Analysis of the steps in single-molecule photobleaching traces by using the hidden markov model and maximum-likelihood clustering.

The step analysis of single-molecule photobleaching data offers a new approach for studying protein stoichiometry under physiological conditions. As such, it is important to develop suitable algorithms that can accurately extract the step events from the noisy single-molecule data. Herein, we report a HMM method that combines maximum-likelihood clustering for initializing the emission-probability distribution of the HMMs with an extended silhouette clustering criterion for estimating the state number of single molecules. In this way, the limitations of standard HMM in terms of processing typical single-molecule data with a short sequence are overcome. By using this method, the number and time points of the step events are automatically determined, without the introduction of any subjectivity. Simulation experiments on the experimental photobleaching data indicate that our method is very effective and robust in the analysis of single-molecule fluorescence photobleaching curves if the signal/noise ratio is larger than 2:1. This method was employed for processing photobleaching data that were obtained from single-molecule fluorescence imaging of transforming growth factor typeII receptors on a cell surface. This method is also expected to be applicable to the analysis of other stepwise events.