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PreprintCC BY-NC-NDChemRxiv

Scale degeneracy: the physical basis of calibration and absolute quantitation in molecular binding

  • Liang Guo1,2
  • Tianjiao Mao3
  • Yipi Xiao4
  • Feiyue Qin5
  • Fanrong Ai6
  • Jiani Wang7
  • Qingxin Song7
  • Shengming Yu8
  • Xiluan Yan7,9,10
  • Huan Li5
10 affiliations
  1. 1State Key Laboratory of Food Science and Resources, Nanchang University
  2. 2Sino German Joint Research Institute, Nanchang University
  3. 3Shanghai Aurefluidics Technology Co., Ltd.
  4. 4Nanchang Hongdu Hospital of TCM
  5. 5Shanghai LiangTa biotech Co., Ltd.
  6. 6School of Advanced Manufacturing, Nanchang University
  7. 7School of Pharmacy, Jiangxi Medical College, Nanchang University
  8. 8The First Affiliated Hospital of Nanchang University
  9. 9The MOE Basic Research and Innovation Center for the Targeted Therapeutics of Solid Tumors, Jiangxi Medical College, Nanchang University
  10. 10Jiangxi Province Key Laboratory of New Drug Evaluation and Transformation
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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.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026scale,
  title = {{Scale degeneracy: the physical basis of calibration and absolute quantitation in molecular binding}},
  author = {Liang Guo and Tianjiao Mao and Yipi Xiao and Feiyue Qin and Fanrong Ai and Jiani Wang and Qingxin Song and Shengming Yu and Xiluan Yan and Huan Li},
  howpublished = {ChemRxiv},
  year = {2026},
  month = sep,
  doi = {10.26434/chemrxiv-2024-19rj6/v11},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv-2024-19rj6/v11},
  note = {CC BY-NC-ND},
}
RIS
TY  - UNPB
TI  - Scale degeneracy: the physical basis of calibration and absolute quantitation in molecular binding
AU  - Liang Guo
AU  - Tianjiao Mao
AU  - Yipi Xiao
AU  - Feiyue Qin
AU  - Fanrong Ai
AU  - Jiani Wang
AU  - Qingxin Song
AU  - Shengming Yu
AU  - Xiluan Yan
AU  - Huan Li
PY  - 2026
DA  - 2026/09/30
PB  - ChemRxiv
DO  - 10.26434/chemrxiv-2024-19rj6/v11
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv-2024-19rj6/v11
AB  - 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.
ER  -