# Hidden Semi-Markov Models for Single-Molecule Conformational Dynamics Source: [Hidden Semi-Markov Models for Single-Molecule Conformational Dynamics]() Collection index: [llms.txt]() Data updated: 2025-10-28T13:56:18.930Z Authors: A. Kovalev, N. Zarrabi, F. Werz, M. Boersch, Z. Ristic, H. Lill, D. Bald, C. Tietz, J. Wrachtrup Published: 2009-02-03T21:21:51.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()