2009
Anal. Chem. 1982, 5 4 , 2009-201 1
Direct Measurement of Fluorescence Polarization or Anisotropy Clarke J. Halfman" and Arthur S. Schneider Department of Pathology, 4Wnlversltyof Health Sclences/The Chicago Medical School, North Chicago, Illinois 60064
We demonstrate that the polarizatlon or anlsotropy of a solution contalnlng fluorescent components can be determined from the ratio V / Z 6 ,where V Is the vertlcai component of the emlsslon and Z 6 Is the Intensity wlth the transmission angle of the polarizer at 6. I n dual channel, ratlo instruments V / Z 6 can be measured directly. Z 6 is measured In the dlvisor channel by settlng 6 so that tan2 6 = C to determine polarizatlon and so that tan2 6 = 2C to determine anlsotropy, where C is the relative transmission of the vertlcal component through the detectlon rrystem wlth respect to that of the horlzontal component. The ratlo V / Z 6 Is linearly related to polarization or anlsotroply in contrast to the more commonly measured ratlo, V / H , where H Is the horlzontal component of the emisslon. A disllnct advantage In measuring V / Z 6 , rather than V / H , Is thal direct instrument readout of poiariration, or anlsotropy, ci3n be acquired In a contlnuous and Instantaneous manner without addltlonal data processing.
When the rotary motion of a fluor is not rapid with respect to the lifetime of the excited state, the emission is polarized. Fluorescence polarization, P, or anisotropy, A , is defined by
P=
vv - CHV -orA= CHV
vv
+
Vv -- CHv Vv f 2CHv
(2)
where Vv and Hv are the measured vertical and horizontal emission components, renpectively, with the excitation beam polarized in the vertical position. Four signals must be measured in order to determine the polarization of a solution. However, since C ideally dlepends only upon the characteristics of the optical system and not upon the polarization of the specimen, it is constant for a particular wavelength and slit width. Thus, once C is determined from measurements of VH and HHon any specimen in a group, the polarization may be determined for the remaining specimens from the measurement of only V" and Hv. I[nstruments are available with two detector systems and which provide direct readout of the ratio of the two signals. Thus, the ratio V / H may be measured directly. Instruments with a single emission detector, but employing a rotating polarizer, also provide direct readout of the ratio V / H . Determinations are more convenient and precise with ratio instruments, and polarization or anisotropy is calculated from
Vv/Hv
+C
or A =
Vv/Hv
+ 2C
(3)
However, since I , = V" + CHv and It = V" + 2 C P , where I, is the measured total intensity, and It is the total emitted intensity (Z), then CHv = I , - Vv = (It - Vv)/2 and
P = 2Vv/I, - 1 or A = 3(Vv/It)/2 - 1 / 2
(4)
which shows that the ratio V"/I, (or V"/It)is linearly related to and completely defines the polarization (of anisotropy). When a polarizer is not present in the divisor detector system and C = 1 (which may be the case when mirrors or gratings are absent), then the signal is proportional to I , and polarization may be measured directly by appropriately adjusting the relative magnitude of the two detector signals and subtracting one from the ratio signal. When C # 1, or to determine anisotropy, a polarizer can be used in the divisor detector system and set at an angle, 6, from the vertical so that the measured intensity, la, is proportional to I, or It. At a transmission angle of 6, the signal intensity, 18, is determined by (3) la= cos2 6[Ivv (IHv,/C) tan2 61. Then, when tan2 6 = C, la= I,/(l + C) and when tan2 6 = 2C, I8 = It/(l+ 2C). It therefore follows from eq 4 that
+
p=- 2 where Ivv and I H v are the vertical and horizontal emission components, respectively, with the incident beam polarized in the vertical direction. The optical system, however, perturbs the relative magnitude of the two components so that in practice a correction factor must be applied to the measured components (1). The correction factor, C, is determined as the ratio of the measured vertical component/horizontal component with the excitation polarizer in the horizontal position, i.e., C = VH/Hn. The corrected polarization or anisotropy is given by
Vv/Hv - C
Vv/Hv - C
P=
-v v -
1 + c Is
1orA=
3 vv - - 1 / 2 (5) 2(1 + 2C) 1 6
Polarization or anisotrppy can thus be determined directly from the ratio signal, according to eq 5, by setting the divisor detector polarizer at a proper transmission angle and appropriately adjusting the relative signal strengths of the two detectors. Experimental verification of eq 4 and the method by which polarization or anisotropy can be determined directly in practice according to eq 5 are demonstrated. EXPERIMENTAL SECTION Chemicals. All reagents used were of highest analytical grade available. Water was glass distilled and deionized. The buffer employed was 0.01 M sodium phosphate in 0.15 M NaCl adjusted to pH of 7.40 h 0.05 with 1 M HC1 or 1 M NaOH. Tetramethylrhodamine B (RB) was purchased from Eastman (Rochester, NY) as the laser grade perchlorate salt. The isothiocyanate derivative of RB was purchased from Research Organics (Cleveland, OH). Concentrations of RB and derivatives were determined from the absorbance at the peak in the vicinity of 550 nm using a molar extinction coefficient ( 4 ) of 1.1 X lo5. RE in an acrylic block (1 cm X 1 cm X 3 cm) was purchased from Perkin Elmer Corp. (Norwalk, CT). The optical density of the block at 552 nm was 0.10. Rabbit antiserum to RB was prepared in our laboratory. Antiserum preparation involved immunizing rabbits with bovine serum albumin (BSA) conjugated with the thiocyanate derivative of RB by subcutaneous injection of 5 mg of the antigen in 1mL of complete Freund's adjuvant. A month later a booster injection was given and after another week, animals were bled by cardiac puncture. Immunoglobulins in the antiserum were precipitated with 40% ammonium sulfate and redissolved in buffer. Binding of fluor by antibody resulted in minimal fluorescence intensity change but the polarization of bound fluor was about 0.45 compared t o 0.09 for the free fluor. The dissociation constant for the antibody-RB interaction was estimated
0003-2700/82/0354-2009$01.25/00 1982 American Chemical Society
2010
ANALYTICAL CHEMISTRY, VOL. 54, NO. 12, OCTOBER 1982
Table Ia Vv
HV
Vn
4.997
1.756
3.767
Hn 3.720
c
Plb 0.475
1.013
A,b 0.376
Im
6.176
p2 0.475
It
8.555
A,C 0.376
P,d 0.475
Asd 0.375
a kkasurements on the rhodamine block as described in the text. Excitation wavelength was 542 nm and matched Corning No. 22 filters were used in both detectors, Calculated according to eq 2 or 3. Calculated according to eq 4. Determined directly according to eq 5 .
to be approximately 2 X lo-'' M by a fluorescent titration technique (5). Fluorescence Measurements. As SLM System 4000 (Champaign, IL) was used for fluorescence measurements. The instrument has two detection channels, each at 90' with respect to the excitation beam and 180' with respect to each other, Le., a T configuration. Photomultiplier tubes were selected for high wavelength sensitivity (Hamamatsu R928-P). The instrument is equipped with two holographic monochromators, one for the excitation beam and the other for one of the emission detector channels. Each monochromator may be driven by a stepping motor whose position is proportional to an output voltage which is applied to the X axis of a recorder for taking spectra. Glann-Thompson polarizers may be positioned in the excitation and detection beams to obtain polarization data. The polarizers are scribed at 35.3' and 54.7' for exact positioning at these two transmission angles. The electronic design provides digital readout of either detection channel or their ratio. The cuvette holder is channeled for temperature control by a circulating water bath. There is a magnetic stirring motor below the cuvette holder. We drilled a small hole in the sample compartmentcover, immediately above the position where a cuvette would be placed, for the purpose of rapidly injecting a reactant for kinetic studies or for slowly infusing a reactant with a constant speed spyringe pump for binding studies.
RESULTS AND DISCUSSION Table I shows data obtained on rhodamine B "frozen" in an acrylic block at a concentration of approximately lo* M. From measurements of p, Hv, VH, and HH in the single channel mode, polarization (P,) and anisotropy (A,) were calculated according to eq 2. The same values for the parameters (P, and A,) were also obtained by calculating according to eq 4. The validity of eq 4 is thus demonstrated. Direct measurement of P or A for a series of specimens with a dual channel instrument i s achieved by adjusting the relative magnitude of V" in the two detector channels to an appropriate value for any specimen and then orienting the divisor detector polarizer to the proper 6. From eq 5 it follows that the proper Vv ratio for determining P is 2/(1 C) and is (3/2)/(1 2C) for determining A. A value of one (or 1/2) is subtracted from the V"/& ratio resulting in a direct readout of P (or A ) . The readout for the remaining specimens is directly P or A . The parameters determined in this manner (P3and As) for the rhodamine block are shown in Table I and are in excellent agreement with the parameters calculated from measurements of the individual emission components. The above procedure requires that the transmission angle is accurately scribed on a polarizer. However, it b also possible to set the orientation of the divisor polarizer in a manner which does not require knowing 6 directly. The individual emission components, or the ratios P / H v and VH/HH,of one of the specimens are measured, and P and A is calculated. Next, the signals from the two detectors are adjusted so that the ratio with both polarizers in the vertical position is 2/(1 + C) for P or is (3/2)/(1 + 2C) for A . Then the transmission angle of the divisor detector polarizer is adjusted so that the ratio, V"/I,,is equivalent to (P 1)or to ( A + 1/2). When the ratio signal is the latter value, then the polarizer is oriented at 6 and the remaining specimens are read with the polarizer set in this position. The specimen employed for setting 6 by the above procedure must be chosen judiciously, however, because the mag-
P 0.000
6
/
( 0 )
38
36
40
Figure 1. Variation in intensity, I * , with respect to the intensity at 6 = arctan (c)"*at various P values as the polarizer transmission angle, 6, is varied. Calculated according to equation 6 with C = 0.60.
0 40-
+
+
+
0 10-
Acx ( nm) 430
460
490
520
Figure 2. Polarization excitation spectrum of rhodamine B (ca. IO-' M) "frozen" In an acrylic block. Both V V I H Vand P were monitored directly. Matched Cornlng R62 filters were used in both detectors.
nitude of changes in I8 with changes in 6 depends upon both P (or A ) and C. Since Ia/Iarctan ~ 1 1 2 )= (Vv cos2 6 + Hv sin2 6)/[(Vv + CHv)/(l + C ) ] apd Vtr /Hv = C ( l + P)/(l- P), it follows that I8
= - i'[C(l
LCtan(C)'/2
2c
+ P) cos2 6 + (1- P ) sin2 61
(6)
The above relationship is illustrated in Figure 1for C = 0.6 and several values of P. It is evident that specimens with intermediate values of P would exhibit a lower dependence of Iaon 6 than would those with low or high values of P. The
ANALYTICAL CHEMISTRY, VOL. 54, NO. 12, OCTOBER 1982
I-----A p L ANTIBODY
"I
0
20
30
Figure 3. Direct monitoring 01 VVIHVor A as an antibody (diluted 1:4) to rhodamine B is infused at a constant rate into 2 mL of 5 X IO-' M rhodamine B (in 0.01 M sodiium phosphate, 0.15 M NaCi, at a pH of 7.40).
sensitivity of lato changw in 6, when C = 0.6, is a maximum and is equivalent for specimens with P values of 0 and 0.5. Specimens with either P value would be equally suitable to use for adjusting 6. Specimens with P in the vicinity of 0.25 would definitely be unsuitable. When C a 0.6 the absolute value of d[la/I,,~ce/z,]/c~6,in the vicinity of 6 = arctan C, for P = 0 is greater than that for P = 0.5. When C > 0.6 the absolute value of the slope (S)is greater for P = 0.5 than for P = 0. The relative sensitivity (!-!&/SI) of Ala to A6 of the two specimens in a group which have the highest P value (Ph)and the lowest (PI) may be determined for any value of C from
(7) The specimen with the greatest sensitivity to changes in la with changes in 6 is used to set 6. The capability to determine A or P directly without additional data processing alllows instantaneous and continuous measurement of the desired parameter. Direct measurement of A or P is useful when a specimen is continuously perturbed in such a way that the fluorescence parameter responds to the perturbation in a characteristic manner. Examples of useful
2011
applications include measurement of the excitation polarization spectrum of a fluor (Figure 2) and monitoring the extent of binding in ligand-protein binding studies (Figure 3). The excitation polarization spectrum of the rhodamine B block, determined by continuous, direct measurement of P as the excitation wavelength is continuously changed, is shown in Figure 2. I,,, was monitored in the divisor channel with the transmission angle of the polarizer set so that V"/Ia= P + 1 at A,, = 540 nm after adjusting the ratio signal to 2/(1 + C) with both polarizers in the vertical position. The Vv/Hv ratio was also monitored and values of P calculated from eq 3 were identical with those measured directly. Direct measurement of P without a polarizer in the divisor channel (not shown) yielded results which were discrepant by as much as 0.01 units at either extreme of the range of P values. When the ratio signal was initially adjusted at low P values, then the direct value was inaccurate at high P values and vice versa. The discrepancy occurred because C was sufficiently different from a value of one. Increased anisotropy associated with binding of rhodamine B to specific antibody is shown in Figure 3. A small volume of antibody (50 pL) was infused into 2 mL of 5 X M fluor with a constant speed syringe pump while directly recording V"/H"or anisotropy. Itwas monitored in the divisor detector channel by setting 6 so that V"/Ia= A 1 / 2 for the cuvette from the prior V"/H"titration after adjusting the ratio signal to (3/2)/(1+ 2C) with both polarizers in the vertical position. Values of A calculated from Vv/Hvwere identical with the directly measured values.
+
ACKNOWLEDGMENT We wish to acknowledge the expert technical assistance of William Pysto.
LITERATURE CITED (1) Weber, G. Blochemistry 1952, 57, 145. (2) Spencer, R. D. In "Nonlsotopic Alteratives to Radioimmunoassay";
Kaplan, L. A., Pesce, A., Eds.; Marcel Dekker: New York, 1981; Chapter 9. (3) Mlelenz, K. D.; Cehelnik, E. D.; McKenzie,R. L.J . Chem. Phys. 1976, 64, 370. (4) Ramette, R. W.; Sandell, E. J . Chem. Soc. 1956, 78, 4872. (5) Halfman, C.; Nlshida, T. Biochemistry 1972, 7 7 , 3493.
RECEIVED for review January 28, 1982. Accepted June 29, 1982. This work was supported in part by the Veterans Administration, by DMMS/NIDA Grant No. 1R03 DA-02775-01, and by Biomedical Research Support Grants No. 2-533-730, No. 2-561-730, and No. 2-582-710, awarded by the Biomedical General Research Support Grant Division of Research Resources, National Institutes of Health.
