the crystal structure. This reaction also occurs at equilibrium (ΔG=0) so that the redox potential of the ubiquinone pool can be measured from the redox potential of bH, calculated from the oxidation state using the Iberius, and the membrane potential calculated from the redox poise of the b-hemes.


Figure 6 Redox poise of the UQ/UQH2 couple and bH in the presence of a membrane potential of 150mV

Redox Potential of the UQ/UQH2 pool



The bc1 complex transfer electrons from the UQ/UQH2 pool to Cytc. It transduces one ΔΨ and two ΔpH of redox energy into the proton motive force so the change in free energy of the reaction, per electron transferred, is given by:



where ΔGIII is the change in free energy, and EhCyt
c is the redox potential of the Cytc pool.

The redox potential of Cyt
c can be calculated from the Cytc oxidation state measured with the Iberius, the redox potential of the UQ/UQH2 pool is measured from the equilibrium with bH and the membrane potential calculated from the redox poise of the b-hemes. Although the bc1 complex works close to equilibrium, the ΔG is typically 10-30mV and so there are two unknowns and the pH gradient cannot be directly calculated from the redox poise. Instead, we use an in-silico model of the bc1 complex and, for a given, EhCytc, EhUQ and ΔΨ, we calculate the ΔpH necessary to match the simulated electron flux to the measured electron flux. The electron flux is measured with the Iberius from the mitochondrial oxygen consumption and the content of the bc1 complex.



References



  1. Kim, N., M.O. Ripple, and R. Springett, Measurement of the Mitochondrial Membrane Potential and pH Gradient from the Redox Poise of the Hemes of the bc1 Complex. Biophys J, 2012. 102(7): p. 1194-1203.
  2. Springett, R., Novel methods for measuring the mitochondrial membrane potential. Methods Mol Biol, 2015. 1264: p. 195-202.
  3. Shinkarev, V.P., A.R. Crofts, and C.A. Wraight, The electric field generated by photosynthetic reaction center induces rapid reversed electron transfer in the bc1 complex. Biochemistry, 2001. 40(42): p. 12584-90.

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