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Diana Davis, Aiguo Zhang, Jim Torrence, and Emily Dale, Bio-Rad Laboratories, Inc., 2000 Alfred Nobel Drive, Hercules, CA 94547 USA
Introduction
Bio-Plex cytokine assays are bead-based quantitative multiplex immunoassays.
The concentrations of analytes in these assays are quantitated using a
calibration or standard curve. A regression analysis is performed to derive
an equation that is used to predict the concentrations of unknown samples.
The specific concentrations of the standards used to construct the standard
curve have a direct effect on the quality of the results. Therefore, selection
of appropriate standards is a critical component of immunoassay performance.
In this tech note, the effect of the selection of standards on the accuracy,
sensitivity, and dynamic range of the results is discussed. The effect
on assay performance of reading assays on a Bio-Plex system set at two
different photomultiplier tube (PMT) voltages as well as criteria for
selecting a custom set of standards are also addressed.
Regression Analysis for Bio-Plex Assays
Because the typical response of an immunoassay is nonlinear, the nonlinear
or logistic regression routine is the preferred method for sandwich immunoassay
data analysis (Baud 1993). The four-parameter (4PL) and five-parameter
(5PL) logistic equations contain parameters (the midpoint of the curve,
the slope where the curve is linear, and the upper and lower points) that
are used to predict the response of the assay (relative median fluorescence
intensity, or MFI; Figure 1). Use of logistic regression yields the widest
range of predictable concentrations for Bio-Plex immunoassays (Nix and
Wild 2001).
Standard Curve Ranges for Bio-Plex Assays
Two sets of standards are recommended for Bio-Plex cytokine assays, a
high-sensitivity range (0.23,200 pg/ml) and a broad range (1.9532,000
pg/ml). The specific concentrations for the two sets of standards are
shown in Table 1. The highsensitivity standards are recommended for use
when the concentrations of the unknowns fall within the physiological
range of cytokines in serum. The highsensitivity standards are suitable
for quantitation of low levels of cytokines and provide the greatest sensitivity.
The broad range standards yield a wide dynamic range and are used when
quantitation of a wide range of cytokine concentrations is desired or
when the range of expected concentrations of cytokines is unknown. The
broad range standards enable the detection of the widest range of concentrations
and yield a wide dynamic range. A comparison of the high-sensitivity and
broad range standard curves plotted as concentration versus fluorescence
intensity is shown in Figure 2.
Effect of Range on Standards Recovery
The overall dynamic range, accuracy, and sensitivity of results obtained
using high-sensitivity vs. broad range standards are quite different.
These differences may be illustrated using a method known as backcalculation
of standards, or standards recovery (Davies 2001). In this method, a regression
model is applied to a set of data and the resulting equation is used to
calculate the concentrations of the standards using the response values
(Nix and Wild 2001). The analysis is performed by calculating the concentration
of each standard and then comparing it to the actual concentration using
the following formula: (observed concentration) / (expected concentration)
x 100. If the regression analysis is accurate, the calculated concentrations
will be very close to the actual concentrations of the standards. This
method yields information about the dynamic range, sensitivity, and accuracy
of calculated concentrations of an assay (Baud 1993). The recovery value
for each standard is an indication of the accuracy of the calculated concentration.
A value within the range of 70130% is considered accurate recovery. The
dynamic range of the assay, or the range where accurate concentrations
may be quantitated, is therefore indicated by the range of standards yielding
a recovery of 70130%.
A comparison of the standards recovery using broad range and high-sensitivity standards for three different cytokines is shown in Tables 2 and 3. The broad range standard concentrations where recovery is 70130% is 1.95 to 8,000 or 32,000 pg/ml, depending on the cytokine assayed. The high-sensitivity standards yield a narrower dynamic range of 0.2 or 0.78 to 3,200 pg/ml. In all three assays, the broad range standards enable the quantitation of a much wider range of concentrations.
A general indication of assay sensitivity is given by the lowest concentration in a set of standards that yields accurate recovery (70130%). Since the lowest concentration of the high-sensitivity standards is lower than the broad range standards (i.e., 0.2 pg/ml vs. 1.95 pg/ml, respectively), it would be expected that the high-sensitivity standards would yield better recovery at a lower concentration, and that the high-sensitivity standards should be chosen to maximize sensitivity in an assay. Tables 2 and 3 illustrate some typical recovery values for broad range and high-sensitivity standards.
Effect of PMT Voltage on Assay Performance
Bio-Plex assays are analyzed on a Bio-Plex system that contains a PMT.
The PMT detects assay signals in the reporter or RP1 channel. The PMT
voltage on the Bio-Plex system is automatically adjusted during CAL2 calibration
using the RP1 target value from a bead with stable fluorescence. This
method yields a reproducible signal output from day to day and between
instruments. Two RP1 target values are recommended for use with Bio-Plex
assays, a low target value for the broad range standards and a high target
value for the high-sensitivity standards. Following calibration, the low
RP1 target value yields a low PMT voltage and the high RP1 target value
yields a higher PMT voltage. Table 4 compares the resulting PMT voltage
on a Bio-Plex system following calibration with the low and high target
values.
The PMT voltage is increased in assays in which higher sensitivity is desired. However, when using the broad range standards, the signals of the high concentration standards on certain cytokines may become saturated and result in a reduced dynamic range. Figures 3 and 4 show a broad range standard IL-8 assay analyzed with the high and low PMT settings. The standard points are labeled with the corresponding recovery. In Figure 3, the recovery at the two highest points is beyond the range of the regression, due to a saturated signal at the high end of the standard curve, and thus OOR (out of range) is displayed. When the same assay is analyzed at the low PMT setting, there is no saturation and the standards recovery is accurate across the entire range of standards (Figure 4).
The high-sensitivity standards yield a much lower fluorescence intensity signal since the concentration range is much lower. When using the low range standards, reading the assay with the high PMT voltage may improve the sensitivity. Table 5 shows a comparison of the recovery of a low range GM-CSF assay run using the low and high PMT voltage settings. The low PMT setting yielded acceptable recovery down to only 3.13 pg/ml. When the same assay was run at the high PMT setting, accurate recovery down to 0.2 pg/ml was achieved.
Guidelines for Running Cytokine Assays
The overall assay performance must be taken into consideration when determining
how to set up both the cytokine assay standards and the Bio-Plex array
reader. In Table 6, the guidelines for optimizing the Bio-Plex system
(including assays and the array reader) are shown. The standards as well
as the PMT voltage chosen for reading the assay may significantly affect
results.
Selecting a Custom Set of Standards
The two sets of standards and RP1 target values discussed in this tech
note have been validated using the Bio-Plex system and have been shown
to yield optimal results. Efficient assay performance may also be achieved
using a custom set of standards as long as a few simple rules are followed.
1. Select a minimum of 8 standard curve points.
The logistic regression model requires a minimum of 5 standards for the
4PL and 6 standards for the 5PL to fulfill the analysis requirements (Motulsky
1996). A total of 8 points are recommended to ensure an accurate fit,
with a maximum of 12 points (Baud 1993). This practice allows the flexibility
to remove standard points with erroneous results due to errors in assay
preparation.
2. Choose standards evenly distributed across the entire range of concentrations.
As noted earlier, the response of a Bio-Plex assay is nonlinear; there
is a flattening of the response near zero and at the high end of the curve
with a linear portion in the middle as shown in Figure 2. Due to the nature
of this response, the chosen standards concentrations should be evenly
distributed across the entire range (Nix and Wild 2001). The regression
routine will then yield the most accurate representation of the assay
response.
3. Choose a 5PL regression routine.
When conditions are optimal, the upper and lower portions of the curve
are symmetrical, and the 4PL logistic routine is appropriate. In reality,
many conditions, such as a high-dose hook effect and inadequate washing,
can cause asymmetry in the curve (Nix and Wild 2001). The 5PL regression
contains an additional parameter to accommodate asymmetry in the curve,
and thus is the more robust type of logistic regression for Bio-Plex assays.
4. Prepare standards using serial dilutions.
When selecting the range of a custom set of standards, determine the lowest
and highest desired concentrations, then determine what dilution series
should be used to yield a total of 8 points within the range. For example,
if the low and high desired values are 5 and 10,000 pg/ml respectively,
a threefold dilution series would yield 8 points (10,000, 3,333, 1,111,
370, 123.4, 41.1, 13.7, and 4.6). A dilution series is simple to prepare
and less prone to errors compared to preparation of individual concentrations.
5. Determine which PMT setting is optimal.
Read the assay on the Bio-Plex array reader after calibrating with the
low RP1 target value, then the high value, to determine which setting
yields the best results. An assay plate may be read a second time by aspirating
the contents of the wells after the first reading and resuspending in
125 l of buffer.
Summary
Bio-Plex assays may be run with a variety of standard curve concentrations.
Two sets of concentrations are recommended, a high-sensitivity range for
maximum sensitivity or for samples such as serum that fall within the
biological range of cytokines, and a broad range for samples where a wide
range of cytokine concentrations are expected. The voltage of the reporter
PMT may also be varied to maximize assay performance. The high-sensitivity
standards should be run following calibration with the high RP1 target
value and the broad range standards perform best following calibration
with the low RP1 target value. Overall, the highsensitivity standards
yield better sensitivity, while maximum dynamic range is achieved using
the broad range standards. Excellent assay performance may also be achieved
using a unique set of standards if a few simple rules are followed: 1)
select a minimum of 8 standard curve concentrations, 2) select a set of
concentrations that are evenly distributed across the entire selected
range, 3) select a 5PL regression in Bio-Plex Manager software for the
most robust assay analysis, 4) prepare the standard curve points using
a serial dilution method, and 5) determine which PMT setting is optimal.
References
Baud M, Data analysis, mathematical modeling, pp 656671 in (Masseyeff
RF et al., eds), Methods of Immunological Analysis Volume 1: Fundamentals
, VCH Publishers, Inc., New York, NY (1993)
Davies C, Concepts, pp 78110 in (David Wild, ed), The Immunoassay Handbook, 2nd ed, Nature Publishing Group, New York, NY (2001)
Motulsky H, The GraphPad guide to nonlinear regression, in GraphPad Prism Software User Manual, GraphPad Software Inc., San Diego, CA (1996)
Nix B and Wild D, Calibration curve-fitting, pp 198210 in (David Wild, ed), The Immunoassay Handbook, 2nd ed , Nature Publishing Group, New York, NY (2001)
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