Direct Determination of Kinetic Rates from Single-Molecule Photon Arrival Trajectories Using Hidden Markov Models
- 1 September 2003
- journal article
- research article
- Published by American Chemical Society (ACS) in The Journal of Physical Chemistry A
- Vol. 107 (38), 7454-7464
- https://doi.org/10.1021/jp035514+
Abstract
The measurement of fluorescence from single protein molecules has become an important new tool in the study of dynamic processes, allowing for the direct visualization of the motions experienced by individual proteins and macromolecular complexes. The data from such single-molecule experiments are in the form of photon trajectories, consisting of arrival times and wavelength information on individual photons. The analysis of photon trajectories can be difficult, particularly if the motions are occurring at rates comparable to the photon arrival rate or in the presence of noise. In this paper, we introduce the use of hidden Markov models (HMMs) for the analysis of photon trajectory data that operate using the photon data directly, without the need for ensemble averaging of the data as implied by correlation function analysis. Using a simple kinetic model, we examine the relationship between the uncertainty in the estimates of the motional rate and the photon detection rate. Remarkably, we obtain relative uncertainties in the rate constants of as little as 3% even when the interconversion rate is equal to the photon detection rate, and the uncertainty increases to only 10% when the interconversion rate is 10 times the photon detection rate. This suggests that useful information can be obtained for much faster kinetic regimes than have typically been studied. We also examine the impact of background photons on the determination of the rate and demonstrate that the HMM-based approach is robust, displaying small uncertainties for background photon arrival rates approaching that of the signal. These results not only are relevant in establishing the theoretical limits on precision, but are also useful in the context of experimental design. Finally, to demonstrate how the methodology can be extended to more complex kinetic models and how it can allow one to make use of the full power of statistics for purposes of model evaluation and selection, we consider a four-state kinetic model for protein conformational transitions previously studied by Schenter et al. (J. Phys. Chem. A1999, 103, 10477). We show how an HMM can be used as an alternative to higher-order correlation function analysis for the detection of “conformational memory” and apparent non-Markovian dynamics arising from such temporally inhomogeneous kinetic schemes.Keywords
This publication has 32 references indexed in Scilit:
- Probing the free-energy surface for protein folding with single-molecule fluorescence spectroscopyNature, 2002
- A Dozen Years of Single-Molecule Spectroscopy in Physics, Chemistry, and BiophysicsThe Journal of Physical Chemistry B, 2002
- Principles of Single Molecule Multiparameter Fluorescence SpectroscopySingle Molecules, 2001
- Single Molecules of Highly Purified Bacterial Alkaline Phosphatase Have Identical ActivityJournal of the American Chemical Society, 2000
- Ten Years of Single-Molecule SpectroscopyThe Journal of Physical Chemistry A, 1999
- Statistical Analyses and Theoretical Models of Single-Molecule Enzymatic DynamicsThe Journal of Physical Chemistry A, 1999
- Fluorescence Spectroscopy, Exciton Dynamics, and Photochemistry of Single Allophycocyanin TrimersThe Journal of Physical Chemistry B, 1998
- Analysis of fluorescence lifetime data for single Rhodamine molecules in flowing sample streamsAnalytical Chemistry, 1994
- A tutorial on hidden Markov models and selected applications in speech recognitionProceedings of the IEEE, 1989
- Monte Carlo sampling methods using Markov chains and their applicationsBiometrika, 1970