A new analysis method of single molecule fluorescence using series of photon arrival times: theory and experiment

Abstract

Up to now, single molecule fluorescence experiments were performed by dividing the time into a set of intervals and to observe the number of fluorescence photons arriving in each interval. It is obvious that the detected photons carry less information than the arrival times of the photons themselves. From the arrival times, one can still calculate the number of photons in any user-defined interval; whereas, when only the number of photons in an interval are recorded, information about their positions in time is lost. Therefore, we present a new analysis method of single molecule fluorescence data based on the positions in time of the detected fluorescence photons. We derive mathematically different statistical characteristics describing the single molecule fluorescence experiment assuming an immobilized molecule. The theory of point processes using the generating functionals formalism is ideally suited for a consistent description, linking the statistical characteristics of the excitation and detected photons to the statistical characteristics of the single motionless molecule. We then use computer-generated data sets mimicking the single molecule fluorescence experiment to explore the parametric estimation of mono- and bi-exponential single molecule impulse response functions (SMIRFs) via the following statistical characteristics: the probability density distributions (pdd) of the single and first photocount time positions in a user-defined detection interval, the probability distribution of the number of photocounts per user-defined detection interval, the time correlation function and the pdd of the time interval between two consecutive photocounts. It is shown that all of the above characteristics ensure a satisfactory recovery of the decay time of mono-exponential SMIRFs for a broad range of excitation intensities and widths of user-defined detection intervals. For bi-exponential SMIRFs, the selection of the experimental conditions is more critical and dependent on the detection procedure. At lower excitation intensities it is advantageous to use the pdds of the single and first photocount time occurrences in the user-defined detection interval. To show the practical usefulness of the new analysis method, series of photon arrival times from immobilized single molecules of DiI and rhodamine 6G were analyzed to estimate triplet lifetimes and intersystem crossing yields.