Section11:Second Experiment-Matrix Compatibility

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Contents 1 Second Experiment-Matrix Compatibility 2 Calibration Curve and Precision Profile for the Three Different Matrix Conditions 3 Calibration Curve Model Selection 4 Importance of Weighting in Calibration Curves 5 Third Development Experiment 6 Experimental Designs for Increasing Calibration Precision 7 Illustration of Experimental Design and Analysis for Sandwich ELISA Optimization

Second Experiment-Matrix Compatibility

Goal: To determine the matrix effect or sample type on the immunoassay method. The matrix is based on what the sample is found in, for instance tissue culture media, serum, cell lysate, buffers, etc. Serum matrix, due to its complexity, can have a significant effect on the method. In this example the samples are in rat serum so the matrix effect of rat serum needs to be determined.

Experiment: The samples that need to be measured in this assay will be in either mouse or rat serum. Use the conditions established in the first experiment for the concentration of the primary capture antibody and the secondary detection antibody. Serially dilute the standard to obtain a full standard curve in 3 different matrices (10% rat serum, 30% rat serum and the original buffer diluent used in the first experiment). This will determine the matrix effect that will be used for the experimental samples.

Reagents:

1. Use all of the reagents and buffers listed in the first experiment.
2. Matrix diluent: 10% rat serum in antibody diluent or 30% rat serum in antibody diluent.

Protocol: Follow the standard protocol changing only the matrix diluent to include rat serum.

1. Dilute the primary antibody in coating buffer at 0.5 µg/ml and add 100 µl to each well of the 96-well microtiter plate.
2. Incubate the plate containing the primary capture antibody overnight at 4°C and use the next day.
3. Stability of the primary capture antibody bound to the plate can be determined in later experiments.
4. Remove the primary capture antibody solution from the microtiter plates by aspirating or dumping the plate.
5. Add 200 µl of blocking buffer to each well of the 96-well microtiter plate.
6. Incubate the plate for one hour at RT.
7. Remove the blocking buffer from the plate by aspirating or dumping the plate.
8. Serially dilute the standard in antibody dilution buffer containing either 10% or 30% rat serum.
9. Add 100 µl of the standard to each well in the microtiter plate and incubate for 2.5 hours at RT.
10. Wash the plates 3 times with wash buffer.
11. Dilute the detection antibody to 1:25,000 in antibody diluent.
12. Add 100 µl of detection antibody diluent to each well of the microtiter plate and incubate for 1 1/2 hours at RT.
13. Wash the plates 3 times with wash buffer.
14. Dilute streptavidin-HRP according to manufacturer instructions in antibody diluent and add 100 µl to each well in the microtiter plate and incubate for 1 hr at RT.
15. For HRP readout add either OPD or TMB as substrate to allow color development and incubate for 10-20 minutes at RT.
16. Add acid stop reagent to stop the enzyme reaction.
17. Read at 405 nm for TMB/HRP.

Results: Use the standard curve data and construct a precision profile. Check background levels. See page 138 for standard or calibration curve model fitting.

Note that the standard curves under all three matrix diluent conditions give the dynamic range and sensitivity necessary for the intended use. For this particular assay, there is no further development needed (based on the standard curve, low background and precision profile).

Precision Profile: Generate the precision profile for the standard curve of the appropriate matrix for the experiment. A web-based tool developed internally is available for computing the calibration curve and the precision profile that gives the estimated working range of the assay. The web address of this tool is http://pascal/statmath/calibration/prd/html/calibration.html.

Calibration Curve and Precision Profile for the Three Different Matrix Conditions

Calibration Curve Model Selection

A significant source of variability in the calibration curves can come from the choice of the statistical model used for the calibration curve. It is therefore extremely important to choose the correct calibration curve model. For most immunoassays, the models commonly available in software are the following.

Linear Model:

Response = a + b*(Concentration) + error,

where a and b are the intercept and slope respectively, and “response” refers to optical density or fluorescence reading from an immunoassay.

Quadratic Model:

Response = a + b*(Concentration) + c*(Concentration)2 + error,

where a, b and c are the intercept, linear and quadratic term coefficients respectively of this quadratic model.

Four Parameter Logistic Model:

where the four parameters to be estimated are Top, Bottom, EC50 and Slope. Top refers to the top asymptote, Bottom refers to the bottom asymptote, and EC50 refers to the concentration at which the response is halfway between Top and Bottom.

Five Parameter Logistic Model:

Asymmetry is the fifth parameter in this model. It denotes the degree of asymmetry in the shape of the sigmoidal curve with respect to “EC50”. A value of 1 indicates perfect symmetry, which would then correspond to the four-parameter logistic model. However, note that the term referred to as “EC50” in this model is not truly the EC50. It is the EC50 when the asymmetry parameter equals 1. It will correspond to something very different such as EC20, EC30, EC80, etc., depending on the value of the asymmetry parameter for a particular data set. Further details are beyond the scope of this chapter.

For most immunoassays, the four or five parameter logistic model is far better than the linear, quadratic or log-log linear models. These models have recently become available in several software packages, and are easy to implement even in an Excel-based program. As illustrated in the plots below, the quality of the model should be judged based on the dose-recovery scale instead of the lack-of-fit of the calibration curve (R2). In this illustration, even though the R2 of the log-log linear model is 0.99, when assessed in terms of the dose-recovery plot, this model turns out to be significantly inferior to the four parameter logistic model. Before the assay is ready for production, the best model for the calibration curve should be chosen based on the validation samples using dose-recovery plots.

Importance of Weighting in Calibration Curves

The default curve-fitting method available in most software packages assigns equal weight to all the response values, which is appropriate only if the variability among the replicates is equal across the entire range of the response. However, for most immunoassays, the variability in the calibration-curve data between replicates increases proportionately with the response mean. Giving equal weight can lead to highly incorrect conclusions about the assay performance and will significantly affect the accuracy of results from the unknown samples. It is therefore extremely important to use a curve-fitting method/software that has appropriate weighting methods/options. See Appendix for more details.

Third Development Experiment

The two-step experiment detailed above is a very simple example of how to develop a sandwich ELISA method. If the dynamic range and sensitivity of the assay does not meet the needs of the experiments then further experimental conditions should be tested using experimental design. With experimental design all of the factors involved in the ELISA including buffers, incubation time and plate type can be analyzed.

In a sandwich ELISA method the antibodies chosen are the major drivers of the assay parameters. If at this point in the method development the precision profile of the standard curve is extremely far from the desired dynamic range and sensitivity, instead of continuing with development experiment, antibodies should be further characterized. Changing some of the variables such as the Ab concentrations can significantly improve the calibration curve and hence it’s precision profile.

Goal: Determine the optimal conditions for the variables in the immunoassay including incubation steps, buffers, substrate, etc. Also, determine the optimal antibody concentrations and the stability of the primary capture antibody bound to the plate.

Experiment: Dilute the standard in the matrix compatible to the sample (as determined in the second experiment). Vary the incubation times, dilution buffers and other variables in order to optimize the immunoassay. Analyze by using experimental design software and precision profiles.

Reagents:

1. Coating buffers
2. Blocking buffers
3. Wash buffers
4. Antibody diluents
5. Substrate

Protocol:

1. Coat the microtiter plate with the primary capture antibody at the concentration determined in the initial experiment. Incubate overnight at 4°C.
2. Discard the primary capture antibody solution from the microtiter plate.
3. Block the plate for 1 hour at RT using various blocking reagents.
4. Store plates at 4°C, desiccated, for several periods of time 0-5 days.
5. Repeat steps 1-3 the day of the actual experiment.
6. Serially dilute, using an 8-point standard curve, the known standard in the appropriate matrix for the experiment. For the control also dilute the standard in the same buffer as was used in the initial experiment. Add 100 µl of standard to each well in the 96-well microtiter plate.
7. Incubate the diluted standard with the primary capture antibody for 1 hour and 3 hours at RT and overnight at 4°C. Each time point will have to be run in a separate plate.
8. Wash plates 3 times (If background or NSB is high try different wash buffers).
9. Add 100 µl of diluted secondary detection antibody. If background is high again different diluents can be tested.
10. Incubate the secondary detection antibody for different time periods and again different plates will have to be used for each time condition.
11. Wash plates 3 times.
12. Add 100 µl of substrate to the plate containing the detection antibody conjugated to the enzyme and allow to incubate according to the manufacturers conditions.
13. Add 100 µl of stop buffer.
14. Read at 405 nm.

Data Analysis: Compute the standard curves and their precision profiles for all the experimental design conditions. Derive the optimization endpoints using the precision profiles. Then analyze the optimization endpoints using software such as JMP to determine the optimum levels of the assay factors. See next section for the details and illustration.

Experimental Designs for Increasing Calibration Precision

Step 1: Identify all the factors/variables that potentially contribute to assay sensitivity and variability. Choose appropriate levels for all the factors (high and low values for quantitative factors, different categories for qualitative factors). Then use fractional-factorial experimental design in software such as JMP to derive appropriate experimental “trials” (combinations of levels of all the assay factors). Run 8-point calibration curves in duplicate for each trial. With each trial taking up two columns in a 96-well plate 6 trials per plate can be tested. All trials should be randomly assigned to different pairs of columns in the 96-well plates. However, certain factors such as incubation time and temperature are inter-plate factors. Therefore, levels of such factors will have to be tested in separate plates.

	Trial 1		Trial 2		Trial 3		Trial 4		Trial 5		Trial 6
	1	2	3	4	5	6	7	8	9	10	11	12
A	8pt. calibration curve; duplicate		8pt. calibration curve; duplicate		8pt. calibration curve; duplicate		8pt. calibration curve; duplicate		8pt. calibration curve; duplicate		8pt. calibration curve; duplicate
B
C
D
E
F
G
H

After the above experiment is run the calibration curves should be fit for each trial using an appropriately weighted-nonlinear regression model. Then the precision profile for the calibration curve of each trial should be obtained along with the important optimization end-points such as working-range, lower quantitation limit and precision area. Now analyze these data to determine the optimal level of all qualitative factors and determine which factors should be further investigated. See Appendix for the definition of these terms/concepts and details on the computations.

Step 2: We now need to determine the optimum levels for the factors determined in the previous step. Choose appropriate low, middle and high levels for each of these factors based on the data analysis results from step 1. Now use software such as JMP to generate appropriate trials (combinations of low, middle and high levels of all the factors) from a central-composite design. Then run duplicate 8-point calibration curves for each trial using a similar plate format as in step 1.

Now obtain the precision profile and the relevant optimization end-points of the calibration curve of each trial. Perform the response-surface analysis of these data to determine the optimal setting of each of the quantitative factors run in this experiment.

Illustration of Experimental Design and Analysis for Sandwich ELISA Optimization

In this table, we have the experiment plan from the second step of the optimization process using experimental design for a sandwich ELISA. These four factors (primary capture antibody, secondary detection antibody, enzyme and volume) were picked out of the six factors considered in the first step of this optimization process (screening phase) for further optimization. We use a statistical experimental design method called central composite design to generate the appropriate combinations of the high, mid and low levels of the four factors in this second step. For example, trial #6 in this table refers to the middle level of the first, third and the fourth factors, and the low level of the second factor.

8-point standard curves in duplicate were generated for each of these trials, in adjacent columns of a 96-well plate. This resulted in six trials per plate, and with 36 trials in 6 plates.

We computed the precision profiles of the calibration curves of each of these 36 trials. From these precision profiles, we computed the working range (lower and upper quantification limits), CV and related variability and sensitivity measures. We then used a statistical data analysis method called "response surface analysis" on these summary measures. This resulted in polynomial type models for all the factors. Using the shape of the curve and other features from this model, the optimum levels for these factors were determined. This gave us the most sensitive dynamic working range possible for this assay.

An experiment was then performed for this ELISA to compare these optimized levels to the pre-optimum levels and the assay kit manufacturer’s recommendation. The results from this comparison are summarized below.

The optimized levels derived from statistical experimental design for this ELISA resulted in the following improvements over the pre-optimum and assay kit manufacturer’s recommendation.

• Lower quantification limit decreased more than two-fold to 13.6 nM.
• Upper quantification limit by up to 10-fold to 1662.3 nM.
• Precision area increased by 2-fold and the working range increased by 2-fold to two log cycles.

This improvement is evident from the precision profiles given above for these three conditions.