ANALYTICA CHIMICA ACTA
Analytica Chimica Acta 336 (1996) 185-l 93
Simultaneous immunoassay using piezoelectric immunosensor array and robust method
Xia Chu, Jian-Hui Jiang, Guo-Li Shen*, Ru-Qin Yu
Institute of Chemometrics and Chemical Sensing Technology and Department of Chemistry and Chemical Engineering, Hunan University,
Changsha 410082, China
Received 13 February 1996; revised 18 June 1996: accepted 20 June 1996
Abstract
A simultaneous immunoassay technique has been developed for the determination of dual analytes, immunoglobulin M (IgM) and C-reactive protein (CRP) by constructing a piezoelectric quartz crystal array system. This array system was composed of five piezoelectric quartz crystals. Each crystal was immobilized with an antibody mixture, which had a fixed ratio of anti-IgM to anti-CRP antibodies but worked under different detection conditions, i.e., in five buffer media with different pH values. The specificity of immunoreactions and the effect of pH on the sensitivity of the immunosensors were investigated. Applications of this array system in the estimation of the concentration of unknown samples using three linear regression methods, i.e., ordinary least squares (OLS), partial least squares (PLS) and least terminated squares (LTS), were presented.
Results of these samples showed that the LTS estimator is a promising tool for multi-analyte piezoelectric immunoassay.
Keywords: Immunoassay; Piezoelectric quartz crystal array; Robust regression; LTS; PLS
1. Introduction
There has been considerable interest in recent years in developing immunoassay techniques that permit the simultaneous determination of multi- analyte in a single sample [l]. Among the most existing techniques for simultaneous immunoassay, it is always necessary to make use of antibodies or antigens with different chemical labels, including, for example, radioactive element labels [2,3], fluorescent
group labels [4,5], enzyme labels [6], and colored
latex particles [7]. Recently, Hayes et al. demon-
* Corresponding author
0003.2670/96/$15.00 ‘: 1996 Elsevier Science B.V. All rights reserved PII SOOO3-2670(96)00308-X
strated a dual analyte immunoassay technique based on two different metal ion labels for simultaneously determining human serum albumin (HSA) and
immunoglobulin G (IgG) [8]. The limitation of all chemical label-based techniques is that a preliminary separation of the labeled antibodies or antigens from the excess labels has to be conducted; and secondly, since the optima1 detection conditions for different
labels are frequently distinguished significantly, the simultaneous determination of different labels in the
final step of the analytical procedure will induce a
loss to the sensitivity of these techniques. A feasible technique to circumvent both the aforementioned limitations is that one can take advantage of multi- channel measurements obtained under various detec-
186 X. Chu et al./Analytica Chimica Acta 336 (1996) 185-193
tion conditions, and make use of high-sensitivity sensors to determine the unlabeled antibodies or antigens directly.
Piezoelectric quartz crystal is a high-sensitivity sensor to the mass deposited on its surface. Recently, piezoelectric quartz crystals have found wide appli-
cations in immunoassay. The use of piezoelectric quartz crystals modified using antigens was first
demonstrated by Shons et al. in 1972 [9]. Many researchers have reported immunosensors using piezoelectric quartz crystals modified by antibodies or antigens [lo-151. Although there is now extensive
literature describing such sensors for immunoassay, there is no published description about multi-analyte
immunoassay with piezoelectric quartz crystal array system, to date. A possible difficulty with this
technique is that the multidimensional data obtained in a piezoelectric immunosensor array system is not free from the occurrence of outliers. To combat this problem, multiple parallel tests usually need be conducted such that the outliers can be easily picked
out. Applications of sensor array systems to multi-
component analysis have been reported by many
researchers [16-l 81. All the reported techniques involved the use of chemometric methods, among
which, the most popular approaches are ordinary least squares (OLS) and partial least squares (PLS)
regressions. PLS is a comparatively new approach for constructing regression equations. The objective of PLS is to construct new explanatory variables, often called latent variables, which can capture most of the information in the X variables that is
useful for predicting the dependent variables [ 19,201. An undesirable feature of PLS is the lack of robustness of the outlying data points. To work with multi-channel measurements, possibly containing
outliers, one has to resort to the robust regression methods so as to offer sufficient credibility to the
results obtained. In particular, when the multi- channel measurements are of relatively low dimen- sion, as in the case of a sensor array system, it is better to use the robust methods having high break- down points.
Many robust regression methods exist in the statistical literature with varying degrees of robust- ness. The first high breakdown point robust regres- sion method introduced to chemists is the least
median squares (LMS) regression method [21,22]. LMS has an asymptotic breakdown point of 50%. A disadvantage of the LMS estimator is its low efficiency. To improve the efficiency of the LMS estimator, an alternative approach-the least trimmed squares (LTS) estimator, which not only
can provide a 50% breakdown point, but also has a higher efficiency-has been proposed by Rous-
seeuw [23]. Consider the regression problem y = x’c + e with observations (xj,y,)(i = 1, . . , n), where e is the random noise, and c is the parameter vector to be estimated. The LTS estimator with a 50% breakdown point for this regression problem is given by:
mint c i=l:..,[n/2]+1 rFi)
where r-f,), t-t2 , . . . , rf,,, d
are the ordered squared residuals, an r$, 5 r(2)2 5 . 5 r$); and [x] denotes the largest integer which is smaller than x. Note that the objective of LTS is quite similar to that of OLS except that the IZ - 1 - [n/2] largest squared residuals are not included in the sum. A common problem with all robust regression methods is that
more than one optimum exist on the response surface of their objective functions, that cause some difficul- ties in developing an appropriate optimization algo- rithm to reach the globally optimal solution. This
local optimization problem is not so severe in cases where the number of observations are relatively small, as in the case of the sensor array system, since
such a problem can be easily approached using the combinational optimization algorithms.
In this paper, a simultaneous immunoassay tech- nique has been developed for the determination of dual analytes, immunoglobulin M (IgM) and C- reactive protein (CRP) by constructing a piezoelectric
quartz crystal array system. This array system composed of five piezoelectric quartz crystals. Each crystal was immobilized with an antibody mixture,
which had a fixed ratio of anti-IgM to anti-CRP antibodies, but worked under different detection conditions, i.e., in five buffer media with different pH values. With a modification in the antibody mixture, the crystals could independently react either with IgM or CRP, which provided an excellent linear response to IgM and CRP. Since the five media with different pH values had different effect on the
X. Chu et al./Analytica Chimica Acra 336 (1996) 185-193 187
crystals’ response characteristics for IgM and CRP, the constructed array system had different response patterns for IgM and CRP, and could be used to determine these dual analytes simultaneously. With a pure component calibration set of various concentra-
tions, eight samples of unknown concentration were determined with the aid of several linear regression methods, including the LTS, PLS and OLS estima-
tors. The concentration of a majority of unknown samples were correctly estimated by all the regres- sion methods. The concentration of the remaining
samples, to which the array’s responses were contaminated by some outliers, were also predicted with satisfactory accuracy by LTS.
2. Experimental
2.1. Reagents and materials
Human immunoglobulin M (IgM) reference serum
and goat anti-(human IgM) diagnostic serum were obtained in the lyophilized form from the Health Department, Shanghai Institute of Biological Pro- ducts (Shanghai, China). C-reactive protein (CRP) reference serum and anti-CRP diagnostic serum were purchased from Zhejiang Yuhuan Biological Re-
agents Factory (Yuhuan, Zhejiang, China). The copolymer of 2-hydroxyethylmethacrylate and
methylmethacrylate (HEMAMMA) was obtained by copolymerizing HEMA and MMA in a ratio of 3 : 1 by volume [24]. Cyanogen bromide (CNBr), for activating the copolymer coating, was prepared from
bromine and sodium cyanide [25]. Other reagents and solvents were of analytical-reagent grade. Fresh, doubly distilled water was used throughout the experiment. All the chemicals were used without
further purification. All the buffer solutions used in this work were prepared following the procedures described in the book [26].
2.2. Apparatus
AT-cut piezoelectric quartz crystals with vacuum- deposited silver electrodes on both sides, giving a fundamental frequency of 9MHz, were purchased from Beijing 707 Factory (Beijing, China). The crystals were powered using a laboratory-made
oscillator circuit constructed from a transistor-
transistor logic integrated circuit (TTL-IC). The crystal frequency was monitored using a nanosecond
Universal Counter (1992 SS 3380) purchased from the Fourth Radio Factory (Shijiazhuang, Hebei,
China). All analyzes were performed at the room temperature, at approximately 25°C.
2.3. Immobilization of antibodies onto quartz crystal
The piezoelectric quartz crystal was immersed in 1.2M NaOH for 25 min. After being washed with doubly distilled water, the crystal was placed in 1.2 M HCl for 20min, and was subsequently washed with
doubly distilled water followed by ethanol and dried. The HEMAMMA copolymer (0.42 g) was dissolved in tetrahydrofuran (THF, 30ml). This THF solution (0.1 ml) containing the HEMAMMA copolymer was uniformly spread on both surfaces of the quartz
crystal and air-dried. The frequency change caused by the copolymer coating was about 1500 Hz. After
being washed with doubly distilled water, the quartz crystal was activated by immersion in a 0.2M CNBr solution for 15 min. During activation, the solution was kept alkaline (pH 1 l-l 3) using NaOH solution and the temperature was kept in the range 15-20°C. Following further washing with water and air-drying,
the quartz crystals were used for antibody immobi- lization.
In the immobilization of single antibody, 50~1 of
IgM antibody (20-fold dilutions) or CRP antibody (5- fold dilutions), diluted with carbonate buffer (pH 9.6), was added to the electrodes on both sides of each quartz crystal. The crystals were incubated at 4°C for 10 h. In the immobilization of dual
antibodies, 5Opl solution consisting of a mixture of an IgM (20-fold dilutions) and CRP antibodies (5- fold dilutions) in a ratio of 1 : 1 by volume, was used to immobilize both anti-IgM anti-CRP antibodies onto the electrodes of each crystal. After incubation, the quartz crystals were rinsed three times with 0.5 M
NaCl solution containing 0.05% Tween-20, and subsequently rinsed three times with doubly distilled
water, followed by a treatment with 0.1 M glycine at 37°C for 20min to the prevent non-specific adsorp- tion of IgM or/and CRP antigen. The quartz crystals were rinsed again in the aforementioned manner and air-dried.
188 X. Chu et al./Analytica Chimica Acta 336 (1996) 185-193
2.4. Immunoreaction
First, a series of pure-component solutions were
prepared by diluting a concentrated IgM reference and CRP reference sera with five buffer media, i.e., two acetate buffers (pH 4.6 and 5.2), one phosphate buffer (pH 6.1), one phosphate buffered saline (pH 7.2), and one borate buffer (pH 8.2). Each solution had five parallels that had the same concentration of IgM or CRP but different pH values. In the calibration step, a pure-component
calibration set was used. That is, the sample solutions were directly obtained by taking 50 ul of one of the above-mentioned parallel solutions. In the prediction step, each sample solution of 50~1 was obtained by mixing one of the above-mentioned
IgM solutions with the other CRP solution having the same pH value. Each sample solution also had five parallels that had the same concentration but different pH values. The five parallel sample solutions were separately dropped onto the electrodes of five quartz crystals on which the antibody mixture had been immobilized. The quartz crystals were incubated at 37°C for 1 h. That is, the immuno-
reactions between the modified crystals and the sample solutions were performed in parallel at five different pH values. After immunoreaction, the
quartz crystals were rinsed three times with 0.5M NaCl solution containing 0.05% Tween-20 followed by three times with doubly distilled water, and air- dried.
2.5. Measurement procedures
Following equilibration in the test chamber for a
few minutes, the stable frequencies (Fi) of the crystals, immobilized with IgM and CRP antibodies, were measured. Since these measurements were
performed in the gaseous phase, the system usually showed an excellent stability, i.e., after equilibration for a few minutes, the maximum frequency change was 5 Hz even after more than 1 h. After the immunoreaction, the crystals were placed in the test chamber and the new frequencies (F2) were mea- sured. The frequency shifts (LW = F, - F2) were related to the total amount of proteins adsorbed onto the crystals. Typically, it took about 3 h to accomplish all the steps needed for the simultaneous immunoas-
say, including the immobilization of antibodies onto the crystals.
In all experiments, the crystals used were regen- erated by soaking them in a THF solution for about
5 min in order to dissolve the copolymer coating; and the fundamental frequencies, therefore, returned to their initial values. By means of such treatments, each crystal could be used repeatedly 20 times without detectable loss of sensitivity. Other regeneration methods, which attempted to remove the adsorbed antigens from the modified crystals (0.2M glycine- HCl, 0.2M ethanolamine, 8M urea), reduced the activity of the immobilized antibodies in this study
significantly, thereby resulting in a loss in the sensitivity and reproducibility of the immunosensors.
3. Results and discussion
3.1. Test of speci$city
Since the crystals were modified using a mixture of anti-IgM and anti-CRP antibodies in a fixed ratio, one would expect that the immunoreactions, either
between IgM and anti-IgM antibody or between CRP and anti-CRP antibody, could proceed indepen- dently. Provided this expectation be true, the total
amount of adsorbed proteins was the sum of the amount of IgM and CRP that had reacted with their corresponding antibodies. Since the frequency shifts resulting from the adsorption of IgM or CRP are usually linearly related to their concentration in a certain range, one can obtain an excellent linear model involving the frequency shifts, and concentra- tions of IgM and CRP. Under most conditions, the requirement of independent immunoreactions can be met because of the high specificity of antigen-
antibody immunoreaction. To test the specificity of the two immunoreactions involved in this work, firstly, we immobilized anti-IgM antibody on the
electrodes of the crystals and compared the frequency responses of pure IgM with that of an antigen mixture of IgM and a fixed concentration of CRP; and secondly, the anti-CRP antibody was immobilized and a similar comparison between the frequency responses of pure CRP, and that of an antigen mixture of CRP and a fixed concentration of IgM was made. As can be seen from Fig. 1, the frequency responses
X. Chu et al./Analytica Chimicu Acta 336 (1996) 185-193 189
Concentration @g/ml)
Fig. I. Relationship between frequency shifts and concentrations.
(0) and ($) represent the frequency shifts after the immunoreac-
tions of pure IgM (0) and IgM mixed with 32.4pgml-’ CRP (@)
with the (anti-IgM antibody)-adsorbed crystals, respectively. ( n ) and (x) represent the frequency shifts after the immunoreactions of
pure CRP ( n ) and CRP mixed with 43.7 pg ml-’ IgM (x) with the
(anti-CRP antibody)-adsorbed crystals, respectively.
of pure IgM and IgM-CRP mixture, or that of pure CRP and CRP-IgM mixture, were nearly identical. These results show that in the sample of a mixture of IgM and CRP, two immunoreactions were carried out in a highly specific manner and no cross-
reaction occurred. This fact gives evidence of a linear model based on the frequency shifts, and IgM and CRP concentrations. In addition, due to the high specificity of immunoreactions, the responses of the
antibody-mixture-modified crystals to the other anti- gens present in the human serum did not differ significantly from blank values, an indication that other antigens did not interfere with the determina- tion of IgM and CRP. This result could be partly shown on the basis of a previous study [27]. The presented results of the specificity test provided a
Table I Effect of antibody dilution ratio on determination of IgM and CRP
Antibody dilution ratio Determination of IgM a
feasibility for the use of the array system in a clinical
test.
3.2. Selection oj’antibody dilution ratio
As the molecular weights of IgM and CRP are about 900 000 and 118 000-144 000, respectively, the frequency shift caused by the adsorption of one IgM
molecule will be larger than that caused by the adsorption of one CRP molecule. Consequently, an appropriate dilution ratio of these two antibodies for the antibody mixture, used to modify the crystals, should be selected in order to obtain comparable sensitivities for the determination of IgM and CRP.
Considering that the single diffusion valence of IgM and CRP antibodies were 1 : 180 and 1 : 80, respec-
tively, three different antibody dilution ratios were used for immobilizing both antibodies onto the quartz crystals, to determine IgM and CRP under pH 7.2, i.e., IgM and CRP reference sera were diluted with phosphate buffered saline. As shown in Table 1, the relative amount of IgM antibody in the antibody mixture has little effect on the determination of IgM.
On the contrary, the relative amount of CRP antibody strongly affected the determination of CRP. When the
relative amount of CRP antibody in the antibody mixture was less than a certain value, good linear
relationship between the frequency shift and the CRP concentration could not be obtained. Only when the antibody dilution ratios were 1 : 40 and 1 : 10 for IgM
antibody and CRP antibodies, respectively, the frequency responses to both IgM and CRP showed good linearity and comparable sensitivities. There- fore, such antibody dilution ratios for anti-IgM and anti-CRP antibodies were used in the subsequent experiments.
Determination of CRP”
IgM antibody CRP antibody Linear range Sensitivity Linear range Sensitivity
(pg ml-‘) (Hzmlpg ‘) (bgml ‘) (Hzmlpg ‘)
I:40 I:20 O-52.4 10.0076 no good linearity 1 : 40 I: 10 O-52.4 9.5261 O-37.8 X.3715 1 : 20 I : 10 O-52.4 11.1274 no good linearity
“The determination of IgM and CRP were performed under pH 7.2 by diluting the IgM and CRP reference sera with phosphate buffered saline.
190 X. Chu et al./Analytica Chimica Acta 336 (1996) 185-193
3.3. Effect of pH on sensitivity
To investigate the effect of pH on the sensitivity of
the antibody-mixture-modified crystals for IgM and CRP, IgM and CRP antibodies were immobilized onto the quartz crystals using the above-mentioned antibody mixture. A series of pure IgM or CRP sample solutions, each having five parallels of the same concentration but different pH values, were
taken to react with the dual antibody-modified crystal at 37°C for 1 h. The frequency shifts resulting from the immunoreaction were measured and the sensitiv-
ity for IgM and CRP at various pH values calculated. The relationship between the sensitivity and pH value
is depicted in Fig. 2. As can be seen, the sensitivity of the antibody-mixture-modified crystal for IgM and CRP first increase and then decrease with increasing
pH values. Two peak-shaped response curves are observed. The sensitivity of the antibody-mixture-
modified crystal for IgM reaches the highest value at pH 5.2, whereas that for CRP is obtained at pH 6.1, for all the pH values examined. Fig. 2 also indicates that there exists significant difference between the sensitivity characteristics of IgM and that of CRP at
these five pH valuesand hence, these antibody- mixture-modified crystals working under the afore- mentioned five pH conditions can be utilized to
construct a five-immunosensor array system for simultaneous assay of IgM and CRP.
An interpretation of why pH affects the sensitivity of the antibody-mixture-modified crystal can be given. Antigens and antibodies are generally amphi-
“4 5 6 7 8 9 PH
Fig. 2. Effect of pH on the sensitivity of immunoreaction of IgM
(0) or CRP (+) with (dual antibodies)-adsorbed crystals.
protic protein, and hence, they have different iso- electric points in different buffer solutions of specific pH values. Only when the pH value of the detection
medium lies between the isoelectric points of the antigen and antibody, the static electricity interac- tion-which is caused by gravitation between two or
more ionogenic parts in the antigenic determinant and the ions with opposite charges in the antibody active
site-will take place between them. As the static electricity interaction will affect the equilibrium constant of the immunoreaction, the amount of
antigen adsorbed onto the crystals at equilibrium is closely related to the pH value of detection medium.
3.4. Calibration plots for IgM and CRP and model- ing of sensor array system
The use of a sensor array for multi-component and the mathematical model used for this task usually
require a linear response model. To determine the linear dynamic range of the five immunosensors for the two proteins, IgM and CRP, a set of pure- component samples, each having the above-men- tioned five parallels, were prepared with various concentrations of IgM or CRP, and the frequency
responses of the sensor array system were measured. To obtain a consistent response for a sample at different tests, all the frequency shifts were first calibrated by reducing the corresponding blank
responses. It is also ensured that the regression line for each component immunosensor had almost the
same intercept. To simplify the linear model, all the calibrated frequency responses were subsequently subtracted from the intercept of the corresponding regression line such that the regression lines for all
the five immunosensors were through the origin. (Note these processing steps of the frequency shifts were consistently used in all the subsequent sections of this study.) The calibration plots for IgM and CRP at various pH values were shown in Figs. 3 and 4, respectively. It can be seen that the response curve of each immunosensor is linear in the ranges O- 52.4ugmll’ and O-37.8 ugmlli for IgM and CRP, respectively. Deviation from the linearity is observed when the concentrations of IgM and CRP were greater than 52.4 pg ml-’ and 37.8 ug ml-‘, respec- tively. The reason why non-linearity occurs at higher concentration is that saturation is encountered due to
X. Chu et al./Analytica Chimica Acta 336 (1996) 185-193 191
-0 20 40 60 IgM concentration (&ml)
Fig. 3. Calibration plots for IgM under different pH conditions;
pH: 4.6 (m), 5.2 (O), 6.1 (B), 7.2 (*) and 8.2 (+).
0 10 20 30 40
CRP concentration @g/ml)
Fig. 4. Calibration plots for CRP under different pH conditions;
pH: 4.6 (m), 5.2 (O), 6.1 (\oplus ), 7.2 (*) and 8.2 (+).
a complete occupancy of the antibodies’ active sites on the electrode surface by antigens.
Having determined the sensitivities of each sensor for IgM and CRP, a simple linear mode1 of this
immunosensor array system, which described the relationship between the frequency shift and concen- tration of IgM and CRP, could be obtained. This model formed the basis of application of OLS and LTS regressions to the estimation of the concentration
of unknown samples. The PLS regression provides another approach for the modeling of this system. Instead of modeling the frequency shifts in terms of the concentration of IgM and CRP, PLS attempts to construct a prediction model for the concentrations using the frequency shifts as the explanatory variables. The calibration set used for PLS modeling was the aforementioned sample set used in calibra-
tion plots in which the concentration of IgM and CRP
lay in their respective linear dynamic ranges. Since the prediction of concentration was of interest in this study, a validation set, which composed of two randomIy selected samples from the calibration set, was used. It revealed that the PLS mode1 with the two
latent components gave the smallest prediction errors for this validation set. Therefore, two latent compo- nents were used for the PLS mode1 in the estimation of the concentration.
3.5. Pattern and data structure analyzes
The frequency responses of the five sensor elements, each working at different pH, can be
combined to generate the characteristic array re-
sponse for each pure analyte. The response patterns for IgM and CRP in the five-channel array system are
shown in Fig. 5. Such an array response pattern of the piezoelectric immunosensor array is unique for each analyte involved and can thus be used tojingerprint
and identify individual components in a sample. As shown in Fig. 5, the response pattern for IgM and CRP are significantly distinguished from each other, which indicates that strong collinearity in the array
system is lacking. One can expect that this fact will bring much convenience to the problem of the estimation of the concentration .
The five-dimensional response of the array system
for an individual pure analyte with concentration in its linear range was governed merely by one free parameter, i.e., the concentration of the pure
0 500 loo0 1.500 2ooo
Component 1
Fig. 5. Sensor array response patterns for IgM and CRP. The
concentrations of IgM and CRP were 26.2 pg ml-’ and
27.0 pg ml-‘, respectively.
192 X. Chu et al./Analytica Chimica Acta 336 (1996) 185-193
component. One could predict that all the responses to an individual pure analyte would lie on a line in the five-dimensional response space. Therefore, all the data points in the pure-component calibration set would lie on two lines in the five-dimensional
response space, each associated with one analyte. This could be confirmed by the two-dimensional projections of the data set along the first two principal components (PCs). By applying principal compo-
nents analysis (PCA) to the pure-component calibra- tion set, it was observed that the first two PCs had
accounted for almost all the total variations of the data. (Variance contribution ratios were 95.26% and
4.44 for the first and second PC, respectively.) One could conclude that all the data points essentially lie on the plane generated by the first two PCs, i.e., the plane on which all the data were projected. Therefore, the two-dimensional projections of the data onto the first two PCs can almost entirely reflect the actual
distribution of all the data points. Such two-dimen- sional projections are shown in Fig. 6. As predicted,
all the projections of the data in the calibration set were distributed on two lines, each corresponding to one pure component, IgM or CRP. Such a two- dimensional representation of the array responses provided a straightforward approach to qualitative
analysis, which could identify whether an unknown sample contains IgM, CRP or both.
3.6. Estimation of concentration of unknown samples
To verify the performance of the developed immunosensor array system in determining unknown
Table 2
Multivariate prediction for IgM and CRP
0 CW w
Fig. 6. Two-dimensional projections of the calibration data set of
pure analytes, IgM and CRP, on the first two principal components
(PCs). The lines through the projections were obtained by data
fitting.
samples, eight samples containing different concen- trations of IgM and CRP (O-52.4 and O-37.8 ug ml-’ for IgM and CRP, respectively) were prepared in parallel with different buffer media. These samples
were used as unknown samples and the responses of the sensor array system were measured. The results of the prediction of these samples using the OLS, PLS and TLS estimators are shown in Table 2. A combinational algorithm, which computes LS, fits
to all possible subsets of the size [n/21+1 and picks out the solution that corresponds to the LS fit giving the smallest sum of squared residuals, was used for the LTS estimator; thus, the concentration estimations obtained using LTS were the exactly the global
optima. It may be observed that for the samples 1, 2, 3, 4 and 7, the predicted concentrations obtained by
No.
1
2
3
4
5
6
7 8
Actual concn.
Qtgmt-‘)
IgM CRP
43.7 36.0
43.7 10.8
26.2 36.0
26.2 10.8
43.7 27.0
26.2 27.0
13.1 10.8 13.1 36.0
Predicted concn. (pgml-‘) Relative error (%)
OLS PLS LTS OLS PLS LTS
‘gM CRP IgM CRP IgM CRP 1gM CRP IgM CRP tgM CRP
44.2 39.6 45.0 37.0 46.3 36.2 1.1 10.0 3.0 2.8 5.9. 0.6
44.3 9.9 44.5 9.2 43.1 12.1 I .4 8.3 1.8 14.8 1.4 12.0
27.8 39.3 28.6 37.1 28.1 31.7 6.1 9.2 9.2 3.1 7.3 4.7
27.3 11.6 27.4 11.3 27.6 11.2 4.2 7.4 4.6 4.6 5.3 3.7
37.5 33.5 38.2 31.4 41.7 28.3 14.2 24.1 12.6 16.3 4.6 4.8
38.8 9.8 38.9 9.4 21.3 29.7 48.1 63.7 48.5 65.2 4.2 10.0
14.1 9.5 14.1 9.6 12.4 10.1 1.6 12.0 7.6 11.1 5.3 6.5 16.5 36.8 17.1 34.9 12.8 39.6 26.0 2.2 30.5 3.1 2.3 10.0
X. Chu et al./Analytica Chimica Acta 336 (1996) 1X5-193
all the estimators are satisfactory. Since the strength
of the collinearities between the explanatory vari- ables, i.e., the sensitivity vectors for IgM and CRP had important influence on the relative prediction performance in the concentration estimation of IgM and CRP, the degree of collinearity in this system was investigated. It was found that the condition number for the explanatory variable matrix was 9.0348, and the variance inflation factors were 0.0221 and 0.0027, which gave the evidence for the fact that no significant collinearity occurs in this system. There-
fore, one could expect that the OLS estimator would provide results almost as good as the PLS estimator, as shown in Table 2. The prediction performance of
LTS estimator for these samples is also favorable. This might be an indication that the random errors had some deviation from the normal distribution. The
prediction errors for the samples 5, 6 and 8 obtained using the OLS and PLS estimators were rather poor. The LTS estimator, however, provided prediction results for these samples with favorable accuracy.
One could infer that the responses of these samples at the immunosensor array system had been contami- nated by one or two outliers such that the perfor-
mance of the OLS and PLS estimators collapsed.
4. Conclusions
This paper proposed a new approach to simulta- neous immunoassay using an antibody-mixture- modified piezoelectric quartz crystal array system. The presented results showed that simultaneous
immunoassay using piezoelectric arrays was feasible. The coupling of piezoelectric immunosensor array and chemometric methods could provide a promising
analytical tool for simultaneous immunoassay. Such combination could enhance the information content of piezoelectric sensing. There is no doubt that the piezoelectric quartz crystal array could lead to the development of new multi-analyte immunoassay techniques.
Acknowledgements
This work was for Ph.D. Thesis
supported by the Foundation research of National Educa-
tion Commission of
I93
the People’s Republic of
China.
References
III I21
[31
[41
ISI
161
[71
[Sl
191
1101
[Ill
1121
[I31
1141
1151 1161
1171
1181
1191 12m
1211
WI ~231 1241
I251
1261
~271
D.S. Hage, Anal. Chem., 63 (1991) 206R.
F.J. Wians, J. Dev, M.M. Powell and J.I. Heald, Clin. Chem.,
32 (1986) 887.
S.M. Cow, G. Caldwell, A.D. Toft and G.J. Beckett, Clin.
Chem., 32 (1986) 2191.
I. Hemmila, S. Holttinen, K. Petterson and T. Lovgren, Clin.
Chem.. 33 (lY87) 2281.
.I. Vuori, S. Rasi, T. Takala and K. Vaananen. Clin. Chem.. 37
(1991) 2087.
C. Blake, M.N. Al-Bassan. B.J. Gould, V. Marks, J.W.
Brtdges and C. Riley, Clin. Chem., 2X (1982) 1469.
S.G. Hadfield. A. Lane and M.B. MeIllmurray, J. Immunol.
Methods, 97 ( 1987) 153.
F.J. Hayes, H.B. Halsall and W.R. Heineman. Anal. Chem.,
66 ( 1994) 1860.
A. Show E Dorman and J. Najarian. J. Biomed. Mater. Kes..
6 (1972) 565.
J.E. Roederer and G.J. Bastiaaans, Anal. Chem.. 55 (I 983)
2333.
E.P. Sochaczewski, J.H.T. Loung and G.G. Guilbault,
Enzyme Microb. Technol.. I2 (1990) 173.
B. Konig and M. Grltzel, Anal. Chem., 66 (1994)
341.
B. Kiinig and M. Gratzel. Anal. Chim. Acta, 309 (lY95)
19.
B. Kiinig and M. Gratrel. Anal. I,ett.. 26 (1093) 2313.
1. Karube and M. Suzuki, Biosensors. 2 (1986) 343.
W.Z. Wei, Z.H. MO and S.Z. Yao. Anal. Chim. Acta, 251
(1991) 143.
Q. Chen, J. Wang, G. Rayson, B. Tian and Y. Lin. Anal.
Chem., 65 (1993) 251.
J. Wang, G.D. Rayson, Z. Lu and H. Wu, Anal. Chem., 62
( 1990) 1924.
P. Hoskuldsson, J. Chemometrics, 2 ( 1988) 21 I
M. Sjostrom, S. Wold, W. Lindberg. J.A. Persson and H.
Martens, Anal. Chim. Acta, 150 (1990) 61.
D. Massart, L. Kaufman, P.J. Rousseeuw and A.M. Leory,
Anal. Chim. Acta, I87 (1986) 171.
P.J. Rousseeuw, J. Chemometrics, 5 I I99 I ) I. P.J. Rnusseeuw, J. Am. Stat. Assoc.. 79 (1984) 871.
Z.H. Lin, G.L. Shen and R.Q. Yu, J. Tranduction Technology
(in Chinese), 8 (1995) 3.
Betjing Medical College. in Experimental Immunology,
People’s Health Press, Beijing, 1980, p. 53.
C.J. Jtang, in Enzyme Immunoassay, People’s Health Press. Betjing. 1984, p. 178.
X. Chu, Z.H. Lin. G.L. Shen and R.Q. Yu, Analyst, 120
(1995) 2829.
