An Experimental Comparison of the Maximum Likelihood Estimation and Nonlinear Least-Squares Fluorescence Lifetime Analysis of Single Molecules

Two procedures based on the weighted least-squares (LS) and the maximum likelihood estimation (MLE) method to confidently analyze single-molecule (SM) fluorescence decays with a total number (N) of 2,500-60,000 counts have been elucidated and experimentally compared by analyzing measured bulk and SM decays. The key observation of this comparison is that the LS systematically underestimates the fluorescence lifetimes by approximately 5%, for the range of 1,000-20,000 events, whereas the MLE method gives stable results over the whole intensity range, even at counts N less than 1,000, where the LS analysis delivers unreasonable values. This difference can be attributed to the different statistics approaches and results from improper weighting of the LS method. As expected from theory, the results of both methods become equivalent above a certain threshold of N detected photons per decay, which is here experimentally determined to be approximately 20,000. In contrast to the bulk lifetime distributions, the SM fluorescence lifetime distributions exhibit standard deviations that are sizably larger than the statistically expected values. This comparison proves the strong influence of the inhomogenuous microenvironment on the photophysical behavior of single molecules embedded in a 10-30-nm thin polymer layer.