Possibilities and limitations of the time-correlated single photon counting technique: a comparative study of correction methods for the wavelength dependence of the instrument response function

One of the principal reasons for poor fits in time-correlated single photon counting fluorescence decay measurements is the wavelength dependence of the instrument response function. Over the years several correction methods have been developed to account for or correct for this effect. The most recent and widely used procedures are critically compared in this paper. A comparison of the channel shift technique, the pseudoscatterer technique, the excitation pulse-shape mimic technique and the delta function convolution method demonstrates that the latter method is the superior one. This method requires the measurement of the fluorescence decay of a reference compound with single exponential decay kinetics under identical conditions as used for the sample. A modified functional form is used to describe the sample decay law. Since no experimental data are altered in any way, a correct residual analysis is possible. Simulations show that fluorescence lifetimes can be recovered accurately, as long as the reference decay time is sufficiently different from that of the sample. Biexponential decays can be resolved successfully when the two decay times are well separated and different from that of the reference. The difference between the standard normal variates of chi-square for single and double exponential fits can be used to distinguish between mono- and bi-exponential decays. The usefulness of the delta function convolution method is demonstrated by fluorescence decay measurements of a series of different samples with very short decay times. Fluorescence lifetimes as short as 10 ps could be resolved accurately and reliably.     

Analysis of S2QA- charge recombination with the Arrhenius, Eyring and Marcus theories

The Q band of photosynthetic thermoluminescence, measured in the presence of a herbicide that blocks electron transfer from PSII, is associated with recombination of the S(2)Q(A)(-) charge pair. The same charge recombination reaction can be monitored with chlorophyll fluorescence. It has been shown that the recombination occurs via three competing routes of which one produces luminescence. In the present study, we measured the thermoluminescence Q band and the decay of chlorophyll fluorescence yield after a single turnover flash at different temperatures from spinach thylakoids. The data were analyzed using the commonly used Arrhenius theory, the Eyring rate theory and the Marcus theory of electron transfer. The fitting error was minimized for both thermoluminescence and fluorescence by adjusting the global, phenomenological constants obtained when the reaction rate theories were applied to the multi-step recombination reaction. For chlorophyll fluorescence, all three theories give decent fits. The peak position of the thermoluminescence Q band is correct by all theories but the form of the Q band is somewhat different in curves predicted by the three theories. The Eyring and Marcus theories give good fits for the decreasing part of the thermoluminescence curve and Marcus theory gives the closest fit for the rising part.     

Mathematical functions for the analysis of luminescence decays with underlying distributions: 2. Becquerel (compressed hyperbola) and related decay functions

The Becquerel (compressed hyperbola) decay law is analyzed in detail and shown to be an interesting approach for the analysis of complex luminescence decays. A decay function unifying the modified Kohlrausch and Becquerel decay laws is also introduced. It is proposed that the analysis of luminescence decays with a sum of Becquerel functions is a powerful alternative to the usual sum of exponentials. It is also shown that some complex decay laws can be written as a sum of an infinite number of exponentials and have for this reason an infinite but discrete spectrum of rate constants.     

Intramolecular monomer and excimer fluorescence with dipyrenylpropanes: double-exponential versus triple-exponential decays

The fluorescence decays of 1,3-di(1-pyrenyl)propane undergoing intramolecular excimer formation can be fitted to a sum of three exponentials, whereas only two exponentials are needed for 1,3-di(2-pyrenyl)propane. It is concluded, from an analysis of the decay parameters, that one monomer and two excimers are involved in the excimer formation for 1,3-di(1-pyrenyl)-propane, in contrast with that for 1,3-di(2-pyrenyl)propane where only one excimer and one monomer are needed in the kinetic scheme. Kinetic and thermodynamic data are presented for both molecules. The significance of the various cases (double and higher) of multi-exponential decay is discussed.     

USE OF A PULSED LASER DIODE TO MEASURE PICOSECOND FLUORESCENCE LIFETIMES

Abstract— The use of an inexpensive pulsed laser diode (Hamamatsu picosecond light pulser PLP-01) as the excitation source for a single photon timing spectrolluorimeter with microchannel plate photomultiplier detection was dem-onstrated. The performance of the instrument was tested with two very short-lived fluorescent dyes and two pho-tosynthetic systems with wcll-defined decay characteristics. Individual fluorescence decays were analyzed by modeling with a convolution of the instrument response function to a sum of exponential decay components. Accurate fluorcscence lifetimcs of the dyes cryptocyanine (55 ps in acetone and 83 ps in ethanol) and 1,1'-diethyl-2,2'-dicarbocyanine iodide (13 ps in acetone and 26 ps in ethanol) were obtained by analysis of the decay kinetics with a single exponential component. Fits to the fluorescence decay kinetics of isolated photosystem I particles and intact cyanobacterial cells required three and four decay components. respectively. The decay kinetics of the isolated photosystem I preparation were dominated (99%) by a very fast 9 ps lifetime, reflecting the preparation's small antenna size of approximately 30 chlorophyll a . The cyanobackria showed decay components of 35 ps, 160 ps, 400 ps and 1.95 ns similar to those described previously by Mullincaux and Holzwarth ( Rinchim. Biophys. Acfa 1098 , 68–78, 1991). The performance of the pulsed laser diode as an excitation source for single photon timing is discussed in comparison with conventional sources of picosecond light pulses.     

Non‐linear least‐squares and chemical kinetics. An improved method to analyse monomer‐excimer decay data

The least squares fitting of experimental results with a non‐linear model can result in a serious loss of accuracy in the model parameters estimation if the statistical nature of the method is not correctly considered. This occurs when the experimental data is fitted to a set of functional parameters that depend in the model parameters to be estimated in the end. A realistic example can be found in the two state model of monomer‐excimer kinetics. The decay curves of the monomer and excimer are a sum and a difference of two exponentials, respectively. It is usual to fit the experimental decays in order to obtain the pre‐exponential factors and decay constants, thus using a reparametrization that is non‐linear with respect to the model parameters. This procedure is thoroughly discussed and a new method to analyse the decay curves that circumvents the problem of reparametrization is presented. The proposed method yields improved results with less than 7% bias in the recovered rate constants. Monte Carlo simulations have been performed in order to obtain confidence intervals for the fitting and model parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Rapid evaluation of the Voigt function and its use for interpreting X-ray photoelectron spectroscopic data

While the Voigt function is recognized as the best function to represent the photoelectron spectroscopic process, it is less frequently used because it cannot be represented as an analytical function and thus has to be evaluated numerically. This paper shows how the true Voigt function can be calculated rapidly with approximately the same speed as pseudo-Voigt functions by using approaches that have been used by the astronomical sciences community. The Voigt function is calculated using code previously published by Wells. The paper describes a method for calculating the function to generate photoelectron peaks for curve fitting X-ray photoelectron spectroscopic data. An appendix is provided with the listing of a Fortran 90 program which uses the subroutine HUMDEV published by Wells. Examples of using this approach for the fitting of experimental core X-ray photoelectron spectroscopic data are presented, and the fits compared with fits using a pseudo Voigt product function. The use of the true Voigt function in the calculation of spectra in the core and valence band region is also described and illustrated by comparing the calculated spectra with experimental spectra.     

AN EVALUATION OF CHARGE EFFECTS ON THE QUENCHING OF TRYPTOPHAN FLUORESCENCE IN SMALL PEPTIDES BY IODIDE ION

Abstract— Charge effects on the quenching of tryptophan fluorescence in small peptides by iodide ion have been analyzed by the conventional "static" quenching model and by a recently proposed competitive quenching model. The former involves a fit of the quenching data using two quenching parameters—one for dynamic and one for static quenching contributions. The latter model involves a single parameter fit in which the fitting parameter is the characteristic rate constant for quenching of the fluorescent state. Both models indicate a clear charge effect on the efficiency of quenching by iodide ion. However, the static model results are obscured by the interdependence of the two fitting parameters and the fact that the true physical meaning of the static parameter is uncertain. Rate constants derived from the competitive model can be converted into relative quenching efficiencies. These efficiencies, which vary by more than a factor of two for the molecules studied, are greatest when the positive charge is on the tryptophan and least when this residue contains a negative charge.     

Theoretical evaluation of methods for extracting retention factors and kinetic rate constants in liquid chromatography

A three-dimensional stochastic simulation is used to provide a detailed understanding of mass transfer processes in liquid chromatography. In this simulation, the migration of individual molecules is established through diffusion and laminar convection within the mobile phase. The molecules interact with the stationary phase by a partition (absorption) mechanism. For these studies, the column length, linear velocity, stationary-phase diffusion coefficient, interfacial mass transfer coefficient, and equilibrium constant are varied in a system with a homogeneous surface. Heterogeneous surfaces are also investigated by having multiple types of interaction sites that are equally or unequally distributed. For each simulation, the molecular distribution is examined and characterized at specified times or column lengths. Five individual methods are then applied to extract the thermodynamic and kinetic information for transport between the mobile and stationary phases. In the first method, all of the molecules are initially distributed in the mobile phase and the fraction remaining is monitored as a function of time. These simulation data are fit to a single exponential decay by nonlinear regression to determine the "true" retention factors and rate constants. The other methods rely on evaluating the shape of the zone profiles along the column. The statistical moments of the profiles are used to calculate the mean and the variance, which are related to the retention factors and the rate constants, respectively. The profiles are also fit to the exponentially modified Gaussian equation, the Giddings equation, and the Thomas equation. The fitting parameters from these equations are then used to calculate the retention factors and rate constants. Comparisons of the accuracy relative to the "true" retention factors and "true" rate constants, as well as the advantages and limitations of each method are discussed.     

PowerSlicing to determine fluorescence lifetimes of water-soluble organic matter derived from soils,plant biomass,and animal manures

Time-resolved fluorescence spectroscopy was used to characterize water-soluble organic matter (WSOM) which plays an important role in soil ecosystem processes. WSOM was extracted from plant biomass, animal manures, and soils from controlled cropping systems studies with known histories of organic amendments. Lifetime constants were derived using the multi-way PowerSlicing method which provides a non-iterative, multi-exponential fitting of decay profiles. The lifetimes obtained by PowerSlicing were not significantly different from those obtained using the traditional discrete components analysis. The three components attributed to WSOM had lifetimes of 0.38 ± 0.14, 2.11 ± 0.72, and 7.08 ± 1.18 ns which are in agreement with previous lifetimes reported for humic substances. This study provides further support for the new paradigm for the structure of soil organic matter where the organic matter is composed of low-molecular-weight components held together by hydrogen bonding and hydrophobic interactions.     

Multi-exponential analysis of the fluorescence decays of 9-cyano-10-t-butylanthracene in PMMA

With the time-correlated single-photon counting technique, the dynamic behaviour of the excited singlet state of the title compound has been investigated under various conditions. In poly(methyl methacryiate) (PMMA) it exhibits temperature-dependent multi-exponential decays, mostly two exponentials below 153 K but three at higher temperatures. The relative fluorescence yields obtained in PMMA from the static measurements disagree with fluorescence quantum yields calculated from the lifetimes of each component. This discrepancy implies a very fast radiationless process from S₁ to S₀ (>10¹⁰ s⁻¹). Its existence could not be deduced without detailed multi-exponential analysis.     

Decay time distribution analysis of Yt-base in benzene-methanol mixtures

Frequency-domain fluorometry was used to measure intensity decays of synthetic Yt-base in mixtures of benzene-methanol at 20 degrees C. Multiexponential analysis shows that the decay of Yt-base fluorescence in benzene and methanol can be well fitted to a single-exponential model with tau = 9.67 ns and 6.25 ns respectively. In mixtures of benzene-methanol the decays became heterogeneous, and the maximum of heterogeneity observed was in a mixture containing 6% methanol. Since we expected a distribution of Yt-base solvation states in the solvent mixtures, and because the decay times of Yt-base are sensitive to solvent, we analyzed the data in terms of decay time distributions. The goodness-of-fit for the unimodal distribution model which has two floating parameters was equivalent to that found using the double exponential model with three floating parameters. The Lorentzian distribution model appears to provide a slightly superior fit relative to the Gaussian distribution model. These results suggest that the intensity decays of solvent-sensitive fluorophores in mixed solvents are described by a distribution of decay times.     

Development of a fluorescence model for the determination of constants associated with binding,quenching, and Förster resonance energy transfer efficiency

Determining accurate dissociation constants for equilibrium processes involving a fluorescent mechanism can prove to be quite challenging. Typically, titration curves and nonlinear least squares fitting of the data using computer programs are employed to obtain such constants. However, these approaches only consider the total fluorescence signal and often ignore other energy transfer processes within the system. The current model considers the impact on fluorescence from equilibrium binding (viz., metal-ligand, ligand-substrate, etc.), quenching, and resonance energy transfer. This model should provide more accurate binding constant as well as insights into other photonic processes. The equations developed for this model are discussed and are applied to experimental data from titrimetric experiments. Since the experimental data are generally in excess of the number of parameters that are needed to define the system, fitting is operated in an overdetermined mode and employs error minimization (either absolute or relative) to define goodness of fit. Examples of how changes in certain parameters affect the shape of the titrimetric curve are also presented. The current model does not consider chelation-enhanced fluorescence.     

A guide to accurate measurement of diffusion using fluorescence correlation techniques with blinking quantum dot nanoparticle labels

Fluctuation-based fluorescence correlation techniques are widely used to study dynamics of fluorophore labeled biomolecules in cells. Semiconductor quantum dots (QDs) have been developed as bright and photostable fluorescent probes for various biological applications. However, the fluorescence intermittency of QDs, commonly referred to as "blinking", is believed to complicate quantitative correlation spectroscopy measurements of transport properties, as it is an additional source of fluctuations that contribute on a wide range of time scales. The QD blinking fluctuations obey power-law distributions so there is no single characteristic fluctuation time for this phenomenon. Consequently, it is highly challenging to separate fluorescence blinking fluctuations from those due to transport dynamics. Here, we quantify the bias introduced by QD blinking in transport measurements made using fluctuation methods. Using computer simulated image time series of diffusing point emitters with set "on" and "off" time emission characteristics, we show that blinking results in a systematic overestimation of the diffusion coefficients measured with correlation analysis when a simple diffusion model is used to fit the time correlation decays. The relative error depends on the inherent blinking power-law statistics, the sampling rate relative to the characteristic diffusion time and blinking times, and the total number of images in the time series. This systematic error can be significant; moreover, it can often go unnoticed in common transport model fits of experimental data. We propose an alternative fitting model that incorporates blinking and improves the accuracy of the recovered diffusion coefficients. We also show how to completely eliminate the bias by applying k-space image correlation spectroscopy, which completely separates the diffusion and blinking dynamics, and allows the simultaneous recovery of accurate diffusion coefficients and QD blinking probability distribution function exponents.     

Experimental design for the estimation of photophysical parameters of the two-state excited-state proton-exchange reaction in the presence of pH buffer

The excited-state proton-exchange reaction of commonly used fluorescent pH probes at physiological pH becomes reversible upon addition of pH buffer. Using computer-generated fluorescence decay surfaces, we investigated under which experimental conditions (pH, buffer concentration, and excitation and emission wavelengths) the rate constants describing the excited-state processes (k(ij)) and the spectral parameters related to excitation ((~)b(1)) and emission ((~)c(1)) can be accurately and precisely estimated by global compartmental curve fitting. It was found that a minimum of three fluorescence decay traces should be collected for the pH probe in the presence of buffer. These three decays should be characterized by at least two different pH values and at least two different buffer concentrations. In addition to these three traces, a minimum of one trace corresponding to the pH probe without buffer has to be recorded. Furthermore, for the accurate estimation of k(ij), (~)b(1), and (~)c(1), at least two of these traces should be collected at the same pH and excitation and emission wavelengths. The experimental conditions should be chosen in such a way that decays with unambiguous biexponential character are obtained. For fluorescent pH probes with pK(a) approximately equal to 7 that are responsive in the near-neutral pH range, it is advisable to use buffers with pK(B)(a) values comparable to or higher than the pK(a) of the probe. Because the changes in the decay times are already apparent with a small quantity of buffer, there is no need to use excessively high buffer concentrations. From a practical point of view, the best experimental design is attained when one combines in a single fluorescence decay surface traces originating from samples characterized by different pH values at the same buffer concentration with traces characterized by different buffer concentrations at the same pH and decays of samples without buffer measured at several pH values.     

Photophysical properties of β-(1-pyrenyl)ethyl p-cyanobenzoate in binary solvents of isooctane-ethyl acetate and ethyl acetate-acetonitrile

The effects of solvent polarity on the fluorescence spectra and fluorescence decays of β-(1-pyrenyl)ethyl p-cyanobenzoate (P2CN) were investigated in detail using binary solvents consisting of various mixing ratios of isooctane-ethyl acetate or ethyl acetate-acetonitrile (dielectric constants ()=1.94–36.2). Whereas both the intensity and wavelength maxima of an intramolecular exciplex emission (EX) are dependent on the solvent polarity, only the intensity of an emission from the locally excited pyrene (LE) is dependent on the solvents used. When monitored at 377 nm, the picosecond SPC (single photon counting) measurements reveal a slow decay (>150 ns) in addition to a fast decay (<1 ns) of the locally excited P2CN. There are also two decays for the EX which vary the intensity ratios by the monitored wavelength. The decay rate constants, k_EX1 and k_EX2, have a good linear correlation with the dielectric constants of the solvents, indicating that there exist two kinds of exciplexes. It is suggested that the decays of the locally excited-state of P2CN are so fast due to result of the efficient electron transfer that the two kinds of intramolecular exciplexes are formed from the two discrete conformers in the ground state.     

Stochastic approach to data analysis in fluorescence correlation spectroscopy

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).     

An Optical Fiber-Based Spectrometer for Measurement of Fluorescence Lifetimes

An instrument is described which measures fluorescence intensity and lifetime properties using a single optical fiber for the development of fiber optic chemical sensors. The instrument utilizes a fast-pulse nitrogen laser for excitation and a digital storage oscilloscope to provide time-resolved fluorescence decay curves. The time-resolved measurements permitted the separation of most of the scattered excitation radiation from the sample signal and allowed for analysis of samples exposed to ordinary room lighting. A method for determination of lifetimes from the time-resolved decays was developed based on the time-correlated single-photon counting method. The new method used reference fluorophore solutions to determine the instrument response function, including the influence of the optical fiber, and multiple decays were averaged to improve signal-to-noise and to provide statistical weighting for the analysis. The accuracy of the lifetime analysis was demonstrated by comparison of results for Stern-Volmer quenching of quinine sulfate by chloride ion (slope = 0.115 ± 0.001, int. = 1.04 ± 0.04, r² = 0.9992) with a literature study on the same system (slope = 0.118 ± 0.002, int. = 1.06 ± 0.05, r² = 0.9986). Measurement of the lifetime of pyrene in ethanol gave 17.8 ± 0.9 ns, while the value for coumarin was 3.82 ± 0.45 ns. When mixed together, two lifetimes with values of 17.43 ± 0.73 and 3.68 ± 1.30 ns were determined.     

Generalized two-dimensional heterocorrelation analysis of spectrally resolved and temporally resolved fluorescence of the 8-anilino-1-naphthalenesulfonate-apomyoglobin complex with pH perturbation

We demonstrate two-dimensional heterocorrelation analysis between spectrally resolved and temporally resolved fluorescence to investigate the decay dynamics of the 8-anilino-1-naphthalenesulfonate- (ANS-) apomyoglobin complex. The dynamic changes of the lifetime components are disclosed across the emission spectrum with an external pH-perturbation. Two different fluorescence lifetime schemes of the ANS-apomyoglobin complex are revealed. From pH 8.5 to 4.5, the transition of protein conformation from the native state to the folding intermediate, a short lifetime component is found to correlate with a short-wavelength emission whose population diminishes with decreasing pH. The lifetime components reflect the excited-state populations of the nascent and the charge-transfer species. From pH 4.2 to 1.0, the transition from the folding intermediate to the acid-unfolded state, the short lifetime is responsible for a long-wavelength emission and the fraction of this component increases when the solution becomes more acidic. In this pH range, the decay components reflect the ground-state populations of microenvironments. The relative decay dynamics across the emission spectrum are revealed without collecting decays at each wavelength. More importantly, these conclusions are reached without the necessity of statistical fitting of the decay data with an a priori decay model.