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A Kinetic and Stochastic Analysis of Crossbridge-Type Stepping Mechanisms in Rotary Molecular Motors

Dieter Walz ^* and S. Roy Caplan 

^* Biozentrum, University of Basel, Basel, Switzerland; and Department of Biological Chemistry, The Weizmann Institute of Science, Rehovot, Israel, and Department of Physiology, McGill University, Montreal, Québec, Canada

Correspondence: Address reprint requests to Prof. S. Roy Caplan, E-mail: r.caplan{at}weizmann.ac.il; or roy.caplan{at}mcgill.ca.

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.