J. Phys. Chem. 1981, 85,953-958
TABLE Ia
common ratio 1.5 2 2.5 a
ps .
precision range O f T , ..., ns 0.5-3
0.1-0.8 0.1-0.7
Precision of lifetimes by phase and modulation
=
rt
5
both absorption and emission spectra that one of them could not be isolated or excluded by means of optical filters, reducing the problem of resolution to that of a binary system. Complementary Character of the Data from Pulse and Phase Fluorometry. As phase and modulation are measured under what may be called stationary conditions, all of the emissions, regardless of the time from excitation, contribute to the measured values of and M. On the other hand, the emissions following an exciting pulse after several fluorescent lifetimes represent a contribution too small to be accurately measured, and the evaluation of the emission a t very short times is limited by the finite instrumental response. The resulting uncertainties at the beginning and the end of the emission preclude the satisfactory closed-form solution that is available with the phase-and-modulation technique. We recall that G and S are respectively the real and imaginary parts of the Fourier transform of the fluorescence impulse response I ( t ) (eq 55). These relations G ( w ) = J m I ( t ) cos ut d t
(55) S ( w ) = - J m I ( t ) sin w t dt
953
suggest ways in which the results of pulse and phase fluorometry can be used to complement and confirm each other. From pulse fluorometry one has available a deconvoluted and truncated impulse response I ( t ) extending from t > 0 to t < a,and by numerical intergration values for G and S can be obtained for any particular frequency. On the other hand, values of G and S that include virtually all emissions from t = 0 to t = a can be computed with minimal propagated error from @ and M. These values from phase fluorometry can be expected to be much more accurate than the approximates from numerical integration of the experimental impulse response, and thus comparison of the two sets of values must permit a direct estimate of the errors owing to deconvolution and truncation in the latter method without regard to the number of components and other complexities of the system. Additionally, the values of G and S obtained from pulse fluorometry employing two or more frequencies could be subjected to the analysis here described to resolve the components of the decay. While the values of S and G from pulse fluorometry are less accurate than those from phase fluorometry, w can be chosen a t will to permit a more thorough analysis6than the one carried out with the two or three fixed frequencies commonly available in phase machines. It should be of considerable interest to compare such a method of resolution of the component lifetimes with others commonly employed for this purpose. (6) A method employing the Fourier transforms of the experimental impulse response (eq 55) and its fitting to expected values of the lifetime has been described by U. Wild, A. Holzwarth, and H. P. Good, Reu. Sci. Instrum., 48, 1621 (1977); O'Connor et al. (ref 3) point out that it does not seem to offer obvious advantage over the fitting to the impulse response itself.
Resolution of the pH-Dependent Heterogeneous Fluorescence Decay of Tryptophan by Phase and Modulation Measurements David M. Jameson and Gregorio Weber* Department of Eiochemistry, School of Chemical Sciences, University of Illinois, Urbana, Illinois 6 180 1 (Received: August 1.2, 1980)
The tryptophan fluorescence emission arises from the zwitterion and the anion, present in amounts determined by the pH of the solution. These forms interconvert in times much longer than the fluorescence lifetime, and their absorption and emission spectra are similar enough to make this an ideal binary system to test the resolution procedure by means of phase and modulation measurements at two excitation frequencies. Measurements were made by employing the excitation frequencies of 6,18, and 30 mHz, in the pH range 8-10,in which the relative zwitterion contribution varies from 0.82 to 0.09. Best resolution was expected and achieved by combining the data at 6 and 30 mHz. Resolved lifetimes were within f0.4 ns of the true lifetimes (3.1,zwitterion; 8.7, anion), and fractional contributions were within 10-2070 of expectancy. Such dispersion is predicted for phase and modulation measured lifetimes with standard deviations of -f50 ps, which in turn correspond to h0.15' phase error and f0.3% modulation error. With some limitations similarly good resolution was reached by fixing the value of one lifetime and employing fewer experimental data: phase and modulation at one frequency, phases at two frequencies, or modulation at two frequencies. For tryptophan no phase delay resulting from difference in energy of the exciting and fluorescence quanta was demonstrable, but correction for such effect may be, in general, needed, and a procedure for this purpose is described.
Introduction The preceding paper gave the theoretical treatment of the analysis of heterogeneous emitting systems by phase and modulation data. Here we describe the experimental verification of the theory and explore the precision and sources of error inherent in present-day instrumentation.
For this study we desired a well-defined, chemically heterogeneous system, i.e., a system wherein the lifetimes and fractional weights of each component are known with precision and in which the relative proportions can be varied in a known fashion. To this end we have analyzed in detail the variation of the components in the fluores-
0022-3654/81/2085-0953$01.25/00 1981 American Chemical Society
954
The Journal of Physical Chemistry, Vol. 85, No. 8, 1981
Jameson and Weber
90 80
80 RELATIVE
W
FLUORESCENCE
ro
70
u
E E 0 3
v) V
GO
k
X
50
LA
40
30
2
2 -I
aW: 20
10
I
2
3
4
5
6
7
8
9
10
I1
12
PH
Flgure 1. Relative yield (X) and lifetimes ( 0 )for tryptophan as a function of pH at 20 OC. I n all cases excitation was 280 nm. Yields were calculated from the total spectral area from 291 to 440 nm. Lifetimes were measured by the phase shift technique at 10-mHz modulation; emission in this case was observed through a Cornlng 0-52 fitter. Buffers used were 0.01 M glycine hydrochloride (pH 13-35), 0.005 M potassium phosphate (pH 6.0-9.0),and 0.005 M sodium pyrophosphate (pH 9.0- 12.5).
cence emission from solutions of tryptophan buffered in the pH range 8-10. The dependence of quantum yield upon pH for tryptophan was demonstrated by Whitel (1959), while lifetime studies were performed by DeLauder and Wah12 (1970) using the pulse technique and Jameson3 (1978) using the phase/modulation technique. The pHdependent forms in equilibrium are the zwitterion and the anionic amino acid. Two pH units below the pK, of the a-amino group (9.39),4 the zwitterion is the only form present, and a fluorescence lifetime of 3.1 ns is recorded a t 20 “C. Near pH 10.8 the overwhelming form is the anion with a lifetime of 8.7 ns. At pH values within 1.5 units of pK,, both forms are present in amounts that can be accurately determined by pH measurements (Figure 1). The anionic and zwitterion forms interconvert in periods that are much longer than the fluorescence lifetime, typically milliseconds (at pH 7), and can therefore be considered as two distinct fluorophors in solution with characteristic lifetimes yet identical absorption and nearly identical emission spectra. In recent years a short-lived (-0.4 ns) component of uncertain origin has been detected in the blue edge (
