Hidden Semi-Markov Models for Single-Molecule Conformational Dynamics

TL;DR

This paper extends Hidden Markov Models to semi-Markovian systems to accurately analyze non-Markovian protein conformational dynamics, demonstrated through single-molecule enzyme kinetics over a wide range of conditions.

Contribution

The paper introduces a semi-Markov extension of HMMs that incorporates dwell time histogram shapes, improving analysis of non-Markovian protein conformational data.

Findings

Successfully modeled F1-ATPase kinetics across six orders of magnitude of substrate concentrations.

Demonstrated the extended HMM's ability to distinguish non-monoexponential dwell times.

Provided a general framework applicable to various protein dynamic studies.

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.