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High-order Michaelis-Menten equations allow inference of hidden kinetic parameters in enzyme catalysis

Author

Listed:
  • Divya Singh

    (Tel Aviv University)

  • Tal Robin

    (Columbia University)

  • Michael Urbakh

    (Tel Aviv University)

  • Shlomi Reuveni

    (Tel Aviv University)

Abstract

Single-molecule measurements provide a platform for investigating the dynamical properties of enzymatic reactions. To this end, the single-molecule Michaelis-Menten equation was instrumental as it asserts that the first moment of the enzymatic turnover time depends linearly on the reciprocal of the substrate concentration. This, in turn, provides robust and convenient means to determine the maximal turnover rate and the Michaelis-Menten constant. Yet, the information provided by these parameters is incomplete and does not allow access to key observables such as the lifetime of the enzyme-substrate complex, the rate of substrate-enzyme binding, and the probability of successful product formation. Here we show that these quantities and others can be inferred via a set of high-order Michaelis-Menten equations that we derive. These equations capture universal linear relations between the reciprocal of the substrate concentration and distinguished combinations of turnover time moments, essentially generalizing the Michaelis-Menten equation to moments of any order. We demonstrate how key observables such as the lifetime of the enzyme-substrate complex, the rate of substrate-enzyme binding, and the probability of successful product formation, can all be inferred using these high-order Michaelis-Menten equations. We test our inference procedure to show that it is robust, producing accurate results with only several thousand turnover events per substrate concentration.

Suggested Citation

  • Divya Singh & Tal Robin & Michael Urbakh & Shlomi Reuveni, 2025. "High-order Michaelis-Menten equations allow inference of hidden kinetic parameters in enzyme catalysis," Nature Communications, Nature, vol. 16(1), pages 1-11, December.
  • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-57327-2
    DOI: 10.1038/s41467-025-57327-2
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    References listed on IDEAS

    as
    1. Tal Robin & Shlomi Reuveni & Michael Urbakh, 2018. "Single-molecule theory of enzymatic inhibition," Nature Communications, Nature, vol. 9(1), pages 1-9, December.
    2. Arun P. Wiita & Raul Perez-Jimenez & Kirstin A. Walther & Frauke Gräter & B. J. Berne & Arne Holmgren & Jose M. Sanchez-Ruiz & Julio M. Fernandez, 2007. "Probing the chemistry of thioredoxin catalysis with force," Nature, Nature, vol. 450(7166), pages 124-127, November.
    3. Gene-Wei Li & X. Sunney Xie, 2011. "Central dogma at the single-molecule level in living cells," Nature, Nature, vol. 475(7356), pages 308-315, July.
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