Optimal Statistical Methods for Analysis of Single-Molecule Data
Time-resolved single molecule fluorescence measurements are important probes for the conformational dynamics of biological macromolecules. The best time resolution in such techniques will only be achieved by measuring the arrival times of individual photons at the detector and by making a detailed statistical analysis of the photon arrival time data. This work presents several general approaches to the estimation of molecular parameters based on individual photon arrival times. In the first, the amount of information present in a data set involving continuous intramolecular motion is quantified by the Fisher information, allowing an algorithm to be constructed which achieves the theoretical limits on time and distance resolution. The second approach is tailored to the analysis of discrete intensity jumps in optical measurements of single molecules or single particles. It uses a recursive generalized likelihood ratio test to determine the location of intensity change points directly from individual photon arrival times. Third, a maximum entropy approach is taken to molecular probability density function estimation. This approach takes advantage of the information measurements previously derived, and avoids the over-fitting produced by straightforward deconvolution methods. All of these analysis methods are applied to measure the persistence length of a series of polyproline oligopeptides.