Signature of (anti)cooperativity in the stochastic fluctuations of small systems: application to the bacterial flagellar motor
Résumé
The cooperative binding of molecular agents onto a substrate is pervasive in living systems.
To study whether a system shows cooperativity, one can rely on a fluctuation analysis of quantities such as the number of substrate-bound units and the residence time in an occupancy
state. Since the relative standard deviation from the statistical mean monotonically decreases
with the number of binding sites, these techniques are only suitable for small enough
systems, such as those implicated in stochastic processes inside cells. Here, 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. First, we elucidate how the strength and
sign of the interaction potential between neighboring bound particles on the lattice determine
the intensity of the fluctuations of the mean occupancy. We then employ this relationship to
compare the theoretical predictions of our model to data from single molecule experiments
on 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. Furthermore, in an attempt to quantify fluctuations
and the adaptability of the BFM, we estimate the stator-stator interaction potential. Finally,
we conclude that the system resides in a sweet spot of the parameter space (phase diagram)
with characteristics suitable for a smoothly and widely adaptive system, while minimizing
fluctuations.
https://arxiv.org/abs/2307.00636v2