Correction for contaminant fluorescence in frequency-domain fluorometry

ANALYTICAL

BIOCHEMISTRY

160,

471-479 (1987)

Correction for Contaminant Fluorescence in Frequency-Domain Fluorometry’ JOSEPH R. LAKOWICZ,~

RANJITH

JAYAWEERA,

NANDA

JOSHI, AND IGANZY

GRYCZYNSIU

Department of Biological Chemistry, University of Maryland School of Medicine, 660 West Redwood Street, Baltimore, Maryland 21201 Received October 10, 1986 We describe a general method to correct for contaminant fluorescence when using the technique of frequency-domain fluorometry. The method can be applied regardless of the origin of the background signal, from scattered light, impurity fluorescence, or both. The procedure requires measurement of the frequency-dependent phase and modulation of the background at enough frequencies to approximate the decay law of the background. We also describe a general method to propagate the uncertainties in the measured phase and modulation values into the corrected values. This propagation is necessary to ensure proper weighting of the frequency-dependent data in the least-squares fitting algorithms. The practical usefulness of this correction method is demonstrated using frequency-domain data for one and two component mixtures which were deliberately contaminated with scattered light and/or other fluorophores. 0 1987 Academic Press. Inc. KEY WORDS: fluorescence spectroscopy; frequency-domain fluorometry; time-resolved fluorescence: background correction; scattered light.

Because of the high sensitivity of fluorescence spectroscopy and the ubiquitous presence of extraneous fluorescence or scattered light, it is frequently necessary to correct fluorescence data for unwanted components. In fact, the background components, and not the sensitivity of the instrumentation, usually limit the lowest allowed sample concentration in the measurements. Correction for background components is straightforward for steady-state measurements, and is accomplished by subtraction of the signal from the unlabeled sample from that of the labeled sample, with due consideration of the ’ This work was supported by Grants PCM-8210878 and DMB-08502835 from the National Science Foundation and Grants GM-293 18 and GM-35 154 from the National Institutes of Health. J.R.L. offers his special thanks to the National Science Foundation for their support for development of the frequency-domain instrument, at a time when others doubted its usefulness. ’ Author to whom correspondence should be addressed.

relative inner filtering effects of the sample and blank solutions. Correction for unwanted signals is similarly easy for time-domain measurements. In this case time-dependent data for the blank are obtained under conditions identical to the sample, and subtracted point by point. In this laboratory we emphasize the alternative technique of frequency-domain fluorometry. We measure the frequency-response of the emission to intensity modulated light, over a wide range of modulation frequencies (1,2). In the measurement of phase angles and modulation factors one cannot simply subtract the values measured for the unlabeled sample. This is because the measured values are a complex weighted average of the desired and the unwanted signals. In this paper we describe the measurements and calculations necessary to correct the frequency-domain data for background components. We became aware of this need 471

0003-2697187 $3.00 Copyright 0 1987 by Academtc Press, Inc All rights of reproduction in any form reserved.

472

LAKOWICZ

in our studies of energy transfer where the donor was highly quenched due to close proximity to the acceptor. We also recognized that the elimination of background by increasing the sample concentration is not practical in many real-world measurements. It appears that continued advances in the design and performance of frequency-domain instruments is resulting in their widespread use. For instance, the wavelength range has been expanded to include protein fluorescence (3,4), and the frequency range has been extended to 2 GHz (5-7). Additionally, frequency-domain fluorometers are now commercially available. Consequently, a general method for background correction is necessary. THEORY Theory and Analysis of Frequency-Domain Data

Consider the emission from a sample excited with light modulated at the circular frequency w, equal to 27r times the frequency in cycles per second. The emission is a forced response at the same frequency, but delayed in phase and demodulated relative to the incident light. The frequency-dependent phase (&) and modulation (m,) values can be calculated from the sine and cosine transforms of the impulse response. The total intensity decay is often described by a sum of exponentials IT(t) = C (YiC”“, [II where ai are the preexponential factors and Ti the decay times. The necessary transforms are N, =

s

Z(t)sin wtdt

where the integral extends from zero to infinity. Analytical expressions for these transforms are given elsewhere (8,9). The phase and modulation values are given by 6, = arc tan(NJD,)

[41

m, = (Ni + Do)“‘.

[51

The data are analyzed by the method of nonlinear least squares (8). The goodness of fit is given by

where the subscript F refers to calculated values for fitted parameters in the decay law, and 6 and m refer to the measured values. For clarity the frequency index (w) was deleted. The value of reduced x2 is given by xi = x2/v, where Y is the number of data points minus the number of floating parameters. For a model adequate to explain the data we expect the values of xi to be near unity. An inadequate model results in elevated values of xi. The uncertainties in the phase and modulation data (66 and 6m) can be estimated in one of two ways. For the present analysis these values were estimated from several years of experience with solutions with known single or double exponential decays. We found that &#I and 6m were mostly independent of frequency, and were approximately equal to 0.2” and 0.005, respectively. Alternatively, one can record the standard deviation of the repetitive measurements of 4 and m. These can be recorded at each modulation frequency. For clarity we used the simpler method of frequency-independent values of &#Jand 6m.

PI s

Z(t)dt

S

Background Correction

Z(t)cos wtdt

D, =

ET AL.

s

9 Z(t)dt

t31

The total emission (T) from the sample can be regarded as being due to two sources; the emission from the desired fluorophore in the sample (c) and that due to the background components (B). The fractional in-

BACKGROUND

CORRECTION

IN

FLUOROMETRY

473

These values (4, and m,) are then used in the usual way to determine the parameters of the decay law describing the sample emission without the background contributions (Eqs. ill-Kl). DT=(l-f)m,cos~,+fm~cos~~. 181 Examination of Eqs. [ 131 and [ 141 reveals that the fraction of the signal due to backIf the background were measured as the only signal in a separate experiment then f = 1.O ground signal (f) must be known. This value must be accurately determined under the and NB = NT = mB Sin ‘$B of the experiment. In [91 precise conditions practice this means that the excitation waveDg= DT=mBcos&. 1101 length, filters, and various gain settings must The desired values are those characteristic of be the same when the sample and blank are the sample, f = 0, compared to determine J: NC = m, sin #, There are two possible methods to deter[Ill mine the decay law of the background or, DC = m,cos&. 1121 equivalently, NB and Dg. To apply Eqs. In these expressions NT and DT are known [7]-[ 141 these values must be known at each from the measurement of the total emission frequency at which the sample was mea(sample plus background, Eqs. [7] and [8]), sured. One approach is to measure the phase and NB and DB are known from an indepenand modulation of the blank at each fredent measurement of the blank. Evidently, quency. Then NB and DB can be determined the desired values (N, and DC) can be calcu- using Eqs. [9] and [lo]. Alternatively, the lated from the total data (Eqs. [7] and [8]) measurements on the blank can be done on a and the background data (Eqs. [9] and [lo]). lesser number of frequencies, say one-fourth N =%+NB of the total. These values are then fit to a c I131 multiexponential model to yield the decay 1 -f law of the background. This decay law is D /h-fDs then used to synthesize the values of NB and c l-f * DB at each desired frequency. In either case, The corrected phase and modulation values the data for the background are likely to have are obtained from N, and DC using Eqs. [4] a higher level of uncertainty due to its weaker and [5]. Substitution yields intensity. Fortunately, this uncertainty becomes less important as f decreases. I [I51 tensities of these sources are 1 - fandJ respectively. At each frequency the total emission can be described by ( lo- 12) NT = (1 -f)m, sin $, +fm~ sin & [7]

m, = &

[(NT -flv,Y

+ CDT -.PB)~I”~.

[I61 In terms of the measured quantities these expressions are mT sin &r - fmB sin &, & = arc tan mT cos$T - fmB cos & I [I71 c

- 2mBmTfcos(h

- 4~11~‘~. 118

Propagation

of Errors

Our analysis of the frequency-domain data relies on nonlinear least squares. It is well known that it is essential to properly weight the data points according to their statistical merit ( 13), as is commonly done in the leastsquares analysis of time-resolved fluorescence data ( 14- 16). Proper weighting is particularly important for samples which display complex decay laws which are near the limits of resolution. Consequently, we deter-

474

LAKOWICZ

mined how the uncertainties in the measured data propagate into the corrected data. Let 6x represent the uncertainties in each of the measured quantities (x = &, &, mT, mB, orf). Then, the uncertainties in the corrected data are given by

ET AL,

tive of the degree of correlation sured values. MATERIALS

AND

in the mea-

METHODS

Phase and modulation data were obtained on a variable frequency instrument previously described (2). The excitation wave&g = F $$ * (6x)* 1191 length was 325 nm from HeCd lasers. The ( 1 modulation was accomplished with a Model smt = T 2 *(6x)*. PO1 1042 electrooptic modulator from Lasermetrics. All solutions were in ethanol, with a ( 1 total optical density below 0.12 at the excitaThese expressions to estimate the uncertaintion wavelength. Samples were equilibrated ties in S, and m, are correct if the errors in x with the atmosphere, and measurements are random and uncorrelated (17). This is were performed at 25°C. The excitation was almost certainly true in our case because the vertically polarized, and the emission was samples (T and B) are measured separately, sampled at 54.7” from the vertical (12,19). the phase and modulation values are meaEmission spectra were measured under the sured with separate electronics, and the fmcsame conditions, except on a scanning spectional intensity of the background is meatrofluorometer. The contribution of scatsured in the steady state. The phase is meatered light was increased by adding microsured with a time interval counter, and the liter amounts of an aqueous suspension of modulation is measured with A/D con- Ludox in water. The maximum water converters in our computer. The analytical centration in the samples was 0.8%. As deforms of these derivatives may be obtained sired, scattered light was eliminated from the from Eqs. [ 171 and [ 181. These expressions signal by use of a Corning 3-75 emission are given in the Appendix. For this report we filter. chose to use the numerical derivatives, which gave essentially identical values for S& and RESULTS 6m, as the analytical expressions. This agreeThe correction method was tested using ment confirms the correctness of these ex(DPA).3 This fluopressions. Equations [ 191 and [20] were used 9, lo-diphenylanthracene rophore was selected because of its convein the present report. If desired, one can determine the upper nient lifetime near 6 ns, its absorption at the bound on S& and am, using 325~nm output of our HeCd laser, and its known single exponential decay of intensity (2,9). The emission from DPA was delibert2 1 ately contaminated with either scattered light (Ludox) or with emission from POPOP or CA (Fig. 1). Scattered light displays a decay time near 0.0 ns. The lifetime of POPOP is These are also the values which would be near 1.35 ns, and that of CA is near 12 ns. found by using all possible values of the pa- Hence, the 6-ns emission of DPA was contaminated with background components rameters (x + 6x), in all possible permutations, and taking the maximum and minimum values of 4, and m, from Eqs. [ 171 and 3 Abbreviations used: DPA, 9,10-diphenylanthracene; [ 181 (18). The uncertainties in $J, and m, POPOP, p-bis[2-(5-phenyloxazolyl)]benzene; CA, 9cannot be larger than these values, irrespec- cyanoanthracene.

BACKGROUND

,’ ----

DPA+SCATTER POPOP

CORRECTION

,’

,,’

g-CA ----;E~Kr ,1’ Cbrning

i

3-75 ! : /’

P-7

350

475

IN FLUOROMETRY

The data from the contaminated sample were corrected using measured values for the frequency-response of the scattering blank and f = 0.13. This latter value is close to the measured value off = 0.11, but the 13% value resulted in a lower value of xi. The correction procedure yields phase and modulation data (0) which are described by a single 6.12~ns decay time, a decrease in X; to 1.9, and random deviations (Fig. 2). It should be noted that our values of xi are not always close to unity because of uncertainties in the precise values of SC$and 6m. Additionally, we are not concerned about minor variations in the decay times of DPA from 6.0 to 6.3 ns in this and other reports (2,9). The DPA decay times are somewhat uncertain due to the solubility and effectiveness of oxygen quenching in ethanol. The results of additional studies of contaminated samples of DPA are summarized in Table 1. The DPA samples were contaminated with either POPOP (1.35 ns), Ludox

__ ,_,~~-~;~~~““.~-~-~ ii90 WAVELENGTH

430 (nml

470

510

FIG. 1. Emission spectra of 9, lo-diphenylanthracene and the background components. Emission spectra are shown for 9,10-DPA with contamination due to scattered light (-), POPOP (---), and 9-CA (* * e). Also shown is the transmission of the bandpass filter used to eliminate scattered light. At 430 nm its transmission is about 70%.

whose decay times were either smaller or larger than the decay time of DPA. In the absence of contamination we expect to be able to fit the data using a single exponential model. In the presence of contamination we expect the single exponential model to fail, and the values of xi should be larger than the expected value. If the correction procedure properly removes the component due to background, then the decay should again be a single exponential near 6 ns. The contamination due to scattered light can also be removed using an emission filter (Fig. l), but this is not possible for contaminants whose emission overlaps with that of the DPA. Frequency-domain data for DPA emission contaminated with scattered light are shown in Fig. 2 (0). The dramatic effect of the scattered light is especially evident from the phase angles at the higher frequencies, which are about 20 degrees smaller than expected for a single exponential decay of 6 ns (0). The contaminated data could not be fit to a single exponential decay law, resulting in an elevated value of xi = 7 17 (Table 1) and large systematic deviations between the measured values and the best single component fit (Fig. 2, lower panels).

z+*"r

b B

1

0

. . . . . . . ..I.

,....

.

LIT;

j??~

]

2

5

10

20

FREQUENCY

50

100

200

(MHZ)

FIG. 2. Frequency-domain data for 9, lo-diphenylanthracene plus scattered light. Top: DPA with scattered light (0) and DPA corrected for the scattered light (0). The bold solid line shows best single exponential fit to the data corrected for scattered light. Bottom: Deviations from the best single exponential fits for the data with (0), and corrected for (0) scattered light.

LAKOWICZ

476

ET AL.

TABLE 1 MEASUREMENT

OF THE DECAY

TIMES OF 9, IO-DPA

IN THE PRESENCE OF BACKGROUND

Background Identity of background

dns)

None Ludox POPOP Ludox and POPOP g-CA

0.001 1.35 0.002 and 1.35 12.0

EMISSION

Uncorrected

0.13 0.14 0.15 0.11

Corrected

f

hs)

Xb

0 (0.11) (0.13) (0.13)b (0.13)

4.21 4.78 4.59 6.72

717.0 186.0 253.0 6.7

4ns) 6.01 6.12 6.16 6.14 6.36

Xl

2.1 1.9 1.9 1.3 2.6

a The first fractional intensity is that used in the analysis yielding the lowest &. The value in parentheses is the independently measured value of the background. b The fractional contributions of the Ludox and POPOP to the total background (f = 15%) were 0.15 and 0.85, respectively.

(0 ns) and POPOP, or CA (12 ns). In each case a single exponential fit to the contaminated data yielded xi near 200, and these values decreased to the value found for the uncontaminated emission (near 2) following correction for the contamination. Prior to correction, analysis of the contaminated data yielded apparent decay times which were shorter or longer than expected for DPA. Of course, this is because of the contaminant. Following correction, the lifetimes of DPA agree with the expected values, which were measured either with no contaminant or with a cutoff filter to eliminate scattered light (Fig. 1). If the correction method is to be generally useful the corrected parameters should not be too sensitive to the correction. We examined this sensitivity by varying the fractional contribution of the background (Fig. 3) and the decay time of the background (Fig. 4). We found that the goodness-of-fit parameter xi is highly sensitive to fractional intensity of the background (Fig. 3). In fact, we used the value offwhich yielded the minimum value of xk, rather than the measured value off: This seems reasonable since it is difficult to accurately determine the background contribution. This steep dependence of xg on f can also be valuable in situations where the decay law of the background is known, but not its

precise intensity. Then, the value offyielding the minimum value of xi can be selected from the xi surface. The value of xi is less sensitive to the decay time for the background (Fig. 4). Fortunately, the decay time of the sample is rather insensitive to both f and the decay time of the background (Figs. 3 and 4). This indicates that the parameters describing the contaminant need not be known precisely to correct the data. As a final example we examined a twocomponent mixture (DPA and POPOP) contaminated with scattered light. This models l3iiic 6. r

LUOOX

-

-POPOP

a-

04, .I0

12

.t4-

.I6

%

RG. 3. Dependence of the decay time of DPA (top) and xi (bottom) on the fractional intensity of the background. The background was due either to scattered light (0) or to POPOP (0).

BACKGROUND

8 LVDOX ‘j; c6 P ‘---

CORRECTION

POPOP == -

4

FIG. 4. Dependence of the decay time of DPA (top) and xi on the decay time of the background. The background was due to either scattered light (0) or POPOP (0).

IN

477

FLUOROMETRY

response expected for this two component mixture (-). This response is the one obtained for the DPA and POPOP sample without scattered light. The two-component fit fails to account for the data even if the lifetimes are variable. This failure is seen from the systematic deviations (Fig. 5, lower panels), the elevated value of xi, and the incorrect values for the decay times (Table 2). Following correction the data are well fit by the two-component model and the correct decay times are recovered. Error Propagation

the situation frequently encountered with biochemical samples, in which the intrinsic decay is multiexponential and the macromolecules result in scattered light which cannot be completely removed using filters or monochromators. The uncorrected data (0) are shown in Fig. 5, along with the frequency

;; 100 mf” Ez 75 “2 ky:: 50

DPA

zg

and

POPOP

. corrected =

for

+

Scattered

Ii

scatter

25

L‘ 2” a

0

It is important to realize that the uncertainties in the phase and the modulation values are altered in a frequency-dependent manner by correcting the data. We initially noticed this in our attempts to analyze the corrected data using the standard value of 64 and 6m. This procedure yielded values of xi severalfold greater than expected and the deviations seemed to be most pronounced in the corrected phase values at the highest frequencies. We now know that the correction procedure results in increased uncertainties in these values, at least for the particular samples chosen for this study. The propagated uncertainties are dependent upon all the parameters describing the sample and the background, and it is not practical to display these numerous possibili-

TABLE RESOLUTION AND POPOP B

-5’ 2

1111’1 5

,,, 10

FREQUENCY

20

50

L,] 100

FIG. 5. Frequencydomain data for a two-component solution of POPOP and DPA contaminated by scattered light. Top: Data with scattered light (0); data corrected for scattered light (0); the bold lines show expected values (-) for T, = 1.36; rr = 6. I9 ns, and fractional contributions of 0.48 and 0.52 (Table 2). Bottom: Deviations between the measured values and the best twocomponent fits (Table 2).

OF A TWO-COMPONENT DECAY OF DPA IN THE PRESENCE OF SCATTERED LIGHT

Data”

Th-4

dns)

Ah

h

xi:

With scatter Corrected for scatter Expected values

0.85

5.04 6.19 6.09

.42 .48 .48

.58 .52 .52

6.78 0.79 0.35

200

(MHz1

2

1.36 1.35

“The data for the background correction was generated using a decay time of 0.001 ns, f= 0.08. and the expected uncertainties of 64 = 0.2 and 6m = 0.005. ‘The fractional intensity of each component in a mixture

is given

by a,~,/2

a,~,.

478

LAKOWICZ

7 g b

The programs for simulation and correction of frequency-domain data have been written in Basic-l 1 (RT-11 or TSX), and are available on request.

f -0.1 ?I-

2 ‘6L

ET AL.

2 df -002

/I/ 0.01

0.00

APPENDIX

Analytical Expressions of the Propagation of Errors in Frequency-Domain Fluorometry

ot ,008

1

r at- - 0.0 to 0.02

E ,006 ‘0 0041

, 2

, 4

\I IO 20 FREQUENCY

50 [MHz1

I00

I

200

FIG. 6. Frequency-dependent values of the weighting factors (84 and am). Values are shown for a decay time of 6 ns and a background of 10% (f= 0.1) with a decay time of 0.001 ns. The values of 66 and 6m for the simulated data prior to correction were assumed to be independent of frequency and equal to 0.2 degrees and OS%, respectively. The uncertainty in the background was 0,O.O 1, or 0.02.

ties. However, it is important to realize this dependence. Hence, values of Srj and 6m appropriate for the present samples are shown in Fig. 6. The uncertainties of the phase values increase with frequency, and are strongly dependent upon the uncertainty in J: These are maximum values of 64. These values will be smaller if the decay time of the background is closer to that of the sample. This is evident from Eqs. [Al]-[Al 11, which show that the values of S$, and am, depend upon the phase angle difference between the total signal and that of the background. The uncertainty in 6m is less sensitive to frequency, and in fact decreases slightly at high modulation frequencies. DISCUSSION

It is not practical to perform and present experiments which use the correction procedure in all conceivable cases. We suggest that simulations be used to mimic the experimental conditions, and thereby reveal the effects of correction on the reliability of the data.

The following expressions were obtained from Eqs. [ 171 and [ 181. These expressions can be computed more quickly than the numerical derivatives. Let A = [m: + f ‘rni

- 2mTmBfcoS(h - h)l-‘.

[A 11

Then the derivatives of & are

-

= AmTIm - mfcoS(& - hdl

[A21

ad+ %B

= AmdIm&

LA31

%T

mT

= -AmBfsin(& amT -ah = AmTfsin(&

cos(d’T

-

d’B)l

- $!JB)

L441

- fpB)

dmB

af

= AmTmB sin(& - &).

WI

The derivatives of m, are as follows. Let B = (1 -f)-‘[(m+

+f*mi

- 2mTmBfcos((bT

- bB))]-“‘.

[A71

Then am, am, = - = -BmBmTf sin(f#.IT- tiB) @B

@T

WI am,

amT

am,

amB

=

B[mT

= Bf[%f-

-

mBfCO@T

mT

-

cos($T

6B)l

-

dB)l

IA91

[A101

BACKGROUND

CORRECTION

am,-j-$&+fmi B af -

(1

+fhmB

10. cos(4-r

-

$B)l-

[Al

11

REFERENCES 1. Gratton, E., and Limkemann, M. (1983) Biophys. J. 44,3 15-324. 2. Lakowicz, J. R., and Maliwal, B. P. (1985) Biophys. Chem. 21,61-78. 3. Lakowicz, J. R., Maliwa!, B. P., and Gratton, E. (1985) Anal. Instrum. 14, 193-223. 4. Lakowicz, J. R., Laczko, G., Gryczynski, I., and Cherek, H. (1986) J. Biol. Chem. 261, 2240-2245. 5. Lakowicz, J. R., Laczko, G., and Gryczynski, I. ( 1986) Biophys. Chem. 24,97- 100. 6. Lakowicz, J. R.. Laczko, G., and Gryczynski, I. (1986) Rev. Sci. Instrum. 57,2499-2506. 7. Lakowicz, J. R., Laczko, G., and Gryczynski, I. (1986) Biochemistry, in press. 8. Lakowicz, J. R., and Gratton, E., Laczko, G., Cherek, H., and Limkemann, M. (1984) Biophys. J. 46,463-477. 9. Gratton, E., Lakowicz, J. R., Maliwal, B., Cherek,

11. 12. 13. 14. 15. 16.

17.

18. 19.

IN FLUOROMETRY

479

H., Laczko, G., and Limkemann, M. (1984) Biophys. J. 46,479-486. Lakowicz, J. R., and Baiter, A. (1982) Biophys. Chem. 16,99- 115. Lakowicz, J. R., and Balter, A. (1982) Biophys. Chem. 16, 117-132. Lakowicz, J. R. (1983) Principles of Fluorescence Spectroscopy, Plenum, New York. Bevington, P. R. ( 1969) Data Reduction and Error Analysis for the Physical Science, McGraw-Hill, New York. Grinvald, A., and Steinberg, I. Z. (1974) Anal. Biothem. 59,583-598. O’Connor, D. V., and Phillips, D. (1984) TimeCorrelated Single Photon Counting, pp. 17 1- 176, Academic Press, New York. Demas, J. N. (1983) Excited State Lifetime Measurements, pp. 70-84, Academic Press, New York. Taylor, J. R. (1982) An Introduction to Error Analysis, The Study of Uncertainties in Physical Measurements, pp. 70-73, University Science Books, Mills Valley, CA. Taylor, J. R., personal communication. Spencer, R. D., and Weber, G. (1976) J. Chem Phys. 52, 1654-1663.