Scale degeneracy: the physical basis of calibration and absolute quantitation in molecular binding
Year: 2026
Type: preprint
Abstract: Quantitative biology, from clinical diagnostics to drug discovery, relies on molecular binding assays. Except digital PCR, these assays require calibration curves and cannot be compared across platforms. All binding assays obey one physical law: an exact finite-site equation of state from statistical mechanics, with two dimensionless variables, the relative target concentration and a regime parameter κ. κ maps assay platforms from the Langmuir limit (κ > 10) to near-complete capture (κ < 0.1). Invariance under joint rescaling of molecule number, capture capacity, and affinity (scale degeneracy) precludes their determination from one equilibrium measurement, explaining calibration. We identify three criteria for calibration-free absolute quantification, met today only by digital PCR, and prove analog assays intrinsically calibration-bound, increasingly so with precision. Validated on six decades of data, from the 1960 radioimmunoassay to single-molecule arrays and clinical samples, it unifies sensitivity standards, explains digital-assay error budgets, and turns calibration into a design parameter.
Source: ChemRxiv
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
Awards: G2395904871, G4098825380
OpenAlex ID: W7214919653