# ESMFold2 SPECTRA Analysis Trace

Tracked on 2026-06-24 as the paper-facing chronology of the ESMFold2 SPECTRA
audit. This document is intended to preserve the analysis path, including axes
that were supported locally, weakened under confirmation, or downgraded before
the final claim boundary.

## Paper Draft Text

We first applied \spectra to ESMFold2~\cite{esmfold2}, a recent foundation model
for monomer structure prediction. \spectra's initial spectral parameter was
evolutionary support, measured by the number of non-query sequences in the input
alignment for ESMFold2. To measure this effect it pulled the CAMEO~\cite{cameo}
dataset. Across 138 CAMEO~2025 targets, \spectra recovered a sharp MSA-depth
threshold: high-support targets attained a mean CA-lDDT of 0.919, whereas
targets below the high-support threshold attained 0.723, a drop of 0.196.

We then asked whether \spectra could identify a non-MSA axis that generalized
beyond CAMEO. The agent first proposed a sequence-intrinsic flexible/non-helical
composition score based on proline enrichment and beta- or turn-favored sequence
propensities. This axis was strong on CAMEO and persisted under held-out CAMEO
confirmation and increased ESMFold2 inference-time sampling; however, when the
same hypothesis was evaluated on an external RCSB~\cite{rcsb} dataset, the
effect weakened substantially. \spectra therefore downgraded the axis from a
broad ESMFold2 failure mode to a CAMEO-local finding.

Continuing across the accumulated ESMFold2 evaluations, and after downgrading
charge, acidic-window, disorder, repeat, and non-portable composition axes,
\spectra converged on high disulfide/cysteine capacity as the broadest
sequence-only degradation proxy. We defined disulfide capacity as:

```tex
\begin{equation}
    \mathrm{disulfide\ capacity}
    = \frac{\lfloor N_{\mathrm{Cys}}/2 \rfloor}{L} \times 100,
    \label{eq:disulfide}
\end{equation}
```

where $N_{\mathrm{Cys}}$ is the number of cysteine residues and $L$ is the
sequence length. Across 652 exact-sequence primary ESMFold2 evaluations, the top
25% of targets by disulfide capacity showed a raw CA-lDDT descriptive decrease
of 0.149 relative to the remaining targets. The effect remained negative after
adjustment for source family, sequence length, and baseline model performance,
and it persisted under approximate cluster-aware validation. In matched-control
analyses the effect was smaller but remained negative overall, indicating that
high disulfide capacity is a broad risk proxy rather than a complete mechanistic
explanation.

Finally, \spectra separated this broad sequence-only proxy from a sharper,
localized failure mode. Among metadata-eligible RCSB rows, viral surface and
envelope proteins showed larger degradation, with class-II-like E/E2/envelope-E
proteins forming the strongest localized subtype. These targets exhibited
substantially lower ESMFold2 confidence as well as lower structural accuracy,
indicating that the audit identified a difficult applicability-domain regime
rather than a hidden overconfidence failure. The final ESMFold2 audit therefore
did not yield a single universal explanation for all errors; instead, it
produced a structured applicability-domain summary: MSA depth is a known
CAMEO-supported axis, high disulfide/cysteine capacity is the broadest
prospective sequence-only risk proxy (cysteine-pair capacity computed from
sequence, not verified disulfide bonds, and correlated with
secreted/extracellular protein classes), and class-II-like viral envelope
proteins represent a sharper, metadata-supported failure regime.

## Artifact Cross-References

- `FINAL_ESMFOLD2_RESULT.md`: final paper-ready claim boundary and reviewer-proofing.
- `prior_axis_reports/01_cameo_msa_depth_final_report.md`: CAMEO MSA-depth result.
- `prior_axis_reports/02_beyond_msa_flexible_nonhelical_report.md`: CAMEO flexible/non-helical axis and inference-time scaling check.
- `prior_axis_reports/03_flexible_nonhelical_external_rcsb_report.md`: external RCSB weakening of the flexible/non-helical axis.
- `prior_axis_reports/07_high_cysteine_fresh_confirmation_report.md`: high-cysteine/disulfide confirmation path.
- `prior_axis_reports/11_surface_lowhelical_and_classII_report.md`: class-II-like viral E/E2/envelope-E localized failure mode.
- `tables/global_hypothesis_effects_primary_sequence.csv`: primary sequence-deduplicated global axis effects.
- `tables/global_hypothesis_adjusted_effects_primary_sequence.csv`: adjusted effects.
- `tables/cluster_aware_disulfide_effects.csv`: approximate cluster-aware validation.
- `tables/matched_control_summary.csv`: matched-control disulfide analysis.
- `tables/confidence_calibration_summary.csv`: pTM/pLDDT calibration checks.