  The conformational kinetics of enzymes can be reliably revealed when they are
governed by Markovian dynamics. Hidden Markov Models (HMMs) are appropriate
especially in the case of conformational states that are hardly
distinguishable. However, the evolution of the conformational states of
proteins mostly shows non-Markovian behavior, recognizable by
non-monoexponential state dwell time histograms. The application of a Hidden
Markov Model technique to a cyclic system demonstrating semi-Markovian dynamics
is presented in this paper and the required extension of the model design is
discussed. As standard ranking criteria of models cannot deal with these
systems properly, a new approach is proposed considering the shape of the dwell
time histograms. We observed the rotational kinetics of a single F1-ATPase
alpha3beta3gamma sub-complex over six orders of magnitude of different ATP to
ADP and Pi concentration ratios, and established a general model describing the
kinetics for the entire range of concentrations. The HMM extension described
here is applicable in general to the accurate analysis of protein dynamics.
