Ultrasensitivity and sharp threshold theorems for multisite systems

Vinckenbosch, Laura (Haute école d’ingénierie et de gestion du canton de Vaud, HES-SO // Haute Ecole Spécialisée de Suisse Occidentale) ; Mazza, Christian (University of Fribourg) ; Dougoud, Michaël (University of Fribourg)

This work studies the ultrasensitivity of multisite binding processes where ligand molecules can bind to several binding sites. It considers more particularly recent models involving complex chemical reactions in allosteric phosphorylation processes and for transcription factors and nucleosomes competing for binding on DNA. New statistics-based formulas for the Hill coefficient and the effective Hill coefficient are provided and necessary conditions for a system to be ultrasensitive are exhibited. It is first shown that the ultrasensitivity of binding processes can be approached using sharp-threshold theorems which have been developed in applied probability theory and statistical mechanics for studying sharp threshold phenomena in reliability theory, random graph theory and percolation theory. Special classes of binding process are then introduced and are described as density dependent birth and death process. New precise large deviation results for the steady state distribution of the process are obtained, which permits to show that switch-like ultrasensitive responses are strongly related to the multi-modality of the steady state distribution. Ultrasensitivity occurs if and only if the entropy of the dynamical system has more than one global minimum for some critical ligand concentration. In this case, the Hill coefficient is proportional to the number of binding sites, and the system is highly ultrasensitive. The classical effective Hill coefficient I is extended to a new cooperativity index Iq, for which we recommend the computation of a broad range of values of q instead of just the standard one I=I0.9 corresponding to the 10%–90% variation in the dose-response. It is shown that this single choice can sometimes mislead the conclusion by not detecting ultrasensitivity. This new approach allows a better understanding of multisite ultrasensitive systems and provides new tools for the design of such systems.

Article Type:
Economie et Services
Institut Interdisciplinaire du Développement de l’Entreprise
Published in:
Journal of physics A: mathematical and theoretical
Numeration (vol. no.):
February 2017, vol. 50, no. 7
Appears in Collection:

 Record created 2017-03-31, last modified 2020-10-27

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