Hidden Markov Modelling of Single Molecule FRET Trajectories

The development of single-molecule fluorescence energy transfer (FRET) microscopy has provided ground-breaking insights to many biological systems. While the acquisition and pre-data processing side of the technique have been much improved since, the data analysis for determining transition rates between states often still relies on simple and arbitrary methods such as applying thresholds and inspection-by-eye. In this project, the application of Hidden Markov Modelling (HMM) for the analysis of single-molecule FRET trajectories was investigated and a method was developed to study the system involving the interactions between Klenow fragment and DNA, using information available from acceptor excitation acceptor emission time trace (AA), donor excitation donor emission time trace (DD), and donor excitation acceptor emission time trace (DA), as well as the proxomity ratio E and stoichiometry ratio S. The results from simulations with known parameters indicate the HMM is very accurate in recovering the true sequence if the difference between FRET states is larger than 0.2 and the standard deviation of the emission probability is less than 0.1, and if there is more than 1 transition per 100 steps. The Akaike and Bayesian information criterion (AIC and BIC) were used to determine the optimal number of states in the system and the results indicate the optimal number of states in E and S to be 4 and 3 states respectively. Based on the HMM analysis on E and S, the presence and dynamics between different populations such as one KF binding on the 5’ or the 3’end of the DNA and two KF binding on the DNA were observed.