Quantifying Specific Antibody Concentrations by Enzyme-Linked Immunosorbent Assay Using Slope Correction

Assessing the magnitude of an antibody response is importantto many research and clinical endeavors; however, there areconsiderable differences in the experimental approaches usedto achieve this end. Although the time-honored approach of endpoint titration has merit, the titer can often be misleadingdue to differences in how it is calculated or when samples containhigh concentrations of low-avidity antibodies. One frequentlyemployed alternative is to adapt commercially available enzyme-linkedimmunosorbent assay kits, designed to measure total antibodyconcentrations, to estimate antigen-specific antibody concentrations.This is accomplished by coating the specific antigen of interestin place of the capture antibody provided with the kit and thenusing the kit's standard curve to quantify the specific antibodyconcentration. This approach introduces considerable imprecision,due primarily to its reliance on a single sample dilution. This"single-point" approach fails to address differences in theslope of the sample titration curve compared to that of thestandard curve. Here, we describe a general approach for estimatingthe effective concentration of specific antibodies, using antiseraagainst foot-and-mouth disease virus VP1 peptide. This was accomplishedby initially calculating the slope of the sample titration curveand then mathematically correcting the slope to that of a correspondingstandard curve. A significantly higher degree of precision wasattained using this approach rather than the single-point method.

INTRODUCTION

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Introduction

Enzyme-linked immunosorbent assays (ELISAs) are among the mostcommonly employed laboratory techniques due to their flexibility,sensitivity, low cost, and ease of automation. ELISAs are usedclinically to assess the magnitude of an immune response fora variety of purposes, including diagnosing disease based uponseroconversion to an infectious agent, assessing the course/statusof an ongoing clinical disease, and predicting protective immunityagainst infectious diseases. In vaccine research, ELISA titersare often used to identify and/or map neutralizing epitopesand to establish correlates of immune protection. In many instances,quantifying the antigen-specific antibody concentration is desirable.

Customarily, end point titration has been used to quantify themagnitude of an antibody response, resulting in an assessmentof "titer." This simple technique suffers from two significantshortcomings. First, there is no universally accepted methodfor assigning titer, resulting in imprecision and ambiguitywhen results obtained by different laboratories are compared.Second, samples containing high concentrations of low-avidityantibodies are often assigned artificially high titers (3, 7).The resulting titers may be misleading, due to the minimum avidityrequirements needed for protection (1). Thus, titers can beunreliable in predicting protection against an infectious diseaseas well as in assessing the magnitude of immune responses.

An alternative to end point titration has emerged over the pastdecade upon commercialization of capture ELISA kits. These kitsuse a sandwich ELISA format to quantify the concentration ofa variety of soluble proteins, including cytokines, hormones,growth factors, and antibodies. Generally, these kits are accurateand precise in that both the solid-phase capture and detectionantibodies are well characterized and bind to their target antigensin a predictable and reproducible manner. In many research publications,substitution of the solid-phase capture antibody with a coatedantigen has been used to determine antigen-specific antibodyconcentrations. In many instances, this approach relies on asingle sample dilution's optical density (OD) falling withinthe bounds of the standard curve. This "single-point" interpolationis fundamentally flawed (8) in that it does not take into accountdifferences in the slope of the sample titration curve comparedto that of the standard curve.

It is generally accepted that the slope of an antibody titrationcurve is proportional to the average antibody avidity (5, 9).To incorporate slope correction into the indirect ELISA system,a mathematical model of avidity differences between sampleswas developed based on the law of mass action (2, 4). This approachyielded a considerably more precise determination of specificantibody concentration.

MATERIALS AND METHODS

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Materials and Methods

Animals and immunizations. Five-week-old Yorkshire pigs of each gender were obtained fromTufts University School of Veterinary Medicine (North Grafton,MA). After a 1-week acclimatization period, each pig was anesthetized(4.4 mg telazol/kg of body weight, 2.2 mg/kg ketamine, and 2.2mg/kg xylazine) and then vaccinated intramuscularly with 100µg of a foot-and-mouth disease virus (FMDV) peptide vaccine(UBITh [10]). Whole blood was collected on a weekly basis andcentrifuged at 1,000 x g, and sera were stored at –20°Cuntil assayed. An identical booster immunization was given 6weeks later, and the animals were sacrificed at week 9 by administrationof Euthasol (Delmarva Laboratories Inc., Midlothian, VA) at0.22 ml/kg (85.8 mg/kg sodium pentobarbital and 11 mg/kg sodiumphenytoin). All animal protocols were approved by the Universityof Connecticut's Institutional Animal Care and Use Committeeprior to the initiation of procedures.

Immunoassays. Plates were coated in one of two ways. On plates receiving thestandard curves, affinity-purified, anti-swine immunoglobulinG (IgG) capture antibodies (Bethyl Laboratories, Montgomery,TX) were diluted in coating buffer (0.05 M sodium carbonate,pH 9.6) and 50 µl was applied to flat-bottomed 96-wellImmulon IV HBX microtiter plates (Thermo Labsystems, Franklin,MA) at concentrations from 1.25 µg/ml to 0.039 µg/mlrepresenting the variable CC. On plates receiving samples, thecapture antibody was substituted with 50 µl of the antigenof interest (FMDV peptide vaccine [UBITh] or bovine serum albumin[BSA] control) at 10 µg/ml in coating buffer. Both setsof plates were tightly sealed with Parafilm and incubated overnightat room temperature (RT).

Standard curves were produced from pig reference serum providedwith the kit and serially (log₂) diluted from 250 ng/ml to 31.25ng/ml. The diluted standards were applied to plates previouslycoated with affinity-purified anti-swine IgG coated at 50 µl/well.

Sample curves were serially (log₂) diluted from pig sera at1:2,000 to 1:8,000 and added to antigen-coated plates. Fromthis point forward, both types of plates were treated identically.

Plates were washed with wash buffer (50 mM Tris, 0.14 M NaCl,0.05% Tween) three times using 125 µl of buffer, withshaking, using a Bio-Tek EL-403 plate washer (Bio-Tek Instruments,Inc., Winooski, VT) between each step. Plates were blocked with100 µl/well of a Tris-buffered saline solution containing0.1% BSA for 30 min at RT. Samples and standards were seriallydiluted (log₂) in Tris-buffered saline (50 mM Tris, 0.14 M NaCl,1% BSA, 0.05% Tween, pH 8.0) and incubated at RT for 1 h.

After the plates were washed, a horseradish peroxidase-conjugatedgoat anti-pig IgG (Bethyl) was applied at a concentration of1:20,000 (50 µl/well) and incubated for 1 h at RT. Plateswere washed, and 50 µl/well of 3,3',5,5'-tetramethylbenzidine(Kirkegaard-Perry, Gaithersburg, MD) microwell peroxidase substratewas added, resulting in the development of a colored product.Plates were allowed to develop at RT for 10 min, at which timethe reaction was stopped upon addition of 50 µl/well of2 N H₂SO₄. The OD of each well was determined by measuring theabsorbance at a ${lambda}$ value of 450 nm using a Bio-Tek EL-311 microplateautoreader (Bio-Tek Instruments, Inc., Winooski, VT).

To determine the slope of each sample's titration curve, a first-orderquadratic formula was fitted to characterize the relationshipbetween OD and log-transformed dilution. Only curves with r²values of $≥$ 0.99 were used in subsequent analyses. Standard curveswere generated using pig reference serum (Bethyl) containinga known concentration of antibodies. The reference serum wasdiluted from a 1-µg/ml stock solution at concentrationsof 250 ng/ml, 125 ng/ml, 62.5 ng/ml, and 31.25 ng/ml, definingthe variable RC. The coating concentration was optimized inorder to obtain a linear slope regression.

Data analysis. (i) Single-point analysis. Specific antibody concentrations were determined by selectingsample dilutions that fell within the upper and lower boundsof the standard curve (generated using the capture ELISA system).The concentrations were calculated using a single-point interpolationwithout slope correction. The resulting value was multipliedby the dilution factor of the sample to correct for the finalconcentration.

(ii) Slope-corrected analysis. In order to determine the slope [m₍_CC₎] and intercept [b₍_CC₎]of each standard curve, the RC and CC values were substitutedinto equation 1. This relationship is illustrated by the fourcurves shown in Fig. 1.

Formula 1 (1)
Theslopes and intercepts determined from equation 1 were then substitutedinto a least-squares formula and plotted against the coatedantigen concentrations (CC), yielding the slope and interceptmatrix:

Formula 2 (2)

Formula 2
This resulted in a log-linear relationshipbetween the coating concentration and the slope/intercept (Fig.2). The relative coating concentration of the predicted, slope-matchedstandard curve (CC_STDcorr) was then determined by substitutingthe slope of the sample titration curve into equation 3.

Formula 3 (3)
This term was used to determinethe intercept (b_STDcorr) as follows:

Formula 4 (4)
Each sample's effective specific antibodyconcentration was then calculated, using any OD reading fromthe sample dilution curve, as follows:

Formula 5 (5)
The dilution factor corresponding to the ODused in equation 5 was then substituted into equation 6 to correctfor each sample's dilution:

Formula 6 (6)

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FIG. 1. The relationship between the optical density and dilution of a series of standard curves at different coating concentrations.

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FIG. 2. Regression of the slopes and intercepts (step 1) versus the coating concentrations (step 2).

RESULTS

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Results

Significant heterogeneity was observed in titration curve slopesfor antisera collected from FMDV peptide-immunized pigs (Fig.3). By applying the formulae in equations 1 to 5, these differencesin slope were corrected, yielding "effective antibody concentrations."The results obtained using this method were then compared tothose obtained using the single-point method. Significantlylower coefficients of variation (CVs) were found using the slopecorrection approach rather than the single-point method. (P< 0.01) (Fig. 4).

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FIG. 3. Serum IgG responses against an FMDV peptide vaccine (UBITh) showing heterogeneity in slopes. Each symbol represents an individual animal.

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FIG. 4. Comparison of CVs using the single-point versus the slope correction method. The single-point method has a significantly higher CV (*, P < 0.01) than the slope correction method.

DISCUSSION

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Discussion

End point titration estimates of titer frequently lead to ambiguousand imprecise results. Thus, many investigators have electedto express the magnitude of humoral immune responses in termsof specific antibody concentration. This is accomplished bysubstituting the coated capture antibody, provided in commerciallyavailable ELISA kits, with the antigen of interest. This approachgenerally results in the OD corresponding to a particular sample'sdilution being interpolated on a standard curve generated usingthe capture antibody. Here, we show that this approach leadsto considerable imprecision, as it does not address differencesin slope that inevitably occur between a given sample's dilutioncurve and the standard curve. To correct for this deficiency,the slopes of both curves were mathematically modeled and thestandard curve was slope matched to the sample curve, therebyproviding an estimate of the sample's concentration.

Lemke et al. recently described an alternative approach forestimating specific antibody concentrations by using an antibodydepletion technique (6). Specific antibodies were depleted ina stepwise fashion by transferring the unbound antibody populationfrom one antigen-coated well to the next. The specific antibodyconcentration was then determined by calculating the differencebetween antibody concentration before and after depletion. Althoughthis method is conceptually sound, it was unreliable in ourhands due to unavoidable loss of sample at each transfer step.In addition, this approach may overestimate the specific antibodyconcentration due to the nonspecific binding that occurs ateach step (data not shown). Further refinement of this approachmay be useful in defining an "absolute" specific antibody concentrationfor a single sample that could then be used as a reference standard.Pairing this method with the slope correction approach describedhere could ultimately improve both the accuracy and precisionof ELISAs.

Although the slope-matching technique described herein is slightlymore cumbersome than either end point titration or the single-pointinterpolation approach using commercial capture ELISA kits,it is considerably more precise. Adopting this approach willlead to better agreement between research groups in assessingthe magnitude of antigen-specific antibody responses.

ACKNOWLEDGMENTS

We thank Debra Rood for critical review of the manuscript, AlanWalfield, United Biomedical Inc., for providing the FMDV peptide,and Roger Zemek for assistance with animal care and handling.

This work was supported in part by USDA grants 58-1940-0-007and NRICGP 2002-02833.

FOOTNOTES

* Corresponding author. Mailing address: University of Connecticut, Center of Excellence for Vaccine Research, 1390 Storrs Rd., ABL Room 302E, Unit 4163, Storrs, CT 06269-4163. Phone: (860) 486-6073. Fax: (860) 486-5067. E-mail: Lawrence.Silbart{at}uconn.edu.

Present address: Cornell University School of Veterinary Medicine,Ithaca, N.Y.

REFERENCES

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