Pulse fluorometry

Obviously, the larger the number of events, the better the accuracy of the decay curve. The required accuracy depends on the complexity of the b-pulse response of the system for instance, a high accuracy is of course necessary for recovering a distribution of decay times. 

When deconvolution is required, the time profile of the exciting pulse is recorded under the same conditions by replacing the sample by a scattering solution (e.g. a suspension of colloidal silica (Ludox)). 

It is important to note that the number of detected fluorescence photons must be kept much smaller that the number of exciting pulses ( 0.01-0.05 stops per pulse), so that the probability of detecting two fluorescence photons per exciting photon is negligible. Otherwise, the TAG will take into account only the first fluo- 

Picosecond diode laser heads offer an interesting alternative to mode-locked lasers. They are much less expensive. They can produce light pulses as short as 50-90 ps with repetition rates from single shot to 40-80 MHz. Peak powers up to 500 mW can be obtained. However, the main disadvantage is the absence of tunability, and the number of wavelengths is limited 375, 400, 440, 635 to 1550 nm. No wavelength below 375 nm is presently available. 

An efficient way of overcoming this difficulty is to use a reference fluorophore (instead of a scattering solution) (i) whose fluorescence decay is a single exponential, (ii) which is excitable at the same wavelength as the sample, and (iii) which emits fluorescence at the observation wavelength of the sample. In pulse fluorometry, the deconvolution of the fluorescence response can be carried out against that of the reference fluorophore. In phase-modulation fluorometry, the phase shift and the relative modulation can be measured directly against the reference fluorophore. 

It is sometimes difficult to totally remove (by the emission monochromator and appropriate filters) the light scattered by turbid solutions or solid samples. A subtraction algorithm can then be used in the data analysis to remove the light scattering contribution. 

Considerable effort has gone into solving the difficult problem of deconvolution and curve fitting to a theoretical decay that is often a sum of exponentials. Many methods have been examined (O Connor et al., 1979) methods of least squares, moments, Fourier transforms, Laplace transforms, phase-plane plot, modulating functions, and more recently maximum entropy. The most widely used method is based on nonlinear least squares. The basic principle of this method is to minimize a quantity that expresses the mismatch between data and fitted function. This quantity /2 is defined as the weighted sum of the squares of the deviations of the experimental response R(ti) from the calculated ones Rc(ti)  

In single-photon counting experiments, the statistics obey a Poisson distribution and the expected deviation r(i) is approximated to [R(b)]1 2 so that Eq. (6.38) becomes 

In practice, initial guesses of the fitting parameters (e.g. pre-exponential factors and decay times in the case of a multi-exponential decay) are used to calculate the decay curve the latter is reconvoluted with the instrument response for comparison with the experimental curve. Then, a minimization algorithm (e.g. Marquardt method) is employed to search the parameters giving the best fit. At each step of the iteration procedure, the calculated decay is reconvoluted with the instrument response. Several softwares are commercially available. 

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The most reliable method for the determination of k3 and k i is based on time-resolved experiments. Either pulse fluorometry or phase fluorometry can be used (see Chapter 6). They provide the values of the decay times from which the rate constants k3 and k i are determined from Eqs (4.52) to (4.53) and the ratio ki/k i yields K. ... 

Dr can be determined by time-resolved fluorescence polarization measurements, either by pulse fluorometry from the recorded decays of the polarized components I l and 11, or by phase fluorometry from the variations in the phase shift between J and I as a function of frequency (see Chapter 6). If the excited-state lifetime is unique and determined separately, steady-state anisotropy measurements allow us to determine Dr from the following equation, which results from Eqs (5.10) and (5.41) ... 

Knowledge of the dynamics of excited states is of major importance in understanding photophysical, photochemical and photobiological processes. Two time-resolved techniques, pulse fluorometry and phase-modulation fluorometry, are commonly used to recover the lifetimes, or more generally the parameters characterizing the S-pulse response of a fluorescent sample (i.e. the response to an infinitely short pulse of light expressed as the Dirac function S). 

Pulse fluorometry uses a short exciting pulse of light and gives the d-pulse response of the sample, convoluted by the instrument response. Phase-modulation fluorometry uses modulated light at variable frequency and gives the harmonic response of the sample, which is the Fourier transform of the d-pulse response. The first technique works in the time domain, and the second in the frequency domain. Pulse fluorometry and phase-modulation fluorometry are theoretically equivalent, but the principles of the instruments are different. Each technique will now be presented and then compared. 

Pulse fluorometry The sample is excited by a short pulse of light and the fluorescence response is recorded as a function of time. If the duration of the pulse is long... 

Fig. 6.6. Principles of pulse fluorometry and multi-frequency phase-modulation fluorometry.

The type of laser source that can be used is exactly the same as for single-photon counting pulse fluorometry (see above). Such a laser system, which delivers pulses in the picosecond range with a repetition rate of a few MHz can be considered as an intrinsically modulated source. The harmonic content of the pulse train - which depends on the width of the pulses (as illustrated in Figure 6.11) - extends to several gigahertz. 

The least-squares method is also widely applied to curve fitting in phase-modulation fluorometry the main difference with data analysis in pulse fluorometry is that no deconvolution is required curve fitting is indeed performed in the frequency domain, i.e. directly using the variations of the phase shift and the modulation ratio M as functions of the modulation frequency. Phase data and modulation data can be analyzed separately or simultaneously. In the latter case the reduced chi squared is given by... 

Typical sets of data obtained by pulse fluorometry and phase-modulation fluo-rometry are shown in Figures 6.12 and 6.13, respectively. 

To answer the question as to whether the fluorescence decay consists of a few distinct exponentials or should be interpreted in terms of a continuous distribution, it is advantageous to use an approach without a priori assumption of the shape of the distribution. In particular, the maximum entropy method (MEM) is capable of handling both continuous and discrete lifetime distributions in a single analysis of data obtained from pulse fluorometry or phase-modulation fluorometry (Brochon, 1994) (see Box 6.1). 

The maximum entropy method has been successfully applied to pulse fluorometry and phase-modulation fluorometry3- . Let us first consider pulse fluorometry. For a multi-exponential decay with n components whose fractional amplitudes are a , the d-pulse response is... 

Time-dependent anisotropy measurements 6.2.7.1 Pulse fluorometry... 

Tab. 6.2. Lifetime of various compounds in deoxygenated fluid solutions at 20 °C. Averages of the values measured by eight laboratories by either pulse fluorometry (four laboratories) or phase fluorometry (four laboratories) ...

In pulse fluorometry, we take advantage of the fact that the amplitudes of the output pulses of the TAC are proportional to the times of arrival of the fluorescence photons on the photomultiplier. Selection of a given height of pulse, i.e. of a given time of arrival, is electronically possible (by means of a single-channel analyzer) and allows us to record the fluorescence spectra at a given time t after the excitation pulse. This is repeated for various times. The method described above for phase fluorometry can also be used in pulse fluorometry. 

Decomposition of the fluorescence spectrum is possible in pulse fluorometry by analyzing the decay with a three-exponential function at each wavelength... 

Pulse fluorometry permits visualization of the fluorescence decay, whereas visual inspection of the variations of the phase shift versus frequency does not allow the brain to visualize the inverse Fourier transform ... 

No deconvolution is necessary in phase fluorometry, while this operation is often necessary in pulse fluorometry and requires great care in recording the instmment response, especially for very short decay times. 

Time-resolved emission anisotropy measurements are more straightforward in pulse fluorometry. 

Time-resolved spectra are more easily recorded in pulse fluorometry. 

The time of data collection depends on the complexity of the (5-pulse response. For a single exponential decay phase fluorometry is more rapid. For complex 5-pulse responses, the time of data collection is about the same for the two techniques in pulse fluorometry, a large number of photon events is necessary, and in phase fluorometry, a large number of frequencies has to be selected. It should be emphasized that the short acquisition time for phase shift and modulation ratio measurements at a given frequency is a distinct advantage in several situations, especially for lifetime-imaging spectroscopy. 

Although satisfactory criteria for deciding whether data are better analyzed by distributions or multiexponential sums have yet to established, several methods for determining distributions have been developed. For pulse fluorometry, James and Ware(n) have introduced an exponential series method. Here, data are first analyzed as a sum of up to four exponential terms with variable lifetimes and preexponential weights. This analysis serves to establish estimates for the range of the preexponential and lifetime parameters used in the next step. Next, a probe function is developed with fixed lifetime values and equal preexponential factors. An iterative Marquardt(18) least-squares analysis is undertaken with the lifetimes remaining fixed and the preexponential constrained to remain positive. When the preexponential... 

The mathematical basis for the exponential series method is Eq. (5.3), the use of which has recently been criticized by Phillips and Lyke.(19) Based on their analysis of the one-sided Laplace transform of model excited-state distribution functions, it is concluded that a small, finite series of decay constants cannot be used to represent a continuous distribution. Livesey and Brouchon(20) described a method of analysis using pulse fluorometry which determines a distribution using a maximum entropy method. Similarly to Phillips and Lyke, they viewed the determination of the distribution function as a problem related to the inversion of the Laplace transform of the distribution function convoluted with the excitation pulse. Since Laplace transform inversion is very sensitive to errors in experimental data,(21) physically and nonphysically realistic distributions can result from the same data. The latter technique provides for the exclusion of nonrealistic trial solutions and the determination of a physically realistic solution. These authors noted that this technique should be easily extendable to data from phase-modulation fluorometry. 

Two techniques, phase and pulse fluorometry, are used for the direct measurement of fluorescence decay rates, and their principles are described by Birks and Munro (1967), Parker (1968), and Birks (1970). The photon sampling method has proved useful and versatile. This is an iterative technique in which single photons are counted as a function of the time at which they appear after excitation and a complete decay curve is built up. (For recent references see e.g. Zimmerman et al., 1973, 1974). Wider use of the photon sampling technique will increase the precision of lifetimes obtained and extend the range of compounds studied to those with shorter lifetimes or very low fluorescence yields. 

The absorption of light is proportional to the scalar product of the incident electric field and of a molecular vector named the transition moment. Thus, excitation of an isotropic population of fluorescent species by polarized light generally creates a temporary anisotropic population of excited molecules. Molecular motions progressively destroy this anisotropy, and affect the polarization of the reemitted fluorescence light which can be studied using pulse fluorometry techniques. 

Wahl, Ph. Itecay fluorescence anisotropy (in Ref. p. 1 Wahl Ph. Nanosecond pulse fluorometry. In New Techniques in Biophysics and Cell Biology, Vol 2. New York ... 

Time-resolved fluorometry fahs into one of two categories, depending on how the fluorescence emission response is measured (1) pulse fluorometry, in which the sample is illuminated with an intense brief pulse of light and the intensity of the resulting fluorescence emission is measured as a function of time with a fast detector system, or (2) phase fluorometry, in which a continuous-wave laser illuminates the sample, and the fluorescence emission response is monitored for impulse and frequency response. ... 

In the first section, steady-state spectroscopy is used to determine the stoichiometry and association constants of molecular ensembles, emphasize the changes due to light irradiation and provide information on the existence of photoinduced processes. Investigation of the dynamics of photoinduced processes, i.e. the determination of the rate constants for these processes, is best done with time-resolved techniques aiming at determining the temporal evolution of absorbance or fluorescence intensity (or anisotropy). The principles of these techniques (pulse fluorometry, phase-modulation fluorometry, transient absorption spectroscopy) will be described, and in each case pertinent examples of applications in the flelds of supramolecular photophysics and photochemistry will be presented. 

Phase fluorometers utilize continuous irradiation by a beam of lighf thaf is sinusoidally modulated. If the frequency of fhe modulation is sef correcfly, there will be a phase difference in the modulation of the fluorescent emission that will depend upon x. Phase fluorometry can yield the same information as does pulse fluorometry.327432,133 gy ysing two or more modulation frequencies the decay rates and fluorescence lifetimes for various chromophores in a protein can be observed. For example, the protein colicin A (Box 8-D) contains three tryptophans W86, W130, and W140. Their fluorescence decays with lifetimes Xj, Xy X3 of -0.6-0.9 ns, 2.0-2.2 ns, and 4.2-4.9 ns at pH 7. While X3 originates mainly from W140, both of the other tryptophans contribute to x and X2. Changes in fluorescence intensify with pH reflect a pfC value of... 

Pulse fluorometry has been favoured over phase techniques since hitherto no general method has been available for determining the proportions and lifetimes of fluorescence components in complex systems. Weberhas presented an exact solution of the problem using the values of the phase shifts and relative modulation of the overall fluorescence of as many light-modulation frequency as there are components. The simplicity and speed of the numerical methods involved... 

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