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Uncertainty in protein–ligand binding constants: asymmetric confidence intervals versus standard errors

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Abstract

Equilibrium binding constants (Kb) between chemical compounds and target proteins or between interacting proteins provide a quantitative understanding of biological interaction mechanisms. Reported uncertainties of measured experimental parameters are critical for decision-making in many scientific areas, e.g., in lead compound discovery processes and in comparing computational predictions with experimental results. Uncertainties in measured Kb values are commonly represented by a symmetric normal distribution, often quoted in terms of the experimental value plus–minus the standard deviation. However, in general, the distributions of measured Kb (and equivalent Kd) values and the corresponding free energy change ΔGb are all asymmetric to varying degree. Here, using a simulation approach, we illustrate the effect of asymmetric Kb distributions within the realm of isothermal titration calorimetry (ITC) experiments. Further we illustrate the known, but perhaps not widely appreciated, fact that when distributions of any of Kb, Kd and ΔGb are transformed into each other, their degree of asymmetry is changed. Consequently, we recommend that a more accurate way of expressing the uncertainties of Kb, Kd, and ΔGb values is to consistently report 95% confidence intervals, in line with other authors’ suggestions. The ways to obtain such error ranges are discussed in detail and exemplified for a binding reaction obtained by ITC.

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Acknowledgements

This research was funded by grant no. S-LLT-20-2 from the Research Council of Lithuania (DM). MB and MJM aknowledge Fundação para a Ciência e Tecnologia (FCT), Portugal, for the financial support to Projects UIDB/00081/2020 and UIDB/00313/2020, respectively. The authors also acknowledge the COST action ARBRE-MOBIEU CA15126 supported by COST (European Cooperation in Science and Technology).

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Authors and Affiliations

  1. Department of Biothermodynamics and Drug Design, Institute of Biotechnology, Life Sciences Center, Vilnius University, Saulėtekio 7, 10257, Vilnius, Lithuania

    Vaida Paketurytė, Vytautas Petrauskas, Asta Zubrienė, Vaida Linkuvienė & Daumantas Matulis

  2. Institute of Biocomputation and Physics of Complex Systems (BIFI), Joint Units IQFR-CSIC-BIFI, and GBsC-CSIC-BIFI, Universidad de Zaragoza, Zaragoza, Spain

    Olga Abian & Adrian Velazquez-Campoy

  3. Aragon Institute for Health Research (IIS Aragon), Zaragoza, Spain

    Olga Abian & Adrian Velazquez-Campoy

  4. Department of Biochemistry and Molecular and Cell Biology, Universidad de Zaragoza, Zaragoza, Spain

    Olga Abian & Adrian Velazquez-Campoy

  5. Centro de Investigación Biomédica en Red en el Área Temática de Enfermedades Hepáticas y Digestivas (CIBERehd), Barcelona, Spain

    Olga Abian & Adrian Velazquez-Campoy

  6. Instituto Aragonés de Ciencias de la Salud (IACS), Zaragoza, Spain

    Olga Abian

  7. Department of Chemistry and Biochemistry, Faculty of Sciences, CIQ-UP, University of Porto, Porto, Portugal

    Margarida Bastos

  8. Department of Chemical and Materials Engineering, National Central University, Taoyüan, Taiwan

    Wen-Yih Chen

  9. Chemistry Department, Faculty of Sciences and Technology, Coimbra Chemistry Center, University of Coimbra, 3004-535, Coimbra, Portugal

    Maria João Moreno

  10. Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK

    Georg Krainer

  11. Protein Technologies, Vienna Biocenter Core Facilities GmbH, Vienna, Austria

    Arthur Sedivy

  12. Fundacion ARAID, Government of Aragon, Zaragoza, Spain

    Adrian Velazquez-Campoy

  13. Department of Biological Sciences, Institute for Structural and Molecular Biology, Birkbeck, University of London, London, UK

    Mark A. Williams

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  1. Vaida Paketurytė
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  8. Georg Krainer
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Correspondence to Margarida Bastos, Arthur Sedivy, Adrian Velazquez-Campoy, Mark A. Williams or Daumantas Matulis.

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Special Issue: COST Action CA15126, MOBIEU: Between atom and cell.

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Paketurytė, V., Petrauskas, V., Zubrienė, A. et al. Uncertainty in protein–ligand binding constants: asymmetric confidence intervals versus standard errors. Eur Biophys J 50, 661–670 (2021). https://doi.org/10.1007/s00249-021-01518-4

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  • DOI: https://doi.org/10.1007/s00249-021-01518-4

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