Oxidative Phosphorylation
Oxidative phosphorylation is the τ-categorical coupling morphism that converts the reducing power of NADH and FADH₂ into ATP via the proton gradient. It is the composition of the electron transport chain (LG-E08) with ATP synthase rotation: electrons traverse Complexes I-IV, protons are pumped across the inner mitochondrial membrane, and the resulting electrochemical potential drives ATP synthesis.
τ-Definition
Oxidative phosphorylation is the τ-categorical coupling morphism that converts the reducing power of NADH and FADH₂ into ATP via the proton gradient. It is the composition of the electron transport chain (LG-E08) with ATP synthase rotation: electrons traverse Complexes I-IV, protons are pumped across the inner mitochondrial membrane, and the resulting electrochemical potential drives ATP synthesis.
Categorical invariant. Coupling morphism: (NADH, FADH₂) ⇒ proton gradient ⇒ ATP; ~2.5 ATP per NADH and ~1.5 ATP per FADH₂; H⁺/ATP ratio ≈ 3.3 (with ATP synthase c-ring stoichiometry n_c = 10).
Primary registry anchor:
VI.D32
τ-Derivation Chain
Empirical Correlate
Biomarker: ATP yield ~2.5 per NADH, ~1.5 per FADH₂; H⁺/ATP stoichiometry ≈ 3.3 (mammalian, n_c = 8 c-ring), ≈ 4.0 (yeast, n_c = 10); inner mitochondrial membrane potential Δψ ≈ 150-180 mV; ΔpH ≈ 0.5-1 unit across cristae.
Measurable range: Coupled mitochondrial respiration (state 3) ≈ 50-200 pmol O₂ s⁻¹ per 10⁶ cells; uncoupled (FCCP) reveals maximal capacity 2-5× state 3; respiratory control ratio (RCR) = state3/state4 ≈ 5-15 in healthy mitochondria; P/O ratio ≈ 2.5 for NADH, ≈ 1.5 for succinate.
Observation method: Seahorse extracellular flux (OCR + drug titrations: oligomycin, FCCP, rotenone/antimycin A), high-resolution respirometry (Oroboros O2k), ³¹P NMR for in-vivo P/O measurement, blue-native PAGE for complex assembly, cryo-EM of supercomplexes.
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.L18 chirality channel
- ATP synthase F₁ rotor stereospecificity (3 catalytic β-subunits cycle in fixed handedness)
- D-ribose handedness of every nucleotide produced
Manuscript reference: manuscript-sources/book-06/part03/ch20-atp.tex
Lean Coverage
Status: Planned