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Identifiability of enzyme kinetic parameters in substrate competition: a case study of CD39/NTPDase1

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Abstract

CD39 (NTPDase1—nucleoside triphosphate diphosphohydrolase 1) is a membrane-tethered ectonucleotidase that hydrolyzes extracellular ATP to ADP and ADP to AMP. This enzyme is expressed in a variety of cell types and tissues and has broadly been recognized within vascular tissue to have a protective role in converting “danger” ligands (ATP) into neutral ligands (AMP). In this study, we investigate the enzyme kinetics of CD39 using a Michaelis–Menten modeling framework. We show how the unique situation of having a reaction product also serving as a substrate (ADP) complicates the determination of the governing kinetic parameters. Model simulations using values for the kinetic parameters reported in the literature do not align with corresponding time-series data. This dissonance is explained by CD39 kinetic parameters previously being determined by graphical/linearization methods, which have been shown to distort the underlying error structure and lead to inaccurate parameter estimates. Modern methods of estimating these kinetic parameters using nonlinear least squares are still challenging due to unidentifiable parameter interactions. We propose a workflow to accurately determine these parameters by isolating the ADPase and ATPase reactions and estimating the respective ADPase parameters and ATPase parameters with independent data sets. Theoretically, this ensures all kinetic parameters are identifiable and reliable for future prospective model simulations involving CD39. These kinds of mathematical models can be used to understand how circulating purinergic nucleotides affect disease etiology and potentially inform the development of corresponding therapies.

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Data availability

Matlab code used for modeling and analysis can be found at the github repository: https://github.com/AndrewDMarquis/CD39-Enzyme-Kinetics

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Funding

This study was supported by National Institutes of Health grant no. K76 AG064426 (awarded to NRS) and the University of Michigan Undergraduate Research Opportunity Program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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Authors and Affiliations

  1. Division of Cardiovascular Medicine, Department of Medicine, Michigan Medicine, Ann Arbor, MI, USA

    Anna N. McGuinness, Aman Tahir & Nadia R. Sutton

  2. Division of Cardiovascular Medicine, Department of Medicine, Vanderbilt University Medical Center, Nashville, TN, USA

    Nadia R. Sutton

  3. Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, USA

    Nadia R. Sutton

  4. Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, MI, USA

    Andrew D. Marquis

  5. Applied BioMath®, MA, Concord, USA

    Andrew D. Marquis

Authors
  1. Anna N. McGuinness
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  2. Aman Tahir
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  3. Nadia R. Sutton
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  4. Andrew D. Marquis
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Contributions

ADM (Marquis) and NS conceived of the presented study. AM (McGuinness), AT, and ADM derived the mathematical model, carried out the computer simulations, and analyzed and interpreted the results. AM and AT took the lead in the original drafting of the manuscript. All figures and tables were prepared by AM, AT, and ADM. ADM and NS provided critical feedback and helped shape the research, analysis, and final manuscript. All authors reviewed and approved of the manuscript.

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Correspondence to Andrew D. Marquis.

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AM and AT are joint first authors.

Appendix

Appendix

Time-varying sensitivities

The time-varying sensitivities are used to calculate the ranked sensitivities for each model state: ATP, ADP, and AMP. These are used to calculate the correlation matrix, which contains the pairwise correlations between the parameters. \({K}_{M1}\), \({K}_{M2}\), \({v}_{\mathrm{max}1}\), and \({v}_{\mathrm{max}2}\). Figure A1 shows the time varying sensitivities of both the nominal and naively estimated parameters in each of the states mentioned.

Fig. A1
figure 10

Time-varying sensitivities

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McGuinness, A. ., Tahir, A., Sutton, N.R. et al. Identifiability of enzyme kinetic parameters in substrate competition: a case study of CD39/NTPDase1. Purinergic Signalling (2023). https://doi.org/10.1007/s11302-023-09942-1

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