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:
motor proteins; single molecule kinetics; enzyme kinetics; flagellar motor;
Markov process; non-equilibrium fluctuations.Comment: revtex, 15 pages, 8 figures, 2 tables. v2: Minor revision, corrected
typos, added references, and moved mathematical parts to new appendice