BIOPHYSICAL THEORY AND MODELING |
Dwell time symmetry in random walks and molecular motors
Martin Lindén 1 and Mats Wallin 2*
1 Royal Institute of Technology
2 Royal Inst of Technology
* To whom correspondence should be addressed. E-mail: wallin{at}kth.se.
Submitted on December 13, 2006
Revised on January 13, 2007
Accepted on 1 February 2007
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Abstract |
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The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this paper, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits.
Key Words:
Markov process, enzyme kinetics, flagellar motor, motor proteins, non-equilibrium fluctuations, single molecule kinetics
