Least Detectable Concentration and Dynamic Range of Three

Anal. Chem. 2007, 79, 1954-1960

Least Detectable Concentration and Dynamic Range of Three Immunoassay Systems Using the Same Antibody Thomas R. Glass, Naoya Ohmura,* and Hiroshi Saiki

Central Research Institute of the Electric Power Industry, Department of Bioscience, 1646 Abiko, Abiko City, Chiba, Japan 270-1194

The least detectable concentration (LDC) and dynamic range (DR) of three immunoassay systems are compared using four distinct antibodies (all specific for estradiol but with different affinities) on each system. The systems evaluated include the industry standard, ELISA, and two biosensors, surface plasmon resonance and kinetic exclusion. In all cases, the measurements of inhibition curves (response vs estradiol concentration) were contracted to outside experts (the biosensor manufacturers themselves in the case of the biosensors), each of whom was supplied with the same blind samples. Each biosensor manufacturer also reported an estimate of the equilibrium dissociation constant (Kd) for each of the antibodies. The LDC and DR observed for the kinetic exclusion biosensor are consistent with an interpretation of Kd limited detection while that from the other biosensor and ELISA show limits of detection somewhat above those expected for Kd limited performance. The determined LDC and DR of each biosensor is self-consistent in the sense that none of the inhibition data contradicts theoretical limits associated with the Kd as measured on that system; however, some contradictions are apparent across platforms. The use of multiple antibodies of differing Kd improves confidence that the observed differences in performance are associated with the immunoassay system rather than the particular analyte. The least detectable concentration (LDC) is a parameter of prime importance in selecting between competing immunoassay techniques. In the field of immunoassay, it is widely recognized that the lowest LDC can be achieved in the “excess reagent” or “sandwich” assays.1,2 This assay format relies on the analyte having two antigenic sites allowing two antibodies to bind simultaneously, and this requirement leaves out a large range of molecules of analytic interest. The alternative immunoassay technique suitable for small molecules is a limited reagent format.1,2 It is well established and generally accepted that, in a limited reagent assay, the LDC is intimately related to, and ultimately limited by, the * To whom correspondence should be addressed. Tel: 81-471-82-8211. Fax: 81-471-83-3347. E-mail; [email protected]. (1) Ekins, R. P. Clin. Chem. 1998, 44, 2015-2030. (2) Gosling, J. P. Clin. Chem. 1990, 36, 1408-1427.

1954 Analytical Chemistry, Vol. 79, No. 5, March 1, 2007

equilibrium dissociation constant (Kd) of the antibody used.3-6 It is also widely appreciated that the relationship is not a simple one and that in order to quantify the LDC it is also necessary to take into account the system reproducibility or noise,5,7,8 as well as some “local factors” such as the degree of certainty required by the analyst.5 Both the Kd limit and the system noise influence can be readily understood from a consideration of the law of mass action. If the antibody concentration is below the Kd value, then the 50% inhibition point will be equal to the Kd and cannot be lowered by any change in experimental conditions.4 Under this condition, if the solution antigen is present at a concentration of 0.01 times the Kd value, then ∼99% of the antibody will be free in solution at equilibrium, implying the signal will only be reduced by 1%. If the system reproducibility is well below 1%, then this signal may be satisfactory for detection. On the other hand, if the system reproducibility is 10% (common in many immunoassay systems), then a 1% signal change cannot be detected. Many immunoassay systems suitable for the detection of small analytes are available, and the LDC and dynamic range (DR) are important parameters in comparing these systems. Several complications arise when attempting to compare systems based on published accounts of the DR and LDC of individual systems. First, if different antibodies are used, then comparisons may reflect the antibody’s contribution to the LDC rather than the immunoassay system’s. Second, even if the antibody is the same, the system noise will usually contain a component reflecting the skill of the practitioner,8 and the comparison may represent differences in the experimental skill. Third, different practitioners may use different nonequivalent methods or assumptions in calculating the LDC and DR, resulting in invalid comparisons. Here we describe a comparison of the DR and the LDC of three commercial immunoassay systems. In an attempt to control the sources of error mentioned above, four antibodies with differing Kd’s were used in the comparison, all measurements were contracted to expert practitioners (the manufacturers themselves in the case of the biosensors), and the data analysis was done (3) O’Connor, T.; Kane, M. M.; Gosling, J. P. Biochem. Soc. Trans. 1995, 23, 393S. (4) Ohmura, N.; Lackie, S. J.; Saiki, H. Anal. Chem. 2001, 73, 3392-3399. (5) Ekins, R.; Edwards, P. Clin. Chem. 1997, 43, 1824-1831. (6) Ekins, R. P. Br. Med. Bull. 1974, 30, 3-11. (7) Pardue, H. L. Clin. Chem. 1997, 43, 1831-1837. (8) Hayashi, Y.; Matsuda, R.; Maitani, T.; Imai, K.; Nishimura, W.; Ito, K.; Maeda, M. Anal. Chem. 2004, 76, 1295-1301. 10.1021/ac061288z CCC: $37.00

© 2007 American Chemical Society Published on Web 01/27/2007

Table 1. Experimental Conditions Kinetic Exclusion Experiments nominal concentrations used antibody A

B

S

D

expt type

Ab

Ag

critical reagent use incubation

sample timing

label

antibody (µg)

β-estradiol (µg)

low [Ab] equilbrium

50 pM

400-1.45 nM, 2.5-fold dilution

1h

120 s, 0.50 mL, 0.25 mL/min

180 s, 0.75 mL, 0.25 mL/min

0.23

0.54

high [Ab] equilibrium

1 nM

400 nM-17 pM, 2.5-fold dilution

1h

30 s, 0.50 mL, 1.00 mL/min

120 s, 0.50 mL, 0.25 mL/min

4.50

0.38

kinetic inject

300 pM

3 µM, 300, 100, 50, 20, 5, and 1 nM, 500 pM

2.9 s

80 s, 1.0 mL, 0.75 mL/min

120 s, 1.0 mL, 0.5 mL/min

1.98

7.56

low [Ab] equilibrium

50 pM


2h

120 s, 0.50 mL, 0.25 mL/min

180 s, 0.75 mL, 0.25 mL/min

0.11

0.13


600 pM


1h

30 s, 0.50 mL, 1.00 mL/min

120 s, 0.50 mL, 0.25 mL/min

1.35

0.09

kinetic inject

25 pM

300, 100, 60, 30, 20, 10, 6, 3, and 1 nM, 500 pM

4.3 s

120 s, 1.0 mL, 0.5 mL/min

120 s, 1.0 mL, 0.5 mL/min

0.09

1.14


10 pM

5 nM-210 fM, 2.5-fold dilution

12 h

720 s, 3.00 mL, 0.25 mL/min

120 s, 0.50 mL, 0.25 mL/min

0.08

0.01


100 pM


6h

120 s, 0.50 mL, 0.25 mL/min

120 s, 0.50 mL, 0.25 mL/min

0.34

0.02

kinetic inject

100 pM

30, 20, 10, 7, 5, 3, and 1 nM, 700, 400, and 100 pM

4.3 s

120 s, 1.0 mL, 0.5 mL/min

240 s, 1.0 mL, 0.25 mL/min

0.12

0.09


50 pM


24 h

2400 s, 10 mL, 0.25 mL/min

240 s, 1.00 mL, 0.25 mL/min

1.16

0.01


500 pM

6.5 nM-273 fM, 2.5-fold dilution

24 h

240 s, 1.00 mL, 0.25 mL/min

240 s, 1.00 mL, 0.25 mL/min

2.25

0.01

kinetic inject

200 pM

15, 6, 3, 2, and 1 nM, 600 pM, 300, 200, 100, 50, and 1 pM

7.2 s

240 s, 1.00 mL, 0.25 mL/min

240 s, 1.00 mL, 0.25 mL/min

0.75

0.08

consistently and identically in our own facility. Systems evaluated included a commercially available surface plasmon resonance biosensor and a flow-based kinetic exclusion biosensor. ELISA, the industry standard in immunoassay, was also included for comparison. The anti-estradiol antibodies and estradiol were distributed as blind samples, and the measurement contracts specified measurement of estradiol inhibition curves (in at least triplicate) for each antibody. Contracts to each of the biosensor manufacturers also specified measurement of each antibody’s Kd for estradiol. The inhibition curves supplied by the contractors were all analyzed identically in our laboratory and used to estimate LDC and DR, assuring that the same methodology and assumptions were applied in all cases. However, Kd values were determined by the manufacturers using their own methodology. This procedure assured that the system comparisons were done using the same antibody and antigen, that the measurements were made by expert users thoroughly familiar with the particular system they were using, and that the data analysis was handled the same way in each case. MATERIALS AND METHODS Antibodies and Chemicals. Monoclonal anti-estradiol antibodies were purchased from the following: Antibody “S”, BiosPacific Inc. (Emeryville, CA) Catalog No. A54060069P; antibodies “A” and “B”, Seradyne (Indianapolis IN) Catalog Nos. MIE 0102 and MIE 0105, respectively; antibody “D”, Biodesign International (Saco ME) Catalog No 2F9. β-Estradiol 6-(carboxymethyl)oxime

BSA (E2-BSA, Catalog No. E5630) came from Sigma Chemical (St. Louis, MO). 17β-Estradiol (Catalog No. 052-04041) came from Wako Pure Chemical Industries (Osaka, Japan). Estradiol-17-BSAhemisuccinate (Catalog No. 80-IE22) came from Fitzgerald Industries (Concord MA). All contractors were supplied with antibodies identified only by the letter designators given above, along with sufficient quantities of estradiol and estradiol conjugates. Each contractor was also given the nominal antibody concentration supplied by the manufacturer. Experimental Details. SPR. For estradiol inhibition experiments, running buffer was PBS with 0.1% BSA, pH 7.4. All samples were applied at 25 °C with a 5 µL/min flow rate and 4 min total time. In between injections, the chip was regenerated with 50 mM NaOH for 1 min (antibodies A and S), with 25 mM NaOH/50% acetonitrile for three 15-s pulses (antibody B), or with 47.5 mM NaOH/5% acetonitrile for three 20-s pulses. For estradiol Kd determination experiments, the same CM5 chip and model S-51 instrument were used. For these experiments, antibody was immobilized on the chip using standard amine coupling protocols of 100 µg/mL antibody in 10 mM sodium acetate pH 5.5. The chip was coated for 10 min while flowing at 5 µL/min. Kd’s were determined in PBS supplemented with 5% DMSO. Beads. Kinetic Exclusion (KE). Particles used on the KE system were 98-µm-diameter poly(methyl methacrylate) (PMMA) and were coated according to Sapidyne Instruments’ standard Analytical Chemistry, Vol. 79, No. 5, March 1, 2007

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procedures. PMMA beads were previously aliquoted into 200-mg portions by Sapidyne Instruments Inc. The beads were rocked in coating solution (100 µg/mL estradiol-17-BSA-hemisuccinate or β-estradiol 6-(O-carboxymethyl)oxime:BSA) for 2-3 h at 37 °C. The beads were then blocked with 10 mg/mL BSA in PBS, pH 7.4, 0.02% sodium azide. Buffers. KE. The running buffer was PBS, pH 7.4, with 0.02% sodium azide. The sample were prepared in the same buffer supplemented with 0.1% BSA. Label. KE. The secondary antibody used for detection was purchased from Jackson ImmunoResearch Laboratories, Inc.: 115175-003, Cy5TM-conjugated AffiniPure goat anti-mouse IgG (H+L) label was used at 1.00 µg/mL. Experimental Details. KE Each contractor was allowed complete freedom to make the measurements in the fashion best suited to their biosensor. Table 1 shows the experimental conditions worked out for each antibody as reported by Sapidyne Instruments. ELISA. ELISA measurements were performed at Kyoto Electronics Manufacturing using a standard 96-well microtitre plate format. Estradiol-BSA was immobilized in the wells, and competition occurred between the immobilized and solution antigens for the primary antibody. Bound antibody was detected using an enzyme-labeled antispecies secondary antibody. Data Analysis Four-Parameter Equation. In the inhibition assays, we required each contractor to provide us with triplicate or greater individual measurements at each concentration. The individual measurements were averaged and then fitted with the following four-parameter logistic equation.

y)

(A1 - A2) [1 + (x/x0)p]

+ A2

(1)

In this equation the term A2 represents the background, or nonspecific binding. Following Hayashi,8 the nonspecific binding term (A2 in eq 1) was subtracted from all measurements. Parameter A1 in eq 1 represents the upper asymptote of the data and includes the nonspecific binding. For this reason, the fitted value of A2 was also subtracted from A1. After subtracting the value A2 from the data, and from parameter A1, A2 was set to zero in the equation. The other parameters (p and x0) remained unchanged. Estimation of the LDC and DR for Inhibition Assays. First Method: Three σ. The LDC is the minimum concentration that can be clearly differentiated from zero concentration. It makes intuitive sense to base the LDC on the noise or variability of the system response at zero analyte. If the measurement error follows a normal distribution, then the system response to zero analyte will be within three standard deviations of the mean 99% of the time. Based on this, we define the LDC to be the concentration of analyte that gives a signal equal to the zero signal minus three times the standard deviation of the zero signal. Analogously, the maximum analyte concentration that can be differentiated from infinite concentration (MDC) represents an upper limit on the usable range of the assay. This can be calculated as the concentration giving a signal three times the standard deviation above the nonspecific binding signal. 1956

Analytical Chemistry, Vol. 79, No. 5, March 1, 2007

Figure 1. ELISA data and theory. Panel A shows the average of the raw measurement data (units of absorbance for ELISA along with error bars of plus and minus one standard deviation (nonspecific binding has been subtracted). The solid curved line is the best fit of eq 4 to the data. The solid vertical lines indicate the LDC and lower and upper limits of the DR as determined from the noise model. The dashed vertical lines show the LDC and MDC as determined from three standard deviation analysis. Panel B shows the RSD, normalized relative to the concentration, along with the best fit of eq 6. The dashed lines indicate the cutoff for the LDC (30% RSD) and DR (10% RSD). Panel C shows the RSD normalized to the signal along with the best fit of eq 3.

Second Method: Noise Theory. Hayashi et al.8 developed a more sophisticated theory allowing ready estimation of both the LDC and DR. They derived an equation to predict their system noise as a function of discrete error sources they identified for their system and experiment. The model they developed describes the relative standard deviation (RSD), the standard deviation divided by the mean of the signal, as a function of the analyte concentration. Equation 2 gives the form of the model they developed.

RSD(x) ) E12 + (E2/y(x))2

(2)

In eq 2, x is the analyte concentration, E1 and E2 are systemspecific constants, and y(x) is given by eq 1. They do not fit their model to their measured noise, though they do show that the theory seems to describe at least some of the noise data reasonably accurately. In the present case, where we sent out samples to the system vendors, we do not have access to the experimental details needed to construct a model equivalent to Hayashi’s. Instead, we fitted a noise model similar to theirs to our measured data. In order to achieve a good fit to all our data, we generalized their model by making the exponent (2 in eq 2)

The slope of the standard curve is given by its derivative with respect to concentration x, or

-A1 p dy (x/x0)p ) dx [1 + (x/x )p]2 x 0

(5)

Multiplying eq 3 by eq 4, dividing by the negative of eq 5 and the concentration x gives the following equation for Hayashi’s “U”shaped curve.

U(x) )

[ ()

1 x E1 p x0

(-p)

+ E1 +

( ) [ [ ( ) ]] [ [ ( ) ]] ] x x0

(-p)

E2 x 1+ A1 x0

p

E2 x ‚ 1+ A1 x0

q

p

+ q

(6)

In this expression, the first term forces U to infinity as x goes to zero, and the last term forces U rapidly to large values as the concentration increases. The overall result is a concave-up open U-shaped curve sometimes referred to as the precision profile.5 Still following Hayashi, the LDC is defined as the minimum concentration giving an RSD of 30% and the DR is defined as the range of values with an RSD less than 10%.

Figure 2. KE data and theory. Panel A shows the average of the raw measurement data (fluorescence intensity) along with error bars of plus and minus one standard deviation (nonspecific binding has been subtracted). The solid curved line is the best fit of eq 4 to the data. The solid vertical lines indicate the LDC and lower and upper limits of the DR as determined from the noise model. The dashed vertical lines show the LDC and MDC as determined from three standard deviation analysis. The dashed lines indicate the cutoff for the LDC (30% RSD) and DR (10% RSD). Panel B shows the RSD, normalized relative to the concentration, along with the best fit of eq 6. Panel C shows the RSD normalized to the signal along with the best fit of eq 3.

a variable of the fit. Letting the exponent become a variable q gives

RSD(x) ) E12 + (E2/y(x))q

(3)

Setting A2 equal to zero in eq 1 gives

y(x) )

A1 1 + (x/x0)p

(4)

Notice y approaches zero for large values of x (the analyte concentration), which results in RSD(x) approaching infinity for large values of x. Following Hayashi, the theoretical RSD given by eq 3 is multiplied by the theoretical system response given by eq 4, to get the theoretical standard deviation. This value is divided by the negative slope of the standard curve, providing a theoretical estimate of the expected variation in concentration due to the standard deviation of the experiment. Finally, this value is divided by the concentration to get the RSD expressed in terms of concentration.

RESULTS AND DISCUSSION Experimental Design. Estradiol, MW 272, is too small for a sandwich assay format. For this reason, it was necessary to use a limited reagent assay format in the case of ELISA and KE. The SPR biosensor can quantify the analyte not only from a competitive assay (binding of soluble antibody to immobilized antigen inhibited by the presence of the analyte) but also by monitoring direct binding of analyte to the immobilized antibody on the sensor chip. Theoretically, direct detection is potentially more sensitive because it can operate in an excess reagent mode; however, the low MW of estradiol makes detection of low concentrations very difficult, even for the most sensitive plasmon resonance detectors (the BIAcore S51 was used in this study). Both methods were evaluated in this study, and for estradiol, the competition mode was found to be more sensitive. Conversely, Kd measurements on the SPR biosensor were estimated from direct binding of the estradiol to immobilized antibody. This was done to prevent spurious effects arising from bivalent binding of the antibody to the solid phase (avidity effects). Four antibodies, labeled A, B, S, and D, were supplied to each biosensor contractor along with soluble estradiol. Estradiol BSA was also supplied in the case of ELISA and KE measurements (estradiol BSA was not used in plasmon resonance measurements). The SPR biosensor was able to measure inhibition curves for all four antibodies, but was able to measure Kd for only two of the antibodies. The other two had “too little response” for Kd estimation. The KE biosensor was able to measure inhibition and Kd for all four antibodies. ELISA was able to measure inhibition for all four antibodies but did not attempt to measure Kd. Figure 1A shows inhibition data for antibody B (Seradyne MIE 0105) from the ELISA system. In the ELISA system, six separate measurements were made at each concentration. The nonspecific binding term has been subtracted and the solid line represents the best fit of the eq 4 to the data. Equation 4 was inverted and used to find concentration estimates for each of the individual Analytical Chemistry, Vol. 79, No. 5, March 1, 2007

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Table 2. Least Detectable Concentration, Dynamic Range, and Binding Constants Measured by Each of 3 Methods for Each Of 4 Antibodiesa SPR

KE

Seradyne 102 (Antibody A) LDC (Noise Model) 14.7 0.05 DR (L) (Noise Model) 22.6 0.2 DR (U) (Noise Model) 661.4 14.6 LDC (3σ) 19.9 0.04 MDC (Noise Model) 789.6 26.3 ka (1/M‚s) 1.3 × 105 1.0 × 108 kd (1/s) 1.6 × 10-3 1.5 × 10-1 Kd 12.6 1.4 BiosPacific (Antibody S) LDC (Noise Model) 10.2 0.003 DR (L) (Noise Model) 13.5 0.01 DR (U) (Noise Model) 1649.6 0.6 LDC (3σ) 20.6 0.002 MDC (Noise Model) 370.8 1.1 ka (1/M‚s) 8.4 × 104 4.1 × 107 kd (1/s) 7.0 × 10-3 1.6 × 10-3 Kd 0.8 0.039 Seradyne 105 (Antibody B) LDC (Noise Model) 32.6 0.02 DR (L) (Noise Model) 42.1 0.1 DR (U) (Noise Model) 524.9 15.4 LDC (3σ) 49.4 0.02 MDC (Noise Model) 598.4 24.2 ka (1/M‚s) n/a 2.5 × 107 kd (1/s) n/a 7.9 × 10-3 Kd n/a 0.3

Figure 3. SPR data and theory. Panel A shows the average of the raw measurement data (units of mass for SPR) along with error bars of plus and minus one standard deviation (nonspecific binding has been subtracted). The solid curved line is the best fit of eq 4 to the data. The solid vertical lines indicate the LDC and lower and upper limits of the DR as determined from the noise model. The dashed vertical lines show the LDC and MDC as determined from three standard deviation analysis. Panel B shows the RSD, normalized relative to the concentration, along with the best fit of eq 6. The dashed lines indicate the cutoff for the LDC (30% RSD) and DR (10% RSD). Panel C shows the RSD normalized to the signal along with the best fit of eq 3.

measurements (six for each nominal concentration in this case), and the mean and standard deviation were computed. Dividing the standard deviation by the mean here gives the RSDconcentration shown in Figure 1B. The solid line in Figure 1B is given by eq 6. Figure 1C shows the standard deviation divided by the mean signal level (RSDresponse) plotted versus concentration. The solid line represents the best fit of eq 3 to the data. The large value of RSD (98.5%) at 367 nM results from the very small average response (0.01 AU) at this concentration. The data fitting was done in two steps. In the first step, eq 1 was fit to the mean inhibition data. The fit was effected by varying the parameters of eq 1 corresponding to the nonspecific binding (A2), the full-scale response (A1), the 50% inhibition concentration (x0), and the “slope factor” (p), which governs the slope of the response. These parameters were determined by a least-squares 1958 Analytical Chemistry, Vol. 79, No. 5, March 1, 2007

Biodesign (Antibody D) LDC (Noise Model) 3.5 0.001 DR (L) (Noise Model) 4.6 0.002 DR (U) (Noise Model) 33.7 0.2 LDC (3σ) 4.3 0.002 MDC (Noise Model) 63.7 0.1 ka (1/M‚s) n/a 6.1 × 107 kd (1/s) n/a 3.6 × 10-4 Kd n/a 0.006

ELISA 2.3 11.7 269.8 7.3 751.5

0.2 0.4 3.7 0.3 9.4

0.6 2.4 94.2 0.6 129.9

0.2 0.6 13.7 0.3 11.9

a Blank entries indicate measurements that were not attempted. n/a indicates failed measurements. Units are nanomolar except where noted.

fit to the mean data. After fitting, the best-fit value for A2 was subtracted from all raw data and from A1. In doing this subtraction, eq 1 reduces to eq 4 and A2 becomes zero. In the second step, parameters E1, E2, and q from eq 3 were varied to minimize the total squared error between eq 3 and the RSDresponse, and between eq 6 and the RSDconcentration. Figures 2A-C and 3A-C show the results for the B antibody for the KinExA system and the SPR system, respectively. The results shown are typical and show that the noise model used has sufficient flexibility to accommodate fairly different noise characteristics. Table 2 and Figure 4 summarize all results for all four antibodies and all three measurement methods. In Figure 4A, the end points of the lines are the LDC and MDC calculated as the concentration giving a signal three standard deviations away from the zero analyte response (LDC) or three standard deviations away from the infinite concentration response (MDC). In Figure 4B, the lines represent the LDC and DR as calculated using the noise model. In both Figure 4A and B, the Kd value is indicated for comparison. It is apparent in Figure 4 that the two methods are in general agreement with both methods showing the most sensitive detection (lowest LDC value) was achieved using the

Figure 4. Least detectable concentration, dynamic range, and Kd for 4 antibodies on 4 measurement platforms. In both panels, antibody D (Biodesign) is represented by diamond markers ((), antibody S (Biospacific) is represented by closed circles (B), antibody B (Seradyne MIE0105) is represented by upright triangles (2), and antibody A (Seradyne MIE0102) is represented by square markers (9). Large open circles indicate the measured Kd for the antibody and technique. The vertical lines in panel A indicate the range from LDC to MDC calculated using three times the standard deviation. The vertical lines in panel B show the LDC (minimum symbol) and DR calculated from the noise theory.

KE system with the Biodesign (D) antibody. This antibody also exhibited the lowest Kd of the antibodies measured by each method. Overall, the trend in LDC follows the trend in antibody Kd values reported by KE (the only method to measure all four Kds), and for the highest Kd values reported, antibodies Seradyne 102 (A) and Seradyne 105 (B) both the ELISA and KE systems may be Kd limited. For the other two antibodies, the KE system still appears to be Kd limited while the ELISA does not, possibly indicating that an instrument/technique limit was reached at a concentration between 0.3 (Kd of the Seradyne 105 antibody) and 0.039 nM (Kd of the Biospacific antibody). In the case of the SPR system, all antibodies were applied at 10 µg/mL (66 nM), which is far above the highest Kd measured by KE (1.4 nM for Seradyne

102) and nearly 10 times higher than the highest Kd reported by SPR (12.6 nM for the same antibody). It is well understood4 that using an antibody above its Kd will prevent Kd-limited detection. All manufacturers were given complete freedom to select the antibody concentration, and 10 µg/mL was chosen for SPR in order to get an adequate signal. It seems reasonable that the relatively low sensitivity of the SPR technique (at least as compared to label-based techniques like fluorescence and enzymeamplified absorbance) required a higher antibody concentration preventing the SPR system from achieving antibody-limited performance. For a Kd-limited immunoassay, it is expected that the Kd of the interaction will be equal in value to a concentration near the Analytical Chemistry, Vol. 79, No. 5, March 1, 2007

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middle of the usable range of the assay. This is exemplified in Figure 4A and B by the KE data. The SPR data show Kd values somewhat below the LDC. This is consistent with a non-Kd-limited detection system and indicates that some parameter other than the antibody Kd is limiting the detection. Conversely, the Kd data are not consistent across platforms, and the experiment performed here did not include any reference method for Kd determination, so it is not possible to say which if any of the Kd results shown is correct. It is interesting to note however that, for the Biospacific antibody, the detection results obtained with KinExA would exceed Kd-limited detection if the Kd supplied by the SPR system were correct. In future work, we hope to improve on the present study by identifying and including a reference method for Kd determination. CONCLUSIONS The present study was designed to compare the performance of two biosensors to each other and to ELISA. In an attempt to get the best possible data for each of the biosensors, the measurement was contracted to the biosensor manufacturers, eliminating our own skill in operation of the biosensor systems as a source of error.

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Analytical Chemistry, Vol. 79, No. 5, March 1, 2007

The least detectable concentration and dynamic range of three systems including enzyme-linked immunosorbent, surface plasmon resonance, and KE assay are compared using the same four anti-estradiol antibodies. The LDC and DR were estimated using two different methods and compared to the corresponding equilibrium dissociation constant (Kd) for each of the antibodies. The determined LDC and DR or each biosensor is self-consistent in the sense that none of the inhibition data contradicts theoretical limits associated with the Kd as measured on that system; however, some contradictions are apparent across platforms. The use of multiple antibodies of differing Kd improves confidence that the observed differences in performance are associated with the immunoassay system rather than any particular analyte. ACKNOWLEDGMENT This study was carried out as part of the project P00058, which was entrusted by the New Energy and Industrial Technology Development Organization (NEDO). Received for review July 17, 2006. Accepted December 6, 2006. AC061288Z

Least Detectable Concentration and Dynamic Range of Three

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