Résumé
The cooperative binding of molecular agents onto a substrate is pervasive in living systems, particularly stochastic processes inside cells. When the number of binding sites is small enough, we can rely on a fluctuation analysis of the number of substrate-bound units, an experimentally accessible quantity, to study whether a system shows cooperativity. First, we present a general-purpose grand canonical Hamiltonian description of a small one-dimensional (1D) lattice gas with either nearest-neighbor or long-range interactions as prototypical examples of cooperativity-influenced adsorption processes. We propose 1) a criterion to determine whether a given adsorption system exhibits cooperative or anti-cooperative behavior and 2) a method to quantify the amplitude of the ligand-ligand interaction potential. Second, we compare the theoretical predictions of our model to bead assay measurements of the bacterial flagellar motors (BFM) of *E. coli*. In this way, we find evidence that cooperativity controls the mechano-sensitive dynamical assembly of the torque-generating units, the so-called stator units, onto the BFM. Finally, we estimate the stator-stator interaction potential and attempt to quantify the *adaptability* of the BFM.References:[1]: https://arxiv.org/abs/2307.00636[2]: https://www.biorxiv.org/content/10.1101/2021.07.05.451114v1