| A Kinetic and Stochastic Analysis of Crossbridge-Type Stepping Mechanisms in Rotary Molecular Motors Biophysical Journal, Volume 89, Issue 3, 1 September 2005, Pages 1650-1656 Dieter Walz and S. Roy Caplan Abstract The bacterial flagellar motor is generally supposed to be a stepping mechanism. The main evidence for this is based on a fluctuation analysis of experiments with tethered bacteria in which rotation frequency was varied by applying an external torque: the variance in time taken for a fixed number of revolutions was found to be essentially proportional to the inverse square of the frequency. This behavior was shown to characterize a Poissonian stepper. Here we present a rigorous kinetic and stochastic analysis of elastic crossbridge stepping in tethered bacteria. We demonstrate that Poissonian stepping is a virtually unachievable limit. To the extent that a system may approach Poissonian stepping it cannot be influenced by an externally applied torque; stepping mechanisms capable of being so influenced are necessarily non-Poissonian and exhibit an approximately inverse cubic dependence. This conclusion applies whatever the torsional characteristics of the tether may be, and contrary to claims, no perceptible relaxation of the tether following each step is found. Furthermore, the inverse square dependence is a necessary but not sufficient condition for Poissonian stepping, since a nonstepping mechanism, which closely reproduces most experimental data, also fulfills this condition. Hence the inference that crossbridge-type stepping occurs is not justified. Abstract | Full Text | PDF (157 kb) |
| Mechanical limits of bacterial flagellar motors probed by electrorotation Biophysical Journal, Volume 69, Issue 1, 1 July 1995, Pages 280-286 R.M. Berry, L. Turner and H.C. Berg Abstract We used the technique of electrorotation to apply steadily increasing external torque to tethered cells of the bacterium Escherichia coli while continuously recording the speed of cell rotation. We found that the bacterial flagellar motor generates constant torque when rotating forward at low speeds and constant but considerably higher torque when rotating backward. At intermediate torques, the motor stalls. The torque-speed relationship is the same in both directional modes of switching motors. Motors forced backward usually break, either suddenly and irreversibly or progressively. Motors broken progressively rotate predominantly at integral multiples of a unitary speed during the course of both breaking and subsequent recovery, as expected if progressive breaking affects individual torque-generating units. Torque is reduced by the same factor at all speeds in partially broken motors, implying that the torque-speed relationship is a property of the individual torque-generating units. Abstract | PDF (744 kb) |
| Helix Rotation Model of the Flagellar Rotary Motor Biophysical Journal, Volume 85, Issue 2, 1 August 2003, Pages 843-852 Rüdiger Schmitt Abstract A new model of the flagellar motor is proposed that is based on established dynamics of the KcsA potassium ion channel and on known genetic, biochemical, and biophysical facts, which accounts for the mechanics of torque generation, force transmission, and reversals of motor rotation. It predicts that proton (or in some species sodium ion) flow generates short, reversible helix rotations of the MotA-MotB channel complex (the stator) that are transmitted by Coulomb forces to the FliG segments at the rotor surface. Channels are arranged as symmetric pairs, S and T, that swing back and forth in synchrony. S and T alternate in attaching to the rotor, so that force transmission proceeds in steps. The sense of motor rotation can be readily reversed by conformationally switching the position of charged groups on the rotor so that they interact with the stator during the reverse rather than forward strokes. An elastic device accounts for the observed smoothness of rotation and a prolonged attachment of the torque generators to the rotor, i.e., a high duty ratio of each torque-generating unit. Abstract | Full Text | PDF (227 kb) |
Copyright © 1996 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 71, Issue 2, 918-923, 1 August 1996
doi:10.1016/S0006-3495(96)79295-0
Research Article
A.D. Samuel and H.C. Berg
Rowland Institute for Science, Cambridge, Massachusetts 02142, USA.
Measurements of the variance in rotation period of tethered cells as a function of mean rotation rate have shown that the flagellar motor of Escherichia coli is a stepping motor. Here, by measurement of the variance in rotation period as a function of the number of active torque-generating units, it is shown that each unit steps independently.