An optimization algorithm for single-molecule fluorescence resonance (smFRET) data processing

Abstract

The single-molecule fluorescence resonance energy transfer (smFRET) technique plays an important role in the development of biophysics. Measuring the changes of the fluorescence intensities of donor and acceptor and of the FRET efficiency can reveal the changes of distance between the labeling positions. The smFRET may be used to study conformational changes of DNA, proteins and other biomolecules. Traditional algorithm for smFRET data processing is highly dependent on manual operation, leading to high noise, low efficiency and low reliability of the outputs. In the present work, we propose an automatic and more accurate algorithm for smFRET data processing. It consists of three parts: algorithm for automatic pairing of donor and acceptor fluorescence spots based on negative correlation between their intensities; algorithm for data screening by eliminating invalid fluorescence spots sections; algorithm for global data fitting based on Baum-Welch algorithm of hidden Markov model (HMM). Based on the law of energy conservation, the light intensity of one pair of donor and acceptor shows a negative correlation. We can use this feature to find the active smFRET pairs automatically. The algorithm will first find out three active smFRET pairs with correlation coefficient lower than the threshold we set. This three active smFRET pairs will provide enough coordinate data for the algorithm to calculate the pairing matrix in the rest of automatic pairing work. After obtaining all the smFRET pairs, the algorithm for data screening will check the correlation coefficient for each pair. The invalid pairs with correlation coefficient higher than the threshold value will be eliminated. The rest of smFRET pairs will be analyzed by the data fitting algorithm. The Baum-Welch algorithm can be used for learning the global parameters. The global parameters we obtained will then be used to fit each FRET-time curve with Viterbi algorithm. The global parameter learning part will help us find the specific FRET efficiency for each state and the curve fitting part will provide more kinetic parameters. The optimization algorithm significantly simplifies the procedures of manual operation in the traditional algorithm and eliminate several types of noises from the experimental data automatically. We apply the new optimization algorithm to the analyses of folding kinetics data for human telomere repeat sequence, the G-quadruplex DNA. It is demonstrated that the optimization algorithm is more efficient to produce data with higher S/N ratio than the traditional algorithm. The final results reveal clearly the folding of G-quadruplex DNA in multiple states that are influenced by the K+ concentration.