Apparent Phase and Modulation Lifetimes

There are several characteristics of the phase and modulation lif mes which are valuatde to know. The ap-parent values areequalonly if the intensity deci is asingle expoo tial, for which case 

For multiexponential or nonexponential decays, the apparent i ase lifetimes are shorter than the a ent modulation lifetimes (ip iSP). Also, and tP gmerally decrease at modulation frequendes. Hence, thdr 

The relationship of and is most easily seen by consideration of a double-exponential decay. Using Eqs. [5.7] and [5.8], one obtains 

It is always posriUe to interpret the phase and modulation values in terms of diea Mrent lifetimes. However, the use of (parent Aase and modulation lifetimes is no longer recommended. Tbese are ouly i iparent values which are the result of a complex weit iting of the individual decay times and an litudes. wludi d eiid on the otperimoital ctmeUtions. Also, one does not actiially measure apparent Uf nres. Tliese values are intopretations of the measurable quantities. which are thephase and modulation values. 

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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. 

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... 

The equations relating the phase and modulation values to the apparent lifetimes (Eqs. [S.3] and [S.4]) are widely known, but the derivation is rarely given. These expres-... 

Figure 7.42. Fluorescence lifaimes and wctra of TNS dissolved in various solvents arxl TNS bound to DOPC vesicles. Apparent phase TNS (O) and modulation ( ) lifetimes were measured at 30 MHz. Normalized emission spectra are shown for TNS in glycerol and bound to DOPC...

One approach to calculating the phase-resolved spectra is based on use of the apparent phase [t (X)] or modulation [t"(X)] lifetimes at each wavelength. Suppose that the san le contains two species, with fractional stea -state intensities of/i(X) and/2(X), and that the two decay times X and X2 are known and are independent of wavelength. Then the ratio of fractimial intensities can be calculated from ... 

Jablonski (48-49) developed a theory in 1935 in which he presented the now standard Jablonski diagram" of singlet and triplet state energy levels that is used to explain excitation and emission processes in luminescence. He also related the fluorescence lifetimes of the perpendicular and parallel polarization components of emission to the fluorophore emission lifetime and rate of rotation. In the same year, Szymanowski (50) measured apparent lifetimes for the perpendicular and parallel polarization components of fluorescein in viscous solutions with a phase fluorometer. It was shown later by Spencer and Weber (51) that phase shift methods do not give correct values for polarized lifetimes because the theory does not include the dependence on modulation frequency. 

It is important to note that if a mixture of fluorophores with different fluorescence lifetimes is analyzed, the lifetime computed from the phase is not equivalent to the lifetime computed from the modulation. As a result, the two lifetimes are often referred to as apparent lifetimes and should not be confused with the true lifetime of any particular species in the sample. These equations predict a set of phenomena inherent to the frequency domain measurement. 

The mobility of tyrosine in Leu3 enkephalin was examined by Lakowicz and Maliwal/17 ) who used oxygen quenching to measure lifetime-resolved steady-state anisotropies of a series of tyrosine-containing peptides. They measured a phase lifetime of 1.4 ns (30-MHz modulation frequency) without quenching, and they obtained apparent rotational correlation times of 0.18 ns and 0.33 ns, for Tyr1 and the peptide. Their data analysis assumed a simple model in which the decays of the anisotropy due to the overall motion of the peptide and the independent motion of the aromatic residue are single exponentials and these motions are independent of each other. 

Figure 7.27. Phase anglei and apparent lifetimes of 3-amino-M-raethylphlhalimide (3-AP) in pure hexM(l). hexane ctxitaitling 0.01% (2), 0.1% (3). 0.3% pyridine (4), and pure pyritSne (3). The modulation frequency was 11.2 MHz. 1 kKs 1000 em Revised from Ref. 63.

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