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Size limits the sensitivity of kinetic schemes

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Listed:
  • Jeremy A. Owen

    (Massachusetts Institute of Technology
    Princeton University)

  • Jordan M. Horowitz

    (University of Michigan
    University of Michigan
    University of Michigan)

Abstract

Living things benefit from exquisite molecular sensitivity in many of their key processes, including DNA replication, transcription and translation, chemical sensing, and morphogenesis. At thermodynamic equilibrium, the basic biophysical mechanism for sensitivity is cooperative binding, for which it can be shown that the Hill coefficient, a sensitivity measure, cannot exceed the number of binding sites. Generalizing this fact, we find that for any kinetic scheme, at or away from thermodynamic equilibrium, a very simple structural quantity, the size of the support of a perturbation, always limits the effective Hill coefficient. We show how this bound sheds light on and unifies diverse sensitivity mechanisms, including kinetic proofreading and a nonequilibrium Monod-Wyman-Changeux (MWC) model proposed for the E. coli flagellar motor switch, representing in each case a simple, precise bridge between experimental observations and the models we write down. In pursuit of mechanisms that saturate the support bound, we find a nonequilibrium binding mechanism, nested hysteresis, with sensitivity exponential in the number of binding sites, with implications for our understanding of models of gene regulation and the function of biomolecular condensates.

Suggested Citation

  • Jeremy A. Owen & Jordan M. Horowitz, 2023. "Size limits the sensitivity of kinetic schemes," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
  • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-36705-8
    DOI: 10.1038/s41467-023-36705-8
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    References listed on IDEAS

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    1. Bahram Houchmandzadeh & Eric Wieschaus & Stanislas Leibler, 2002. "Establishment of developmental precision and proportions in the early Drosophila embryo," Nature, Nature, vol. 415(6873), pages 798-802, February.
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