  Time series of conformational dynamics in proteins are usually evaluated with
hidden Markov models (HMMs). This approach works well if the number of states
and their connectivity is known. However, for the multi-domain protein Hsp90, a
standard HMM analysis with optimization of the BIC (Bayesian information
criterion) cannot explain long-lived states well. Therefore, here we employ
constrained hidden Markov models, which neglect transitions between states by
including assumptions. Gradually tuning a model with justified and focused
changes allows us to improve its effectiveness and the score of the BIC. This
became possible by analyzing time traces with several thousand observable
transitions and, therefore, superb statistics. In this scheme, we also monitor
the residences in the states reconstructed by the model, aiming to find
exponentially distributed dwell times. We show how introducing new states can
achieve these statistics but also point out limitations, e.g., for substantial
similarity of two states connected to a common neighbor. One of the states
displays the lowest free energy and could be the idle open "waiting state", in
which Hsp90 waits for the binding of nucleotides, cochaperones, or clients.
