Cellular Respiration
Cellular respiration is the τ-categorical composite morphism that closes the metabolic fiber: glycolysis ∘ Krebs ∘ electron-transport-chain ∘ ATP-synthase yields the full Loop_L orbit — net 30-32 ATP per glucose, terminal electron acceptor O₂ → H₂O. It is the canonical witness of VI.T05 (Metabolic Fiber Theorem) at the eukaryotic-mitochondrial scale.
τ-Definition
Cellular respiration is the τ-categorical composite morphism that closes the metabolic fiber: glycolysis ∘ Krebs ∘ electron-transport-chain ∘ ATP-synthase yields the full Loop_L orbit — net 30-32 ATP per glucose, terminal electron acceptor O₂ → H₂O. It is the canonical witness of VI.T05 (Metabolic Fiber Theorem) at the eukaryotic-mitochondrial scale.
Categorical invariant. Respiration = composite of (γ_Gly · γ_Krebs · γ_ETC · γ_ATPsyn) realising a γ+η-balanced Loop_L instance with maximal source winding under O₂-terminal-acceptor constraint.
Primary registry anchor:
VI.T05
τ-Derivation Chain
Empirical Correlate
Biomarker: Oxygen consumption rate (OCR); respiratory quotient (RQ = CO₂ produced / O₂ consumed); P/O ratio (~2.5 for NADH, ~1.5 for FADH₂); proton motive force across the inner mitochondrial membrane.
Measurable range: Whole-organism O₂ consumption ~250-400 mL·min⁻¹ (resting adult); per-cell O₂ flux ~10⁻¹⁶ mol·s⁻¹; P/O ratio 2.5 (theoretical max ~3); proton motive force ~200 mV (Δψ ~150-180 mV + ΔpH ~0.5-1).
Observation method: Indirect calorimetry (whole organism); Seahorse extracellular flux analyzer (cellular OCR); Clark-electrode respirometry (isolated mitochondria); TMRM imaging (Δψ); ³¹P-NMR (ATP turnover).
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.L18 chirality channel
- stereospecificity of complex I (NADH:ubiquinone) and complex II (succinate dehydrogenase)
- F₁F₀-ATP synthase rotor handedness preserved across all eukaryotic taxa
Manuscript reference: manuscript-sources/book-06/part03/ch19-metabolism.tex
Lean Coverage
Status: Planned