Direct observation of steps in rotation of the bacterial flagellar motor

Abstract

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel many species of swimming bacteria. The rotor is a set of rings up to 45 nm in diameter in the cytoplasmic membrane; the stator contains about ten torque-generating units anchored to the cell wall at the perimeter of the rotor. The free-energy source for the motor is an inward-directed electrochemical gradient of ions across the cytoplasmic membrane, the protonmotive force or sodium-motive force for H+-driven and Na+-driven motors, respectively. Here we demonstrate a stepping motion of a Na+-driven chimaeric flagellar motor in Escherichia coli at low sodium-motive force and with controlled expression of a small number of torque-generating units. We observe 26 steps per revolution, which is consistent with the periodicity of the ring of FliG protein, the proposed site of torque generation on the rotor. Backwards steps despite the absence of the flagellar switching protein CheY indicate a small change in free energy per step, similar to that of a single ion transit.

A Delicate Nanoscale Motor Made by Nature—The Bacterial Flagellar Motor

“…An optical trapping system with high temporal and spatial resolution was used while a small indicator (a latex bead of diameter 0.2–0.5 microns) was attached to the flagellum. Finally, 26 steps per revolution were observed for the first time,40 consistent with the 26‐fold stoichiometry of the FliG protein on the C ring.…”

Reconstruction of noisy signals by minimization of non-convex functionals

“…A second domain is defined by PWS signals corrupted with White Gaussian noise, both alone and jointly with Impulsive noise. These denoising problems might result from scientific and engineering areas such as cross-hybridization of DNA [24], molecular bioscience [25], reconstruction of brain stimuli [26], among others. From a practical point of view, impulsive noises may appear due to sensor malfunctioning, while White Gaussian noise is mainly caused by poor illumination, high temperature, transmission errors, among others.…”

“…The first bound can be straightforwardly inferred from the boundedness ofû(x) and g(x). The second one follows from (24) and (25). Let us define now two other numbers:…”

A simple backscattering microscope for fast tracking of biological molecules

“…Measurements with sufficiently high spatial and temporal resolution have helped elucidate information about the kinetics and stepping behavior of molecular motors. [1][2][3][4] In an optical microscope, sparse particles can be tracked with arbitrary precision provided that sufficient photons are collected. 5 Probes, such as fluorophores, microbeads, or nanoparticles, have been tracked with nanometer accuracy and time resolution of milliseconds or better.…”