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A sandwich ELISA for properdin in clinical specimens
Journal of Immunological Methods, 98 (1987) 161-172 Elsevier
161
JIM 04281
A sandwich ELISA for properdin in clinical specimens * L o u i s G . H o f f m a n n 1, A. K a y Pitts 2, P e t e r D e n s e n 2, J o h n M. Weiler 2, J o h n E. Butler 1 a n d J e f f r e y H. P e t e r m a n 1 Departments of ~ Microbiology and 2 Internal Medicine, University of Iowa, Iowa City, IA 52242, U.S.A. (Received 3 November 1986, accepted 3 December 1986)
We have developed a symmetrical sandwich ELISA for measuring human properdin (P) in serum by using the globulin fraction from a commercial antiserum as the capture antibody adsorbed on the plastic. The detecting reagent was a glutaraldehyde conjugate of this Ig fraction with alkaline phosphatase. Two types of inhibition were observed in this study. First, inhibition was observed when > 2.5 ~ g / m l of the globulin fraction was used to coat the plates. A second type of inhibition was observed for serum dilutions < 1 / 4 0 0 ; it was independent of the concentration of capture Ab and did not occur when purified P was assayed. The data generated with this assay could be fitted in log-log mode by a quadratic equation. The coefficient of the linear term in this equation was found to be the same for serum and purified P, within the limits of experimental error. The results for different samples run on the same plate were expressed in terms of the relative concentration of each sample required to produce an OD405 = 0.2. A sample of pooled normal h u m a n serum was run on each plate as a reference; it was assigned a titer of 100 ELISA u n i t s / m l ( E U / m l ) . The titers of the unknown samples were expressed in terms of E U / m l by reference to this standard. For purified P, the assay could readily detect 10 n g / m l . By comparing purified P with our reference serum pool, we found that 1 EU equals 0.57 ~g. Day-to-day variation for a group of nine normal sera showed a mean difference of - 0 . 8 5 E U / m l , SD 5.85 E U / m l . The mean titer for these normal sera was 78.9 E U / m l , SD 15.7 E U / m l . In three recovery experiments in which purified P was mixed with pooled normal serum, the recoveries ranged from 96 to 117%. We conclude that the sandwich ELISA constitutes an adequate immunochemical assay for human P in serum specimens. Key words: ELISA; Complement; Properdin
Introduction Properdin is a component of the alternative pathway of complement activation which funcCorrespondence to: L.G. Hoffmann, Department of Microbiology, University of Iowa, Iowa City, IA 52242, U.S.A. * Supported by Merit Review Awards and Clinical Investigatorships from the Veterans' Administration to P.D. and J.M.W., and by NIH Grants nos. A1-16476 and HL-22676. Abbreviations: Ab, antibody; ELISA, enzyme-linked immunoassay; EU, ELISA unit; Ig, immunoglobulin; P, properdin; RC, relative concentration.
tions by stabilizing the alternative pathway C3 convertase, C3b,Bb, from spontaneous decay (Fearon and Austen, 1977). Its measurement in serum samples presents difficulties when presently available methods are used. Hemolytic assays are complicated by the presence in serum of variable concentrations of complement factors B and H, which together with P determine the rate and extent of formation of the C3 convertase of the alternative p a t h w a y . A ' r o c k e t ' i m m u n o e lectrophoresis procedure has been described by Schrager et al. (1976), but this procedure requires
0022-1759/87/$03.50 © 1987 Elsevier Science Publishers B.V. (Biomedical Division)
162 large quantities of antiserum to P, and we have found it difficult to reproduce; after several attempts with the same normal samples, we were able to obtain visible precipitates only once. Therefore, we have developed a sandwich ELISA for P, using the Ig fraction from a commercial antiserum to P to capture P and a glutaraldehyde conjugate of alkaline phosphatase with the same Ig fraction (symmetrical configuration) as the detection system. Our goals in developing this assay were sensitivity, precision, and accuracy. The precision of an assay depends on its dose-response curve. In a model ELISA system studied by Butler et al. (1986), the log-log plot of antigen captured vs. antigen input was found to be linear with a slope equal to 1 when the capture Ab was in excess; the plot approaches a plateau at high inputs of antigen where Ab becomes limiting. The range of antigen concentrations over which the dose response is linear reflects the concentration and affinity of the capture Ab. Hence, the ideal sandwich ELISA is one which yields a log-log dose-response curve that is linear with a slope close to 1 over a wide range of antigen concentrations. We examined various parameters of the assay in order to establish conditions under which this ideal is approached most closely. Accuracy in any assay requires that the dose-response lines of different samples be parallel to each other and to that of the standard; we established conditions under with this requirement is met. The accuracy of the assay was examined further by recovery experiments in which chromatographically purified P was added to serum samples to determine whether the added P could be measured accurately.
Materials and methods
Reagents Goat antiserum to human P (lot no. 026) was purchased from Atlantic Antibodies. Its specificity was checked by immunoelectrophoresis, which showed a single arc against normal human serum; this arc corresponded to that produced by pure P. Properdin was purified from outdated, pooled human plasma (Fearon and Austen, 1977). Bovine alkaline phosphatase and its substrate, p-
nitrophenyl phosphate, were purchased from Sigma Chemical Co. Human serum samples were prepared from blood collected from healthy consenting volunteers, and stored at - 7 0 ° C. A pool of 20 normal sera was divided into small aliquots which were also stored at - 7 0 ° C and used only once. Buffer A: 0.1 M NaHCO3/Na2CO3, pH 9.6. Buffer B: 0.15 M NaC1, 10 mM N a H 2 P O 4 / Na2HPO4, 0.05% Tween 20, pH 7.1. Buffer C: 50 mM N a H C O 3 / N a 2 C O 3, 1 mM MgC12, pH 9.8. Rinsing solution: 0.15 M NaC1, 0.05% Tween 20. A crude globulin fraction was prepared from the anti-P antiserum by precipitation with an equal volume of saturated (NH4)2SO 4. The precipitate was collected by centrifugation, washed with 50% saturated (NH4)2SO 4, and redissolved in the original volume of buffer B without Tween; it was then dialyzed for 3 days against three changes of the same buffer. The final preparation contained ca. 5 r a g / m l of protein as determined spectrophotometrically on the basis of an extinction coefficient of 1.36 m l / m g at 278 nm. Glutaraldehyde conjugation with alkaline phosphatase was performed according to Avrameas (1972) at 1 m g / m l of globulins and 1.5 m g / m l of enzyme.
Methods Except for variations indicated in the results section, the sandwich ELISA was performed as described by Butler et al. (1986). Briefly, the anti-P globulin fraction was diluted 1/4000 in buffer A. We dispensed 0.2 ml of this dilution per well into Immulon 2 microtiter plates for overnight adsorption at room temperature. The plates were washed with rinsing solution by means of a 16-well microtiter plate washer described by Butler et al. (1985). Two-fold serial dilutions of P samples were made in buffer B, and 0.2 ml of each was pipetted into duplicate wells. The plates were incubated on a rotary shaker for 2 h at room temperature and washed. The enzyme-antibody conjugate was diluted 1 / 7 5 0 in buffer B; this dilution was established as optimal in a preliminary experiment. We pipetted 0.2 ml of the diluted enzyme-antibody conjugate into each well and incubated the plates on a rotary shaker for 2 h as before. After another wash, 0.2 ml of substrate solution (1 m g / m l pnitrophenyl phosphate in buffer C) was added to
163 each well. T h e OD405 of the well c o n t a i n i n g the highest i n p u t of the s t a n d a r d was m o n i t o r e d o n a B i o T e k M o d e l EL-310 p l a t e r e a d e r until it rea c h e d 1.2; at that time, the O D value of each well was m e a s u r e d a n d recorded. E a c h p l a t e i n c l u d e d c o n t r o l s w i t h o u t antigen (to m e a s u r e b a c k g r o u n d activity) a n d serial d i l u t i o n s of a s t a n d a r d serum pool.
Results
Inhibition at high serum concentrations R e p r e s e n t a t i v e results for an a s s a y on p o o l e d n o r m a l h u m a n serum, d i l u t e d f r o m 1 / 1 0 1 to 1 / 6464, are shown in Fig. 1 in s e m i - l o g a r i t h m i c
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Relative Concentration Fig. 1. Inhibition of the dose response at high serum concentration. The ordinate shows OD405 as a function of relative antigen concentration, which is plotted on a logarithmic axis. A relative antigen concentration of 1.0 represents a 1/6464 dilution of serum. The dilution of capture Ab was 1/4000 (ca. 1.25 /~g/ml of Ig). The points represent OD readings from duplicate wells receiving the same serum solution, corrected for background readings from wells receiving no antigen. The solid line depicts the quadratic equation fitted to the data in log-log mode as described in the results section under 'Analysis of the Data'. The dashed horizontal line represents an OD = 0.200.
form. T h e abscissa shows relative serum conc e n t r a t i o n (the inverse of dilution) on a logarithmic scale. (This scale was a d o p t e d s i m p l y to imp r o v e the clarity of the graph.) T h e o r d i n a t e shows O1:)405 c o r r e c t e d for b a c k g r o u n d in wells receiving no antigen, on a linear scale. T h e solid line was fitted as discussed in the next section. The dose response clearly passes through a m a x i m u m at a s e r u m dilution of ca. 1 / 4 0 0 . It seemed of interest to d e t e r m i n e whether the i n h i b i t i o n o b s e r v e d in Fig. 1 was inherent in the assay, or whether it was an artefact due to inhibition of some step in the assay b y an u n k n o w n s e r u m constituent; in the l a t t e r case, we also wished to d e t e r m i n e whether the i n h i b i t i o n might be a c o n s e q u e n c e of p o o l i n g several sera. W e therefore a n a l y z e d p o o l e d n o r m a l serum, a r a n d o m l y selected i n d i v i d u a l n o r m a l serum, a n d purified P on the s a m e plate. The serum dilutions ranged f r o m 1 / 1 0 1 to 1 / 1 2 813, a n d the c o n c e n t r a t i o n s of purified P from 2.2 to 282 n g / m l . The results are shown in log-log form (the form in which the d a t a were a n a l y z e d ) in Fig. 2. The titration plot for p o o l e d n o r m a l serum clearly shows i n h i b i t i o n at high serum c o n c e n t r a t i o n s , (i.e., at dilutions < 1 / 4 0 0 ) when c o m p a r e d to the titration plot o b t a i n e d for p u r i f i e d P. T h e curve for the i n d i v i d u a l n o r m a l s e r u m shows less inhibition, suggesting that p o o l i n g sera m a y c o n t r i b u t e to the o b s e r v e d inhibition. However, o t h e r i n d i v i d u a l sera (not shown) y i e l d e d variable degrees of inhibition, some of which were as great as those seen with the p o o l e d serum. These results indicate that the inh i b i t i o n o b s e r v e d with n o r m a l s e r u m is due to the presence of interfering substance(s). T h e degree of i n h i b i t i o n is to some extent m a s k e d b y the log-log m o d e of p l o t t i n g the data; it is m o r e evident when one considers the increase in O D on going from the lowest p o i n t in the assay to the highest point, a 128-fold increase in c o n c e n t r a t i o n . T h e corres p o n d i n g increase in O D is 29-fold for p o o l e d n o r m a l serum, 42-fold for the i n d i v i d u a l n o r m a l serum, a n d 107-fold for purified P.
Analysis of the data T h e i n h i b i t i o n o b s e r v e d at high serum conc e n t r a t i o n s was f o u n d to p r e c l u d e analysis of the d a t a b y either linear regression or logit plots as p r o p o s e d b y P e t e r m a n (1986). Both of these p r o -
164
Pooled Normal Serum
Individual Normal Serum
Purified P
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cedures led to fitted fines that were not parallel for different serum samples. The reason for the failure of both the linear and logit equations to fit the data adequately is that neither of these equations predicts a maximum. We therefore used an empirical quadratic equation to fit the data by linear regression of log O D on log concentration. The choice of a quadratic equation was based on the following considerations: (1) By McLauren's Theorem, any well-behaved (i.e., analytic) function can be approximated by a power series. (2) The equation of lowest degree that predicts a maximum is the quadratic. (3) The use of an equation of degree higher than 2 is justified only if the quadratic does not fit, and requires more data since more parameters must be estimated. The equation is shown in eq. 1: Y= a + bX+ cX 2
(1)
where: Y = log (corrected OD); X = log (relative concentration = RC); a = log (corrected O D at R C = 1); b = 'slope', i.e., the slope of the straight line that would result when c = 0 ; and c = parameter that compensates for deviation from linearity. Inspection of numerous sets of data like those in Fig. 2 suggested that the log differences between duplicates are roughly independent of serum
concentration over the range of concentrations tested; therefore, all points were weighted equally. A program was written in Radio Shack BASIC (cf. listing in the appendix) to analyze the data on a personal computer. The printed output provides: (1) the fitted equation; (2) a list of the parameters a, b and c, together with their standard errors and coefficients of variation; (3) a list of the input data, the calculated value of the corrected O D at each RC, and the difference between calculated and observed OD; and (4) the RC value at which the calculated O D = 0.200. On a log-log plot, the choice of an end-point is necessarily arbitrary; we chose an O D value (corrected for background) of 0.2 as the end-point. This choice presents a compromise between two considerations: one is to choose an O D value that can be measured accurately, the other is to choose an O D value where the contribution of inhibition to the dose response is minimized. For an O D value of 0.2, this contribution, as measured by the square term in the equation, averaged 5.6% of the log O D (range 0.1%-10.6%) for a representative set of samples. The ' r a w ' ELISA titer of a sample was defined as the reciprocal of the sample dilution which produced an O D of 0.2, interpolated from the fitted curve. The pooled serum sample was arbitrarily assigned a value of 100 E U / m l , and the titers of all samples were normalized on
165
the basis of this pool, which was assayed as a reference on each plate to eliminate the effect of day-to-day variations in incubation time and enzyme activity. We illustrate these calculations by applying them to the data shown in the left and center panels of Fig. 2. For pooled normal serum (left panel): RC = 1 corresponds to a 1 / 1 2 8 1 3 dilution; O D = 0.2 is obtained with a R C = 4.446, which corresponds to a dilution of 4.446/12 813 = 1/2882; the raw titer is 2882. For the individual normal serum (center panel): R C = 1 corresponds to a 1 / 1 2 813 dilution; O D = 0.2 is obtained with a R C = 8.065, which corresponds to a dilution of 8.065/12813 = 1 / 1 5 8 9 ; the raw titer is 1589. The normalized titer of the individual serum is: 100 × (1589/2882) = 55.1
dilutions, ranging from 1 / 1 0 0 0 (ca. 5 ttg p r o t e i n / ml) to 1 / 3 2 000. The same set of serial dilutions of pooled normal serum, ranging from 1 / 1 0 1 to 1/6464, was then analyzed at each antibody concentration. The results are shown in Fig. 3. Each panel shows the dose response obtained for the same pooled serum (as log O D vs. log sample concentration) at the dilution of capture Ab indicated in the panel. It is clear that the inhibition at high sample concentrations observed in Fig. 1 is independent of the concentration of capture Ab. The m a x i m u m in the dose-response line occurs at about the same sample dilution in each case. An apparent exception is observed for the 1 / 1 0 0 0 dilution of Ab, which seems to yield a linear response; but in this case the deviations are so large that inhibition, if present, could easily be masked. Fig. 3 also shows that the response of the system depends markedly on Ab concentration; it appears optimal at Ab dilutions from 1 / 2 0 0 0 to 1/8000, whereas the O D values produced by a given serum concentration decrease outside this range. At a capture Ab dilution of 1 / 1 0 0 0 (5
EU/rra. Effect of capture antibody concentration The effect of variations in the concentration of antibody used to coat the plate was studied by coating duplicate rows of wells with different Ab
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166
F g / m l ) , there is an 8-fold increase in the sample concentration required to yield an O D = 0.2 compared to the 1 / 2 0 0 0 dilution; at 1 / 3 2 000, there is not enough capture Ab to achieve an O D = 0.2 at any sample concentration. This effect is seen more clearly when one examines the effect of Ab dilution on the parameters a and b of the fitted equation, and on the raw titers calculated from those parameters. These results are shown graphically in Fig. 4. All three parameters have broad maxima in the range of Ab dilutions from 1 / 2 0 0 0 to 1/8000. Furthermore, the standard errors are smaller in this range; this means that the quadratic equation fits the data better, permitting more precise estimation of the parameters. Inspection of Fig. 3 suggests that at least part of the improved fit is due to better reproducibility between duplicate data points. The raw titers are ca. 6000 in the range of optimal Ab concentrations but drop abruptly to less than 2000 outside it. The 'slope' is close to 1 at optimal Ab concentrations but decreases at both higher and lower Ab concentrations. This fact is important because it shows that at these Ab concentrations, the system comes closest to ideal behavior, and it means that a given difference in P concentration will result in the greatest difference in OD. The intercepts are also higher at optimal Ab concentrations, reflecting the fact that all O D values are higher in this range. On the basis of these results, a capture Ab dilution of 1 / 4 0 0 0 was chosen as standard. Evaluation and results for normal sera To determine how well the proposed quadratic equation fits the data, residual plots were constructed for a series of assays. The residual plot shows the difference between observed O D and the corresponding O D computed from the fitted line, as a function of relative sample concentration. Its purpose is to test qualitatively for goodness of fit. If the equation fits the data well, the residuals should be comparable to the differences between duplicate observed O D values, and should be distributed evenly about a mean of zero throughout the range of the data. Conversely, poor fit would be indicated by residuals greater than the difference between duplicates, or by a tendency for positive or negative residuals to clus-
D e p e n d e n c e of P a r a m e t e r s on Ab Dilution
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167
ter around particular X values, or by both. Such a plot is shown for pooled normal serum, 4 individual normal serum samples, and pure P in Fig. 5. The residual errors are generally within the range of the differences between duplicates and appear to be distributed randomly. This indicates that the empirical equation we propose fits the data satisfactorily. The residual errors tend to increase somewhat at the highest sample concentrations; but even in this range, the residual errors are comparable to the differences between duplicates. The increase in residual errors at high sample concentrations, i.e., at high OD values, is due to the fact that the data were fitted in log-log mode. This means that the regression process minimizes the sum of squares of differences between calculated and observed log OD values. Since a given difference in log OD corresponds to a difference in OD that is proportional to OD, the same difference in log OD will translate into a small difference in OD at low OD and into a large difference in OD at high OD. RESIDUAL PLOT
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Fig. 5. Residual plot for data from a representative plate on which pooled normal human serum, four individual sera, and pure P were analyzed. A relative concentration of 1.0 represents a 1/25664 dilution of normal serum or 5.5 n g / m l of purified P. Data sets 1-4 were obtained with different individual normal sera; data set 5 with the reference pooled normal serum, and data set 6 with purified P. The ordinate shows, for each of the duplicate points in the assay, the difference between the observed OD and the OD calculated according to the fitted equation.
To evaluate the assay further, we analyzed nine individual normal serum samples and a sample of purified P and repeated this experiment on different days. On one of these occasions, a capture Ab dilution of 1 / 8 0 0 0 was used instead of the standard 1 / 4 0 0 0 dilution. The results were analyzed to determine: (a) whether the fitted dose-response lines were parallel, and (b) whether the observed P titers were reproducible. The question whether the lines are parallel was examined in terms of the coefficient, b, of the linear term of the fitted equation. This coefficient corresponds to the slope of a straight line. For each set of points corresponding to one sample, we computed the variance of this 'slope' internally, i.e., from the regression analysis. This variance measures the uncertainty in the 'slope' due to deviations of the data from the fitted line and to differences between duplicates. Table I shows the values and variances of the 'slope' for both experiments, and illustrates the calculations that follow. The internal estimates of the variance of the 'slope' were pooled separately for each experiment to provide an expected value of the variance for comparison with the variance between the 'slope' of the dose-response lines for the individual samples in the experiment. If the dose-response lines are not parallel, the 'slopes' should vary more widely than expected on the basis of the pooled internal variance. This question was answered by performing an F-test on the variance between samples over the pooled variance. For both experiments, the variance ratio was found to be non-significant, P > 0.3. Furthermore, when the average slopes for the two experiments were compared in a t-test, the difference was found to be non-significant, t < 1.0. The reproducibility of the assay is illustrated in Table II. The raw titers obviously vary considerably between experiments since they are strongly influenced by variations in incubation time for the enzymatic reaction step. But with one exception (sample 1), the normalized titers are quite reproducible. The mean differences between the normalized titers of the remaining eight samples in the two experiments is 0.85 E U / m l . The associated standard deviation, representing an estimate of the standard deviation due to day-to-day differences in assay results for a given sample, is 5.85
168 TABLE I C O E F F I C I E N T S OF T H E L I N E A R T E R M IN T H E F I T T E D E Q U A T I O N Plate
Sample
Experiment 1 Variance
' Slope'
Variance
1 2 3 4 5 Pool
0.9937 1.310 1,340 0,7146 0,6043 1,075
0.05140 0.006655 0.02827 0.06216 0.3301 0.03028
0,4761 0.5631 0,9391 1,037 0.9595 1.208
0.5095 a 0.06768 0.008911 0.005783 0.02610 0.008333
6 7 8 9 Pool P
1,115 1,340 1,264 1.340 1.309 1.128
0.09654 0.05658 0.01803 0.006662 0.01208 0.006466
0.9240 0.7729 0.9649 0.9645 1.101 1.029
0.02571 0.06943 0.04197 0.003990 0.01730 0.01183
Mean Variance between ' slopes' (1) Pooled internal variance (2) F = (1)/(2) a
Experiment 2
' Slope'
1.128
0.9511
0.06231
0.02853 0.05877
0.02609
1.060
1.094
Results for sample 1, experiment 2, were anomalous and therefore omitted (cf. Table 1I).
TABLE II ASSAY RESULTS F O R N O R M A L SERA Plate
Sample
Titer
Difference a
Experiment 1
A
Mean SD
Experiment 2
(Exp. 2 - 1)
Raw
Normalized
Raw
Normalized
1 2 3 4 5 Pool
3 210 4 166 3 641 4 723 3 309 5 226
61.4 79.7 69.7 90.4 63.3 (100.0)
5 019 2 744 2 142 2 995 1 702 3 150
159.3 b 87.1 68.0 95.1 54.0 (100.0)
97.9 7.40 1.71 4.67 -- 9.28
6 7 8 9 Pool P
2 848 2 826 2 765 3 987 3 657 8725
77.9 77.3 75.6 109.0 (100.0) 238.6 c
2 204 2 534 2 283 3 350 3124 7464
70.5 81.1 73.1 107.2 (100.0) 238.9 c
- 7.44 3.82 - 2.52 - 1.76
79.5 16.8
-0.85 5.85
78.3 14.5
0.33
Difference between normalized titers. b This data set contained four anomalous readings (' hot wells') and was excluded from the average. c D a t a for pure P were not included in the average. a The mean difference is not the same as the difference between the means because the mean for experiment 1 includes the value from plate A, sample 1; the mean difference does not. a
169
E U / m l , i.e., 7.4% of the average titer. The standard deviation between individual sera averages 15.7 E U / m l , or 20% of the average titer; this represents an estimate of the range of variation between individuals. The data shown for purified P in Table II permit us to relate our arbitrary EU values to absolute P concentration as determined spectrophotometrically. This calculation shows that 1 EU = 570 ng of P; furthermore, the end-point, i.e., O D = 0.2, is achieved with 17 n g / m l . As a final criterium for the validity of the assay, we performed three separate recovery experiments by titrating mixtures of pooled normal serum and pure P in various proportions. These titrations were compared with measurements on pooled normal serum and on pure P, run on the same plate. The results are summarized in Table III. The first three lines in the upper portion of the table show the calculated P content of the mixture in each experiment, expressed as E U / m l of the highest dilution (i.e., RC = 1) of the mixture tested, based on the control titrations of pooled serum and pure P. The data for the mixture were fitted as described and used to determine the relative concentration (RC) of the mixture re-
quired to produce an O D =0.2, our standard end-point. The values of these standard end-points are shown in line 4 of Table III. The concentration of P present at the standard end-point should be the same for the mixtures and for the reference pooled normal serum (containing 100 E U / m l of P by definition), which was titrated on the same plate. The 'observed' P concentration present in the dilution of the mixture that produces O D = 0.2, in E U / m l , is therefore calculated from the dilution of pooled normal serum that produces this OD; this value is shown for each experiment in line 5. The expected P content of that RC of the mixture which produces O D = 0.2 is calculated from the expected P content of the same mixture at RC = 1 which was calculated in lines 1-3. This is done by multiplying the expected P content at R C = 1 (line 3) by the RC found to produce O D = 0.2 (line 4). The result is given in line 6. The ratio of line 5 to line 6 (shown on line 7) equals the recovery of P in the mixture as measured by this ELISA. Ideally, this recovery should be 1.0, i.e., 100%; a lower value would indicate that pooled normal serum contains a substance that inhibits some phase of the reaction, whereas a higher value would show that the assay is measuring something
TABLE III RECOVERY EXPERIMENTS Experiment 1
2
3
(1) From pooled serum a (2) From purified P b
Expected P content ( E U / m l ) of highest dilution of mixture (RC = 1) 0.00370 0.01266 0.00622 0.00322
0.01226 0.00706
(3) Total: (1)
0.00992
0.01548
0.01932
5.832
2.625
2.253
0.0583
0.0476
0.0417
0.0578
0.0406
0.0435
1.01
1.17
0.958
(4) Observed RC of mixture producing OD = 0.2: (2) (5) Observed P content a required c to produce O D = 0.2: (3) (6) Expected P content a at this RC: (4) = (1) x (2) (7) Observed/expected P content of mixture: (3)/(4) a b c a
Based on dilution used (undiluted pooled serum = 100 E U / m l ) . Based on titration of pure P. Based on calibration for pooled serum. In E U / m l .
170
besides P. The average recovery is 105% with a standard deviation of 11%; both appear reasonable in view of the 5.9% day-to-day reproducibility obtained from Table II.
Discussion
The experiments described in this report establish an ELISA for P that satisfies the criteria of sensitivity, precision and accuracy which we set out to achieve. The data generated by the assay can be fitted by an empirical quadratic equation. The coefficient of the linear term in this equation (i.e., the 'slope') does not vary between samples and standards by more than one would expect from its experimental error. Therefore, the doseresponse curves are parallel, at least at high dilutions where the square term contributes little; this permits valid comparisons of data from different samples. However, even though the differences in the 'slopes' of the lines are not statistically significant, Table I shows that they are substantial and certainly greater than those observed by Butler et al. (1986) in a model system. This is probably due to inexact fit of the quadratic equation, which produces large estimates for the variances of the parameters and substantial variation between experiments in the parameters themselves. The solution to this problem would require a larger number of data points per sample and the use of a polynomial of higher degree to fit them. But the resulting increase in the amount of work required per sample would make the assay less attractive as a tool for measuring large numbers of samples, and would in most cases not be justified by the increase in precision beyond what was achieved in this study. The precision of this assay is characterized by a standard deviation between repetitive assays of the same sample of 7.4% of the average titer. Assays on a series of nine serum samples from healthy donors produced a standard deviation between samples of 20% of the average titer. The sensitivity of the assay is such that in an average experiment, a P concentration of 17 n g / m l produces an O D = 0.2. Two anomalous results were obtained which deserve consideration. Inhibition was observed at
high inputs (more than 2.5 /~g/ml) of capturing Ab, and also at high serum concentrations. The inhibition seen at high inputs of capture Ab seems analogous to inhibition two of us (J.E.B. and J.H.P.) have observed in a direct ELISA when plates are coated with high amounts of antigen. We believe that the inhibition in the direct ELISA is due to loss of antigen from the plate into solution during subsequent incubation with Ab, where it competitively binds the Ab, preventing the latter from reacting with the solid-phase antigen. The percentage of antigen lost from the solid phase is roughly independent of the amount of antigen applied; it can be decreased but not eliminated by prolonged washing (Peterman, 1986). In the experiments shown here, we are describing a sandwich ELISA where the reagent adsorbed to the solid phase in Ab instead of antigen, but studies in one of our laboratories have shown that the loss of adsorbed protein occurs regardless of the nature of the protein. The inhibition observed at high serum concentrations appears to be due to a serum constituent. The serum dilution at which it is observed is independent of the dilution of capture Ab used to coat the plate; therefore, the inhibition is not related to the ratio of antigen to capture Ab. This conclusion is further supported by the fact that no inhibition is seen with pure P, even when the amount of P applied is enough to equal or exceed the maximal OD value observed for serum on the same plate. Furthermore, the extent of inhibition varies for different serum samples, again implicating the presence of variable amounts of an unidentified inhibitor in serum as the cause. This inhibitor may act in two ways. One is by direct interference with the antigen-antibody reaction; the other possibility is that the inhibitor is bound to the plate or to the antigen-antibody complexes adsorbed on the plate in a manner that is not reversed by subsequent washing, enabling it to interfere with either the binding or the function of the antibody-enzyme conjugate used for detection of bound antigen. At present, we do not have data that would permit us to discriminate between these possibilities. Similar inhibition has also been observed with other crude materials in other systems. The practical implication of this serum inhibitor is that it prevents successful analysis at serum
171
dilutions below 1 / 4 0 0 . This is particularly important for the analysis of sera deficient in P to which the assay has been applied. In spite of this limitation, the assay was successful in identifying
individuals with a genetic P deficiency as well as their relatives who appear to be heterozygous for this defect (Densen et al., submitted for publication).
Appendix PROGRAM
B I VAF~
10 PRINT "THIS PROGRAM FITS A QUADRATIC EQUATION BY LINEAR REGRESSION.":PRINT TA B(20) "THIS I S DONE IN LOG MODE." 20 CLEAR IO00:DEFINT I,J,N:DEFDBL R,A~K,V,D:DEFSTR C,S:DIM S P C ( I O O ) , X ( 2 , 2 0 ) , Y ( 3 , 2 0 ) , R ( 3 , 3 ) : I N P U T "PLEASE ENTER TITLE, ENCLOSED IN QUOTES";ST 30 LPRINT CHR$(27)"@":LPRINT CHR$(27)"O":LPRINT CHR$(12) 40 LPRINT:LPRINT:L%=(80-LEN(ST))/2:LPRINT STRINGS(L%, . . . . )+ST:LPRINT 50 INPUT "ENTER NUMBER OF OBSERVATIONS, THEN BACKGROUND,SEPARATED BY COMMA";NO,B G 60 FOR J=O TO NO-I:INPUT "ENTER RELATIVE CONCENTRATION, THEN OD VALUE, SEPARATED BY C O M M A " ; X ( O , J ) , Y ( O , J ) : I F X(O,J)>O AND Y(O,J)>O THEN 80 70 PRINT TAB(22) " I CAN'T HANDLE ZERO OR NEGATIVE VALUES.":INPUT "PLEASE ENTER C ORRECT DATA NOW";X(O,J),Y(O,J) 80 X ( O , J ) = L O G ( X ( O , J ) ) : Y ( O , J ) = L O G ( Y ( O , J ) - B G ) : X ( 1 , J ) = X ( O , J ) [ 2 : R ( O , O ) = R ( O , O ) + X ( O ,J) : R ( O , 1 ) = R ( O , 1 ) + X ( 1 , J ) : R ( O , 2 ) = R ( O , 2 ) + Y ( O , J ) : R ( 1 , 1 ) - R ( 1 , 1 ) + X ( O , J } [ 3 : R ( 1 , 2 ) - R ( 1 , 2+)
X(O,J)[4 90 R(2,0)=R(2,0)+X(O,J)*Y(O,J):R(2,1)=R(2,1)+X(1,J)*Y(O,J):R(2,2)=R(2,2)+Y(O, J)[ 2:NEXT J 100 R ( 1 , 0 ) = R ( O , 1 ) : A V ( O ) = R ( O , 2 ) / N O : A V ( 1 ) = R ( O , O ) / N O : A V ( 2 ) = R ( O , 1 ) / N O : R ( 1 , 0 ) = R ( I0, ) R ( O , O ) * A V ( 1 ) : R ( 1 , 1 ) = R ( 1 , 1 ) - R ( O , 1 ) * A V ( 1 ) : R ( 1 , 2 ) - R ( I ~ 2 ) - R ( O , 1 ) * A V ( 2 ) : R ( 2 , 0 ) = R ( 2O) ~ -R(O,2)*AV(1) 110 R ( 2 , 1 ) = R ( 2 ~ I ) - R ( O , 2 ) * A V ( 2 ) : R ( 2 , 2 ) = R ( 2 , 2 ) - R ( O ~ 2 ) * A V ( O ) : D = R ( 1 , 0 ) * R ( 1 , 2 ) - R ( 11) , [2:K(1)=(R(2~)*R(1~2)-R(2~1)*R(1v1))/D:K(2)=(R(1~)*R(2~1)-R(1~1)*R(2~))/D:K(~ )=AV(O)-K(1)*AV(1)-K(2)*AV(2) 120 V ( 4 ) = ( R ( 2 , 2 ) - K ( 1 ) * R ( 2 , 0 ) - K ( 2 ) * R ( 2 , 1 ) ) / ( N O - 3 ) : V ( 1 ) = V ( 4 ) * R ( 1 , 2 ) / D : V ( 2 ) = V ( 4 ) * R ( 1,0)/D:V(O)=V(4)*(1/NO+(AV(1)[2*R(1,2)+AV(2)[2*R(1,0)+2*AV(1)*AV(2)*R(1,1))/D) 130 H$=CHR$(9):C(1)="Y = # # # # . # # +##.####X +##.####X":LPRINT STRINGS(34, . . . . ) + " F I TTED L I N E : " : L P R I N T 140 LPRINT STRINGS(24," ")~ 150 LPRINT USING C ( 1 ) ; K ( O ) ; K ( 1 ) | K ( 2 ) ; 160 LPRINT CHR$(27)"SO2";CHR$(27)"T" 170 I F V(4)
Y(O~J)-EXP(Y(O,J)):Y(2~J)=Y(O,J)-Y(1,J) 3&O 370 380 390 400 410 420 430
LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT
H$; USING HSH$| USING HSH$; USING H$; USING
"####.#";X(O,J); "###.@@@";Y(O,J); "###.@###";Y(1,J); "#@#.####";Y(2,J):NEXT J
172 440 D = 4 * K t 2 ) * ( L O S t O . 2 ) - K ( O ) ) + K t l ) [ 2 : I F D
References Avrameas, S. (1972) Enzyme markers: Their linkage with proteins and use in immune histochernistry. Histochem. J. 4, 321. Butler, J.E., Peterman, J.H. and Koertge, T.E (1985) The amplified enzyme-linked immunosorbent assay (a- ELISA). In: T.T. Ngo and H.M. Lenhoff (Eds.), Enzyme-Mediated Immunoassay (Plenum, New York) pp. 241-276. Butler, J.E., Spradling, J.E., Suter, M., Dierks, S.E., Heyermann, H. and Peterman, J.H. (1986) The immunochemistry of sandwich ELISAs. The binding characteristics of immunoglobuhns to monoclonal and polyclonal antibodies adsorbed on plastic and their detection by symmetrical and
asymmetrical antibody-enzyme conjugates. Mol. lmmunol. 23, 971. Fearon, D.T. and Austen, K.F. (1977) Activation of the alternative complement pathway due to resistance of zymosanbound amplification convertase to endogenous regulatory mechanisms. Proc. Natl. Acad. Sci. U.S.A. 74, 1683. Peterman, J.H. (1986) Factors which influence the binding of antibody to solid phase antigens: Theoretical and experimental investigations. Ph.D. Thesis, University of Iowa. Schrager, M.A., Chapitis, J., Rothfield, N.F. and Lepow, I.H. (1976) Electroimmunoassay for properdin: A comparison with radioimmunoassay. Clin. Immunol. Immunopathol. 5, 258.
161
JIM 04281
A sandwich ELISA for properdin in clinical specimens * L o u i s G . H o f f m a n n 1, A. K a y Pitts 2, P e t e r D e n s e n 2, J o h n M. Weiler 2, J o h n E. Butler 1 a n d J e f f r e y H. P e t e r m a n 1 Departments of ~ Microbiology and 2 Internal Medicine, University of Iowa, Iowa City, IA 52242, U.S.A. (Received 3 November 1986, accepted 3 December 1986)
We have developed a symmetrical sandwich ELISA for measuring human properdin (P) in serum by using the globulin fraction from a commercial antiserum as the capture antibody adsorbed on the plastic. The detecting reagent was a glutaraldehyde conjugate of this Ig fraction with alkaline phosphatase. Two types of inhibition were observed in this study. First, inhibition was observed when > 2.5 ~ g / m l of the globulin fraction was used to coat the plates. A second type of inhibition was observed for serum dilutions < 1 / 4 0 0 ; it was independent of the concentration of capture Ab and did not occur when purified P was assayed. The data generated with this assay could be fitted in log-log mode by a quadratic equation. The coefficient of the linear term in this equation was found to be the same for serum and purified P, within the limits of experimental error. The results for different samples run on the same plate were expressed in terms of the relative concentration of each sample required to produce an OD405 = 0.2. A sample of pooled normal h u m a n serum was run on each plate as a reference; it was assigned a titer of 100 ELISA u n i t s / m l ( E U / m l ) . The titers of the unknown samples were expressed in terms of E U / m l by reference to this standard. For purified P, the assay could readily detect 10 n g / m l . By comparing purified P with our reference serum pool, we found that 1 EU equals 0.57 ~g. Day-to-day variation for a group of nine normal sera showed a mean difference of - 0 . 8 5 E U / m l , SD 5.85 E U / m l . The mean titer for these normal sera was 78.9 E U / m l , SD 15.7 E U / m l . In three recovery experiments in which purified P was mixed with pooled normal serum, the recoveries ranged from 96 to 117%. We conclude that the sandwich ELISA constitutes an adequate immunochemical assay for human P in serum specimens. Key words: ELISA; Complement; Properdin
Introduction Properdin is a component of the alternative pathway of complement activation which funcCorrespondence to: L.G. Hoffmann, Department of Microbiology, University of Iowa, Iowa City, IA 52242, U.S.A. * Supported by Merit Review Awards and Clinical Investigatorships from the Veterans' Administration to P.D. and J.M.W., and by NIH Grants nos. A1-16476 and HL-22676. Abbreviations: Ab, antibody; ELISA, enzyme-linked immunoassay; EU, ELISA unit; Ig, immunoglobulin; P, properdin; RC, relative concentration.
tions by stabilizing the alternative pathway C3 convertase, C3b,Bb, from spontaneous decay (Fearon and Austen, 1977). Its measurement in serum samples presents difficulties when presently available methods are used. Hemolytic assays are complicated by the presence in serum of variable concentrations of complement factors B and H, which together with P determine the rate and extent of formation of the C3 convertase of the alternative p a t h w a y . A ' r o c k e t ' i m m u n o e lectrophoresis procedure has been described by Schrager et al. (1976), but this procedure requires
0022-1759/87/$03.50 © 1987 Elsevier Science Publishers B.V. (Biomedical Division)
162 large quantities of antiserum to P, and we have found it difficult to reproduce; after several attempts with the same normal samples, we were able to obtain visible precipitates only once. Therefore, we have developed a sandwich ELISA for P, using the Ig fraction from a commercial antiserum to P to capture P and a glutaraldehyde conjugate of alkaline phosphatase with the same Ig fraction (symmetrical configuration) as the detection system. Our goals in developing this assay were sensitivity, precision, and accuracy. The precision of an assay depends on its dose-response curve. In a model ELISA system studied by Butler et al. (1986), the log-log plot of antigen captured vs. antigen input was found to be linear with a slope equal to 1 when the capture Ab was in excess; the plot approaches a plateau at high inputs of antigen where Ab becomes limiting. The range of antigen concentrations over which the dose response is linear reflects the concentration and affinity of the capture Ab. Hence, the ideal sandwich ELISA is one which yields a log-log dose-response curve that is linear with a slope close to 1 over a wide range of antigen concentrations. We examined various parameters of the assay in order to establish conditions under which this ideal is approached most closely. Accuracy in any assay requires that the dose-response lines of different samples be parallel to each other and to that of the standard; we established conditions under with this requirement is met. The accuracy of the assay was examined further by recovery experiments in which chromatographically purified P was added to serum samples to determine whether the added P could be measured accurately.
Materials and methods
Reagents Goat antiserum to human P (lot no. 026) was purchased from Atlantic Antibodies. Its specificity was checked by immunoelectrophoresis, which showed a single arc against normal human serum; this arc corresponded to that produced by pure P. Properdin was purified from outdated, pooled human plasma (Fearon and Austen, 1977). Bovine alkaline phosphatase and its substrate, p-
nitrophenyl phosphate, were purchased from Sigma Chemical Co. Human serum samples were prepared from blood collected from healthy consenting volunteers, and stored at - 7 0 ° C. A pool of 20 normal sera was divided into small aliquots which were also stored at - 7 0 ° C and used only once. Buffer A: 0.1 M NaHCO3/Na2CO3, pH 9.6. Buffer B: 0.15 M NaC1, 10 mM N a H 2 P O 4 / Na2HPO4, 0.05% Tween 20, pH 7.1. Buffer C: 50 mM N a H C O 3 / N a 2 C O 3, 1 mM MgC12, pH 9.8. Rinsing solution: 0.15 M NaC1, 0.05% Tween 20. A crude globulin fraction was prepared from the anti-P antiserum by precipitation with an equal volume of saturated (NH4)2SO 4. The precipitate was collected by centrifugation, washed with 50% saturated (NH4)2SO 4, and redissolved in the original volume of buffer B without Tween; it was then dialyzed for 3 days against three changes of the same buffer. The final preparation contained ca. 5 r a g / m l of protein as determined spectrophotometrically on the basis of an extinction coefficient of 1.36 m l / m g at 278 nm. Glutaraldehyde conjugation with alkaline phosphatase was performed according to Avrameas (1972) at 1 m g / m l of globulins and 1.5 m g / m l of enzyme.
Methods Except for variations indicated in the results section, the sandwich ELISA was performed as described by Butler et al. (1986). Briefly, the anti-P globulin fraction was diluted 1/4000 in buffer A. We dispensed 0.2 ml of this dilution per well into Immulon 2 microtiter plates for overnight adsorption at room temperature. The plates were washed with rinsing solution by means of a 16-well microtiter plate washer described by Butler et al. (1985). Two-fold serial dilutions of P samples were made in buffer B, and 0.2 ml of each was pipetted into duplicate wells. The plates were incubated on a rotary shaker for 2 h at room temperature and washed. The enzyme-antibody conjugate was diluted 1 / 7 5 0 in buffer B; this dilution was established as optimal in a preliminary experiment. We pipetted 0.2 ml of the diluted enzyme-antibody conjugate into each well and incubated the plates on a rotary shaker for 2 h as before. After another wash, 0.2 ml of substrate solution (1 m g / m l pnitrophenyl phosphate in buffer C) was added to
163 each well. T h e OD405 of the well c o n t a i n i n g the highest i n p u t of the s t a n d a r d was m o n i t o r e d o n a B i o T e k M o d e l EL-310 p l a t e r e a d e r until it rea c h e d 1.2; at that time, the O D value of each well was m e a s u r e d a n d recorded. E a c h p l a t e i n c l u d e d c o n t r o l s w i t h o u t antigen (to m e a s u r e b a c k g r o u n d activity) a n d serial d i l u t i o n s of a s t a n d a r d serum pool.
Results
Inhibition at high serum concentrations R e p r e s e n t a t i v e results for an a s s a y on p o o l e d n o r m a l h u m a n serum, d i l u t e d f r o m 1 / 1 0 1 to 1 / 6464, are shown in Fig. 1 in s e m i - l o g a r i t h m i c
I"t
,.4 13
<5 '~ "d
o o
Relative Concentration Fig. 1. Inhibition of the dose response at high serum concentration. The ordinate shows OD405 as a function of relative antigen concentration, which is plotted on a logarithmic axis. A relative antigen concentration of 1.0 represents a 1/6464 dilution of serum. The dilution of capture Ab was 1/4000 (ca. 1.25 /~g/ml of Ig). The points represent OD readings from duplicate wells receiving the same serum solution, corrected for background readings from wells receiving no antigen. The solid line depicts the quadratic equation fitted to the data in log-log mode as described in the results section under 'Analysis of the Data'. The dashed horizontal line represents an OD = 0.200.
form. T h e abscissa shows relative serum conc e n t r a t i o n (the inverse of dilution) on a logarithmic scale. (This scale was a d o p t e d s i m p l y to imp r o v e the clarity of the graph.) T h e o r d i n a t e shows O1:)405 c o r r e c t e d for b a c k g r o u n d in wells receiving no antigen, on a linear scale. T h e solid line was fitted as discussed in the next section. The dose response clearly passes through a m a x i m u m at a s e r u m dilution of ca. 1 / 4 0 0 . It seemed of interest to d e t e r m i n e whether the i n h i b i t i o n o b s e r v e d in Fig. 1 was inherent in the assay, or whether it was an artefact due to inhibition of some step in the assay b y an u n k n o w n s e r u m constituent; in the l a t t e r case, we also wished to d e t e r m i n e whether the i n h i b i t i o n might be a c o n s e q u e n c e of p o o l i n g several sera. W e therefore a n a l y z e d p o o l e d n o r m a l serum, a r a n d o m l y selected i n d i v i d u a l n o r m a l serum, a n d purified P on the s a m e plate. The serum dilutions ranged f r o m 1 / 1 0 1 to 1 / 1 2 813, a n d the c o n c e n t r a t i o n s of purified P from 2.2 to 282 n g / m l . The results are shown in log-log form (the form in which the d a t a were a n a l y z e d ) in Fig. 2. The titration plot for p o o l e d n o r m a l serum clearly shows i n h i b i t i o n at high serum c o n c e n t r a t i o n s , (i.e., at dilutions < 1 / 4 0 0 ) when c o m p a r e d to the titration plot o b t a i n e d for p u r i f i e d P. T h e curve for the i n d i v i d u a l n o r m a l s e r u m shows less inhibition, suggesting that p o o l i n g sera m a y c o n t r i b u t e to the o b s e r v e d inhibition. However, o t h e r i n d i v i d u a l sera (not shown) y i e l d e d variable degrees of inhibition, some of which were as great as those seen with the p o o l e d serum. These results indicate that the inh i b i t i o n o b s e r v e d with n o r m a l s e r u m is due to the presence of interfering substance(s). T h e degree of i n h i b i t i o n is to some extent m a s k e d b y the log-log m o d e of p l o t t i n g the data; it is m o r e evident when one considers the increase in O D on going from the lowest p o i n t in the assay to the highest point, a 128-fold increase in c o n c e n t r a t i o n . T h e corres p o n d i n g increase in O D is 29-fold for p o o l e d n o r m a l serum, 42-fold for the i n d i v i d u a l n o r m a l serum, a n d 107-fold for purified P.
Analysis of the data T h e i n h i b i t i o n o b s e r v e d at high serum conc e n t r a t i o n s was f o u n d to p r e c l u d e analysis of the d a t a b y either linear regression or logit plots as p r o p o s e d b y P e t e r m a n (1986). Both of these p r o -
164
Pooled Normal Serum
Individual Normal Serum
Purified P
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Relative Concentration Fig. 2. Comparison of dose-response data for pooled normal serum, an individual normal serum, and purified P. The data are presented in log-log form; a relative antigen concentration of 1.0 represents a 1/12 813 dilution of serum or 2.2 ng/ml of purified P. Other details are explained in the legend for Fig. 1.
cedures led to fitted fines that were not parallel for different serum samples. The reason for the failure of both the linear and logit equations to fit the data adequately is that neither of these equations predicts a maximum. We therefore used an empirical quadratic equation to fit the data by linear regression of log O D on log concentration. The choice of a quadratic equation was based on the following considerations: (1) By McLauren's Theorem, any well-behaved (i.e., analytic) function can be approximated by a power series. (2) The equation of lowest degree that predicts a maximum is the quadratic. (3) The use of an equation of degree higher than 2 is justified only if the quadratic does not fit, and requires more data since more parameters must be estimated. The equation is shown in eq. 1: Y= a + bX+ cX 2
(1)
where: Y = log (corrected OD); X = log (relative concentration = RC); a = log (corrected O D at R C = 1); b = 'slope', i.e., the slope of the straight line that would result when c = 0 ; and c = parameter that compensates for deviation from linearity. Inspection of numerous sets of data like those in Fig. 2 suggested that the log differences between duplicates are roughly independent of serum
concentration over the range of concentrations tested; therefore, all points were weighted equally. A program was written in Radio Shack BASIC (cf. listing in the appendix) to analyze the data on a personal computer. The printed output provides: (1) the fitted equation; (2) a list of the parameters a, b and c, together with their standard errors and coefficients of variation; (3) a list of the input data, the calculated value of the corrected O D at each RC, and the difference between calculated and observed OD; and (4) the RC value at which the calculated O D = 0.200. On a log-log plot, the choice of an end-point is necessarily arbitrary; we chose an O D value (corrected for background) of 0.2 as the end-point. This choice presents a compromise between two considerations: one is to choose an O D value that can be measured accurately, the other is to choose an O D value where the contribution of inhibition to the dose response is minimized. For an O D value of 0.2, this contribution, as measured by the square term in the equation, averaged 5.6% of the log O D (range 0.1%-10.6%) for a representative set of samples. The ' r a w ' ELISA titer of a sample was defined as the reciprocal of the sample dilution which produced an O D of 0.2, interpolated from the fitted curve. The pooled serum sample was arbitrarily assigned a value of 100 E U / m l , and the titers of all samples were normalized on
165
the basis of this pool, which was assayed as a reference on each plate to eliminate the effect of day-to-day variations in incubation time and enzyme activity. We illustrate these calculations by applying them to the data shown in the left and center panels of Fig. 2. For pooled normal serum (left panel): RC = 1 corresponds to a 1 / 1 2 8 1 3 dilution; O D = 0.2 is obtained with a R C = 4.446, which corresponds to a dilution of 4.446/12 813 = 1/2882; the raw titer is 2882. For the individual normal serum (center panel): R C = 1 corresponds to a 1 / 1 2 813 dilution; O D = 0.2 is obtained with a R C = 8.065, which corresponds to a dilution of 8.065/12813 = 1 / 1 5 8 9 ; the raw titer is 1589. The normalized titer of the individual serum is: 100 × (1589/2882) = 55.1
dilutions, ranging from 1 / 1 0 0 0 (ca. 5 ttg p r o t e i n / ml) to 1 / 3 2 000. The same set of serial dilutions of pooled normal serum, ranging from 1 / 1 0 1 to 1/6464, was then analyzed at each antibody concentration. The results are shown in Fig. 3. Each panel shows the dose response obtained for the same pooled serum (as log O D vs. log sample concentration) at the dilution of capture Ab indicated in the panel. It is clear that the inhibition at high sample concentrations observed in Fig. 1 is independent of the concentration of capture Ab. The m a x i m u m in the dose-response line occurs at about the same sample dilution in each case. An apparent exception is observed for the 1 / 1 0 0 0 dilution of Ab, which seems to yield a linear response; but in this case the deviations are so large that inhibition, if present, could easily be masked. Fig. 3 also shows that the response of the system depends markedly on Ab concentration; it appears optimal at Ab dilutions from 1 / 2 0 0 0 to 1/8000, whereas the O D values produced by a given serum concentration decrease outside this range. At a capture Ab dilution of 1 / 1 0 0 0 (5
EU/rra. Effect of capture antibody concentration The effect of variations in the concentration of antibody used to coat the plate was studied by coating duplicate rows of wells with different Ab
Ab 1/1000
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Fig. 3. Dependence of the dose response for pooled normal serum on the concentration of capture Ab; the 1 / 1 0 0 0 dilution contains ca. 5 ~tg p r o t e i n / m l , A relative antigen concentration of 1.0 represents a 1 / 6 4 6 4 dilution of serum. Other features are explained in the legend of Fig. 1.
166
F g / m l ) , there is an 8-fold increase in the sample concentration required to yield an O D = 0.2 compared to the 1 / 2 0 0 0 dilution; at 1 / 3 2 000, there is not enough capture Ab to achieve an O D = 0.2 at any sample concentration. This effect is seen more clearly when one examines the effect of Ab dilution on the parameters a and b of the fitted equation, and on the raw titers calculated from those parameters. These results are shown graphically in Fig. 4. All three parameters have broad maxima in the range of Ab dilutions from 1 / 2 0 0 0 to 1/8000. Furthermore, the standard errors are smaller in this range; this means that the quadratic equation fits the data better, permitting more precise estimation of the parameters. Inspection of Fig. 3 suggests that at least part of the improved fit is due to better reproducibility between duplicate data points. The raw titers are ca. 6000 in the range of optimal Ab concentrations but drop abruptly to less than 2000 outside it. The 'slope' is close to 1 at optimal Ab concentrations but decreases at both higher and lower Ab concentrations. This fact is important because it shows that at these Ab concentrations, the system comes closest to ideal behavior, and it means that a given difference in P concentration will result in the greatest difference in OD. The intercepts are also higher at optimal Ab concentrations, reflecting the fact that all O D values are higher in this range. On the basis of these results, a capture Ab dilution of 1 / 4 0 0 0 was chosen as standard. Evaluation and results for normal sera To determine how well the proposed quadratic equation fits the data, residual plots were constructed for a series of assays. The residual plot shows the difference between observed O D and the corresponding O D computed from the fitted line, as a function of relative sample concentration. Its purpose is to test qualitatively for goodness of fit. If the equation fits the data well, the residuals should be comparable to the differences between duplicate observed O D values, and should be distributed evenly about a mean of zero throughout the range of the data. Conversely, poor fit would be indicated by residuals greater than the difference between duplicates, or by a tendency for positive or negative residuals to clus-
D e p e n d e n c e of P a r a m e t e r s on Ab Dilution
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o
d-
m
~o
o
4 I
i'#
.
.
.
.
.
.
i'0'
'
Ab Dilution Factor Fig. 4. Effect of dilution of capture Ab on the parameters of the fitted regression line and on the observed titer of pooled normal serum, zx: Raw liter (reciprocal of dilution producing O D = 0.2) of pooled normal serum. This titer depends primarily on the intercept and slope of the fitted curve and is defined as the inverse of the dilution producing an OD = 0.2. No titer can be calculated at an Ab dilution of 1/32000 since the fitted curve does not reach this OD value (cf. Fig. 3). O : Slope of the fitted curve, i.e., the coefficient of the linear term of the quadratic equation. 0: Intercept of the fitted fine; this represents the regression estimate of the log of the OD at a relative antigen concentration of 1.0 (a 1/6464 dilution). Error bars show fitted values + 1 SE; no standard errors could be computed for the titers.
167
ter around particular X values, or by both. Such a plot is shown for pooled normal serum, 4 individual normal serum samples, and pure P in Fig. 5. The residual errors are generally within the range of the differences between duplicates and appear to be distributed randomly. This indicates that the empirical equation we propose fits the data satisfactorily. The residual errors tend to increase somewhat at the highest sample concentrations; but even in this range, the residual errors are comparable to the differences between duplicates. The increase in residual errors at high sample concentrations, i.e., at high OD values, is due to the fact that the data were fitted in log-log mode. This means that the regression process minimizes the sum of squares of differences between calculated and observed log OD values. Since a given difference in log OD corresponds to a difference in OD that is proportional to OD, the same difference in log OD will translate into a small difference in OD at low OD and into a large difference in OD at high OD. RESIDUAL PLOT
io i 1
:
I
I
B
/5
g
|o* o
2?' 0 .......
I~
Relative C o n c e n t r a t i o n s = D a t a Set 1 o = D a t a Set 2 = D a t a Set :3
+ = D a t a Set 4 × = D a t a Set 5 o = D a t a Set 6
Fig. 5. Residual plot for data from a representative plate on which pooled normal human serum, four individual sera, and pure P were analyzed. A relative concentration of 1.0 represents a 1/25664 dilution of normal serum or 5.5 n g / m l of purified P. Data sets 1-4 were obtained with different individual normal sera; data set 5 with the reference pooled normal serum, and data set 6 with purified P. The ordinate shows, for each of the duplicate points in the assay, the difference between the observed OD and the OD calculated according to the fitted equation.
To evaluate the assay further, we analyzed nine individual normal serum samples and a sample of purified P and repeated this experiment on different days. On one of these occasions, a capture Ab dilution of 1 / 8 0 0 0 was used instead of the standard 1 / 4 0 0 0 dilution. The results were analyzed to determine: (a) whether the fitted dose-response lines were parallel, and (b) whether the observed P titers were reproducible. The question whether the lines are parallel was examined in terms of the coefficient, b, of the linear term of the fitted equation. This coefficient corresponds to the slope of a straight line. For each set of points corresponding to one sample, we computed the variance of this 'slope' internally, i.e., from the regression analysis. This variance measures the uncertainty in the 'slope' due to deviations of the data from the fitted line and to differences between duplicates. Table I shows the values and variances of the 'slope' for both experiments, and illustrates the calculations that follow. The internal estimates of the variance of the 'slope' were pooled separately for each experiment to provide an expected value of the variance for comparison with the variance between the 'slope' of the dose-response lines for the individual samples in the experiment. If the dose-response lines are not parallel, the 'slopes' should vary more widely than expected on the basis of the pooled internal variance. This question was answered by performing an F-test on the variance between samples over the pooled variance. For both experiments, the variance ratio was found to be non-significant, P > 0.3. Furthermore, when the average slopes for the two experiments were compared in a t-test, the difference was found to be non-significant, t < 1.0. The reproducibility of the assay is illustrated in Table II. The raw titers obviously vary considerably between experiments since they are strongly influenced by variations in incubation time for the enzymatic reaction step. But with one exception (sample 1), the normalized titers are quite reproducible. The mean differences between the normalized titers of the remaining eight samples in the two experiments is 0.85 E U / m l . The associated standard deviation, representing an estimate of the standard deviation due to day-to-day differences in assay results for a given sample, is 5.85
168 TABLE I C O E F F I C I E N T S OF T H E L I N E A R T E R M IN T H E F I T T E D E Q U A T I O N Plate
Sample
Experiment 1 Variance
' Slope'
Variance
1 2 3 4 5 Pool
0.9937 1.310 1,340 0,7146 0,6043 1,075
0.05140 0.006655 0.02827 0.06216 0.3301 0.03028
0,4761 0.5631 0,9391 1,037 0.9595 1.208
0.5095 a 0.06768 0.008911 0.005783 0.02610 0.008333
6 7 8 9 Pool P
1,115 1,340 1,264 1.340 1.309 1.128
0.09654 0.05658 0.01803 0.006662 0.01208 0.006466
0.9240 0.7729 0.9649 0.9645 1.101 1.029
0.02571 0.06943 0.04197 0.003990 0.01730 0.01183
Mean Variance between ' slopes' (1) Pooled internal variance (2) F = (1)/(2) a
Experiment 2
' Slope'
1.128
0.9511
0.06231
0.02853 0.05877
0.02609
1.060
1.094
Results for sample 1, experiment 2, were anomalous and therefore omitted (cf. Table 1I).
TABLE II ASSAY RESULTS F O R N O R M A L SERA Plate
Sample
Titer
Difference a
Experiment 1
A
Mean SD
Experiment 2
(Exp. 2 - 1)
Raw
Normalized
Raw
Normalized
1 2 3 4 5 Pool
3 210 4 166 3 641 4 723 3 309 5 226
61.4 79.7 69.7 90.4 63.3 (100.0)
5 019 2 744 2 142 2 995 1 702 3 150
159.3 b 87.1 68.0 95.1 54.0 (100.0)
97.9 7.40 1.71 4.67 -- 9.28
6 7 8 9 Pool P
2 848 2 826 2 765 3 987 3 657 8725
77.9 77.3 75.6 109.0 (100.0) 238.6 c
2 204 2 534 2 283 3 350 3124 7464
70.5 81.1 73.1 107.2 (100.0) 238.9 c
- 7.44 3.82 - 2.52 - 1.76
79.5 16.8
-0.85 5.85
78.3 14.5
0.33
Difference between normalized titers. b This data set contained four anomalous readings (' hot wells') and was excluded from the average. c D a t a for pure P were not included in the average. a The mean difference is not the same as the difference between the means because the mean for experiment 1 includes the value from plate A, sample 1; the mean difference does not. a
169
E U / m l , i.e., 7.4% of the average titer. The standard deviation between individual sera averages 15.7 E U / m l , or 20% of the average titer; this represents an estimate of the range of variation between individuals. The data shown for purified P in Table II permit us to relate our arbitrary EU values to absolute P concentration as determined spectrophotometrically. This calculation shows that 1 EU = 570 ng of P; furthermore, the end-point, i.e., O D = 0.2, is achieved with 17 n g / m l . As a final criterium for the validity of the assay, we performed three separate recovery experiments by titrating mixtures of pooled normal serum and pure P in various proportions. These titrations were compared with measurements on pooled normal serum and on pure P, run on the same plate. The results are summarized in Table III. The first three lines in the upper portion of the table show the calculated P content of the mixture in each experiment, expressed as E U / m l of the highest dilution (i.e., RC = 1) of the mixture tested, based on the control titrations of pooled serum and pure P. The data for the mixture were fitted as described and used to determine the relative concentration (RC) of the mixture re-
quired to produce an O D =0.2, our standard end-point. The values of these standard end-points are shown in line 4 of Table III. The concentration of P present at the standard end-point should be the same for the mixtures and for the reference pooled normal serum (containing 100 E U / m l of P by definition), which was titrated on the same plate. The 'observed' P concentration present in the dilution of the mixture that produces O D = 0.2, in E U / m l , is therefore calculated from the dilution of pooled normal serum that produces this OD; this value is shown for each experiment in line 5. The expected P content of that RC of the mixture which produces O D = 0.2 is calculated from the expected P content of the same mixture at RC = 1 which was calculated in lines 1-3. This is done by multiplying the expected P content at R C = 1 (line 3) by the RC found to produce O D = 0.2 (line 4). The result is given in line 6. The ratio of line 5 to line 6 (shown on line 7) equals the recovery of P in the mixture as measured by this ELISA. Ideally, this recovery should be 1.0, i.e., 100%; a lower value would indicate that pooled normal serum contains a substance that inhibits some phase of the reaction, whereas a higher value would show that the assay is measuring something
TABLE III RECOVERY EXPERIMENTS Experiment 1
2
3
(1) From pooled serum a (2) From purified P b
Expected P content ( E U / m l ) of highest dilution of mixture (RC = 1) 0.00370 0.01266 0.00622 0.00322
0.01226 0.00706
(3) Total: (1)
0.00992
0.01548
0.01932
5.832
2.625
2.253
0.0583
0.0476
0.0417
0.0578
0.0406
0.0435
1.01
1.17
0.958
(4) Observed RC of mixture producing OD = 0.2: (2) (5) Observed P content a required c to produce O D = 0.2: (3) (6) Expected P content a at this RC: (4) = (1) x (2) (7) Observed/expected P content of mixture: (3)/(4) a b c a
Based on dilution used (undiluted pooled serum = 100 E U / m l ) . Based on titration of pure P. Based on calibration for pooled serum. In E U / m l .
170
besides P. The average recovery is 105% with a standard deviation of 11%; both appear reasonable in view of the 5.9% day-to-day reproducibility obtained from Table II.
Discussion
The experiments described in this report establish an ELISA for P that satisfies the criteria of sensitivity, precision and accuracy which we set out to achieve. The data generated by the assay can be fitted by an empirical quadratic equation. The coefficient of the linear term in this equation (i.e., the 'slope') does not vary between samples and standards by more than one would expect from its experimental error. Therefore, the doseresponse curves are parallel, at least at high dilutions where the square term contributes little; this permits valid comparisons of data from different samples. However, even though the differences in the 'slopes' of the lines are not statistically significant, Table I shows that they are substantial and certainly greater than those observed by Butler et al. (1986) in a model system. This is probably due to inexact fit of the quadratic equation, which produces large estimates for the variances of the parameters and substantial variation between experiments in the parameters themselves. The solution to this problem would require a larger number of data points per sample and the use of a polynomial of higher degree to fit them. But the resulting increase in the amount of work required per sample would make the assay less attractive as a tool for measuring large numbers of samples, and would in most cases not be justified by the increase in precision beyond what was achieved in this study. The precision of this assay is characterized by a standard deviation between repetitive assays of the same sample of 7.4% of the average titer. Assays on a series of nine serum samples from healthy donors produced a standard deviation between samples of 20% of the average titer. The sensitivity of the assay is such that in an average experiment, a P concentration of 17 n g / m l produces an O D = 0.2. Two anomalous results were obtained which deserve consideration. Inhibition was observed at
high inputs (more than 2.5 /~g/ml) of capturing Ab, and also at high serum concentrations. The inhibition seen at high inputs of capture Ab seems analogous to inhibition two of us (J.E.B. and J.H.P.) have observed in a direct ELISA when plates are coated with high amounts of antigen. We believe that the inhibition in the direct ELISA is due to loss of antigen from the plate into solution during subsequent incubation with Ab, where it competitively binds the Ab, preventing the latter from reacting with the solid-phase antigen. The percentage of antigen lost from the solid phase is roughly independent of the amount of antigen applied; it can be decreased but not eliminated by prolonged washing (Peterman, 1986). In the experiments shown here, we are describing a sandwich ELISA where the reagent adsorbed to the solid phase in Ab instead of antigen, but studies in one of our laboratories have shown that the loss of adsorbed protein occurs regardless of the nature of the protein. The inhibition observed at high serum concentrations appears to be due to a serum constituent. The serum dilution at which it is observed is independent of the dilution of capture Ab used to coat the plate; therefore, the inhibition is not related to the ratio of antigen to capture Ab. This conclusion is further supported by the fact that no inhibition is seen with pure P, even when the amount of P applied is enough to equal or exceed the maximal OD value observed for serum on the same plate. Furthermore, the extent of inhibition varies for different serum samples, again implicating the presence of variable amounts of an unidentified inhibitor in serum as the cause. This inhibitor may act in two ways. One is by direct interference with the antigen-antibody reaction; the other possibility is that the inhibitor is bound to the plate or to the antigen-antibody complexes adsorbed on the plate in a manner that is not reversed by subsequent washing, enabling it to interfere with either the binding or the function of the antibody-enzyme conjugate used for detection of bound antigen. At present, we do not have data that would permit us to discriminate between these possibilities. Similar inhibition has also been observed with other crude materials in other systems. The practical implication of this serum inhibitor is that it prevents successful analysis at serum
171
dilutions below 1 / 4 0 0 . This is particularly important for the analysis of sera deficient in P to which the assay has been applied. In spite of this limitation, the assay was successful in identifying
individuals with a genetic P deficiency as well as their relatives who appear to be heterozygous for this defect (Densen et al., submitted for publication).
Appendix PROGRAM
B I VAF~
10 PRINT "THIS PROGRAM FITS A QUADRATIC EQUATION BY LINEAR REGRESSION.":PRINT TA B(20) "THIS I S DONE IN LOG MODE." 20 CLEAR IO00:DEFINT I,J,N:DEFDBL R,A~K,V,D:DEFSTR C,S:DIM S P C ( I O O ) , X ( 2 , 2 0 ) , Y ( 3 , 2 0 ) , R ( 3 , 3 ) : I N P U T "PLEASE ENTER TITLE, ENCLOSED IN QUOTES";ST 30 LPRINT CHR$(27)"@":LPRINT CHR$(27)"O":LPRINT CHR$(12) 40 LPRINT:LPRINT:L%=(80-LEN(ST))/2:LPRINT STRINGS(L%, . . . . )+ST:LPRINT 50 INPUT "ENTER NUMBER OF OBSERVATIONS, THEN BACKGROUND,SEPARATED BY COMMA";NO,B G 60 FOR J=O TO NO-I:INPUT "ENTER RELATIVE CONCENTRATION, THEN OD VALUE, SEPARATED BY C O M M A " ; X ( O , J ) , Y ( O , J ) : I F X(O,J)>O AND Y(O,J)>O THEN 80 70 PRINT TAB(22) " I CAN'T HANDLE ZERO OR NEGATIVE VALUES.":INPUT "PLEASE ENTER C ORRECT DATA NOW";X(O,J),Y(O,J) 80 X ( O , J ) = L O G ( X ( O , J ) ) : Y ( O , J ) = L O G ( Y ( O , J ) - B G ) : X ( 1 , J ) = X ( O , J ) [ 2 : R ( O , O ) = R ( O , O ) + X ( O ,J) : R ( O , 1 ) = R ( O , 1 ) + X ( 1 , J ) : R ( O , 2 ) = R ( O , 2 ) + Y ( O , J ) : R ( 1 , 1 ) - R ( 1 , 1 ) + X ( O , J } [ 3 : R ( 1 , 2 ) - R ( 1 , 2+)
X(O,J)[4 90 R(2,0)=R(2,0)+X(O,J)*Y(O,J):R(2,1)=R(2,1)+X(1,J)*Y(O,J):R(2,2)=R(2,2)+Y(O, J)[ 2:NEXT J 100 R ( 1 , 0 ) = R ( O , 1 ) : A V ( O ) = R ( O , 2 ) / N O : A V ( 1 ) = R ( O , O ) / N O : A V ( 2 ) = R ( O , 1 ) / N O : R ( 1 , 0 ) = R ( I0, ) R ( O , O ) * A V ( 1 ) : R ( 1 , 1 ) = R ( 1 , 1 ) - R ( O , 1 ) * A V ( 1 ) : R ( 1 , 2 ) - R ( I ~ 2 ) - R ( O , 1 ) * A V ( 2 ) : R ( 2 , 0 ) = R ( 2O) ~ -R(O,2)*AV(1) 110 R ( 2 , 1 ) = R ( 2 ~ I ) - R ( O , 2 ) * A V ( 2 ) : R ( 2 , 2 ) = R ( 2 , 2 ) - R ( O ~ 2 ) * A V ( O ) : D = R ( 1 , 0 ) * R ( 1 , 2 ) - R ( 11) , [2:K(1)=(R(2~)*R(1~2)-R(2~1)*R(1v1))/D:K(2)=(R(1~)*R(2~1)-R(1~1)*R(2~))/D:K(~ )=AV(O)-K(1)*AV(1)-K(2)*AV(2) 120 V ( 4 ) = ( R ( 2 , 2 ) - K ( 1 ) * R ( 2 , 0 ) - K ( 2 ) * R ( 2 , 1 ) ) / ( N O - 3 ) : V ( 1 ) = V ( 4 ) * R ( 1 , 2 ) / D : V ( 2 ) = V ( 4 ) * R ( 1,0)/D:V(O)=V(4)*(1/NO+(AV(1)[2*R(1,2)+AV(2)[2*R(1,0)+2*AV(1)*AV(2)*R(1,1))/D) 130 H$=CHR$(9):C(1)="Y = # # # # . # # +##.####X +##.####X":LPRINT STRINGS(34, . . . . ) + " F I TTED L I N E : " : L P R I N T 140 LPRINT STRINGS(24," ")~ 150 LPRINT USING C ( 1 ) ; K ( O ) ; K ( 1 ) | K ( 2 ) ; 160 LPRINT CHR$(27)"SO2";CHR$(27)"T" 170 I F V(4)
Y(O~J)-EXP(Y(O,J)):Y(2~J)=Y(O,J)-Y(1,J) 3&O 370 380 390 400 410 420 430
LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT LPRINT
H$; USING HSH$| USING HSH$; USING H$; USING
"####.#";X(O,J); "###.@@@";Y(O,J); "###.@###";Y(1,J); "#@#.####";Y(2,J):NEXT J
172 440 D = 4 * K t 2 ) * ( L O S t O . 2 ) - K ( O ) ) + K t l ) [ 2 : I F D
References Avrameas, S. (1972) Enzyme markers: Their linkage with proteins and use in immune histochernistry. Histochem. J. 4, 321. Butler, J.E., Peterman, J.H. and Koertge, T.E (1985) The amplified enzyme-linked immunosorbent assay (a- ELISA). In: T.T. Ngo and H.M. Lenhoff (Eds.), Enzyme-Mediated Immunoassay (Plenum, New York) pp. 241-276. Butler, J.E., Spradling, J.E., Suter, M., Dierks, S.E., Heyermann, H. and Peterman, J.H. (1986) The immunochemistry of sandwich ELISAs. The binding characteristics of immunoglobuhns to monoclonal and polyclonal antibodies adsorbed on plastic and their detection by symmetrical and
asymmetrical antibody-enzyme conjugates. Mol. lmmunol. 23, 971. Fearon, D.T. and Austen, K.F. (1977) Activation of the alternative complement pathway due to resistance of zymosanbound amplification convertase to endogenous regulatory mechanisms. Proc. Natl. Acad. Sci. U.S.A. 74, 1683. Peterman, J.H. (1986) Factors which influence the binding of antibody to solid phase antigens: Theoretical and experimental investigations. Ph.D. Thesis, University of Iowa. Schrager, M.A., Chapitis, J., Rothfield, N.F. and Lepow, I.H. (1976) Electroimmunoassay for properdin: A comparison with radioimmunoassay. Clin. Immunol. Immunopathol. 5, 258.