Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 183
Table 5.3. Global Analysis of a Two-Component
Mixture of Anthranilic Acid and 2-Aminopurine
Measured at Five Emission Wavelengths a,b
2-AP AA c
Observation τ 1 = 8.19 ns τ 2 = 11.18 ns
wavelength (nm) α 1 f 1 α 2 f 2
360 0.117 0.089 0.883 0.911
380 0.431 0.357 0.569 0.643
400 0.604 0.528 0.396 0.472
420 0.708 0.640 0.292 0.360
440 0.810 0.758 0.190 0.242
aAnalysis of the data in Figure 5.33. f = 0.2 and δm = 0.005. From
[116].
b For the one-component fit χR 2 = 37.4, for the two-component fit χ R 2 =
1.33.
cLifetimes assigned to these fluorophores based on measurements of
the individual fluorophores (Figure 5.31).
wavelength. Hence the global analysis is performed as
described in eqs. 5.13 to 5.15, where the α i (λ) values are
assumed to be different at each wavelength, but the τ i values
were assumed to be independent of wavelength.
Results of the global analysis are shown in Figure 5.33
and Table 5.3. The value of χ R 2 = 37.4 for the one-component
fit is easily rejected. Use of the two-component model
results in a decrease of χ R 2 to 1.33. For the global analysis,
the frequency responses at each emission wavelength are in
good agreement with the calculated curves when using two
wavelength-independent decay times. Use of three decay
times does not improve χ R 2, so the two-decay-times model
is accepted.
Global analysis results in less uncertainty in the recovered
parameters. The lifetime χ R 2 surfaces from the global
Figure 5.34. Lifetime χ R 2 surfaces for the mixture of anthranilic acid
(AA) and 2-aminopurine (2-AP). The 67% line refers to the F χ values
for global analysis. From [116].
analysis are much steeper when calculated using the data at
six emission wavelengths (Figure 5.34, ——). The elevated
values of χ R 2 are more significant because of the larger
degrees of freedom. For this global analysis there are
approximately 200 datapoints, and seven variable parameters.
Hence the F statistic is 1.16 (Table 4.4), and the F >
value is 1.04 (eq. 5.24). Global analysis also results in
improved estimates of the amplitudes. The fractional intensities
(f i ) and decay times (τ i ) recovered from the global
analysis closely match those expected from the spectral
properties of the individual fluorophores (Figure 5.30).
5.7.4. Analysis of a Three Component Mixture:
Limits of Resolution
A three-component mixture with less than a threefold range
in lifetime represents the practical limit of resolution for
both time and frequency domain measurements. Analysis of
the data from such a sample illustrates important considerations
in data analysis at the limits of resolution. Frequency-domain
intensity decay data for the mixture of indole
(IN, 4.41 ns), anthranilic acid (AA, 8.53 ns) and 2-aminopurine
(2-AP, 11.27 ns) are shown in Figure 5.35. The data
cannot be fit to a single decay time, resulting in χ R 2 = 54.2,
so this model is easily rejected. The situation is less clear
for the two- and three-decay-time fits, for which the values
Figure 5.35. Frequency-domain intensity decay for a three-component
mixture of indole (IN), 2-aminopurine (2-AP), and anthranilic
acid (AA) in water, 20°C, pH 7, observed at 380 nm. The χ R 2 values
for one-, two-, and three-decay-time fits are 54.2, 1.71, and 1.81,
respectively. From [116].