Pathway satisfiability

A pathway module is a boolean formula over steps; a context (tissue, cell zone,
genome) supplies the truth values. The same engine then answers "is this pathway wired
up here?" — and, when a pathway is independently known to run but the logic says no,
turns the gap into a reviewable hypothesis.

Motivation

Pathway-completeness tools (KEGG/Reactome module coverage) ask a genome-level question:
does the organism have the pathway? That is the right question for a microbe but the
wrong one for a metazoan, where every cell carries the whole genome and the discriminating
variable is which isozyme is expressed in which context. Gluconeogenesis is "present"
in every human cell, yet free-glucose output is restricted to a few tissues — and, within
the liver, to a few cell layers.

This project treats a curation module (modules/*.yaml, the ModuleReview schema) as
a monotone boolean circuit and evaluates it against a context oracle:

a module's parts / annotons are AND; its variant_sets are OR;
a leaf annoton (a step) is an atom whose truth value comes from the oracle;
the engine enumerates routes (one branch per variant set), tests satisfiability
in a context, finds the gate atoms required by every route, and reports the
unsatisfied steps (gaps).

The logic core carries no biological data; only the oracle changes between contexts. This
is deliberately the eukaryotic analogue of GapMind's prokaryotic step-finding.

Architecture

flowchart LR M[Module YAML\nparts=AND, variant_sets=OR] --> C[compile_module\n→ boolean circuit] C --> E{module_logic engine\nroutes · gate · gaps · abduction} O1[GTEx bulk tissue] --> E O2[Halpern liver zonation] --> E O3[GTEx substrate entry] --> E O4[KEGG genome presence] --> E E --> R[per-context result:\nsatisfiable? which route?\nwhich gate / gap?] P[independent activity\nphenotype / flux] --> A[abduce] E --> A A --> H[reviewable gap hypothesis]

The engine lives at src/ai_gene_review/module_logic.py (frozen Atom; compile_module,
enumerate_routes, is_satisfied, core_atoms, unsatisfied_steps, abduce; doctested,
mypy-clean) with tests/test_module_logic.py. The oracles and per-context resolvers are in
modules/experimental/gluconeogenesis-context/ (see its RESULTS.md for full output).

Results

Between organs (GTEx bulk tissue)

Evaluating the human gluconeogenesis module across 54 tissues recovers exactly the textbook
gluconeogenic set — liver, kidney cortex, small intestine — with no false positives and
no misses. Every non-gluconeogenic tissue fails at the same gate atom, the gluconeogenic
glucose-6-phosphatase catalytic subunit, and the engine resists the ubiquitous paralog
(expressed everywhere but not gluconeogenic). The gate is graded: raising the expression
threshold drops tissues in the order liver → kidney → intestine, matching their known
quantitative contribution.

Within an organ (Halpern 2017 liver zonation)

Reusing the same engine with a liver-lobule zonation oracle, the gluconeogenesis route is
satisfiable only toward the periportal pole and is blocked at the pericentral pole —
at the same gate atom. The porto-central orientation is inferred from landmark genes (not
assumed), so the periportal restriction is a derivation, not a restatement.

Which precursor? (substrate-entry routes)

A precursor-resolved module makes lactate / alanine (via pyruvate) and glycerol (bypassing
the carboxylation backbone) explicit. Because glycerol skips that backbone, the only
universally required step is the terminal glucose-6-phosphatase system. Per tissue the engine
then reports which precursors are usable, with physiologically faithful skews (kidney
lactate-dominant; liver highest alanine capacity).

Across genomes (KEGG genome presence) — the GapMind reproduction

The same engine reconstructs L-methionine biosynthesis from KEGG orthologs across genomes.
It selects the encoded route per organism (succinyl vs acetyl acylation; trans-sulfuration vs
direct sulfhydrylation; cobalamin-dependent vs -independent methylation), completes
C. glutamicum through the alternative branch despite a missing trans-sulfuration enzyme, and
flags genome-reduced organisms as gaps.

Abduction — a gap is a hypothesis

Crossing satisfiability with an independent activity phenotype:

outcome	meaning	example
CONSISTENT_ACTIVE	reconstructable & known prototroph	E. coli, B. subtilis, C. glutamicum
ABDUCTION_TARGET	makes methionine but a step has no candidate	Synechocystis, M. jannaschii
CONSISTENT_INACTIVE	gap correctly predicts a known auxotrophy	Rickettsia prowazekii

The two abduction targets are real metabolic dark matter: both are autotrophs that synthesise
methionine yet encode none of the canonical acylation/sulfur enzymes, so the engine emits a
structured lead ("an unannotated / non-orthologous enzyme must fill this step"). The same
machinery does not over-call Rickettsia, whose gap is correctly read as its auxotrophy.

The same abduce() runs on the eukaryotic side against GTEx, with the independent claim
now a documented tissue function (and an extra "not cell-autonomous" explanation, since a
metazoan pathway can be split across organs):

outcome	meaning	example
CONSISTENT_ACTIVE	tissue oxidises ketones, enzymes expressed	heart, brain, muscle, kidney
CONSISTENT_INACTIVE	gap correctly predicts the function's absence	liver ketolysis → gap at OXCT1/SCOT
ABDUCTION_TARGET	function reported but a step's gene barely expressed	intestinal gluconeogenesis → G6PC1

Ketone-body oxidation pinpoints why the liver cannot consume the ketones it makes — it is the
one tissue lacking OXCT1/SCOT (GTEx liver = 0 TPM) — reproducing a textbook fact from
expression alone. Intestinal gluconeogenesis, genuinely debated because intestinal
glucose-6-phosphatase is low, surfaces as a lead localised to one gene, which is exactly the
form a reviewer can act on.

Epistemics

Presence ≠ flux. Expression/genome presence is used asymmetrically: absence excludes a
route (strong), presence only permits it. A satisfiable set is an upper bound on capacity.
Derived, not assumed. Zonation orientation comes from landmark genes; tissue/zone
identity from data — never from the answer being sought.
Abduction is independent. The activity column (growth phenotype) is independent of the
ortholog oracle, so a scored gap is a genuine prediction, and "the assertion is wrong" is
always retained as an explicit hypothesis.

Reproduce

# engine + tests
uv run pytest tests/test_module_logic.py -q
uv run pytest --doctest-modules src/ai_gene_review/module_logic.py

# per-context resolvers (from modules/experimental/gluconeogenesis-context/)
uv run python resolve_context.py       # between organs (GTEx)
uv run python resolve_zonation.py      # within liver (Halpern zonation)
uv run python resolve_substrates.py    # which precursor per tissue
uv run python resolve_genomes.py       # methionine across genomes (KEGG)
uv run python resolve_abduction.py     # microbial gaps vs phenotype → leads / auxotrophy
uv run python resolve_eukaryotic_abduction.py   # tissue gaps vs function (ketolysis, gluconeogenesis)

Artifacts

Engine: src/ai_gene_review/module_logic.py; tests: tests/test_module_logic.py
Modules: modules/gluconeogenesis_human.yaml, modules/gluconeogenesis_human_substrates.yaml,
modules/methionine_biosynthesis.yaml, modules/ketone_body_oxidation.yaml
Oracles & resolvers + full results: modules/experimental/gluconeogenesis-context/
(RESULTS.md)

Next steps

A human liver zonation oracle to remove the mouse-ortholog step in the zonation result.
Apply the engine to additional curated modules (it is module-agnostic).
Promote the resolvers from modules/experimental/ into a small CLI once the oracle
interfaces stabilise.