Fluorescence cumulants analysis with non-ideal observation profiles.

One of the challenges of fluorescence fluctuation fpectroscopy (FFS) is an adequate approximation of a brightness profile. The key feature of fluorescence intensity distribution analysis (FIDA) is a polynomial approximation of a brightness profile. A broad range of brightness profile shapes can be well described by this approximation. A different approach consisting of the introduction of additional fitting parameters, defined as a relative difference between integrals of the actual brightness profile and its Gaussian approximation, is used in photon counting histogram (PCH) analysis. It is sufficient to introduce only one additional fitting parameter (first-order correction) to get an adequate fit to the experimental data in many practical applications. In the current study, we apply these approaches to the theory of time integrated fluorescence cumulants analysis. We demonstrate that developed corrections improve results of FFS analysis applied to simulated and experimental data. The use of different brightness profile approximations and normalizations in PCH and FIDA leads to different estimates of brightness and the number of molecules, even though they represent the same physical quantities. Based on the developed theory, we derive equations that relate brightness and the number of molecules in PCH and FIDA.

Global analysis of time-resolved fluorescence data.

In this chapter, we describe the global analysis approach for processing time-resolved fluorescence spectroscopy data of molecules in the condensed phase. Combining simultaneous analysis of data measured under different experimental conditions (spatial coordinates, temperature, concentration, emission wavelength, excitation intensity, etc.) with the fitting strategy, enabling parameter linkage and thus decreasing the total amount of estimated variables, makes global analysis more robust and more consistent compared to a sequential fit of single experimental data. We consider the main stages of the global analysis approach and provide some details that are important for its practical implementation. The application of the global approach to the analysis of time-resolved fluorescence anisotropy is demonstrated on experimental data of (enhanced) green fluorescent protein in aqueous solution.

Simulation of autocorrelation function and photon counting distribution in fluorescence fluctuation spectroscopy.

In modern fluorescence fluctuation spectroscopy, the autocorrelation function and photon counting distribution are two widely used statistical characteristics of the measured fluctuating fluorescence intensity signal. Applying special analysis methods such as fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) to these properties, it is possible to recover values of different parameters of fluorescent molecules such as the concentration, diffusion coefficient, molecular brightness, and kinetic rate constants. The development of new analysis methods is senseless without testing their validity, accuracy, and robustness. The most appropriate check of a method is its application to experimental data. However, sometimes it is more convenient and easier to verify a method on simulated data. Simulation is also useful for better understanding the processes that were modeled during the development of analysis methods. Here, we present two simulation models providing an autocorrelation function and photon counting distribution of a sequence of photon arrival times detected in fluorescence fluctuation spectroscopy.

Global analysis of autocorrelation functions and photon counting distributions in fluorescence fluctuation spectroscopy.

In fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis, the same experimental fluorescence intensity fluctuations are used, but each analytical method focuses on a different property of the signal. The time-dependent decay of the correlation of fluorescence fluctuations is measured in FCS yielding molecular diffusion coefficients and triplet-state parameters such as fraction and decay time. The amplitude distribution of these fluctuations is calculated by PCH analysis yielding the molecular brightness. Both FCS and PCH give information about the molecular concentration. Here we describe a global analysis protocol that simultaneously recovers relevant and common parameters in model functions of FCS and PCH from a single fluorescence fluctuation trace. Application of a global analysis approach allows increasing the information content available from a single measurement that results in more accurate values of molecular diffusion coefficients and triplet-state parameters and also in robust, time-independent estimates of molecular brightness and number of molecules.

Simultaneous diffusion and brightness measurements and brightness profile visualization from single fluorescence fluctuation traces of GFP in living cells.

Fluorescence correlation spectroscopy (FCS) and photon-counting histogram (PCH) analysis use the same experimental fluorescence intensity fluctuations, but each analytical method focuses on a different property of the signal. The time-dependent decay of the correlation of fluorescence fluctuations is measured in FCS yielding, for instance, molecular diffusion coefficients. The amplitude distribution of these fluctuations is calculated by PCH analysis yielding information about the molecular brightness of fluorescent species. Analysis of both FCS and PCH results in the molecular concentration of the sample. Using a previously described global analysis procedure we report here precise, simultaneous measurements of diffusion constants and brightness values from single fluorescence fluctuation traces of green-fluorescent protein (GFP, S65T) in the cytoplasm of Dictyostelium cells. The use of a polynomial profile in PCH analysis, describing the detected three-dimensional shape of the confocal volume, enabled us to obtain well fitting results for GFP in cells. We could visualize the polynomial profile and show its deviation from a Gaussian profile.

A mathematical model of actin filament turnover for fitting FRAP data.

A novel mathematical model of the actin dynamics in living cells under steady-state conditions has been developed for fluorescence recovery after photobleaching (FRAP) experiments. As opposed to other FRAP fitting models, which use the average lifetime of actins in filaments and the actin turnover rate as fitting parameters, our model operates with unbiased actin association/dissociation rate constants and accounts for the filament length. The mathematical formalism is based on a system of stochastic differential equations. The derived equations were validated on synthetic theoretical data generated by a stochastic simulation algorithm adapted for the simulation of FRAP experiments. Consistent with experimental findings, the results of this work showed that (1) fluorescence recovery is a function of the average filament length, (2) the F-actin turnover and the FRAP are accelerated in the presence of actin nucleating proteins, (3) the FRAP curves may exhibit both a linear and non-linear behaviour depending on the parameters of actin polymerisation, and (4) our model resulted in more accurate parameter estimations of actin dynamics as compared with other FRAP fitting models. Additionally, we provide a computational tool that integrates the model and that can be used for interpretation of FRAP data on actin cytoskeleton.

FRET study of membrane proteins: determination of the tilt and orientation of the N-terminal domain of M13 major coat protein.

A formalism for membrane protein structure determination was developed. This method is based on steady-state FRET data and information about the position of the fluorescence maxima on site-directed fluorescent labeled proteins in combination with global data analysis utilizing simulation-based fitting. The methodology was applied to determine the structural properties of the N-terminal domain of the major coat protein from bacteriophage M13 reconstituted into unilamellar DOPC/DOPG (4:1 mol/mol) vesicles. For our purpose, the cysteine mutants A7C, A9C, N12C, S13C, Q15C, A16C, S17C, and A18C in the N-terminal domain of this protein were produced and specifically labeled with the fluorescence probe AEDANS. The energy transfer data from the natural Trp-26 to AEDANS were analyzed assuming a two-helix protein model. Furthermore, the polarity Stokes shift of the AEDANS fluorescence maxima is taken into account. As a result the orientation and tilt of the N-terminal protein domain with respect to the bilayer interface were obtained, showing for the first time, to our knowledge, an overall alpha-helical protein conformation from amino acid residues 12-46, close to the protein conformation in the intact phage.

FRET study of membrane proteins: simulation-based fitting for analysis of membrane protein embedment and association.

A new formalism for the simultaneous determination of the membrane embedment and aggregation of membrane proteins is developed. This method is based on steady-state Förster (or fluorescence) resonance energy transfer (FRET) experiments on site-directed fluorescence labeled proteins in combination with global data analysis utilizing simulation-based fitting. The simulation of FRET was validated by a comparison with a known analytical solution for energy transfer in idealized membrane systems. The applicability of the simulation-based fitting approach was verified on simulated FRET data and then applied to determine the structural properties of the well-known major coat protein from bacteriophage M13 reconstituted into unilamellar DOPC/DOPG (4:1 mol/mol) vesicles. For our purpose, the cysteine mutants Y24C, G38C, and T46C of this protein were produced and specifically labeled with the fluorescence label AEDANS. The energy transfer data from the natural tryptophan at position 26, which is used as a donor, to AEDANS were analyzed assuming a helix model for the transmembrane domain of the protein. As a result of the FRET data analysis, the topology and bilayer embedment of this domain were quantitatively characterized. The resulting tilt of the transmembrane helix of the protein is 18 +/- 2 degrees. The tryptophan is located at a distance of 8.5 +/- 0.5 A from the membrane center. No specific aggregation of the protein was found. The methodology developed here is not limited to M13 major coat protein and can be used in principle to study the bilayer embedment of any small protein with a single transmembrane domain.

Initial guesses generation for Fluorescence Intensity Distribution Analysis.

The growing number of applications of Fluorescence Intensity Distribution Analysis (FIDA) demands for new approaches in data processing, aiming at increased speed and robustness. Iterative algorithms of parameter estimation, although proven to be universal and accurate, require some initial guesses (IG) of the unknown parameters. An essential component of any data processing technology, IG become especially important in case of FIDA, since even with apparently reasonable, and physically admissible but randomly chosen IG, the iterative procedure may converge to situations where the FIDA model cannot be evaluated correctly. In the present work we introduce an approach for IG generation in FIDA experiments based on the method of moments. IG are generated for the sample parameters: brightness, concentration, and for the parameters related to experimental set-up: background, observation volume profile. A number of analytical simplifications were introduced in order to increase the accuracy and robustness of the numerical algorithms. The performance of the developed method has been tested on number of simulations and experimental data. Iterative fitting with generated IG proved to be more robust and at least five times faster than with an arbitrarily chosen IG. Applicability of the proposed method for quick estimation of brightness and concentrations is discussed.

Global analysis of fluorescence fluctuation data.

Over the last decade the number of applications of fluorescence correlation spectroscopy (FCS) has grown rapidly. Here we describe the development and application of a software package, FCS Data Processor, to analyse the acquired correlation curves. The algorithms combine strong analytical power with flexibility in use. It is possible to generate initial guesses, link and constrain fit parameters to improve the accuracy and speed of analysis. A global analysis approach, which is most effective in analysing autocorrelation curves determined from fluorescence fluctuations of complex biophysical systems, can also be implemented. The software contains a library of frequently used models that can be easily extended to include user-defined models. The use of the software is illustrated by analysis of different experimental fluorescence fluctuation data sets obtained with Rhodamine Green in aqueous solution and enhanced green fluorescent protein in vitro and in vivo.

Artificial neural network modification of simulation-based fitting: application to a protein-lipid system.

Simulation-based fitting has been applied to data analysis and parameter determination of complex experimental systems in many areas of chemistry and biophysics. However, this method is limited because of the time costs of the calculations. In this paper it is proposed to approximate and substitute a simulation model by an artificial neural network during the fitting procedure. Such a substitution significantly speeds up the parameter determination. This approach is tested on a model of fluorescence resonance energy transfer (FRET) within a system of site-directed fluorescence labeled M13 major coat protein mutants incorporated into a lipid bilayer. It is demonstrated that in our case the application of a trained artificial neural network for the substitution of the simulation model results in a significant gain in computing time by a factor of 5 x 10(4). Moreover, an artificial neural network produces a smooth approximation of the noisy results of a stochastic simulation.