Auditable Algebraic Counting Field for Cryptic-Pocket Detection from Apo Structures

Shan Yu; Xuening Wu

Source-linked AI summary

Auditable Algebraic Counting Field for Cryptic-Pocket Detection from Apo Structures

Shan Yu, Xuening Wu

arXiv:2610.00988v1Oct 1, 2026cs.LGq-bio.BM

TL;DR

Cryptic pockets may be closed or absent in apo structures, and the measurements and learned evidence behind predictions are not always directly inspectable. ACF provides a compact, decomposable structural predictor; it showed an external ROC-AUC advantage on Set A, but gains were not consistent across evaluations.

Problem
Cryptic ligand-binding sites may be absent or closed in apo structures, while researchers seek predictions whose evidence is directly inspectable.
Source: §1 · pp. 1–2
Method
ACF represents structural evidence explicitly with a compact, exactly decomposable readout and separates ranking evaluation from operating-point effects.
Source: §1 · p. 2
Results
On Set A, ACF’s mean paired ROC-AUC advantage over P2Rank was 0.0443 (adjusted 95% CI [0.0102, 0.0792]), while official-fold ROC-AUC and matched-budget F1 differences remained unresolved.
Source: §6 · p. 12
Takeaways & Limitations
The findings support an auditable supervised predictor, without establishing lookup-table superiority or a causal explanation of pocket opening.
Source: §6 · p. 12
Set A contains only 57 units and excludes ambiguous intermediate-displacement cases, while the second external read contains only 45 scorable units.
Source: §4.2 · p. 11

Abstract

from arXiv · show

Cryptic ligand-binding pockets are not apparent in experimentally determined apo structures, making them difficult to identify from unbound receptor geometry. A complementary challenge is to make the structural measurements and learned evidence behind each prediction directly inspectable. We introduce a supervised algebraic counting field (ACF) for predicting cryptic-pocket residues from apo structures. ACF compiles explicit geometric, physicochemical, and topological features into compact, integer-weighted lookup tables. Each prediction score can be reconstructed from feature values, training counts, table weights, and spatial aggregation, without sequence search, structural-template transfer, or a protein language model at inference. We evaluate ACF on CryptoBench and two locked external collections, separating ranking performance from the effects of residue-calling budgets. On an external set of 57 post-CryptoBench apo-holo units, ACF exceeded P2Rank by +0.044 in mean paired ROC-AUC (multiplicity-adjusted 95% CI [+0.010, +0.079]). The advantage was dataset-dependent: official-fold ROC-AUC and matched-budget F1 differences against P2Rank remained unresolved, and a second external evaluation did not confirm gains from added structural features. ACF thus provides a compact predictor with externally validated signal and an inspectable path from structural measurements and training counts to residue scores.

1. Introduction

Cryptic pockets may be absent or closed in apo structures, even when local geometry and chemistry suggest where opening is possible. ACF addresses the demand for directly inspectable structural predictions with a compact, decomposable readout.

1. Introduction

Cryptic-pocket residues may be absent or closed in apo structures, so identifying them tests structural inference beyond sequence or template transfer.Local geometry and chemistry may still indicate where opening is possible.Source: §1 · p. 1
Prior approaches span geometric, energetic, and learned methods, motivating a predictor whose scores are mechanically reconstructable from measurements and training counts.The cited landscape includes cavity detection, physicochemical and energetic scoring, convolutional networks, graph learning, and a protein-language-model baseline.Source: §1 · pp. 1–2
ACF rank-discretizes structural features within each chain and combines compact lookup tables with bounded integer weights derived from training-fold counts.The deployed score does not require a neural-network pass or external database search, but the method uses training-derived parameters.Source: §1 · p. 2
ACF contributes an explicit structural representation with an exactly decomposable readout, evaluated against strong baselines while separating ranking from operating-point effects.Figure 1 contrasts training, which freezes label-derived parameters, with prediction from a new apo chain using table lookup and spatial aggregation.Source: §1 · p. 2, Figure 1 · p. 2

2. Materials and Methods

The methods define chain-level CryptoBench evaluation with leakage controls, compile explicit local structural features into weighted lookup tables, and specify matched-budget and external comparisons with paired uncertainty analyses.

2.1. Benchmark, evaluation units, and leakage controls

192 single-chain units from 190 PDB entries define the official analysis; 38 multi-chain cases and one unretrievable chain are excluded, and predictors receive apo coordinates only.Multi-chain cases are excluded because benchmark labels do not unambiguously assign residues to individual chains; a runtime guard rejects non-solvent heteroatoms and other non-polymer atoms.Source: §2.1 · p. 3

2.2. Local quantities, wires, and ACF compilation

Each residue has 43 base quantities—35 geometric and topological descriptors, seven fixed physicochemical constants, and one training-fold residue-type propensity—expanded into 645 wires, each discretized separately within the scored chain.Source: §2.2 · p. 3
Each table stores training-fold cryptic-residue counts by cell; regularized fitting yields rounded integer table weights, and an 18 Å neighborhood gate augments residue scores.The gate was selected on a UniProt accession-disjoint training half and frozen; its internal split does not guarantee sequence-cluster separation.Source: §2.2 · p. 4

2.3. Baselines and operating points

Comparisons include local P2Rank, PocketMiner, pLM-NN, and a geometry baseline; ACF and P2Rank use a matched top-9% per-chain budget for binary calls.The deployed ACF call uses the top 0.09 fraction selected on training data; applying the same training-fold grid search to P2Rank also selects 0.09.Source: §2.3 · p. 5

2.4. External validation

External validation uses a frozen, cluster-disjoint set of 57 post-CryptoBench apo–holo units and a second set of 45 cryo-EM units to test added feature families.Set A uses three prespecified co-primary comparisons with Bonferroni correction; Sets B+C prespecify four comparisons of the expanded field and baselines.Source: §2.4 · p. 5

2.5. Statistical analysis

Per-unit ROC-AUC and PR-AUC are averaged across units, with paired unit-bootstrap intervals; the mean paired ROC-AUC is primary and adjusted intervals determine whether co-primary differences are resolved.Undefined per-unit metrics are excluded rather than imputed as zero; the training-selected 20% trimmed mean is exploratory because indexed reads preceded its registration.Source: §2.5 · p. 6

2.6. Training-only structural-family probes

Training-only probes append predefined feature families across 12 accession-disjoint training halvings and compare their lift with size-matched controls without changing the deployed detector.Additional atom-level data also receive a within-chain row-permutation control; these exploratory probes do not use official or external folds for candidate selection.Source: §2.6 · p. 6

3. Results

The official-fold comparison with P2Rank and the F1 conclusion depend on evaluation conventions, while a locked external set provides the principal confirmatory accuracy result. Added feature families showed training-fold signal without a confirmed held-out gain, and the field’s auditability does not translate into faster warm inference.

3.1. Official-fold ranking and strong baselines

On the official fold, ACF reached ROC-AUC 0.799 versus P2Rank’s 0.793, but their paired difference (+0.0058) remained unresolved.ACF scored lower than pLM-NN in ROC-AUC and at a common calling budget, while both ACF and P2Rank exceeded PocketMiner.Source: §3.1 · pp. 6–7, Table 2 · p. 7, Figure 2 · p. 7

3.2. The F1 conclusion depends on the operating convention

At a matched top-9% calling budget, the F1 difference was +0.0140 [-0.0085, +0.0364], an unresolved result that does not support a convention-independent advantage.Across 39 thresholds, ACF’s F1 was directionally above P2Rank’s, but intervals excluded zero at only 10 thresholds; pLM-NN remained above ACF throughout.Source: §3.2 · pp. 7–8, Figure 3 · p. 8

3.3. First locked external validation

+0.0443 was the ACF advantage over P2Rank in mean ROC-AUC on the 57-unit locked external set (Bonferroni-adjusted 95% CI [+0.0102, +0.0792]).ACF was ahead on 42 of 57 units; matched top-9% external F1 against P2Rank remained unresolved.Source: §3.3 · p. 8, Figure 4 · p. 9

3.4. Second external read of the expanded representation

On 45 cryo-EM units, expanded ACF’s mean per-unit ROC-AUC was 0.7980; its +0.0063 difference from deployed ACF remained unresolved.The evaluation did not confirm gains from the four added feature families; expanded ACF also remained ahead of PocketMiner but behind pLM-NN.Source: §3.4 · p. 9, Figure 4 · p. 9

3.5. Discarded atom-level structure carries training-fold signal

On training-fold halvings, atom-level backbone, side-chain, and void descriptors improved ROC-AUC, while size-matched controls remained near zero.The combined backbone–side-chain family yielded +0.0072 and adding void geometry produced +0.0095; these results do not establish held-out accuracy gains.Source: §3.5 · pp. 9–10

3.6. Architecture sensitivity, auditability, and cost

Exact recomputation matched stored residue scores within 5 × 10^-16, but the audited score decomposition is not a causal biological explanation.Warm end-to-end ACF runtime was 0.298 s per chain versus 0.162 s for P2Rank; the supported efficiency advantage was model size, 1.79 MiB versus 22.01 MiB.Source: §3.6 · p. 10, Figure 5 · p. 11

4. Discussion

ACF’s accuracy advantage over P2Rank is dataset-dependent, and the authors position its contributions as numerical traceability and compact storage rather than leading accuracy or faster warm inference. The discussion limits claims about expanded features, test-set confirmation, and the benchmark target.

4.1. Positioning the contribution

ACF’s accuracy advantage over P2Rank is specific to Set A; the cryo-EM comparison did not confirm gains from the expanded representation.Same-wire logistic comparisons also do not establish a benefit of the table readout.Source: §4.1 · p. 11

4.2. Limitations

Set A contains only 57 units, excludes ambiguous intermediate-displacement cases, and may be easier than CryptoBench; the second external read has 45 scorable cryo-EM units.Both external collections are spent and cannot confirm a future revision.Source: §4.2 · p. 11
The sensitivity and family-addition analyses do not establish that all 645 wires are essential or quantify their redundancy; systematic deletion ablations remain absent.Coordinate-perturbation robustness and individual-weight stability across training splits and pairing seeds also remain untested.Source: §4.2 · p. 12
The analysis excludes 38 multi-chain units and does not establish performance at interfaces or in assemblies; its target is benchmark cryptic-residue labels, not ligand identity or efficacy.The authors call for broader locked datasets, frozen chain-aware mapping, and prospective experimental or simulation follow-up.Source: §4.2 · p. 12

5. Reproducibility

The reproducibility record pins the manuscript’s artifacts and deployed configuration to a repository snapshot and documents checks for regenerated metrics, artifact integrity, and history. It also bounds these checks by their dependence on frozen inputs and an environment-specific runtime record.

The original results, macros, and deployed configuration are pinned to commit 5d1726a, distinguishing manuscript artifacts from later development.The frozen table artifact records wire names, pairs, counts, weights, propensity, operating point, and code and manifest hashes.Source: §5 · p. 12
make recompute regenerates metrics from archived predictions, while make verify checks artifacts and make extorder checks ancestry in retained Git history.Inference and compilation require frozen inputs, caches, baseline binaries and weights, and the environment; ancestry checks cannot exclude unrecorded reads.Source: §5 · p. 12
Runtime measurements specify the Apple M4 software environment and separate warm and cold timing, CPU time, threading, extraction, scoring, and peak RSS.The measurements are environment-specific, and artifact checks are not experimental reruns.Source: §5 · p. 12

6. Conclusion

ACF provides compact, numerically traceable structure-based prediction without homology or template searches at inference. Its external advantage over P2Rank was not consistent across evaluations, limiting the conclusion to an auditable predictor with externally validated signal.

ACF’s mean paired ROC-AUC advantage over P2Rank on Set A was 0.0443 (adjusted 95% CI [0.0102, 0.0792]).Official-fold ROC-AUC and matched-budget F1 differences against P2Rank remained unresolved, and cryo-EM evaluation did not confirm gains from added features.Source: §6 · p. 12