Phase and Modulation Lifetimes

With the rate constant in hand, the lifetime can be reported. Rearrangement of these expressions yields the more familiar expression for phase and modulation lifetimes in terms of t. 

To summarize the results of multiple cells, 2D histograms of the phase and modulation lifetimes can be used (Fig. 2.4c). Such 2D... 

The apparent lifetimes calculated by these expressions are the true lifetimes only if the fluorophore obeys single exponential decay kinetics. In the case of a single exponential decay, the apparent lifetimes as determined from the two equations should be the same. If the apparent phase and modulation lifetimes are not equal, more than one decay process is indicated. 

In discussing the FD data, we have deliberately avoided the use of phase (t ) or modulation (x ) Hfetiines. These values are the lifetimes calculated fr om the measured phase and modulation values at a given frequency. The use of phase and modulation lifetimes can be misleading and is best avmded. The characteristics of and are discussed in Section 5.10. 

An example of the use of apparent phase and modulation lifetimes is given in Figure 535. for the mixture of ACF and AFA. This figure shows die diase-angle and modulation spectra in terms of xjf and xj i. The fact that xjf < xj for a hetero oeous deci is evident by comparison die iqiper and low panels. Also, one immediately notices fiiat the lif me by phase or... 

Effect of Heterogeneity on Apparent Phase and Modulation Lifetimes Sappote that you have samples which display a double-exponendal decay law. with lifetimes of 0.5 and 5.0 ns. For one sample the pieexponential factors are equal (aj = ot2 = 0.5), and for the other san le the fractional intensities art equal ifi fi- Calculate the apparent phase and modulation lifetimes for these two decay laws at modulation frequencies of 50 and 100 MHz. Explain the relative values of the apparent lifetimes. 

A. Effect of an Exetted-State Reaction on the Apparent Phase and Modulation Lifetimes... 

Tablc5.7. Apparent Phase and Modulation Lifetimes for the Odofide Probe SFQ... 

Practically speaking, these expressions allow the prediction of the phase and modulation for an arbitrary mixture of noninteracting fluorophores and the respective modulation and phase lifetimes. 

This procedure involves selecting a fluorophore of known lifetime and placing it in the microscope and measuring the phase and modulation depth [11]. Rearranging Eqs. (2.5 and 2.6) allows the expected phase and modulation to be predicted. These may then be used to compute the position of zero phase and the modulation depth of the light source. An advantage of the method is that it may be done under conditions exactly matching those of a sample. 

Prior to describing the possible applications of laser-diode fluorometry, it is important to understand the two methods now used to measure fluorescence lifetimes these being the time-domain (Tl)/4 5 24 and frequency-domain (FD) or phase-modulation methods.(25) In TD fluorometry, the sample is excited by a pulse of light followed by measurement of the time-dependent intensity. In FD fluorometry, the sample is excited with amplitude-modulated light. The lifetime can be found from the phase angle delay and demodulation of the emission relative to the modulated incident light. We do not wish to fuel the debate of TD versus FD methods, but it is clear that phase and modulation measurements can be performed with simple and low cost instrumentation, and can provide excellent accuracy with short data acquisition times. 

In the case of a single lifetime with no interference from ambient or backscattered light only a single frequency is necessary to determine the lifetime of the luminescence. Determination of the phase and modulation at multiple frequencies is necessary to characterize complex decays in fiberoptic sensors. 

Figure 10.5. Schematic of phase angle and modulation lifetime measurements, to = Frequency of modulation. r = lifetime.

Figure 10.10. Frequency responses of intensity decays of possible oxygen sensors with various lifetimes. The arrows indicate the magnitude of changes in phase and modulation in the range from 0% oxygen (N2, deaerated solution) to about 20% oxygen (Air, equilibrium with air).

Figure 11.9. Phase and modulation measurement of fluorescence lifetime, tan = 2 jr/r = phase difference.

In the upper panel of Figure 13.6, the emission is drawn assuming a modulation frequency of 30 MHz and a lifetime of 9 nsec. Using the equations above, the phase angle is 59.5° and the demodulation factor is 0.5. (For further details, the reader is referred to Lakowicz(66)). Additionally, multifrequency phase and modulation instruments that operate over a range of frequencies have been described(67, flS) and simple instruments are possible if only one or several discrete frequencies are required (Figure 13.6, lower panel). 

For a single fluorophore with an exponential decay, the phase and modulation are related to the fluorescence lifetime by the expressions... 

PFIAs and fluorescence lifetime immunoassays (FLIAs) are uniquely based on measurement of probe emission properties other than the intensity. The phase and modulation are measured, and they directly reflect the fluorescence lifetime of the fluorophore. This provides a major advantage, since the intensity can vary over a broad range, with only minor effects on the results. Phase-modulation measurements can be... 

P. B. Garland, Phase and modulation optical spectroscopic methods for determining triplet lifetimes and slow rotational diffusion coefficients, Biochem. Soc. Trans. 15, 838-839 (1986). 

Membranes and vesicles were labeled at a DPH/lipid ratio of 1/400 and measured using phase-modulation fluorometry at ten frequencies between 5 and 90 MHz at 37°C. y2 values were calculated assuming errors of 0.2 and 0.002 in the phase and modulation, respectively, except where otherwise noted. /, 2, Fraction of Exponential term or Lorentzian t, 2, lifetime (ns) cu, center of Lorentzians (ns) w12, half-width of Lorentzians (ns). 

T. Parassassi, F. Conti, E. Gratton, and O. Sapora, Membrane modification of differentiating proerythroblasts. Variation of l,6-diphenyl-l,3,5-hexatriene lifetime distributions by multifrequency phase and modulation fluorimetry, Biochim. Biophys. Acta 898, 196-201 (1987). 

Steady-state and multifrequency phase and modulation fluorescence spectroscopy are used to study the photophysics of a polar, environmentally-sensitive fluorescent probe in near- and supercritical CF3H. The results show strong evidence for local density augmentation and for a distribution of cluster sizes. These results represent the first evidence for lifetime distributions in a "pure solvent system. 

Time-resolved emission spectra were reconstructed from a set of multifrequency phase and modulation traces acquired across the emission spectrum (37). The multifrequency phase and modulation data were modeled with the help of a commercially available global analysis software package (Globals Unlimited). The model which offered the best fits to the data with the least number of fitting parameters was a series of bi-exponential decays in which the individual fluorescence lifetimes were linked across the emission spectrum and the pre-exponential terms were allowed to vary. 

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