Where thermodynamics wins: a regime contrast

The starting point

EnergyFingerprint combines two axes: an evolutionary one (the log-likelihood ratio of a protein language model, ESMC) and a thermodynamic one (the mRNA stacking energy profile). For months we worked with an internal figure stating that the evolutionary axis, on its own, barely discriminated clinical variants (AUC ≈ 0.5). From that came an attractive hypothesis: if each channel is weak alone but together they reach AUC ≈ 0.88, the only explanation would be a multiplicative interaction between signal and shape — the heart of our Λ = S ⊗ Φ framework.

Before building an entire paper on that idea, we decided to verify the number everything depended on. That is what a glass-box approach demands: audit the number before building on it.

The audit: the number was wrong

We recomputed the AUC of the evolutionary channel alone, read at the exact position of the variant and unnormalized, over the 5,023 confident variants of the 42-gene panel. Result:

The evolutionary channel does discriminate, and very well (AUC ≈ 0.90, in line with published ESM-1v). The decisive clue: even the reference ESM-1v came out at ~0.52 in the original table, when the literature places it at 0.75–0.85 — the fault hit even the control model, so it was a computation artifact (window aggregation instead of point reading), not a property of any model.

With the signal read correctly: what does thermodynamics add in missense?

With the figure corrected, the question changes. It is no longer "why do two weak channels add up to so much?", but "does thermodynamics add anything on top of a correctly-read evolutionary signal?". We refit four nested models (signal only, shape only, additive, with interaction) with per-gene cross-validation and multiple-comparison correction (FDR).

The honest answer: in missense, adding the thermodynamic channel improves AUC by +0.000. The signal×shape interaction exists — it is statistically detectable after FDR — but it is of practically null effect: it does not change the classification. In missense, the language model already sees what there is to see.

A note on the AUCs: they are computed on ClinVar, where the value may reflect gene identity or variant position rather than the effect of the variant itself. The 42-gene panel results are unpublished.

The contrast: where the language model is blind

Here is the twist. A synonymous variant does not change the protein — the protein language model has nothing to read, blind by construction. We applied exactly the same thermodynamic channel to 5,531 synonymous variants across 8 genes:

The same channel that is inert in missense carries the classification in synonymous variants. Not because the method changes — the regime changes. Where there is no evolutionary signal to read, the mRNA physics is what remains, and it discriminates.

Thermodynamics does not compete with language models on their turf. It is the axis that lights up the ground where they cannot see.

What this means for EnergyFingerprint

It reorders the story in a way that strengthens it. Our positioning was always to operate "where REVEL and AlphaMissense are blind" — and those are missense predictors. The audit confirms it with numbers: the distinctive value of thermodynamics is not competing in missense (where the evolutionary signal already wins), but in the silent regime — synonymous variants, mRNA, non-coding — where no protein language model has an entry point.

And there is a method lesson: a result that looked extraordinary (multiplicative super-additivity) rested on a figure no one had verified. Auditing it saved us from publishing an artifact and gave us something more solid — a clean, falsifiable regime contrast. In a glass-box company, correcting your own record is not a weakness; it is the product.

Honesty note: the synonymous validation is limited by the scarcity of confident pathogenic variants (tens); the robust high-power figure (AUC 0.71) comes from the expanded set. We state it because rigor is the point.