Modeling Torque Versus Speed, Shot Noise, and Rotational Diffusion of the Bacterial Flagellar Motor
Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey, USA.Physical Review Letters (Impact Factor: 7.51). 12/2009; 103(24):248102. DOI: 10.1103/PhysRevLett.103.248102
We present a minimal physical model for the flagellar motor that enables bacteria to swim. Our model explains the experimentally measured torque-speed relationship of the proton-driven E. coli motor at various pH and temperature conditions. In particular, the dramatic drop of torque at high rotation speeds (the "knee") is shown to arise from saturation of the proton flux. Moreover, we show that shot noise in the proton current dominates the diffusion of motor rotation at low loads. This suggests a new way to probe the discreteness of the energy source, analogous to measurements of charge quantization in superconducting tunnel junctions.
Full-text previewDOI: · Available from: ncbi.nlm.nih.gov
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.
- [Show abstract] [Hide abstract]
ABSTRACT: Author Summary Many species of bacteria swim to find food or to avoid toxins. Swimming motility depends on helical flagella that act as propellers. Each flagellum is driven by a rotary molecular engine–the bacterial flagellar motor–which draws its energy from an ion flux entering the cell. Despite much progress, the detailed mechanisms underlying the motor's extraordinary power output, as well as its near 100% efficiency, have yet to be understood. Surprisingly, recent experiments have shown that, at low speeds, the motor proceeds by small steps (∼26 per rotation), providing new insight into motor operation. Here we show that a simple physical model can quantitatively account for this stepping behavior as well as the motor's near-perfect efficiency and many other known properties of the motor. In our model, torque is generated via protein-springs that pull on the rotor; the steps arise from contact forces between static components of the motor and a 26-fold periodic ring that forms part of the rotor. Our model allows us to explain some curious properties of the motor, including the observation that backward steps are shorter on average than forward steps, and to make novel, experimentally testable predictions on the motor's speed and diffusion properties.
- [Show abstract] [Hide abstract]
ABSTRACT: Cells of Escherichia coli are able to swim up gradients of chemical attractants by modulating the direction of rotation of their flagellar motors, which spin alternately clockwise (CW) and counterclockwise (CCW). Rotation in either direction has been thought to be symmetric and exhibit the same torques and speeds. The relationship between torque and speed is one of the most important measurable characteristics of the motor, used to distinguish specific mechanisms of motor rotation. Previous measurements of the torque-speed relationship have been made with cells lacking the response regulator CheY that spin their motors exclusively CCW. In this case, the torque declines slightly up to an intermediate speed called the "knee speed" after which it falls rapidly to zero. This result is consistent with a "power-stroke" mechanism for torque generation. Here, we measure the torque-speed relationship for cells that express large amounts of CheY and only spin their motors CW. We find that the torque decreases linearly with speed, a result remarkably different from that for CCW rotation. We obtain similar results for wild-type cells by reexamining data collected in previous work. We speculate that CCW rotation might be optimized for runs, with higher speeds increasing the ability of cells to sense spatial gradients, whereas CW rotation might be optimized for tumbles, where the object is to change cell trajectories. But why a linear torque-speed relationship might be optimum for the latter purpose we do not know.