Metabolic constants: sources, and what may be encoded¶

This page ties each quantitative constant used around the digestion and redox route modules to its source, and — separately — to a rule about whether the engine is allowed to compute with it.

Those are two different questions, and conflating them is the failure mode this repository exists to prevent. A number can be well sourced and still be illegal to multiply by a meal field.

The three tiers¶

Tier	Meaning	Engine rule
Identity	Fixed by chemistry or structure. Does not vary between people.	May be encoded as a constant.
Teaching constant	An accepted physiological value with real spread around it.	May be named as identity. Never multiplied by a meal field.
Population statistic	A cohort average that masks large individual variation.	Must stay OPEN per packet. Evidence, not law.

The tier, not the quality of the citation, decides what the code may do. Hinkle's P/O ratios are excellent science and still may not be applied to a gram of fibre.

Tier 1 — Identity (encoded)¶

Structural stoichiometry. These are already constants in the package.

Constant	Value	Where encoded	Source
SOD dismutation	2 O₂•⁻ + 2 H⁺ → H₂O₂ + O₂	`SOD_O2_PER_H2O2 = 2`	McCord & Fridovich 1969
GPx reduction	H₂O₂ + 2 GSH → 2 H₂O + GSSG	`GPX_GSH_PER_H2O2 = 2`	Lubos et al. 2011
Oxidative PPP	G6P + 2 NADP⁺ → Ru5P + 2 NADPH + CO₂	`PPP_NADPH_PER_G6P = 2`	Stanton 2012
Glutathione reductase	GSSG + NADPH + H⁺ → 2 GSH + NADP⁺	`GR_GSH_PER_GSSG = 2`, `GR_NADPH_PER_GSSG = 1`	Deponte 2013

Documented, not yet encoded — no module needs them:

Constant	Value	Source
SMCT1 symport	1 SCFA⁻ : 2 Na⁺	Miyauchi et al. / den Besten et al. 2013
H⁺ translocated per 2e⁻	Complex I: 4, Complex III: 4, Complex IV: 2	Chemiosmotic consensus
H⁺ per NADH / FADH₂ oxidised	10 / 6	as above
ATP synthase c-ring	c₈ → 8 H⁺ per 3 ATP = 2.67 H⁺/ATP	Mammalian structural biology
Transport surcharge	+1 H⁺/ATP (ANT + Pᵢ) → 3.67 H⁺/ATP total	as above

Tier 2 — Teaching constants (named, never applied)¶

Constant	Value	Status in code	Source
P/O ratio, NADH-linked	~2.5 (mechanistic ceiling ~2.72)	`PO_NADH = 2.5`, emitted as `po_identity` only	Hinkle 1991, 2005
P/O ratio, FADH₂-linked	~1.5 (mechanistic ceiling ~1.63)	`PO_FADH2 = 1.5`, same	Hinkle 1991, 2005

dig/mitochondrial_routes.py returns these in a po_identity field while every entry in amounts stays None. The ratio is reported as a fact about the respiratory chain; it is never used to turn a nutrient mass into ATP moles.

The ceilings (2.72, 1.63) follow from the tier-1 identities above: 10 H⁺ ÷ 3.67 H⁺/ATP ≈ 2.72, and 6 H⁺ ÷ 3.67 ≈ 1.63. The accepted 2.5 / 1.5 sit below the ceilings because basal proton leak dissipates part of the gradient — which is precisely why they are a range in disguise and belong in tier 2.

Tier 3 — Population statistics (must stay OPEN)¶

None of these are encoded, and none may be. They are recorded here so that a future contributor can see they were considered and rejected as law, rather than overlooked.

Constant	Reported value	Why it cannot be law	Source
SCFA molar ratio	~60:20:20 acetate : propionate : butyrate	Population average over individual microbiomes	Miller & Wolin 1996
Total colonic SCFA yield	400–600 mmol/day	Depends on substrate, transit, and community	den Besten et al. 2013
Electron leak, State 4	~1.0–2.0% of O₂ consumption	Isolated-mitochondria assay condition	Boveris & Chance 1973; St-Pierre 2002
Electron leak, State 3	~0.1–0.2% of O₂ consumption	as above	St-Pierre et al. 2002
Maximal H₂O₂ flux	~20 nmol·min⁻¹·mg protein⁻¹	Isolated pigeon heart, hyperoxic buffer	Boveris & Chance 1973
Total cellular glutathione	1–10 mM	Tissue-specific; a host seat, not a meal output	Lu 2013
GSH:GSSG at rest	> 100:1	Host redox state, not a function of a food packet	Lu 2013
Glutathione redox poise	−240 to −280 mV	Derived from the above; same objection	Lu 2013

The sources say so themselves¶

The strongest argument against encoding tier 3 comes from the reviews that report it:

The 60:20:20 SCFA ratio remains a population average that mathematically masks vast individual stoichiometric variations based on local colonic micro-environments, transit times, and the efficiency of resident methanogens. Universal constants for exact RS-to-butyrate molar yields in a given human are technically impossible without mapping the specific metagenomic structure of that individual's colonic ecosystem.

and, on respiratory state:

In real, intact human myocytes experiencing highly variable, often hypoxic metabolic demands, mitochondria do not exist in pure State 3 or State 4, but rather fluctuate dynamically between them. Mapping the precise temporal percentage of electron leak over a 24-hour physiological cycle in vivo remains beyond current methodological capabilities.

A per-meal engine that emits a butyrate mass or a leak percentage is asserting exactly the measurement its own sources say does not exist. That is why dig/respiratory_control.py returns a direction (state_3 / state_4, leak_direction low/high) and no percentage, and why dig/colon_fermentation.py returns SCFA identity with amounts all None.

What a tier-3 number would need to become tier 2¶

Not a better citation — a declared seat. Tier 3 constants are properties of a host and its microbiota, not of a food. They can enter a computation only when the packet or host state actually declares the relevant field (measured GSH pool, sequenced community, measured transit time), and then they are evidence attached to that declaration, not a default. Silence stays UNEVALUABLE.

The tiers are enforced, not described¶

This page used to be the only place the tier of a constant was recorded. That made it unenforceable: SOD_O2_PER_H2O2 = 2 and PO_NADH = 2.5 sat in dig/ as bare literals, emitted in to_dict() payloads, with nothing in the tree saying which paper backed them or whether the engine could multiply by them.

Each now carries its own warrant:

SOD_O2_PER_H2O2 = grounded(
    2,
    tier="identity",
    pmid="5389100",
    supports="SOD dismutates two superoxide anions per hydrogen peroxide",
)

grounded() returns an int or float subclass, so arithmetic, equality and JSON serialisation are unchanged and the emitted payload keeps its shape. What changed is that the number cannot exist without a tier and a resolved PMID.

Two gates hold it. tools/check_constants.py refuses a bare literal at module level in dig/ and refuses a PMID that is not in the resolved cache; tools/check_pmids.py proves that cache still names the right papers. Tier 3 is refused at construction — a population statistic does not become encodable by acquiring a citation, and annotating one would make it look as though it had.

Verification status¶

Every PMID on this page and in src/biology_as_code/dig/ was resolved against PubMed on 2026-09-07 and diffed against the claim it is attached to. The page previously recorded them as unverified; that pass has now been run.

It found what the ontology pass found. Twelve of seventeen identifiers named a different paper. They were not near-misses — the id attached to Regulation of short-chain fatty acid production resolved to a paper on transducing cells on solid surfaces, and the id attached to Murphy's ROS review resolved to a case report on non-Hodgkin lymphoma. Every one passed a regex. tools/check_pmids.py now runs this diff as a gate, for the same reason tools/check_curies.py exists: an identifier that has not been resolved is decoration.

Corrected — code (`src/biology_as_code/dig/`)¶

Source	Was	Resolved to	Now
Macfarlane & Macfarlane 2003	`12740047`	In situ transduction of target cells…	`12740060`
den Besten et al. 2013	`24347302`	Modulatory effects of L-carnitine on tamoxifen…	`23821742`
Stilling et al. 2016	`26859755`	Tree Age Effects on Fine Root Biomass…	`27346602`
Lubos et al. 2011	`21924744`	Novel laparoscopic hernia of Morgagni repair…	`21087145`
Rich 2003	`14668792`	no PubMed record	`14641005`
Brand 2010	`20463404`	Mitochondrial amyloid-beta levels…	`20064600`
Deponte 2013	`23380711`	Anaerobic co-digestion of grease sludge…	`23036594`
Murphy 2009	`19052988`	Synchronous presentation of systemic and brain NHL	`19061483`

Corrected — this page¶

Source	Was	Resolved to	Now
Miller & Wolin 1996	`8962261`	Differential effects of interleukin-10…	`8633856`
Hinkle 1991	`1939103`	Covalent linkage between nucleotides and PD-ECGF	`2012815`
Hinkle 2005	`15639704`	Cost-utility analysis of imatinib mesylate…	`15620362`
St-Pierre et al. 2002	`12417066`	[Changes of inflammatory factors…]	`12237311`

Confirmed as supplied¶

Source	PMID
McCord & Fridovich 1969	`5389100`
Stanton 2012	`22431005`
Mitchell 1961	`13771349`
Boveris & Chance 1973	`4749271`
Lu 2013	`22995213`

Closed conflict: den Besten et al. 2013¶

Three ids had been offered for this review — 24023713, 24347302 and 23985657. The page said at most one could be right. None of them is. All three resolve to unrelated papers; the J Lipid Res review is 23821742.

That outcome is the argument for the tier table above. Three independent sources agreed on the shape of a citation and every one of them was wrong, which is exactly the failure mode a number cannot survive if it is allowed to drive a computation.