Statistical methods in single particle fluorescence microscopy

Doctoral thesis, 2013

The aim of this thesis is stochastic modeling and statistical inference in single particle fluorescence microscopy related to the experimental observation of randomly moving particles. A central theme is the use of single particle microscopy for estimation of absolute concentration of nanoparticles performing Brownian motion. In Papers I and II, the monodisperse case, i.e.\ one single diffusion coefficient, is considered. The key idea is to estimate the absolute concentration by first estimating the size of the three-dimensional detection region in which particles are observed. In earlier works, this has been estimated in separate calibration experiments. In Paper I, the detection region size is estimated by modeling the distribution of trajectory lengths (durations) as a function of the size. In Paper II, an alternative method is suggested by studying transition probabilities in a time series of particle counts known as a Smoluchowski process. It is demonstrated that both methods provide very good agreement with reference values and with each other. Paper III is partly based on Paper I, generalizing the results to the polydisperse case, i.e.\ with a distribution of diffusion coefficients. It is shown that the distribution of diffusion coefficients as well as the total absolute concentration can be satisfactorily estimated. One crucial step in single particle microscopy is the correct classification of particles and noise in microscope images, since both false negatives and false positives can have a substantial impact on all further analysis. Typically, a plausible set of particles is obtained from a larger set of candidate particles by filtering using manually selected threshold values for intensity, size, shape, and other parameters. In Paper IV, a novel method for automatic selection of such threshold values is introduced, based on an analysis of the correlation structure of a Smoluchowski process distorted by false negatives and false positives. The method shows promise and provides a new paradigm in automated image analysis for single particle microscopy.