KineticTurbidimetricMethod for the ... - Clinical Chemistry

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Concentra- tions quantified in 14 pathological sera by the proposed .... ' Presentaddress:The Upjohn Company,Kalamazoo,MI. 2Adth. ... standard deviation (±1 SD). ..... Measurementobjective. Rate. Two-point. RKb. Rate. Two- point. R-K#{176}.
CLIN. CHEM. 34/2, 309-315 (1988)

KineticTurbidimetricMethod for the ImmunochemicalQuantificationof Immunoglobulins, IncludingSamples with Excess Antigen John W. Skoug1 and Harry L Pardue2 Here we describe a kinetic approach for quantification of the immunoglobulins (lgG, IgA, 1gM) in all regions of the immunoprecipitin curve. We use centrifugal mixing and report results for maximum-velocity, two-point, and multipoint curve-fitting methods as wellas the use ofratecoefficients obtainedfrom the curve-fitting process to differentiate among regionsof excess antibody, equivalence,and excess antigen.We show thatitis possibleto quantifyeach immunoglobulinover a concentrationrange from a large excess of antibodyto moderate excesses ofantigenwitha singleset of measurements made on a single dilution of each sample. Results for standard additions of the immunoglobulinsto pooled sera have relative standard deviations (coefficients of variation) in the range of 1% to 3%, with analytical recoveries in the range of 95% to 106%. Correlations among determined and reported values in individual sera are quite good, with slopes ranging from 0.86 to 1.03 and no intercepts differing from zero by more than two standard deviation units. Concentrations quantified in 14 pathological sera by the proposed method correlated well with concentrations quantified by a fluorescenceimmunoassay method. Additional

Keyphrase: fluorescence immunoassay compared

In a companion paper (1), we describe results of detailed kinetic studies of the immunoprecipitin reactions of IgG,

IgA, and 1gM. Reaction conditions were identified that accommodated the mixing speed of a centrifugal mixing system and gave good sensitivityof the calibration curves in regions of excess antibody, equivalence, and excess antigen. In this paper, we describe the use of kinetic data not only to differentiate among the regions of excess antibody, equivalence, and excess antigen,but also to quantify antigen concentration in each of these regions with a single set of measurements for a single dilution of each sample. We have found that kinetic response curves can be fit satisfactorily with a zero-order/first-order model and that a ratioof first-order to zero-order rate coefficients is the most useful parameter to differentiate among the three regions of the dose-response curves. In addition, the first-orderrate .

coefficient is the most useful calibration parameter for the region of equivalence for all three analytes and the region of

excessantigen for 1gM. A varietyof data-processing options can be used to quantify all three immunoglobulins in the regions

of excess antibody.

Materials and Methods Instrumentation and Software We have previously

described the centrifugal

mixing and

computer systems as well as media used to filter antibody

and polyethylene

glycol (PEG) solutions (1).

Reagents

with distilled, de-ionized water. stated otherwise,we report concentrations and dilution factors as those in the measurement cuvettes. Diluents. Unless stated otherwise, we prepared both antigen and antibody diluents to contain, per liter, 65 mmol of phosphate buffer at pH 7.5 and 0.3 mol of NaC1; the antibody diluent also contained 48 g of PEG per liter. The final We prepared all solutions

Unless

concentration of PEG in the reaction mixture was 40 gIL. Antibodies. We used “nephelometric”-grade monospecific goat antiserum (Atlantic Antibodies Inc., Scarborough, ME) to human IgG, IgA, and 1gM. Antigens. We used reference sera CAl and CA4 and a custom calibrator (Atlantic Antibodies) to prepare standard and control solutions of the immunoglobulins as described

earlier (1). Serum samples. We used pooled and individual sera from three hospital laboratories. Of 52 individual sera, obtained on several different days, 23 included reported concentrations of IgG, IgA, and 1gM (as determined with the Beckman ICS instrument); three had abnormally high concentrations of IgG, and five had known monoclonal gammopathies of the immunoglobulins. All sera were stored frozen until used. Reference method. For the pathological sera, we used as a comparison method a fluorescence-excitation-transfer immunoassay kit (Syva Advance, IgG; Syva Co., Palo Alto, CA) adapted to a conventional fluorometer (Model LS-5, Perkin Elmer Corp.). Data Processing

Kinetic data. We processed the data for turbidity(T = -log I/L3) vs time with the same kinetic options as described for nephelometric data (2). We refer to those three options as the “rate,” “two-point,” and “regression-kinetic” options. For the rate option, we used the maximum of the derivative (3) of each response curve, which is analogous to the approach used by Anderson and Sternberg (4) for nephelometric data. For the two-point option, we used the change in turbidity = T1) between two specified points in time. In the special case when t1 = 0, we computed T1 = T0 as the intercept (t = 0) of a fit of the firstfive to 10 data points of the response curve to a quadratic model. For the regression-kinetic option, we used a quadratic -

model to compute T0 and a nonlinear least-squaresmethod to compute the best fit of experimental data after the induction period to a parallel first-order/zero-order model (5). Parameters computed in the fitting process are the

Department of Chemistry, Purdue University, West Lafayette, IN 47907. ‘Presentaddress:The Upjohn Company, Kalamazoo,MI. 2Adth. correspondenceto this author. ReceivedMay 7,1987; acceptedNovember 30,1987.

Nonstandard abbreviations: RSD, relative standarddeviation (coefficientof variation);RK, regressionkinetic; PEG, polyethylene glycol; T, turbidity; turbidity change.

T,

measured turbidity

change;

‘,

computed

CLINICALCHEMISTRY, Vol. 34, No. 2, 1988 309

computed turbidity, t, at t = an#{231}l the apparent first- and zero-order rate coefficients, k1 and k0, respectively. Procedure We mixed 500 1zL of antibody in PEG/buffer solution (outer well) with 100 L of sample or standard prepared in buffer. Measurements were made at 340 nm (±5 nm) by using data rates of 2.5 s per point for IgG and 3.Os per point for IgA and 1gM. We controlled the temperature at 25.0 ±0.1 #{176}C. Results

and Discussion

Unless stated

otherwise,

are reported as one

uncertainties

standard deviation (±1 SD).

for IgG and IgA do not. As was the case with nephelometric monitoring of the IgG reaction (2), a combined zero-order/ first-order/quadratic model gave better fits of the data than the combined zero-order/first-order model, but it offered no advantage relative to the latter for quantitative applications and was not used further. Calibration curves. Figure 2 includes several calibration plots for IgG and 1gM with superimposed least-squares fits of the data. For IgG, we observed a reproducible break in the calibration curve at about 10 mgIL for all data-processing options because the reaction velocity is too fast relative to the mixing speed of the centrifugal system for accurate measurements. Accordingly, we used two quadratic equations and fit the curve in the region of excessantibody using piecewise regression:

Response Curves Figure 1, A and B, presents typical response curves for IgG and 1gM for near-optimal conditions chosen for quantification of these species (1); response curves for IgA were similar to those for IgG. The principal differences are as noted earlier (1); plots for 1gM continue to yield increasing values of turbidity

as concentration

increases whereas plots

A

=

b0 + b1x1 + bbx2 + b3(x1

-

c)x2 + b4[x1

where x1 is IgG concentration, x2 is an with the values, 0 if x1 c or 1 if x1 concentration value at which the break equation occurs.Other data were fit with equations. Our goal was to identify

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T1mQ (s) FIg. 1. Turbidity-tIme curvesforconditionsrangingfromlargeexcess of antibodyto excess of antigen A,& PEG,40 g/L. (A) lgG reaction; ail curves, antibody at 80-told dilution;lgG concentrations forcurvesa- respectively, 1.5, 6.0, 12, 24, 40, 55, 79, 103, and 120 mg/I.. ( 1gMreaction.All curves: antibody at 120-fold dilution. 1gM concentrations forcurvesa- respectively, 2.9,5.9,10,18,26,33,40,60, and 80 mg/L

310 CLINICALCHEMISTRY,Vol. 34, No. 2, 1988

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measurement

objectives

(Vm,

us to identify the transition region between excess antibody and excess antigen and to quantify the immunoglobulins throughout the concentration ranges of physiological interest. There is no single measurement objective that will satisfy all these criteria. Therefore, our plan was to use different measurement objectives to achieve the above-stated goals. Although the velocity (Figure 2A) can be used to quantify the immunoglobulins in the regions of excess antibody or excess antigen, it can not be used to quantify antigen in the region of equivalence, because the plot passes through a maximum. In Figure IA, it is noted that the slopes of response curves at 250s (vertical dashed line) are very small up to curve e, and then begin to increase steadily as antigen concentration increases (curves f-i). This behavior is illustrated by the data in Figure 2A (right-hand ordinate), in which the rate remains very small and constant for IgG up to abotit 40 mg/L and then increases for IgG up to about 100 mg/L. In principle, the rate measured at some time near 250 s could be used both to detect the region of equivalence and to quantify IgG in that region (vertical dashed lines in Figure 2A). However, in practice, the rates are so small (note the ordinate scales) that they may not be sufficiently reliable for either purpose. Similar reasoning applies to turbidity changes, at fixed times and the difference between these changes, (T = iT), as illustrated in Figure 2B. Persons not prepared to use the curvefitting methods discussed below might profitably consider these options. However, we believe the curve-fitting method offers better choices, and the remainder of our attention is focused on that approach. Figure 2, C and D, illustrates different types of information available from the curve-fitting process. The turbidity changes computed with the curve-fitting method, T, behave similarly to those in Figure 2B computed as differences between two discrete points, T; the first-order rate coefficient (right ordinate) exhibits analogous behavior, with the maximum shiftedto lower concentrations relative to those for or T. Figure 2D shows that both the zero-order rate coefficient (curve 0) and the ratio of rate coefficients (k1/k0) (curve D) exhibit different types of behavior that can be used to detect the transition region between excess antibody and T, k1, k0, etc.) that would enable

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excess antigen. We prefer to use the ratio, because of the smooth, unidirectionalchange from a point well below the equivalence region throughout the remainder of the concentration range examined. Ratios between the intersections of the first-order rate coefficient with the two vertical dashed lines (Figure 2C) corresponded to the transition region; larger ratios corresponded to excess antibody and smaller ratios corresponded to excess antigen. We used the first-order ratecoefficient to quantify immunoglobulin concentrations in the transition region and a variety of quantities (V,,., ATE, and i1) to quantify concentrations outside that region. The program also detects and identifies responses that are outside the useful range (low and high) of the proposed procedure. The behavior of IgA is similar to that for IgG and we used

Fig. 2. Calibration plotsforthevarious processing options FramesA-O, lgG; frameE gM. (A) rate option; ( tiurbldftychangeto 608 () and 1808(0) and between60 and 180s(O); (C reeeaion4dnetic option,data fit with a Sstorder/zem-ordar model, 250-sprocessing range, t (0) and k1(s); (1 ratio ofratecoefficients, k,/k0 (0), andk,, (0), (E)same sa C,exceptfor l, 300-sprocessing range

analogous proceduresfor this component. The principo.l problem with IgA is that there is less overlap between k1 and other calibration options in the interface between the regions of excess antibody and equivalence. Calibration data for 1gM are presented in Figure 2E. We used the computed turbidity change, t, up to some predetermined upper limit (e.g., T = 0.12) to quantify lower 1gM concentrations (to the left of the dashed vertical line in Figure 2E) and the first-order rate coefficient, k1, to quantify higher 1gM concentrations (to the right of the dashed line). Imprecision/Recovery

We assessedthe reproducibility, linearity, and efficacy of the proposed quantitative procedure in the following manner. A known amount of antigen from the appropriate CLINICAL CHEMISTRY, Vol. 34, No. 2, 1988 311

reference serum CA1 for IgG and the custom serum for IgA and 1gM (1)1 was added to a serum pool to give samples with concentrations corresponding to regions of excess antibody, equivalence, and excess antigen. We made measurements on each of two or three replicates for each concentration prepared over a two- and three-day period and selected appropriate calibration equations as describedin the previous section. We computed the mean value of the determined concentration (no grouping by days), the average within-run relative standard deviation (RSD), and the average “recovery” of known amounts of antigen added to a serum pool, based on the determined concentration of the pool before and after adding antigen. The between-run RSD was computed by dividing the pooled standard deviation for all runs by the average determined concentration. These and other results are summarized for each iinmunoglobulin and each data-processing option in Table 1 and are discussed below. IgG. Results forIgG are summarized in the first six rows of Table 1. The within- and between-run RSDs were less than 3% for all data-processing options. Average recoveries ranged from 96% to 102% except for the highest concentration computed with the two-point option, for which the recoverywas 108%. This concentration was close to the maximum of the calibration curve and was just outside the lower limit of the calibration equation for excess antigen, and the less-than-ideal performance is not surprising. For samples near the equivalence region (42.6 and 63.6 mg/L added), we recommend the use of k1 to compute concentrations; however, for comparison purposes, we computed results by using all the calibration options. It is noted that reasonable agreement is achieved for all the options, with those for k1, T, and Vm showing better agreement than those for It should be noted that we used iT and Vm to quantify IgG in these supplemental samples only Table 1. Results for Quantification

we had prior knowledge of their approximate concentrations. In practice they would be identified as being in the range in which k1 should be used as the calibrator. IgA. For IgA, the within-run imprecision for each region of the calibration curve was typically