Mitochondria & Chemiosmotic Coupling

1. The Proton-Motive Force

The free energy per proton translocated across the inner mitochondrial membrane is

\[ \Delta\tilde\mu_{\mathrm{H}^+}/F = \Delta\psi - (2.303\,RT/F)\,\Delta\mathrm{pH} \]

Under physiological conditions with Δψ ≈ −180 mV and ΔpH ≈ 0.5 (matrix basic), the total pmf ≈ −210 mV, or about 20 kJ/mol per proton. ATP synthesis under cellular ΔG_ATP ≈ 50 kJ/mol therefore requires the translocation of ≥ 3 protons, and the F₁F₀ ATP synthase evolved as a rotary motor with stoichiometry of 8–15 c-subunits (per rotation) and 3 β-catalytic sites producing three ATP. The matching between these integers is not accidental.

Simulation: pmf Decomposition

2. Cristae as Geometric Optimisation

Inner-membrane area in a mitochondrion exceeds outer-membrane area by a factor of 5–10. This is achieved by folding the inner membrane into cristae: lamellar or tubular invaginations that maximise the surface density of ETC complexes while maintaining a constrained intermembrane space where cytochrome c is retained.

The cristae junctions — where the invagination meets the inner boundary membrane — are saddle-shaped (K < 0; Module 1) and are stabilised by the MICOS complex (Mitofilin/MIC60) and by cardiolipin, a cone-shaped tetra-acyl lipid with strongly negative spontaneous curvature (C₀ < 0). Cardiolipin is unique to mitochondria and is the remnant of the bacterial origin: it is synthesised at the matrix face of the inner membrane and stays there.

Cristae geometry is not fixed — cristae remodel in response to energetic demand (starvation tightens cristae, apoptosis opens cristae junctions releasing cyt c). The OPA1 protein (an inner-membrane dynamin-related GTPase) controls this remodelling and its loss causes dominant optic atrophy.

3. The Electron Transport Chain

The mitochondrial ETC is four complexes (plus ubiquinone and cytochrome c as mobile carriers) organised in linear sequence and, in part, in quaternary supercomplexes (“respirasomes”, I+III₂+IV, Schägger 2000). Each complex transfers electrons from a lower to a higher redox potential and uses the free-energy release to pump protons:

• Complex I (NADH:ubiquinone oxidoreductase): 4 H⁺/2e⁻; the largest and most fragile of the complexes. Mutations in complex I subunits cause Leigh syndrome.
• Complex II (succinate:ubiquinone): 0 H⁺/2e⁻, feeds electrons from the TCA cycle without pumping.
• Complex III (cytochrome bc₁): 4 H⁺/2e⁻; performs the Q-cycle that bifurcates electron flow between the Rieske Fe–S centre and cytochrome b_L/b_H.
• Complex IV (cytochrome c oxidase): 4 H⁺/4e⁻(with additional 4 H⁺ consumed from the matrix for water formation); the terminal O₂-reduction step. Uses Cu_A, haem a, haem a₃–Cu_B binuclear centre.

Total: ~10 H⁺ pumped per NADH (Hinkle 2005 modern revision; earlier estimates were higher), ~6 per FADH₂. Divided by the 3 H⁺/ATP of the synthase, this gives the familiar but approximate P/O ratio of 2.5 / 1.5.

4. Quantum Coherence in Electron Transport

The ETC is a sequence of single-electron hops between metal and quinone centres whose edge-to-edge distances range from 4 to 14 Å. At such distances, electron transfer is quantum tunnelling, and is well-described by the Marcus–Hush semiclassical rate:

\[ k_{ET} = \dfrac{2\pi}{\hbar}|H_{DA}|^2 \dfrac{1}{\sqrt{4\pi\lambda k_B T}} \exp\!\left[-\dfrac{(\Delta G^\circ + \lambda)^2}{4\lambda k_B T}\right] \]

with |H_DA|² the electronic coupling (exponentially sensitive to distance, |H|² ∝ e^−βr with β ~ 1.4 Å⁻¹), λ the reorganisation energy, and ΔG^° the driving force.

The famous “inverted region”(−ΔG^° > λ), where further exergonicity slows the reaction, has been mapped experimentally in photosynthetic reaction centres and is conserved as a design principle in the mitochondrial ETC: successive hops are engineered so that no transition sits deep in the inverted region, thereby keeping electron flux high and back-reactions suppressed (Moser, Page & Dutton 1995).

Simulation: Marcus Parabola & ETC Hops

5. F₁F₀ ATP Synthase — The Rotary Motor

F₁F₀ ATP synthase is two coupled rotary engines. F₀ is a membrane-embedded proton-driven rotor (the c-ring, 8–15 subunits depending on species; 8 in vertebrates, 15 in spinach chloroplast); F₁ is the catalytic head, an α₃β₃ hexamer with a central γ-shaft whose rotation drives the three β-subunits through the binding-change cycle (Boyer 1997 Nobel; Walker 1994 structure; Yasuda 1998 direct rotation observation).

Each c-ring revolution drives 3 ATP syntheses. The H⁺/ATP ratio is therefore n_c/3 where n_c is the ring size. Organisms in low-pmf environments have larger rings: Propionigenium modestum(11) and spinach chloroplast (15) use larger rings to extract more work per proton.

Operating backward — ATP hydrolysis driving proton pumping — the same machine functions as a V-type or F-type ion pump; the bacterial V-ATPase cousin is what Module 5 uses to acidify the lysosome. The family relation is explicit: rotor geometry and a basic E/K dicysteine residue in the c-subunit are conserved across F, V, and A-ATPases.

6. Open Research: Vibrationally Assisted Tunnelling

Recent work has asked whether vibrationally assisted tunnelling — in which specific protein modes are coupled resonantly to the electron transfer coordinate — plays a role in ETC efficiency, as it now clearly does in the Fenna–Matthews–Olson photosynthetic complex (Engel 2007; Ishizaki & Fleming 2009). If so, the mitochondrial cristae would be not only geometric but spectroscopic optimisations, tuning local dielectric and vibrational environments to match the Marcus parameters of each hop. This remains one of the live frontier questions in quantum biology.