Auditing Haldane Consistency in Reversible Enzyme Kinetics: A Curated Two-Sided Backbone and a Labeled Fold-Error Benchmark

Abstract

Reversible enzyme kinetic constants can be audited through the Haldane relation: the apparent equilibrium constant implied by the rate law should match biochemical thermodynamics under matched conditions. We use the reciprocal cost $C_{\mathrm{Haldane}}=J(K'_{\mathrm{eq,kin}}/K'_{\mathrm{eq,thermo}})$, with $J(x)=\tfrac12(x+x^{-1})-1=\cosh(\ln x)-1$, as a calibrated, direction-symmetric reporting scale. The score is zero at agreement, penalizes reciprocal over- and underestimates equally, encodes the free-energy discrepancy in $RT$ units, and ranks records identically to $|\Delta\Delta G|$; the contribution is therefore biochemical curation, a reproducible workflow, and fold-error calibration rather than a new ordering. We apply the score to a curated demonstration set and, under prespecified inclusion criteria, assemble a two-sided backbone of twenty-one audited single-study records. Eight genuinely independent tests pair kinetics fit without a thermodynamic prior against separately measured equilibria; all eight fall within twofold (maximum $C_{\mathrm{Haldane}}=0.069$), although this remains a feasibility demonstration. Across the full backbone, eighteen records fall within twofold and three are flagged. The backbone is concentrated in carbohydrate isomerases and epimerases, so these results are within-family observations. Because real records carry no ground-truth labels, a semi-synthetic benchmark (twenty-nine within-twofold seeds, $1{,}885$ injected known-error cases) quantifies detectability: AUC $0.784$ ($95\%$ bootstrap CI $0.725$--$0.838$), conditional on the injected error taxonomy and invariant under monotone rescaling of $|\ln x|$. All data, code, protocol, and benchmark generator are archived for exact reproduction.