Stochastic Approach to Data Analysis in Fluorescence Correlation Spectroscopy

Abstract

Fluorescence correlation spectroscopy (FCS) has emerged as a powerful technique for measuring low concentrations of fluorescent molecules and their diffusion constants. In FCS, the experimental data is conventionally fit using standard local search techniques, for example, the Marquardt-Levenberg (ML) algorithm. A prerequisite for these categories of algorithms is the sound knowledge of the behavior of fit parameters and in most cases good initial guesses for accurate fitting, otherwise leading to fitting artifacts. For known fit models and with user experience about the behavior of fit parameters, these local search algorithms work extremely well. However, for heterogeneous systems or where automated data analysis is a prerequisite, there is a need to apply a procedure, which treats FCS data fitting as a black box and generates reliable fit parameters with accuracy for the chosen model in hand. We present a computational approach to analyze FCS data by means of a stochastic algorithm for global search called PGSL, an acronym for Probabilistic Global Search Lausanne. This algorithm does not require any initial guesses and does the fitting in terms of searching for solutions by global sampling. It is flexible as well as computationally faster at the same time for multiparameter evaluations. We present the performance study of PGSL for two-component with triplet fits. The statistical study and the goodness of fit criterion for PGSL are also presented. The robustness of PGSL on noisy experimental data for parameter estimation is also verified. We further extend the scope of PGSL by a hybrid analysis wherein the output of PGSL is fed as initial guesses to ML. Reliability studies show that PGSL and the hybrid combination of both perform better than ML for various thresholds of the mean-squared error (MSE).

Automatic Analysis of Composite Physical Signals Using Non-Negative Factorization and Information Criterion

“…The objective function given by Eq. (6) represents the divergence between I ji and ( wh ) ji , and the objective function of the fitting method is usually represented using the LSE [14]. Thus, we propose an objective function for BzNMF to minimize LSE, as follows:In BzNMF, the time constants τ r and the non-negative coefficients h are optimized to estimate the approximations.…”

“…In [13], the objective function of BzNMF was defined by the generalized Kullback-Leibler (KL) divergence. However, in physical chemistry [14], optimization problems are usually solved using the method of least square error (LSE).…”

Systematic evaluation of fluorescence correlation spectroscopy data analysis on the nanosecond time scale

“…Stochastic approaches were developed to enable highthroughput fitting procedures independent of manually chosen starting values. 32 Model functions are also optimized in a more general way by using maximum likelihood estimation or maximum entropy methods. For rating a finite number of competing model functions Bayesian inference testing was employed.…”

Information Content in Fluorescence Correlation Spectroscopy: Binary Mixtures and Detection Volume Distortion

“…The general utility of FCS has been widely recognized for decades. Both the older and more-recent FCS literature contains considerable discussion regarding the reliability and interpretation of FCS information. − Although these studies explore various aspects of the measurement technique or data analysis individually, the principal factors contributing to systematic bias in FCS are inherently inter-related. These factors include (1) a lack of correspondence between the 3D geometry of the experimental DV and the geometry assumed in the mathematical model; (2) a lack of correspondence between the presumed molecular dynamics and the dynamics actually occurring in the sample; (3) the effectiveness of the mathematical fit and its tolerance to local minima for a given number of model parameters; and (4) the signal-to-noise ratio present in the correlation data.…”