Signature of (anti)cooperativity in the stochastic fluctuations of small systems: application to the bacterial flagellar motor

TL;DR

This paper develops a theoretical model to analyze how cooperativity influences fluctuations in small biological systems, specifically applying it to bacterial flagellar motors to understand their adaptive assembly and fluctuation behavior.

Contribution

It introduces a grand canonical Hamiltonian model for small lattice gases with interactions, linking interaction strength to fluctuation intensity, and applies it to experimental data from bacterial flagellar motors.

Findings

Cooperativity affects fluctuation intensity in small systems.

Experimental data suggests stator units exhibit cooperative behavior.

The system operates near a phase space point that balances adaptability and fluctuation minimization.

Abstract

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) suitable for a smoothly adaptive system while minimizing fluctuations.