Inventory-aware whole contact patterns

Frozen candidate, original residue score retained

This separate experimental arm adds a dimensionless conditional pattern log ratio once per original scored CDR:peptide residue edge. Original TCRen and both bundled potential tables remain unchanged. No assay labels, assay weights, source weights, cohort normalization, distance regression or default promotion enter estimation. The reference resource and immutable scoring package must be frozen before any new benchmark score is inspected.

For a contacting directed residue pair with amino acids a,b, let A and B be its selected observed heavy-atom inventories. Their Cartesian product contains M physical atom-pair opportunities. Missing atoms are never built. For each physical pair t=(i,j), z_t=1 when its distance is at most the existing 5 A contact cutoff, and z_t=0 otherwise. Chemical equivalence pools parameter categories, retaining every physical pair and its opportunity multiplicity. The observed state is the whole binary vector z, conditional on A,B,a,b and K=sum(z)>0.

Native class-I CDR:peptide and curated antibody:peptide references supply integer contact counts c_abij and available-pair counts n_abij across their contacting residue edges. Actual counts are pooled, with separate source accounting. The fixed Jeffreys Beta(1/2,1/2) posterior means are

p_abij = (c_abij + 1/2) / (n_abij + 1)
q_ab   = (sum_ij c_abij + 1/2) / (sum_ij n_abij + 1).

These are reference estimates, not coefficient-free quantities. P assumes independent Bernoulli states with probabilities p_t. Q assumes exchangeable Bernoulli states with the common q_ab. Both distributions are normalized on the same physical inventory and conditioned on at least one contact. Define

P_+(z) = product_t p_t^z_t (1-p_t)^(1-z_t) / (1-product_t(1-p_t))
Q_+(z) = product_t q_ab^z_t (1-q_ab)^(1-z_t) / (1-(1-q_ab)^M).

The edge correction and retained-residue score are

D_edge = -log(P_+(z)/Q_+(z))
       = -sum_t [z_t log(p_t/q_ab)
                 +(1-z_t) log((1-p_t)/(1-q_ab))]
         +log[(1-product_t(1-p_t))/(1-(1-q_ab)^M)]
E_inventory = E_original + sum_scored_CDR_edges D_edge.

Every logarithm is natural. The correction has coefficient one; it is summed once per whole residue pattern, without atom-pair averaging. No pattern is silently restricted to contacting endpoints. Noncontacting atom pairs and the nonempty normalization are essential terms. Counts, inventory size, contacting pairs and whole-edge abstentions are reported separately.

An unseen amino-acid/category opportunity abstains for the entire edge with a zero correction and an explicit unsupported-edge count. This is a support policy, not a likelihood for an invented subset. Original framework and missing matrix-entry policies remain in effect. Invalid or inconsistent inventories, duplicate physical pairs and contacts outside their inventories are errors.

Meaning and limits

This normalized conditional model is a deliberately sparse first approximation: independent atom-pair Bernoulli variables cannot reproduce geometrical exclusion, bonds or correlated packing. Empirical frequencies come from already contacting residue edges; the model is not maximum-likelihood fitting of a truncated Bernoulli family. Q describes exchangeable cells within these edges, not bulk solvent, free atom exposure or a binding/nonbinding ensemble. Full observed inventories do not establish protonation, hydrogen bonds or solvent exposure. No physical free-energy units or assay-specific interpretation are assigned.

Antibody references augment actual available-pair chemistry; their greater sample count remains visible. Transfer does not establish exchangeability of antibody and TCR recognition contexts. No source-only classifier or source-weight search is implied by the pooled resource.