Time-Resolved Detection of Energy Transfer: Theory and … · 2008. 2. 22. · 102 LARRY E. MORRISON acceptor may be minimized by selecting the excitation wavelength such that it

ANALYTICALBIOCHEMISTRY 174, 101-120(1988)

Time-Resolved Detection of Energy Transfer: Theory and Application to lmmunoassays

LARRY E. MORRISON Amoco Research Center, P.O. Box 400. Naperville, Illinois 60566

Received February 22, I988

Energy-transfer measurements based upon acceptor fluorophore emission are plagued with background fluorescence resulting from absorption of the excitation light by the acceptor fluorophore. The present work examines the use of a long-lifetime donor fluorophore and a short- lifetime acceptor fluorophore, combined with pulsed-laser excitation and electronic gating of detector signals, to separate the component of acceptor emission due to energy transfer from the component due to absorption of the excitation light. Theoretical equations describing the acceptor fluorescence and integrated acceptor fluorescence show that increasing the integration delay relative to the excitation pulse should greatly enhance detection of the energy-transfer component. The time-resolved detection ofenergy transfer was tested in a competitive immunoassay format in which antibodies to human immunoglobulin G (IgG) F(ab’)* fragments were covalently labeled with pyrenebutyrate (T = 100 ns) and IgG Fab’ fragments were covalently labeled with B-phycoerythrin (T = 2.5 ns). Solutions containing these two conjugates exhibited energy transfer from the pyrenebutyrate to the B-phycoerythrin upon excitation with a nitrogen laser. Acceptor emission was measured with 0- and 20-ns integration delays and the ratios of the energy-transfer component to the laser-excited component were found to increase by 9- to 15- fold when the 20-ns delay was used in three series of immunoassays. Good agreement between the experimental data and theory was obtained following convolution of the theoretical fluorescence responses with the instrumental response of the fluorometer. 0 1988 Academic press, hc.

KEY WORDS: fluorescence, nanosecond; binding assays; instrumentation; laser methods: im- munochemical methods: energy transfer; fluorescence, time-resolved.

Long-range nonradiative energy-transfer measurements have become a common means to determine distance relationships within and between biological molecules (1). Such measurements have also become the basis for biological assays including immunoassays (2-5) and DNA hybridization assays (6). Energy transfer is detected as a decrease in the fluorescence efficiency of an energy donor fluorophore and an increase in the fluorescence efficiency of an energy acceptor fluorophore. Although measurement of the decrease in donor emission is sufficient to calculate the efficiency of energy transfer, it is preferable to monitor the acceptor emission as well since processes other than nonradiative energy transfer

may contribute to quenching of the donor emission (7,8,3).

Unfortunately, the acceptor fluorophore emission resulting from energy transfer is al- ways accompanied by a background emission component resulting from direct absorption of the excitation light intended for excitation of the donor fluorophore. Since it is a require- ment for energy transfer that the acceptor absorbance overlap the donor emission, the do- nor excitation energy necessarily exceeds that of the longest wavelength absorption band of the acceptor. Light intended for excitation of the donor, therefore, will be absorbed to some extent by the acceptor owing to the existence of energy transitions from the ground state to higher excited states. Light absorption by the

101 0003-2697188 $3.00 Copyright 0 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.

102 LARRY E. MORRISON

acceptor may be minimized by selecting the excitation wavelength such that it coincides with a minimum in the acceptor absorption spectrum. However, this will not eliminate the problem.

Absorption of excitation light by the acceptor fluorophore is avoided when a chemiluminescent compound is used as the donor species and excitation of the donor is performed through a chemical reaction instead of via light absorption. This technique has been applied to energy-transfer-based immunoassays and DNA hybridization assays (6,9) and not only eliminates direct excitation of the acceptor substituent but also avoids interference resulting from scattered excitation light. Chemical excitation, however, generally provides a greater variability in the intensity of emitted light, relative to excitation by light absorption, and consequently leads to less precise emission measurements. In addition, relatively few chemiluminescent com- pounds are available in a form which may be conjugated to biological molecules of in- terest.

The present work describes a technique which allows the use of a fluorescent donor molecule by reducing the background acceptor fluorescence resulting from absorption of the excitation light. This technique requires the selection of donor and acceptor fluorophores such that the fluorescence lifetime of the donor (mu) is greater than the fluorescence lifetime of the acceptor (TV), thereby impart- ing a temporal distinction between acceptor fluorescence resulting from energy transfer and acceptor fluorescence resulting from light absorption. Time-resolved detection of acceptor fluorescence can then be used to distinguish the two temporally distinct components. In this paper we demonstrate that time-resolved detection of energy transfer reduces fluorescence background in an energy- transfer-based immunoassay. Theoretical equations relevant to time-resolved detection of energy transfer are presented and predictions using these equations are compared to

experimental results in order to establish the predictive capability of the equations.

THEORETICAL CONSIDERATIONS

Time-resolved detection of fluorescence can be performed using several methods of detection including time-correlated photon counting, multifrequency phase fluorometry, gated integration, and phase sensitive detection. Gated integration is perhaps the sim- plest of the detection methods, requiring a source of pulsed excitation light and one to several gated integrators. Gated integration was used here to isolate the energy-transfer component of the acceptor fluorescence from the component of the acceptor fluorescence resulting from absorption of excitation light. The ability of gated integration to differenti- ate these two components can be predicted from an examination of the several first-order deexcitation processes involved in energy transfer between fluorophores.

When a donor and an acceptor fluorophore are excited by light absorption, the rates at which the excited state populations change are dictated by

dD*/dt = IDabs - kDD* - kTD* [II dA*ldt = ZAabs - kAA* + k,D*, PI

where D* and A* are the respective numbers of donor and acceptor excited states at a particular time t, IDabs and IAabs are the respective rates of donor and acceptor light absorption, kD and kA are the respective rate constants of donor and acceptor deexcitation in the absence of energy transfer, and kT is the rate constant of energy transfer from excited donor to acceptor. When excitation light is provided as a pulse of infi- nitely short duration (delta function), integrations using Eqs. [l] and [2] provide the impulse responses of the donor and acceptor excited state populations,

[31

TIME-RESOLVED ENERGY-TRANSFER IMMUNOASSAY 103

A* = kTD$(kA - kD - k&l

X [e- (k,+f+ - e-(k,t)] + &Ne-(k,&, [4]

where A$ and D$ are the numbers of excited donors and acceptors initially formed by the excitation pulse (t = 0). Equation [4] is identi- cal to the equation for acceptor fluorescence presented by Schiller (7) except that the terms in Eq. [4] are arranged to separate A* formed by light absorption (last term) from A* formed by energy transfer (remaining terms). The temporal distinction between acceptor fluorescence resulting from the two different excitation processes is clear upon examination of Eq. [4]. Since fluorescence is proportional to the number of excited states (see below), acceptor fluorescence resulting from light absorption decays with a lifetime 7A = 1 /kA , while acceptor fluorescence resulting from energy transfer varies as the difference of two exponentials. When t becomes large, acceptor fluorescence decays with a lifetime of either l/kA or l/(kn + kT). whichever is larger. Therefore, selection of a long-lived do- nor and short-lived acceptor (kA > kD) causes the acceptor fluorescence to persist longer in the presence of the energy donor than in the absence of the energy donor, as long as the rate of energy transfer is not exceedingly large. This persistent fluorescence is due solely to excitation of the acceptor by energy transfer and can be selectively measured by gating the detection system such that fluorescence measurements are delayed with re- spect to the time of the excitation pulse.

A gated integrator integrates a portion of the signal produced by a detector, the portion integrated being defined by a delay period, d, and an integration period, w. In the case of a light-sensing detector, such as a photomultiplier tube, the signal is proportional to the number of photons impinging on the detector per second, d[hv]/dt. When an optical filter is used to pass only wavelengths of light emitted by the acceptor, the signal from an ideal detector at any time t is proportional to

the instantaneous acceptor fluorescence, FA(t), defined in

F*(t) = d[hv,]/dt = kAEA*, [51

where [hv,J is the number of photons emitted by the acceptor and kAE is the emissive lifetime of the acceptor molecule. Combining Eqs. [4] and [5], and integrating between the limits of d and d + w, provides the antic- ipated result of a gated integration of the acceptor fluorescence, as shown in Eqs. [6] and [7] where the acceptor fluorescence resulting from energy transfer, FAT(t), and light absorption, FAabs(t), have been integrated separately:

s

d+ M’

FAdf)df d

k/w kT Do* e-(k,+k,)d

= k, - kD - k, k, + kT ( 1 - e-(k,,+kT’y

e-(kAd)

+ kA - (e-(kA”‘) - 1) 1 [(j]

s d+ fi’

Fad Wt d

= (k,, Ad/k,& (k,d)( 1 - e-(kAW)). [71

It may be noted that for any positive non- zero value of d, the integrated acceptor fluorescence resulting from direct absorption of the excitation light is attenuated relative to the integrated acceptor fluorescence resulting from energy transfer, when kA is greater than kD + kT. Gated integration, therefore, provides an enrichment of the measured signal in the component of acceptor emission due to energy transfer.

It may also be noted that when k,, + kT > kA, gated integration does not distinguish between the two components of acceptor emission; however, the integrated donor fluorescence is attenuated relative to the integrated acceptor emission, for positive values of d. This latter condition could be used to advantage in situations where the donor and acceptor emission spectra overlap and


optical filtering is insufficient to separate the donor and acceptor fluorescence.

MATERIALS AND METHODS

Chemicals. Affinity-purified IgG’ fractions of (goat) anti-human IgG (F(ab’), fragment specific), lots 19965 and 18958, were obtained from Cappel Laboratories (Malvern, PA). Also obtained from Cappel Laboratories were (goat) anti-human IgG (Fab fragment specific), lot 20542, and human IgG, lots 20492, 20787, and 20869. B-Phycoerythrin, succinimidyl 1 -pyrenebutyrate, 1 -pyrenebutyric acid (99+%), and l-pyrenebutyrylcholine bromide were purchased from Molecular Probes, Inc. (Junction City, OR). Quinine sulfate, dihydrate, Ultrex grade, was obtained from J. T. Baker Chemical Co. (Phillipsburg, NJ). The heterobifunctional crosslinkers SMCC and SPDP were obtained from Pierce Chemical Co. (Rockford, IL). Rhodamine B, pepsin (2X crystallized), and Tris were purchased from Sigma Chemical Co. (St. Louis, MO). Gel permeation chromatography me- dia, including Sephadex G-25 and Sephacryl S-200 and S-300, were obtained from Phar- macia Fine Chemicals (Piscataway, NJ). Concentration of protein solutions was performed using stirred concentrator cells and Diaflo ultrafiltration membranes (PM 10 and PM 30) obtained from Amicon Corp. (Lex- ington, MA).

Preparation ofpyrenebutyrate-labeledanti- bodies. Donor fluorophore-labeled antibodies were prepared by reacting the IgG fraction of (goat) anti-human IgG (F(ab’), or Fab fragment specific) in 0.05 M boric acid, pH 9.3, with a one- to eightfold molar excess of succinimidyl pyrenebutyrate. The labeling reagent was added as a 0.02 M solution in ace-

’ Abbreviations used: IgG, immunoglobulin G; B-PE, B-phycoerythrin; BSA, bovine serum albumin; SMCC, succinimidyl 4-(N-maleimidomethyl)cyclohexane- l- carboxylate; SPDP, TV-succinimidyl 3-(2-pyridyldithio)- propionate; Ab, antibody: Ag, antigen.

tone and the reaction was allowed to proceed for 2 h at room temperature. Labeled antibody was separated from unreacted fluorophore by gel permeation chromatography using Sephadex G-25. Labeled antibody preparations were dialyzed in buffer containing 0.02 M Tris and 0.15 M NaCl at pH 7.5. Puri- fied conjugates were sterile filtered and stored at 4°C. The amounts of labeling reagents uti- lized in a number of different preparations are listed in Table 1 together with the extents of labeling achieved.

Preparation of human Fab’ particles. Fab particles were prepared by digesting human IgG with pepsin (3 mg/lOO mg antibody) at 37°C for 16 to 20 h in 0.1 M sodium acetate/ HCl at pH 4.3 (10). The resultant F(ab’)z particles were isolated by gel permeation chromatography using Sephacryl S-200 or S-300 as the chromatography medium and 0.1 M

sodium acetate/HCl elution buffer at pH 5.0. The F(ab’), fraction was then cleaved in a solution containing 0.0 15 M dithiothreitol and the pH 5.0 buffer. At this point the thiol-containing Fab’ particles were either used for conjugation with derivatized phycobiliprotein or alkylated for use as unlabeled antigen. When used in a subsequent conjugation reaction, the Fab’ particles were first isolated on a Sephadex G-25 column eluted with buffer containing 0.1 M NaH2P04 and 0.1 M NaCl at pH 7.0. When the Fab’ particles were used as unlabeled antigen, the reactive-thiol groups were alkylated by adding sufficient iodoacetamide to the cleavage-reaction mixture to obtain a 0.036 M solution. The alkylated protein was then purified on Sephacryl S-200 or S-300 columns, eluted with the Tris/ sodium chloride buffer.

Preparation of B-phycoerythrin-labeled antigen. B-Phycoerythrin-labeled human IgG Fab’ particles were prepared using the heterobifunctional crosslinker SMCC in a procedure similar to that reported by Yoshitake et al. (11). A 4.5 mM solution of SMCC in diox- ane was added to B-phycoerythrin dissolved in 0.1 M NaH2P04 at pH 7.0. The SMCC was


TABLE 1

ANTI-HUMAN IgG (F(ab’)* OR Fab FRAGMENT SPECIFIC) LABELING WITH SUCCINIMIDYL l-WRENEBUTYRATE

Conjugate reference

no. Ab form

mol succinimidyl pyrenebutyrate added/m01 Ab

mol pyrenebutyrate attached/m01 Ab

Percentage exciplex emission

I w 1.0 0.68 6 2 IgG’ 1.5 1.1 16 3 IgG y 2.0 1.4 17 4 IgG” 5.0 2.9 26 5 IgG’ 7.1 3.4 27 6 Fab’b I.0 0.56 14 7 Fab’“,b 2.0 0.87 22 8 Fab’b 15 2.5 82

’ Indicates that immunoaffinity-purified antibodies were used in the preparation. Immunoaffinity-purified antibodies were F(ab’)* fragment specific while other antibodies were Fab’ fragment specific.

b Fab’ fragments of antibodies were prepared by the same procedure as the human Fab’ particles (see Materials and Methods).

added in nine separate additions, each separated by 5 min. The resultant solution was allowed to stir for 1.5 h and the protein fraction recovered in the void volume of a Sephadex G-25 column eluted with buffer containing 0. I M NaH,P04 and 0.1 M NaCl, at pH 7.0. The phycobiliprotein, containing maleimide substituents, was then mixed with an Fab preparation of human IgG, containing free thiol groups (see above). The coupling reaction was allowed to proceed with stirring overnight (-20 h) at 4°C. The conjugate was isolated by gel permeation chromatography using Sephacryl S-200 chromatography medium eluted with 0.02 M Tris buffer at pH 7.5 containing 0.15 M NaCl. The product was sterile filtered and stored at 4°C.

Alternatively, B-phycoerythrin-labeled human IgG Fab’ particles were prepared using the heterobifunctional crosslinker, SPDP, using the crosslinking procedure of Carlsson et al. (12). SPDP (2 mM in ethanol) was added to B-phycoerythrin in 0.1 M NaH2P04 buffer containing 0.1 M NaCl at pH 7.5 and allowed to react for 1 h at room temperature. Follow- ing isolation on a G-25 column the disulfide- modified phycobiliprotein was mixed with the thiol-containing Fab’ preparation and al-

lowed to react overnight at room temperature. This was followed by purification of the conjugate on a Sephacryl S-200 column. The amounts of reactants used in the B-phycoerythrin conjugation procedures are listed in Ta- ble 2 together with the extents of labeling achieved.

Immunoassay procedure. Immunoassays were performed by separately adding the B- phycoerythrin-human Fab’ and pyrenebutyrate-anti-human F(aIQ to solutions containing human Fab’ in buffer containing 0.02 M Tris, 0.15 M NaCl, and 1% BSA at pH 7.5. The assay mixture was allowed to equilibrate for 2 h at which time the fluorescence data were collected. The time course of antibody- antigen binding was evaluated in a solution containing 140 nM pyrenebutyrate-antibody (conjugate No. 5) and 9.7 nM B-phycoerythrin-Fab’ (conjugate No. 2).

Absorbance spectroscopy. Conjugate compositions and concentrations were determined from absorbance spectra recorded with a Cary 17D spectrophotometer (Varian Associates, Palo Alto, CA). The extinction coefficients of 0.1% protein solutions at 280 nm were determined to equal 1.32 and 1.25 cm-’ for goat IgG and Fab’ particles thereof’,


TABLE 2

HUMAN Fab’ LABELING WITH B-PHYCOERYTHRIN (B-PE)

Conjugate reference

no. Crosslinking

reagent mol crosslinker

added/m01 B-PE mol Fab

added/m01 B-PE mol Fab

attached/mol B-PE

I SPDP 10 10 3.0 2 SMCC 10 13 1.0 3 SMCC 20 34 4.5

respectively. Extensively desalted and lyophi- ton-counting detector. The photon-counting lized proteins were used for these determina- detector consisted of a Hamamatsu (Middle- tions. Assuming molecular weights of ton, NJ) Model R928 side-on photomulti- 150,000 and 49,000 for goat IgG and Fab plier tube in a Model TE- 177RF thermoelec- fragments, respectively, molar extinction co- tric-cooled housing from Products for Re- efficients of 1.98 X lo4 and 6.12 X lo4 Me1 search, Inc. (Danvers, MA). The associated cm-’ were calculated. Literature values of 4.0 electronics were obtained from EG & G OR- X lo4 and 2.41 X lo6 M-’ cm-’ were used for TEC (Oak Ridge, TN) and consisted of a the molar extinction coefficients of pyrenebu- Model 9301 fast preamplifier, a Model 9302 tyric acid (13) and B-phycoerythrin (14) at amplifier/discriminator, and a Model 874 their long wavelength absorption maxima of quad counter/timer. Quantum yields were 346 and 545 nm, respectively. Absorbance determined in the immunoassay buffer using contributions at 280 nm were determined to corrected emission spectra referred to the equal 4.2 X lo4 M-’ cm-’ for pyrenebutyric emission of quinine sulfate in 0.1 M HzS04 acid and 5.00 X lo5 M-’ cm-’ for the pycobi- (16). A value of 0.70 4 0.02 was used for the liprotein. quantum yield of quinine sulfate (17).

Fluorescence measurements. Corrected fluorescence excitation spectra, corrected emission spectra, and fluorescence lifetimes were measured using a Model 4800 spectrofluorometer from SLM Instruments, Inc. (Urbana, IL). A quantum counter consisting of a rhodamine B solution in glycerol (3 mg/ ml) was used in the fluorometer’s reference channel when the excitation spectra were recorded. in order to correct for the wavelength dependence of the excitation light intensity (15). In addition, sample absorbance was kept below a value of 0.02 over the wavelength range of an excitation spectrum so that the fluorescence excitation spectrum should be proportional to the sample absorbance spectrum (see Eqs. [5] and [S]). For some spectra, the spectrofluorometer was modified for greater sensitivity by replacement of the analog photomultiplier detector with a pho-

Time-resolved fluorescence was measured with a pulsed laser fluorometer. A schematic representation of the fluorometer is presented in Fig. 1. The pulsed nitrogen laser portion of an EG&G Princeton Applied Research (Princeton, NJ) Model 2 100 tuneable dye laser was used as the source of excitation light. The pulse duration of the nitrogen laser is specified at 1.2 ns, full width at half maximum, and was operated at a 1 O-Hz repetition rate. A portion of the beam was directed to- ward an EG&G Princeton Applied Research Model 2 100/99 fast diode edge trigger which was used to trigger the gated integrators. The remainder of the laser beam passed through a Uniblitz (Rochester, NY) Model 225 me- chanical shutter and entered the sample compartment. Within the sample compartment a portion of the beam was reflected onto a photomultiplier tube, for measuring laser pulse

FIG. I. Schematic representation of the pulsed-laser fluorometer using gated detectors. M, Front surface to- tally reflecting mirror: F, , F4, F5, neutral density filters; BS, beam splitter (uncoated quartz plate); PD, photodi- ode trigger unit; L, ,500 mm focal length lens; S, shutter; I, iris; PMTi , PMTz , PMT3, photomultiplier tubes; L2, focusing lens; L3, 25-mm focal length collimating lens; L., , 50-mm focal length focusing lens; Fz , F, , combina- tions of color, interference, and neutral density filters.

intensity, and the main portion of the beam was focused onto the sample cell (l-cm-path- length cuvette) located within a thermostated cell holder. Emission from the sample cell was collected in two directions, each at 90” relative to the path of the excitation light, and focused onto the two remaining photomultiplier tubes. Light reaching these detectors was attenuated with a combination of neutral density and color filters to isolate either the pyrenebutyrate or the B-phycoerythrin fluorescence. A high current voltage divider, pat- terned after Harris et al. (18), was employed with each of the three photomultiplier tubes which were contained in Products for Re- search ambient temperature housings, Model PR 1405RFSH-005, custom designed for this purpose. The photomultiplier tube anodes were connected to Model SR 250 gated integrators from Stanford Research Systems, Inc. (Palo Alto, CA). Connections from the gated integrators to a Techtronics (Beaverton, OR) Model 475 oscilloscope allowed viewing of fluorescence transients and gating signals. In- tegrated photomultiplier currents were digi- tized, following each laser pulse, with an Ana- log Devices (Norwood, MA) Model 363 12- bit integrated circuit data acquisition system, and transferred to a Hewlett-Packard 9836

Pyrenebutyrate fluorescence was isolated using Corning glass filters No. 7-60 and O-5 1 and neutral density filters in the optical density range of 2 to 3. B-Phycoerythrin fluorescence was isolated using a sodium nitrite liq- uid prefilter (2 M NaN02, 2.8 mm thick), a Corning glass filter No. 3-67, and neutral density filters in an optical density range of 3 to 4. The photomultiplier current corresponding to B-phycoerythrin emission was integrated for 300 ns following each laser pulse. Either a 0-ns delay (pseudo-steady- state detection) or 20-ns delay (time-resolved detection) was imposed between the arrival of the laser pulse and the start of the integration period.

Calculation of theoretical fluorescence responses. The theoretical impulse responses of the acceptor and donor fluorescence were calculated using Eqs. [3] through [5] (and the donor equivalent of Eq. [5]). In dilute solutions, D$ and A$ may be evaluated from Eqs. [8] and [9] where [ hv,,] is the number of photons contained in the short pulse of excitation light and an and aA are the donor and acceptor absorbances, respectively:

&f = 2.3[hv&, PI

A$ = 2.3[hu,,]a,. [91

Separate calculations were performed for the fractions of donors emitting from monomeric excited states and excited-state complexes and the fluorescence due to each donor excited state summed.

The value of kT was calculated from the re- _ lationship derived by Theodor Forster ( 19):


computer (Palo Alto, CA) through an ex- panded 16-bit parallel interface. The computer maintained a running average of the net gated photomultiplier signals which were obtained by taking measurements alternately with the shutter open and closed. Net integrated fluorescence was normalized to integrated laser pulse intensities.


kT = 8.79 x 10-25~2&,kDo-4~-6

X s

O” E&+,(X)X4dX, [IO] 0

where K is an orientation factor, &, is the do- nor fluorescence quantum yield, kD is the first-order rate constant for deexcitation of the donor in the absence of energy transfer, n is the refractive index of the medium, R is the distance separating the energy donor and acceptor, En(X) is the nomalized fluorescence emission spectrum of the donor species, and t*(X) is the spectrum of the acceptor molar extinction coefficient for light absorption, both spectral distributions being functions of the wavelength, A. The value of K is determined by the relative orientation ofthe donor emission dipole, the acceptor absorption dipole, and the vector joining them (19,20). The average value of K* = 3 for randomly oriented donors and acceptors in solution was used for the calculation of kT. The integral in Eq. [lo] was evaluated according to Conrad and Brand (8) except that the corrected acceptor fluorescence excitation spectrum, normalized to a value of 2.4 1 X lo6 M-’ cm-’ at 545 nm (t545), was used for c*(h).

Convolutions of the fluorescence impulse responses with the instrumental response were performed by multiplying values of F*(t), obtained from Eqs. [4] and [5], by values of the instrument response function L(t) and integrating according to

s

t R(t) = qt - u)F(u)du [Ill

0

(see Ref. (2 1) for a general description of convolutions applied to fluorescence). Products of F*(u) and L(t - U) were calculated at OS- ns intervals and summed to effect integration. L(t) was determined from oscilloscope tracings of the detector anode current in response to scattered light.

RESULTS

The time-resolved energy-transfer measurements required a donor fluorophore

3ou 350 400 450 500 550 600 650 Wavelength lnml

FIG. 2. Corrected fluorescence excitation and emission spectra of 2.9: 1 pyrenebutyrate-anti-human F(ab’)z (conjugate No. 4, Table 1) and 1: 1 B-phycoerythrin-human Fab’ (conjugate No. 2, Table 2) recorded in buffer containing 0.0 1 M KH,P04 and 0.15 M NaCl at pH 7.5.

possessing a long fluorescence lifetime and an acceptor fluorophore possessing a short fluorescence lifetime. Pyrenebutyrate was selected as the donor fluorophore because of its unusually long fluorescence lifetime. B- Phycoerythrin was selected as the acceptor fluorophore because of its relatively short fluorescence lifetime and its large absorbance throughout the ultraviolet and visible wavelengths where pyrenebutyrate fluoresces. The reagents required for the homogeneous competitive immunoassay were prepared by labeling antibody with pyrenebutyrate and antigen with B-phycoerythrin. Fab’ fragments of human IgG were chosen as the antigen in the model immunoassay system.

Spectral and temporal characteristics of do- nor and acceptor labels. The spectral information pertinent to the fluorescence immunoassay is presented in Fig. 2 and Table 3. Efficient energy transfer requires overlap of the donor emission spectrum and the acceptor absorbance or excitation spectrum, as ex- pressed by the integral in Eq. [lo]. The excitation and corrected emission spectra of repre- sentative donor-labeled antibody conjugates and acceptor-labeled antigen conjugates are shown in Fig. 2. Good spectral overlap is not obvious from a comparison of the donor emission spectrum and acceptor excitation


TABLE 3

FLUORESCENCE CHARACTERISTICS OF PYRENEBUTYRATE AND B-PHYCOERYTHRIN CONJUGATES

Lifetime analysis

Fluorophore Frequency

(MHz) ~phare (ns) Quantum yield Ro 6) b

Pyrenebutyrate Monomer Exciplex

B-Phycoerythrin

6 101 * 1 103 fl 0.72 k 0.04 60 6 46 +l 58 +I 0.66 kO.05 94

30 2.6 kO.1 2.2kO.l 0.98 kO.05' 0.89 * O.Osd

0 Pyrenebutyrate exciplex emission was obtained using donor-labeled conjugate No. 4 (see Table 1) correcting for the amount of monomer emission present; pyrenebutyrate monomer emission was obtained from unconjugated pyrenebutyric acid which was free ofexciplex emission, pH 7.5; and B-phycoerythrin fluorescence was obtained from acceptor-labeled conjugate No. 2 (see Table 2).

b R. values refer to energy transfer from the indicated emissive form of the pyrenebutyrate to B-phycoetythrin. ’ Literature value from Ref. (22). d Literature value from Ref. (23).

spectrum until it is noted that the peak ex- were determined for pyrenebutyrate since the tinction coefficient for B-phycoerythrin ab- antibody conjugates exhibited significant sorbance is 2.4 X lo6 M-’ at 545 nm (14), pro- emission from both monomer and excited viding extinction coefficients greater than 3 state complexes. Since no conjugates could X lo4 M-’ over the range of pyrenebutyrate be obtained free of excited-state complex emission (360-450 nm). Also of note in Fig. emission, unconjugated pyrenebutyric acid 2 is the long wavelength tail of the pyrenebu- was used to approximate the monomer emis- tyrate emission resulting from the formation sion of the conjugate. The presence of the of excited-state complexes. Ideally, pyrene- negative charge on the free pyrenebutyrate butyrate emission should be entirely from the which is not present in the conjugated form monomeric excited state, since fluorescence should not lead to large errors since the greater than 500 nm would be negligible, charge is four carbons removed from the py- thereby allowing measurement of the B-phy- rene ring system. To confirm this point, the coerythrin fluorescence without interference quantum yields of pyrenebutyric acid in 0.0 1 from the donor emission. Attempts to elimi- M HCl (uncharged) and pyrenebutyrylcho- nate the excited-state complex emission by line bromide at pH 7.5 (positively charged lowering the degree of pyrenebutyrate label- pendant group) were measured and found to ing were unsuccessful, as may be seen in the be within experimental error of the pyrene- last column of Table 1 where the percentage butyrate quantum yield at pH 7.5 (4 = 0.68 of excited-state complex emission is listed for + 0.05 for both neutral pyrenebutyric acid each pyrenebutyrate-antibody preparation. and pyrenebutyrylcholine bromide).

The fluorescence lifetimes and quantum yields of the donor and acceptor species are listed in Table 3. The relative long and short lifetimes of the donor and acceptor, respectively, were verified by phase fluorometry. Two sets of lifetimes and quantum yields

The lifetime of free pyrenebutyrate was essentially homogeneous. In contrast, the lifetime of the excited-state complexes of conjugated pyrenebutyrate (donor conjugate No. 4), measured at wavelengths greater than 500 nm to isolate the exciplex emission, showed


considerable lifetime heterogeneity. The fact that the lifetime determined from modulation measurements was greater than the lifetime determined from phase measurements shows that the lifetime discrepancy results from a heterogeneous population of excited states rather than from excited-state products. Excited-state heterogeneity is expected since emission could result from complexes of pyrenebutyrate with different amino acids of the antibody as well as with other pyrenebutyrate labels. Even though less than the monomer lifetime, the lifetimes of the excited-state complexes were still considerably longer than the B-phycoerythrin lifetime. The measured lifetimes of B-phycoerythrin were within the range of previously reported values (22-24) and the similarity in lifetimes determined from phase and modulation measurements indicate that the emission was nearly homogeneous.

As a measure of the suitability of the pyrenebutyrate species for energy transfer, critical distances for energy transfer, &, were calculated for monomeric and complexed pyrenebutyrate and listed in Table 3. The critical distance is defined as the separation distance at which deexcitation of the donor by energy transfer and fluorescence are equally likely and is obtained by equating kT and kD in Eq. [lo]. The uncertainty in the R0 values is estimated at l-2% exclusive of the uncertainty in ,K’/B. While the refractive indices of label environments are not expected to differ greatly from that of water, the value of K2 can range from 0 to 4. However, since an individ- ual antibody-antigen complex contains several antibodies, each randomly labeled with multiple pyrenebutyrate donor molecules, and an antigen labeled with a B-phycoerythrin molecule, which itsself contains about 38 independent chromophores (14) with various orientations (22), the value of K2 for com- pletely random orientations should provide a reasonable approximation. For randomly oriented donors and acceptors, ~~ = 4 if the donors and acceptors have rapid (relative to

7donor) and unrestricted rotation. In rigid me- dia ~~ has been estimated as 0.476 for random orientations (see Ref. (20) for a discussion of K~). Since the motion of the donor and acceptor labels should be hindered to some degree, the applicable value of K’ may be in error by 33% which leads to an uncertainty in the R. values of 56%. Additional errors result from treating the excited-state complexes of pyrenebutyrate as a single species. In spite of these uncertainties, however, the relatively large values of R. calculated for both donor forms indicate that pyrenebutyrate and B- phycoerythrin are good labels for energy- transfer experiments.

The measured lifetimes of the donor- and acceptor-labeled conjugates indicate that gated integration should provide good temporal distinction between B-phycoerythrin fluorescence resulting from direct absorption of light (T approximately 2.5 ns) and B-phycoerythrin fluorescence resulting from energy transfer (7 approximately 50- 100 ns for small values of kT). The recorded fluorescence responses of pyrenebutyrate - anti -human F(ab’)* and B-phycoerythrin-Fab’ to a short pulse of nitrogen laser light are shown in Fig. 3, together with a tracing of the integrator gating signal. The initial rapid rise in the fluorescence of each label (negative voltage deviation) occurs upon excitation by the light pulse from the nitrogen laser. Prior to the pulse arrival, the integrating circuits are inactive as indicated by the low voltage level of the gating signal. Following arrival of the light pulse, the integrators remain inactive for 20 ns, at which time integration of the fluorescence signal begins, as indicated by the high voltage level of the gating signal. From the oscilloscope tracings it appears that a 20-ns integration delay should exclude nearly all of the short-lived B-phycoerythrin emission while allowing integration of a large portion of the longer lived acceptor emission resulting from energy transfer. It may be noted that the average lifetime of the pyrenebutyrate fluorescence, indicated by the top trace in Fig. 3, is

TIME-RESCLVED ENERGY-TRANSFER IMMUNOASSAY 111

Pyrene-anti-Fab’

Delayed gate

B-phycoerythrin-Fab’

H 20 n set

FIG. 3. Oscilloscope traces of fluorescence and integrator timing signals following a nitrogen laser pulse. Volt- ages generated by photomultiplier detector currents are displayed in the upper and lower traces (vertical displacement) as a function oftime (horizontal displacement). In the upper trace, fluorescence reaching the detector was first filtered to pass short-wavelength pyrenebutyrate emission, while in the lower trace, fluorescence was first filtered to pass long-wavelength B-phycoerythrin emission. The center trace is the gating voltage applied to the integrators. Integrators were inactive when the gating voltage was low and active when the gating voltage was high.

shorter than 100 ns. This results from the fact that optical filters used to isolate the pyrenebutyrate emission attenuated the monomer emission relative to the shorter lived excited- state complex fluorescence.

Time-resolved energy-transfer immunoassays. Reagent concentrations for the time-resolved energy-transfer immunoassays were optimized by titrating B-phycoerythrin-human Fab’ preparations with pyrenebutyrate- anti-human F(ab’), preparations. At each concentration, the amount of B-phycoerythrin fluorescence resulting from energy transfer was measured relative to the amount of background fluorescence. The total background fluorescence comprised the B-phycoerythrin fluorescence, resulting from direct absorption of the laser light, and the long wavelength emission of the pyrenebutyrate excited-state complexes which overlapped the wavelength region ofthe B-phycoerythrin

fluorescence. All measurements of the acceptor fluorescence were made using 20-ns integration delays and the background was determined as the sum of the long wavelength fluorescence resulting from each conjugate in the absence of the other conjugate. The pyrenebutyrate emission intensity was essentially unchanged in the presence or absence of the B-phycoerythrin-labeled antigen, showing an average variation in these experiments of about 2% which was uncorrelated the presence of the acceptor. This was expected since affinity tests showed that only 30% or less of the antibody was bound to antigen and the efficiency of energy transfer within an antigen-antibody complex was estimated at about 14%. The fluorescence data from the titrations are plotted in Figs. 4A and 4B, as functions of the labeled antibody to labeled antigen ratio. Common plotting symbols and connecting lines are used olu- tions containing the same conjugate ?ara- tions and the same concentration of the B- phycoerythrin-human Fab’. Generally, the antibody excess required to optimize the signal-to-background ratio was between 5- and IO-fold. At lower antibody excess, the low amount of energy transfer limited the signal level, while at higher excess, background fluorescence resulting from excess pyrenebutyrate limited the sensitivity. It may be noted in Fig. 4A that lower antibody excess was required when antibody preparations with higher degrees of pyrenebutyrate labeling were used. Comparisons of the data sets in Fig. 4B show that a IO-fold dilution of the acceptor-labeled antigen did not greatly alter the optimum antibody excess but signifi- cantly reduced the signal-to-background ratios.

Several competitive immunoassays were performed using optimum concentrations of labeled reagents. In these experiments, concentrations of human Fab’, ranging between 5 X 10P” and 5 X 10e6 M, were mixed with fixed amounts of B-phycoerythrin- human Fab’ and pyrenebutyrate-anti-hu-

112 LARRY E MORRISON

.8

.4

5 .2

i

z 1.2 z p 1.0

2 .8

.6

ii.52 3 5 10 15 20 30

FIG. 4. Effect of conjugate compositions and concentrations on the energy-transfer component of B-phycoerythrin emission. The ratio of the integrated B-phycoerythrin emission, resulting from energy transfer, to the background emission level is plotted at various relative concentrations of pyrenebutyrate-labeled anti-human F(ab’)* and B-phycoerythrin-labeled human Fab’, in the absence of unlabeled antigen (20-ns integration delay). Common plotting symbols indicate a particular combination ofconjugates as follows: (A) 9.7 X 10m9 M antigen conjugate No. 2 combined with antibody conjugate No. 5, 0; antibody conjugate No. 4. 0, antibody conjugate No. 3, A; and antibody conjugate No. 2, A. (B) 9.7 X lO-9 M antigen conjugate No. 2 combined with antibody conjugate No. 5, 0 (repeated from (A)); 9.7 X IO-” M antigen conjugate No. 2 combined with antibody conjugate No. 5,0,9.0 X 10e9 M antigen conjugate No. 3 combined with antibody conjugate No. 5, A; 9.0 X IO-” M antigen

conjugate No. 3 combined with antibody conjugate No. 5, A; and 9.0 X 10e9 M antigen conjugate No. 3 combined with antibody conjugate No. 4, 0. Conjugate reference numbers refer to listings in Tables 1 and 2. Error bars indicate 1 standard deviation of propogated errors.

man F(ab’)z. After an equilibration period, the B-phycoerythrin emission was measured in each sample. Data derived from one of the assays are plotted in Fig. 5. Each data point is the ratio of the integrated long-wavelength fluorescence to the integrated intensity of the excitation pulse. The integrated fluorescence was recorded with either no delay relative to the laser pulse (triangular symbols) or with a 20-m integration delay (circular symbols).

The data sets plotted as open symbols use the total integrated long-wavelength fluorescence which includes a portion of the fluorescence emitted from excited-state complexes of pyrenebutyrate. The data sets plotted as solid symbols use the net B-phycoerythrin emission, obtained by subtracting the long-wavelength pyrenebutyrate emission. Separate measurements of the pyrenebutyrate fluorescence, filtered to remove B-phycoerythrin emission, showed the pyrenebutyrate fluorescence to be essentially independent (2% standard deviation) of antigen concentration. For ease of comparison, the various data sets in Fig. 5 have been normalized to the same value for the long-wavelength emission in the absence of unlabeled antigen.

Fab’ concentration InM)

FIG. 5. Energy-transfer-based competitive immunoassay for human Fab’. Assay conditions are described in Table 4, under assay No. 3. Each data point is normalized to the integrated laser pulse intensity and all data sets are scaled to the same initial value ofthe long-wavelength emission in the absence of unlabeled antigen. Data represented by triangular symbols were recorded with no integration delay. Data represented by circles were recorded with a 20-ns integration delay. Total long-wavelength emission is denoted with open symbols. Long-wavelength emission due only to B-phycoerythrin is denoted with solid symbols. Error bars indicate I standard deviation of propogated error.


TABLE 4

EXPERIMENTALIMMUNOASSAYCONDITIONSANDOBSERVEDRATIOSOFB-PHYCOERYTHRIN (B-PE) FLUORESCENCERESULTINGFROMENERGYTRANSFERANDBACKGROUNDFLUORESCENCE,

WITHANDWITHOUTTIME-RESOLVEDDETECTION

Assay no.

1 2 3 4

B-PE-human Fab Reference no.“ [Fab’] (no)

Pyrene-anti-human F(ab’)z Reference no.a 1.W (nM)

Abou.d/Ag [Human Fab)lmidpoint (nM) J FA,(t)/totaI backgroundb

Integration delay, 0 Integration delay, 20 ns

5 ~AT(0I.r F*aLm(f) b Integration delay, 0 Integration delay, 20 ns

2 3 2 2 9.7 9.0 9.7 9.7

5 5 5 4 150 45 97 150

4.1 3.2 3.3 3.7 41 14 24 40

- 0.22 _t 0.0 1 0.23 t 0.01 0.24 t 0.0 I 1.20 f 0.05 0.65 f 0.04 1 .OO -+ 0.08 1.10?0.06

- 0.36 + 0.02 0.28 f 0.01 0.30 t 0.01 5.0 kO.4 4.0 +0.6 4.1 20.6 2.8 50.2

LI Reference numbers refer to conjugates listed in Tables I and 2. b Total background equals J FAabs(l) plus the integrated pyrenebutyrate emission transmitted by the long pass filters

used to isolate B-PE emission. J FAabs(f) and J FAr(f) are defined in Eqs. [6] and [7] where the integration was carried out between d and d + w (w = 300 ns).

The expected sigmoidal relationship between acceptor fluorescence and antigen concentration was observed in all the data sets plotted in Fig. 5 as a result of the competition between unlabeled human Fab’ and B-phycoerythrin-human Fab’ for binding to the pyrenebutyrate-anti-human F(ab’), . Delay- ing the integration period relative to the excitation pulse considerably improved the relative size of the fluorescence change obtained in response to antigen concentration. The effectiveness of the time-resolution technique can best be judged from the net B-phycoerythrin fluorescence since the technique was not designed to remove the long-lived donor emission. As shown by the solid symbols, a 20-ns integration delay greatly enhanced the energy-transfer component of the acceptor fluorescence relative to the component resulting from light absorption.

The results of four energy transfer immunoassays are listed in Table 4. The data plot-

ted in Fig. 5 correspond to assay No. 3 in this table. Included in the table are the conjugate preparations and their concentrations employed in each assay, the number of pyrenebutyrate-anti-human F(ab’)z bound per B-phycoerythrin-Fab’ in the absence of unlabeled antigen (A&&Ag), the observed human Fab’ concentration at the midpoint of each titration curve, and the signal-to-background ratios obtained in the absence of unlabeled antigen, with 0- and 20-ns integration delays. Signal-to-background ratios are listed for total long-wavelength fluorescence (s FAT(t)/total background) and net B-phycoerythrin fluorescence (s FAr(t)/J FAab(t)). The binding ratios of labeled reagents at the reagent concentrations used in the four assays were determined from titrations of the specified B-phycoerythrin-human Fab’ with the respective pyrenebutyrate-anti-human F(ab’)* preparations and assuming five antibody molecules bind per antigen molecule at


high antibody excess. The saturation value of five antibodies/antigen was estimated from values reported for other antigens of similar molecular weight (25).

DISCUSSION

Binding of a donor fluorophore-labeled antibody reagent to an acceptor fluorophore- labeled antigen reagent greatly reduces the average distance separating the donor and acceptor fluorophores and long-range nonradiative energy transfer becomes detectable. Im- munoassays based upon this principle have been reported by others (2-5). The fact that acceptor fluorescence is usually not moni- tored in these assays is an indication that background fluorescence associated with acceptor measurements is large, particularly when the acceptor-labeled reagent is used in excess. In the energy-transfer immunoassays reported here, high acceptor background fluorescence was also observed. Using pyrenebutyrate-labeled antibodies in excess, the maximum amount of B-phycoerythrin fluorescence resulting from energy transfer was only 18% of the total long-wavelength fluorescence detected in three different immunoassays. Correcting for the amount of long- wavelength donor emission included in these measurements, the energy-transfer component of the acceptor emission was still only 22 to 26% of the total acceptor fluorescence measured.

Taking advantage of the long fluorescence lifetime of the pyrenebutyrate donor label, delaying the period over which the acceptor fluorescence was measured provided a considerable enhancement of the energy-transfer component of the B-phycoerythrin fluorescence. Gated integration of the long-wavelength fluorescence, using a 20-ns integration delay relative to the excitation pulse, provided 3- to 4.6-fold improvement in the ratio of the energy-transfer component of acceptor fluorescence to the remaining long-wavelength fluorescence. With the 20-ns delay, the

energy-transfer component of acceptor emission comprised 39 to 54% of the integrated fluorescence. Subtracting the background component due to long-wavelength donor fluorescence, gated integration of acceptor fluorescence provided a 9.3- to 15-fold increase in the ratio of acceptor fluorescence resulting from energy transfer to acceptor fluorescence resulting from direct absorption of excitation light. The energy-transfer component comprised 74 to 83% of the integrated acceptor fluorescence when the 20-ns integration delay was imposed.

From the above information it is apparent that time-resolved detection of acceptor fluorescence greatly enhanced the relative amount of energy transfer detected. How- ever, for the particular donor fluorophore used here, long-wavelength donor emission limited the enhancement obtained by time- resolved detection. Eliminating excited-state complexes of pyrenebutyrate labels would reduce this interference to negligible amounts but efforts to do this by reducing the degree of donor labeling were ineffective. Excited-state complex formation can be avoided in immunoassays of many nonprotein antigens by using pyrenebutyrate for the antigen label. Switching the donor label to the antigen would reduce the donor background even if excited-state complexes were present since the acceptor-labeled antibodies would be used in excess. However, acceptor excess would lead to increased amounts of directly excited acceptor fluorescence.

The performance of time-resolved detection of energy transfer under different assay conditions should be predictable given Eqs. [6] and [7], the spectral characteristics of the donor and acceptor labels, and the antibody affinity for antigen. Tables 3 and 4 and Fig. 3 provide the required information for predict- ing the results of the immunoassays examined here. Comparison of the predictions with the actual results in Table 4 will allow verification of the theory and justify its use in


TABLE 5

COMPARISON OF EXPERIMENTAL RESULTS WITH THEORETICAL PREDICTIONS OF THE INTEGRATED ACCEPTOR IMPULSE RESPONSE AND THE IMPULSE RESWNSE CONVOLUTED WITH THE INSTRUMENTAL RESPONSE FOR

SEVERAL DONOR-ACCEPTOR DISTRIBUTION MODELS

Assay no.

Gate delay (ns) Observed

Theoretical impulse response, two-point

model

Convoluted impulse response for various distribution models

Two-point Concentric Nonconcentric

1 0 - 0.31 0.28 0.035 0.21 20 5.0 kO.4 560 6.3 0.88 6.1 40 - I ,ooo,ooo 2,600 420 2,600

2 0 0.36 + 0.02 1.1 0.99 0.12 0.95 20 4.0 kO.6 2.000 22 3.1 22 40 - 3,600,OOO 9,300 1,500 9,100

3 0 0.28 k 0.01 0.25 0.23 0.029 0.22 20 4.1 rt0.6 460 5.1 0.71 4.9 40 - 820,000 2,100 340 2,100

4 0 0.30 It 0.0 1 0.23 0.21 0.026 0.20 20 2.8 kO.2 430 4.8 0.66 4.6 40 - 770,000 2,000 320 2,000

a J FAT(t) and J F,&f) are defined in Eqs. [6] and [7] for integration between d and d + w where w = 300 ns.

evaluating untried fluorescent label combina- tions and labeling strategies.

Evaluation of Eqs. [6] and [7] first requires the determination of the rate constant for energy transfer, kr , using the relationship derived by Theodor Forster (19) (Eq. [lo]). The donor and acceptor separation distance required for the calculation of kT can be ap- proximated using the molecular distance relationships of an antibody-antigen complex pictured in Fig. 10. From the dimensions shown in the figure, the distance between the center of a randomly donor-labeled antibody and the center of the B-phycoerythrin acceptor molecule is approximately 100 A. The use of a single value for the separation distance will be referred to as the two-point model since it considers all donor molecules within a complex to be concentrated at one point in space and all acceptor molecules to be concentrated at a second point (26).

Table 5 lists the predicted ratios of the acceptor fluorescence resulting from energy

transfer to the acceptor fluorescence resulting from direct absorption of light. Predictions based upon the two-point model are listed in the fourth column of Table 5 and were calculated using the conditions of each experimental immunoassay, as indicated in the first column, and each of three integration delays, listed in the second column. The observed ratios are listed in the third column, repeated from Table 4. Immediately obvious from the comparison of predicted and observed ratios is that reasonable predictions were obtained only for the pseudo-steady-state condition (integration delay = 0). Calculations using delayed integrations predicted much better discrimination between energy-transfer and directly excited acceptor fluorescence than actually was obtained.

The discrepancy between prediction and experiment is caused by the finite width ofthe excitation pulse and the fluorometer response time. These factors can be corrected for by performing convolutions between the re-


i

FIG. 6. Theoretical fluorescence impulse response for a model system using parameters equivalent to those used in assay No. 3 (see Table 4). Total acceptor emission, F*(t), is represented by the solid line. The portion of acceptor emission due to energy transfer, F&), is represented by the stippled line and the portion due to direct excitation, F&t), is shown as a double-dashed line. Do- nor emission, F,(t), is represented by the dashed line and is scaled to the same value as the total acceptor emission att=O.

sponse of the fluorometer detectors to scattered excitation light, L(t), and the predicted impulse responses of the acceptor fluorescence, F*(t), as shown in Eq. [ 1 I] (see Materi- als and Methods). F*(t) is plotted in Fig. 6 for the experimental conditions of assay No. 3, together with the two components of acceptor emission, FAT(t) and FAabs(t), and the relative donor fluorescence, F,(t). The corresponding convolution of F*(t) and FAabs(t) with L(t) are plotted in Fig. 7, together with the experimental recording of L(t).

Comparisons of the curves in Figs. 6 and 7 show that the excitation pulse width and fluorometer response cause the detected acceptor fluorescence to persist longer than expected based upon the fluorescence impulse response. The greatest effect of the time- broadening is on the component of acceptor fluorescence due to direct absorption of light, since this component has the shortest lifetime, resulting in the observed reduction in discrimination between the energy-transfer and directly excited components of the acceptor fluorescence. This is emphasized by comparing the solid lines in Figs. 8 and 9

Time ,nanarecon*s,

FIG. 7. Convolution of theoretical fluorescence impulse response with instrumental response. The double- dashed line represents the recorded anode current produced in response to light scattered from the dye laser excitation pulse. The convolution of the fluorometer response with the theoretical acceptor emission is represented by the solid line, for the conditions of assay No. 3. The convolution of the component due to direct excitation of the acceptor is represented by the dashed line. All peak intensities are normalized to a value of 1.

which describe the composition of the integrated acceptor fluorescence as a function of the integration delay for the fluorescence impulse response and the convoluted impulse response, respectively. With a 20-ns integration delay, nearly 100% of the integrated impulse response results from energy transfer, in contrast to a value of 84% predicted from the

FIG. 8. Integrated theoretical fluorescence intensities as a function of gate delay for a model of assay No. 3. The corresponding theoretical fluorescence curves are presented in Fig. 6. The percentage of the integrated fluorescence resulting from energy transfer is represented by the solid line. The percentage of the total fluorescence integrated is represented by the stippled line.


FIG. 9. Integration of convoluted acceptor fluorescence plotted as a function ofgate delay. The corresponding convoluted curves are presented in Fig. 7. The percentage of the integrated fluorescence resulting from energy transfer is represented by the solid line. The percentage of the total fluorescence integrated is represented by the stippled line.

convoluted response. Ratios of the integrated convoluted components of acceptor fluorescence are listed in the fifth column of Table 5 and show considerably better agreement with the experimentally determined ratios. In fact, good agreement between predicted and experimental values was obtained in three of the four assays.

The reason for the large disagreement between observed and predicted ratios in assay No. 2 can be explained by the different spatial arrangements of donor and acceptor labels in the antibody-antigen complexes. In assays No. 1, 3, and 4 the antigen conjugate consisted of a single Fab’ fragment attached to a molecule of B-phycoerythrin. In assay No. 2 the antigen conjugate consisted of multiple Fab’ fragments attached to a molecule of B- phycoerythrin. The spatial arrangement of an antibody-antigen complex in assay No. 2 may better be described by Fig. 11. In assay No. 2, the B-phycoerythrin label would be at the center of a sphere with radius R, which contained the pyrenebutyrate-labeled antibodies bound to the Fab’ fragments. The mul- tiply appended Fab’ fragments may serve to exclude the antibodies and their labels from a sphere of radius R2 around the B-phycoerythrin. Although a larger number of antibodies

surround the acceptor in this complex, donor labels obtain closer approach to the acceptor when only one Fab’ fragment is attached to the acceptor (see Fig. 10). This would explain the discrepancy between predictions made using the two-point model above. Factors other than spatial arrangement which affect energy transfer would appear to be unchanged between the different B-phycoerythrin-antigen conjugates. An estimated 33% uncertainty in the value of K’ (see Results) would not be sufficient to account for the discrepancy between assay No. 2 and the other assays and it would be difficult to rationalize a larger variation in K’ between the antibody- antigen complexes described in Figs. 10 and 11.

Better estimation of the energy transfer rate constants may be obtained by considering the distribution of separation distances within an antibody-antigen conjugate (2,269. - - this calculation kT is summed over all d ‘-acceptor separation distances accordin Gv

kT = k,,NA s

* P,(Ro/r)6dr, 1121 0

where P, is the ‘probability of finding a donor

Nonconcentric

I-llOA-I -llOA+ Hd-i

FIG. 10. Spatial model for antibody-antigen complexes involving 1: 1 B-phycoerythrin-human Fab’ conjugates. Molecular dimensions for IgG class antibodies and B-phycoerythrin (B-PE) were obtained from Refs. (2) and (27). The shaded circles represent Fab’ fragments with diameters of approximately 50 A. Antibody (Ab) molecules are assumed to be randomly labeled with pyrenebutyrate. The signilicances of r, R, , and R2 are described in the text.


Concentric

FIG. 11. Spatial model for antibody-antigen complexes involving B-phycoerythrin-human Fab’ conjugates containing multiple Fab’ fragments. See Fig. 10 for further details.

and acceptor label separated by a distance r and NA is the number of acceptor labels present in each antibody-antigen complex. For the antibody-antigen complex pictured in Fig. 11, where the donor labels are concentri- cally distributed about the acceptor label, kT is given by

kdL% kT =

s RI

rm4dr R2

s

RI r2dr

R2

= k&/WG)3. [I31

For the antibody-antigen complex pictured in Fig. 10, where the donor labels are noncon- centrically distributed about the acceptor label, kT is given by

ICDNd~ s

25 re4(2R, - r)dr

kT = R2

s 25

r2(2R, - r)dr R2

k,R$(R; + 16R: - 12R:R,)

= 2R;R:( 16R’: - 8R,R: + 3R:) ’ iI41

when the center of the sphere with radius R, coincides with the center of the Fab’ frag-

ment. Both equations only approximate the actual spatial characteristics of the respective antibody-antigen complexes; however, considering other approximations used in the energy-transfer calculations, Eqs. [ 131 and [ 141 should provide adequate accuracy.

Predicted ratios of the integrated and convoluted components of the acceptor fluorescence are listed in the last two columns of Ta- ble 5 for each of the two distributions. Predic- tions based upon the nonconcentric label distribution of Fig. 10 provide reasonable agreement with the experimental results of assays No. 1, 3, and 4 and are very similar to the predictions using the simple two-point model. Predictions based upon the concentric label distribution of Fig. 11 provide reasonable agreement with the experimental results of assay No. 2 but not with the other three assays, as expected since only assay No. 2 used an antigen conjugate in which multiple Fab’ fragments were attached per B-phycoerythrin. These results support the hypoth- esis that multiple antigens attached to the acceptor label shield the acceptor from close approach of the donor labels. Reasonable predictions for assay No. 2 are obtained using the two-point model if shielding of the acceptor is taken into account. When the separation distance is chosen to be the distance between the center of the two circles in Fig. 11 and a point halfway between the circumfer- ences of the two circles (about 150 A), then a ratio of 3.2 is calculated which is nearly iden- tical to the value determined using the concentric distribution.

The preceding analysis has demonstrated that gated detection of energy transfer can be properly modeled using the theoretical fluorescence impulse response and the instrumental response of the detection system. Looking beyond the conditions under which assays No. 1 through 4 were performed, the theoretical predictions offer insight into how these experiments may be improved and predict the performance of other label combina- tions. For example, lengthening the delay of


the integration period from 20 to 40 ns would have provided considerably more discrimination between the energy-transfer and directly excited components of B-phycoerythrin emission. In Table 5 predictions for gate delays of 40 ns are included and show about a 400-fold increase in the ratio of the two emission components when the gate delay is dou- bled from 20 to 40 ns. The accompanying decrease in the magnitude of the integrated acceptor fluorescence upon doubling the integration delay is only 50% (see dashed lines in Figs. 8 and 9).

Unfortunately, in the donor-acceptor system examined in the present work, increasing the integration delay would only slightly increase the overall signal-to-background level due to the long-wavelength background emission of the pyrenebutyrate excited-state complexes. The donor background component was emphasized in the immunoassays since a large excess of donor-labeled antibody to acceptor- labeled antigen was required to obtain optimal amounts of energy transfer. In this situation it might be more advantageous to label the antibodies with B-phycoerythrin and label the antigen with pyrenebutyrate. The theoretical relationships can be used to determine if a higher or lower overall signal-to-background ratio would be obtained in this hypothetical situation. A hypothetical situation analogous to the conditions of assay No. 3 with reversal of the labels would contain the following: 3.3 antibodies bound per Fab’ fragment, antibody present in lo-fold excess to antigen, antibody and B-phycoerythrin conjugated in a 1: 1 ratio, and pyrenebutyrate and Fab’ fragments conjugated in a 1: 1 ratio (since larger labeling ratios produce unusually high levels of excimer emission-see last two entries in Table 1). A concentric label distribution is expected to adequately describe this system where the Fab’ antigen is placed at the center of a sphere with a radius of 130 A and accep tor labels are excluded from a concentric sphere of 50 A diameter. Following convolution of the impulse response with the fluorometer response. the ratio of the integrated acceptor

component to the directly excited acceptor component was predicted to equal 0.15 for an integration delay of 20 ns. Increasing the integration delay to 40 ns improved the ratio to a value of 34. Although this value is low when compared to the value predicted for the conditions of assay No. 3 with a 40-ns integration delay (see Table 5), the overall signal-to-background ratio of the assay, which includes the pyrenebutyrate background component, was predicted to be 29:1, considerably larger than the observed ratio of 4.1 using excess donor- labeled antibodies. For a donor/acceptor pair of pyrenebutyrate and B-phycoerythrin, the ability of gated detection to distinguish between the energy-transfer and directly excited components of the acceptor emission outweighs the poor ability of the optical filtering to distinguish between donor and acceptor emission.

As a final note, the midpoint concentrations of the antigen titration curves, listed Ta- ble 4, show that the sensitivities of the energy- transfer assays are on the order of 10 nM. While this is a moderate sensitivity level for immunoassays, the object of this work was not to obtain high sensitivity but to (i) demonstrate enhancement of the energy-transfer component of acceptor fluorescence using time-resolved detection in conjunction with a long-lifetime donor, and (ii) demonstrate that the time-resolved detection of energy transfer could be effectively modeled. Lowering the assay sensitivity level would require reducing the concentration of labeled antigen and antibody reagents. While the fluorometer can de- tect the acceptor fluorescence at concentrations IOOO- to lO,OOO-fold lower than those used here, the formation of appreciable amounts of antibody-antigen complexes at lower reagent concentrations would require the use of antibodies with affinity constants considerably higher than those used here.

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