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Probing thyroglobulin in undiluted human serum based on pattern recognition and competitive adsorption of proteins Ran Wang, 1,a) Shuai Huang, 2 Jing Li, 3 and Junseok Chae 1 1 School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA 2 Department of Industrial and Systems Engineering, University of Washington, Seattle, Washington 98195, USA 3 School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona 85281, USA (Received 20 September 2013; accepted 28 September 2014; published online 10 October 2014) Thyroglobulin (Tg) is a sensitive indicator of persistent or recurrent differentiated thyroid cancer of follicular cell origin. Detection of Tg in human serum is challenging as bio-receptors, such as anti- Tg, used in immunoassay have relatively weak binding affinity. We engineer sensing surfaces using the competitive adsorption of proteins, termed the Vroman Effect. Coupled with Surface Plasmon Resonance, the “cross-responsive” interactions of Tg on the engineered surfaces produce uniquely distinguishable multiple signature patterns, which are discriminated using Linear Discriminant Analysis. Tg-spiked samples, down to 2 ng/ml Tg in undiluted human serum, are sensitively and selectively discriminated from the control (undiluted human serum). V C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4897630] Biosensors aiming at detection of target analytes, such as proteins, microbes, and virus, are widely needed for vari- ous applications including detection of chemical and biologi- cal warfare (CBW) agents, environmental monitoring, and drug screening. 1 Proteins are often targeted for detection as their relative and absolute levels of concentrations may be correlated to specific disease states and as such be used to assess the progress of disease and monitor the effects of treatment. 26 Many biosensors aiming at probing protein bio- markers impose challenges of insufficient sensitivity and se- lectivity in human serum, in which there are more than 20 000 different proteins with concentrations ranging more than 10 orders of magnitude. 69 In traditional biosensors, the selectivity is provided by bio-receptors possessing highly specific binding affinity to capture target analytes. Many bio-receptors, such as antibod- ies, peptides, and aptamers, exist, yet their use in biosensors is often limited by their relatively weak binding affinity with analyte, non-specific adsorption, need for optimization con- ditions, low reproducibility, and difficulties integrating onto the surface of transducers. 1012 In order to circumvent the use of bio-receptors, we instead utilize the competitive adsorption of proteins, termed the Vroman effect. The Vroman effect was reported by Vroman and Adams in 1969, 13 and its various aspects have been largely studied since then. 1416 The competitive adsorp- tion targeted here occurs among different proteins competing to adsorb to a surface, when more than one type of proteins are present. When lower-affinity proteins are adsorbed on the surface first, they can be displaced by higher-affinity pro- teins arriving at a later point in time. 17 Moreover, only low- affinity proteins can be displaced by high-affinity proteins, typically possessing higher molecular weight, yet the reverse sequence does not occur. Therefore, we can design the selec- tivity of detection primarily depending on proteins’ affinity strength and engineer surface characteristics to change the adsorption affinity according to the energy preference to fur- ther increase selectivity. 18 Because this process occurs at the vicinity of the sur- face, it is appropriate to couple the process with a surface- sensitive analytical tool such as Surface Plasmon Resonance (SPR). SPR offers detection limits up to a few ppt (pg/ ml). 19,20 Through SPR, the process of competitive protein adsorption may be monitored in real-time, 21 and transduced into an SPR angle shift, as shown in Figs. 1(a) and 1(b). This unique technique bypasses the time-consuming, labor-inten- sive labeling processes, such as radioisotope and fluores- cence labeling. More importantly, the method avoids the modification of the biomarker’s characteristics and behaviors by labeling that often occurs in traditional biosensors. 22,23 This competitive adsorption biosensing technique led the detection of fibrinogen at a concentration of 0.5–2.5 mg/ ml in undiluted human serum. 18 Despite the success, it is dif- ficult to adopt this method to detect other protein biomarkers as the concentrations of many target proteins of interest are extremely low, ng/ml even down to pg/ml. In this work, we aim to detect thyroglobulin (Tg, 660 kDa), a sensitive indica- tor of persistent or recurrent differentiated thyroid cancer (DTC) of follicular cell origin after total thyroidectomy, 24,25 down to 2 ng/ml, in undiluted human serum. Tg is produced by and used entirely within the thyroid gland. After total thyroidectomy, its normal concentration in serum is extremely low, less than 3 ng/ml when receiving thyroid hormone. 24 The current standards to measure Tg in serum are radioimmunoassay (RIA) and enzyme-linked immune sorbent assay (ELISA). 24 Both are technically matured and commercialized. However, RIA involves com- plicated and time-consuming processes, including specific binding of antibody, labeling of gamma-radioactive isotopes, a) Author to whom correspondence should be addressed. Electronic mail: [email protected] 0003-6951/2014/105(14)/143703/5/$30.00 V C 2014 AIP Publishing LLC 105, 143703-1 APPLIED PHYSICS LETTERS 105, 143703 (2014) This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.219.25.29 On: Wed, 25 Feb 2015 17:45:00

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Page 1: Probing thyroglobulin in undiluted human serum based on ...jchae2/Research_files/Tg-HumanSerum_APL14.pdf · Probing thyroglobulin in undiluted human serum based on pattern recognition

Probing thyroglobulin in undiluted human serum based on patternrecognition and competitive adsorption of proteins

Ran Wang,1,a) Shuai Huang,2 Jing Li,3 and Junseok Chae1

1School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe,Arizona 85287, USA2Department of Industrial and Systems Engineering, University of Washington, Seattle, Washington 98195,USA3School of Computing, Informatics, and Decision Systems Engineering, Arizona State University,Tempe, Arizona 85281, USA

(Received 20 September 2013; accepted 28 September 2014; published online 10 October 2014)

Thyroglobulin (Tg) is a sensitive indicator of persistent or recurrent differentiated thyroid cancer of

follicular cell origin. Detection of Tg in human serum is challenging as bio-receptors, such as anti-

Tg, used in immunoassay have relatively weak binding affinity. We engineer sensing surfaces using

the competitive adsorption of proteins, termed the Vroman Effect. Coupled with Surface Plasmon

Resonance, the “cross-responsive” interactions of Tg on the engineered surfaces produce uniquely

distinguishable multiple signature patterns, which are discriminated using Linear Discriminant

Analysis. Tg-spiked samples, down to 2 ng/ml Tg in undiluted human serum, are sensitively and

selectively discriminated from the control (undiluted human serum). VC 2014 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4897630]

Biosensors aiming at detection of target analytes, such

as proteins, microbes, and virus, are widely needed for vari-

ous applications including detection of chemical and biologi-

cal warfare (CBW) agents, environmental monitoring, and

drug screening.1 Proteins are often targeted for detection as

their relative and absolute levels of concentrations may be

correlated to specific disease states and as such be used to

assess the progress of disease and monitor the effects of

treatment.2–6 Many biosensors aiming at probing protein bio-

markers impose challenges of insufficient sensitivity and se-

lectivity in human serum, in which there are more than

20 000 different proteins with concentrations ranging more

than 10 orders of magnitude.6–9

In traditional biosensors, the selectivity is provided by

bio-receptors possessing highly specific binding affinity to

capture target analytes. Many bio-receptors, such as antibod-

ies, peptides, and aptamers, exist, yet their use in biosensors

is often limited by their relatively weak binding affinity with

analyte, non-specific adsorption, need for optimization con-

ditions, low reproducibility, and difficulties integrating onto

the surface of transducers.10–12

In order to circumvent the use of bio-receptors, we

instead utilize the competitive adsorption of proteins, termed

the Vroman effect. The Vroman effect was reported by

Vroman and Adams in 1969,13 and its various aspects have

been largely studied since then.14–16 The competitive adsorp-

tion targeted here occurs among different proteins competing

to adsorb to a surface, when more than one type of proteins

are present. When lower-affinity proteins are adsorbed on

the surface first, they can be displaced by higher-affinity pro-

teins arriving at a later point in time.17 Moreover, only low-

affinity proteins can be displaced by high-affinity proteins,

typically possessing higher molecular weight, yet the reverse

sequence does not occur. Therefore, we can design the selec-

tivity of detection primarily depending on proteins’ affinity

strength and engineer surface characteristics to change the

adsorption affinity according to the energy preference to fur-

ther increase selectivity.18

Because this process occurs at the vicinity of the sur-

face, it is appropriate to couple the process with a surface-

sensitive analytical tool such as Surface Plasmon Resonance

(SPR). SPR offers detection limits up to a few ppt (pg/

ml).19,20 Through SPR, the process of competitive protein

adsorption may be monitored in real-time,21 and transduced

into an SPR angle shift, as shown in Figs. 1(a) and 1(b). This

unique technique bypasses the time-consuming, labor-inten-

sive labeling processes, such as radioisotope and fluores-

cence labeling. More importantly, the method avoids the

modification of the biomarker’s characteristics and behaviors

by labeling that often occurs in traditional biosensors.22,23

This competitive adsorption biosensing technique led

the detection of fibrinogen at a concentration of 0.5–2.5 mg/

ml in undiluted human serum.18 Despite the success, it is dif-

ficult to adopt this method to detect other protein biomarkers

as the concentrations of many target proteins of interest are

extremely low, ng/ml even down to pg/ml. In this work, we

aim to detect thyroglobulin (Tg, 660 kDa), a sensitive indica-

tor of persistent or recurrent differentiated thyroid cancer

(DTC) of follicular cell origin after total thyroidectomy,24,25

down to 2 ng/ml, in undiluted human serum.

Tg is produced by and used entirely within the thyroid

gland. After total thyroidectomy, its normal concentration in

serum is extremely low, less than 3 ng/ml when receiving

thyroid hormone.24 The current standards to measure Tg in

serum are radioimmunoassay (RIA) and enzyme-linked

immune sorbent assay (ELISA).24 Both are technically

matured and commercialized. However, RIA involves com-

plicated and time-consuming processes, including specific

binding of antibody, labeling of gamma-radioactive isotopes,

a)Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0003-6951/2014/105(14)/143703/5/$30.00 VC 2014 AIP Publishing LLC105, 143703-1

APPLIED PHYSICS LETTERS 105, 143703 (2014)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.219.25.29 On: Wed, 25 Feb 2015 17:45:00

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and separation of analytical labeled components from the

mixture via precipitation and centrifugation. ELISA utilizes

colorimetric signals to measure the antigen-antibody reaction

instead of a radioactive method, which is more practical to

supplant RIA.26 These two techniques both suffer from non-

specific interference in the process of specific binding

between antigen and antibody.26,27

The non-specific interference is a challenge to the

Vroman effect based detection scheme as well. Only relying

on the specific adsorption behavior is not sufficient to dis-

criminate such minute concentrations of a target analyte (i.e.,

Tg in the range of <3 ng/ml) in human serum. In order to

address the challenge, we combined the Vroman effect with

a pattern recognition technique, a strategy based on the

“chemical nose-tongue,”28–30 discriminating specific finger-

prints generated by a large array of biosensors. In the pattern

recognition technique, an array of individual biosensor ele-

ments are used to provide sensing based on “differential”

receptors. “Cross-responsive” interactions between biosen-

sors in the array and the target proteins generate a unique

composite pattern, which allows the recognition of the target

proteins.31–34

Selection of the sensing surfaces to generate the pattern

is critical as it affects the sensitivity and selectivity of a pat-

tern recognition technique. Ten different sensing surfaces are

designed to deliver large differences in adsorption affinity

quantified by dissociation constant (KD) and the change in

Gibbs energy (DG�). Among many statistical methods,

Linear Discriminant Analysis (LDA), a robust pattern recog-

nition technique, is adopted for this work.35 Two kinds of

results are produced to estimate the classification accuracy.

The first is the original classification result that indicates

how well the functions discriminate the given samples. The

second is the cross-validation on the basis of the leave-one-

out option. This result can be used to estimate how well the

functions should predict a new sample.

FIG. 1. Illustration of the competitive

adsorption of proteins (Vroman effect)

and the schematics of SPR profile. (a)

Low-affinity proteins pre-adsorbed on

a surface are displaced by high-affinity

proteins arriving later, resulting in a

large SPR angle shift, Dh. (b) High-

affinity proteins pre-adsorbed on a sur-

face are not displaced by subsequent

low-affinity proteins. (c) The SPR

angle profile describing the competi-

tive adsorption of proteins on two sur-

face features (gold and COOH-SAM

modified), and the distinctively differ-

ent SPR angle shift patterns.

143703-2 Wang et al. Appl. Phys. Lett. 105, 143703 (2014)

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The bare gold or COOH-SAM (self-assembled mono-

layer) modified sensing surface is mounted above the SPR,

which is then coupled with the flow cell. After thorough cal-

ibration, each one of the five known-affinity protein (IgM,

IgG, Transferrin, Albumin, and Lysozyme) samples is

injected to be pre-adsorbed on a bare gold and COOH-SAM

modified surfaces. These five different proteins and two dif-

ferent surfaces provide ten surface features (shown in Table

S1) for Tg detection, establishing the array that generates a

pattern.36 When pre-adsorption is completed, Phosphate

Buffered Saline (PBS) rinses the surface to sweep excess

weakly bound proteins to establish a stable baseline. Tg-

spiked (100, 10, and 2 ng/ml) serum samples (shown in

Table S2) flow across the pre-adsorbed surfaces.36 The SPR

angle shift increases simultaneously as some pre-adsorbed

proteins are replaced by Tg via the competitive adsorption

of proteins. After rinsing and sweeping with PBS, the SPR

angle shift reaches steady state. Subtracting the baseline

from this angle shift, a final angle shift caused by Tg-spiked

samples is obtained (Fig. 1(c)). Every sample is repeated 6

times on every surface feature and ten average values of

SPR angle shifts from ten surface features are obtained to

form a distinguishing pattern for each sample. Different pat-

terns are compared and analyzed to discriminate the

Tg-spiked samples as a function of Tg concentrations in

undiluted serum.

Five different proteins, IgG (150 kDa), Transferrin

(80 kDa), Albumin (67 kDa), Lysozyme (14.7 kDa), and IgM

(900 kDa), are utilized to be pre-adsorbed on the surfaces of

gold chips. Lysozyme, Transferrin, Albumin, and IgG pow-

ders are prepared in PBS with concentrations of 1 mg/ml

each. Tg powders are dissolved in human serum at three dif-

ferent concentrations: 100, 10, and 2 ng/ml. The concentra-

tions gradually decrease to attempt the lowest limitation of

this biosensor. Glass slides (BK7, n¼ 1.517, 150 lm thick, 18

� 18 mm) are first immersed in ethanol and cleaned in an ul-

trasonic cleaner for 5 min. Subsequently, the slides are rinsed

sequentially with ethanol and deionized (DI) water, and dried

by a N2 stream. Cr/Au (2 nm/47 nm) is sputtered on the glass

chips. The slides are cleaned in a plasma cleaner at 10.15 W

for 1 min.20 To form COOH-terminated chips, the gold chips

fabricated above are immersed in an ethanol of alkane-thiols

(1 mM) for 24 h. Before use, they are rinsed with ethanol and

dried by a N2 stream. Compared with hydrophobic bare gold

surfaces, COOH-SAM modified chips are hydrophilic, which

leads to different interaction with proteins.37,38

With k classes, LDA produces k-1 discriminant func-

tions that produce the greatest discriminations between these

k classes. If there are more than three functions produced,

three of them, which contain as many of the distinguishing

signals of the original data set as possible and are uncorre-

lated to each other, are picked up to build a plot in three

dimensions. Particularly, in this work, a kind of sample rep-

resents a class. The data set contains SPR angle shift patterns

representing different samples, generated from the ten sur-

face features. In the plot, every data point, or training case,

represents a replication generated from the ten surface fea-

tures. The data points (six points produced by six replica-

tions) representing the same sample are separated from

others, if they can be successfully recognized.36

Proteins are differently adsorbed on the surfaces based

upon their thermodynamic energy preferences, and naturally

behave to minimize the overall system energy.17 Their reac-

tions can be interpreted as the natural outcome to achieve the

equilibrium point. Therefore, the change in Gibbs energy

caused by protein adsorption on a surface reflects the chemi-

cal potential and reaction process in the system.39,40

The change in Gibbs energy for the reversible part of

the adsorption process can be expressed as

DG ¼ DGo þ RTð½AB�=ð½A�½B�ÞÞ: (1)

At equilibrium

DGo ¼ �RTlnð½AB�=ð½A�½B�ÞÞ¼ �RTlnðDh=ðCðDhmax � DhÞÞÞ ¼ RTlnðKDÞ; (2)

where DG and DG� represent the changes in adsorption free

energy and in standard state adsorption free energy, respec-

tively; R is the ideal gas constant (1.985 cal/K mol); and T is

the absolute temperature (298 K). [A] is the molar concentra-

tion of the protein in solution; [B] and [AB] are the mole

fraction of surface sites occupied by a surface and adsorbed

protein, respectively. Dh is the SPR angle shift; Dhmax is the

SPR angle shift at the saturation; C is the protein concentra-

tion; KD is the dissociation constant.17,40

Through Eq. (2), a Langmuir-like feature (shown in Fig.

S1) can be described by36,40

Dh ¼ DhmaxC=ðKD þ CÞ: (3)

Noticeably, as SPR signal changes are unlikely at truly equi-

librium states, the extracted dissociation constants (KD) are

apparent and useful only for the purpose of comparing

results obtained under similar experimental conditions.41

Table I lists maximum SPR angle shift (at saturation), Dhmax,

equilibrium dissociation constant, KD, and Gibbs energy

change, DG�, measured on ten different surface features.36

The normal concentration of Tg in human serum is

3 ng/ml for a patient after treatment for DTC. In order to

characterize the sensitivity of biosensor for diagnosis, three

different Tg-spiked samples, 100, 10, and 2 ng/ml, are

attempted, and undiluted human serum is used as the control.

The ten surface features produce 6� 10¼ 60 SPR angle

shifts that together form a group representing a single sample.

As such, the four samples (100, 10, 2 ng/ml Tg-spiked sam-

ples and the control) are represented by four groups of SPR

angle shifts, as shown in Table S3.36 In Fig. 2(a), ten average

values with error bars (standard deviation) taken from the ten

surface features and measured over six repetitions are shown

to form a pattern. Depending on the specific response on one

kind of surface feature, the difference between the sample and

the control are usually too minute to be discriminated. These

SPR angle shift patterns are further analyzed by LDA to be

discriminated and formally classified into different groups.

After LDA, three discriminant functions are generated

(90.0%, 9.6%, and 0.4%) to represent the linear combina-

tions of the ten-dimensional data set including four sam-

ples� ten surface features� six replications. Based on the

three functions, a three dimensional plot is built in Fig. 2(b),

in which 24 training cases (4 samples� 6 replications) are

143703-3 Wang et al. Appl. Phys. Lett. 105, 143703 (2014)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.219.25.29 On: Wed, 25 Feb 2015 17:45:00

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classified into four groups representing four samples, respec-

tively. In Table II, the original classification of 91.7% indi-

cates how well the functions discriminate these four given

samples, while the cross-validations of 66.7% is used to esti-

mate how well the functions derived from all 24 cases should

predict a new sample.

We further analyze the separate discriminating accuracies

for the three Tg samples, as shown in Tables S4–S6.36 100,

10, and 2 ng/ml Tg-spiked samples that are discriminated

from the control show the original classification of 100%,

100%, and 100%, and the cross-validation of 83.3%, 53.3%,

and 41.7%, respectively. In other words, for an unknown sam-

ple, a higher concentration evidently provides a higher possi-

bility to discriminate Tg samples from the control. In Fig.

2(b), 100 and 10 ng/ml Tg-spiked serum samples are shown

farther away from the control, but the 2 ng/ml Tg-spiked se-

rum sample has a finite overlap with the control, which high-

lights the difficulty of discrimination. The reason is apparent

in the case where more differences between higher concentra-

tion Tg samples and the control result in more distinctively

different patterns that are easier for LDA to discriminate. All

the points, mapped on an x-y plane, are composed of two

most significant functions. This demonstrates that these four

samples can be discriminated on the two functions. Only the

discrimination between the 2 ng/ml Tg-spiked sample and the

control needs the assistance of the third function.

A set of experiments for selectivity of SPR biosensor

are designed and executed. IgM is chosen to demonstrate the

selectivity characterization as the affinity strength of IgM

TABLE I. Ten surfaces described by protein characteristics, equilibrium dis-

sociation constants (KD), and the changes in Gibbs energy (DGo).

Proteins (MWa, kDa) Surface

Dhmax

(mdeg)

KD

(10�5 M)

DGo

(kcal/mol)

IgM (970) bare gold 501 1.0 6 0.1 �6.8 6 0.04

COOH-SAM 222 6.0 6 0.3 �5.7 6 0.03

IgG (150) bare gold 517 3.1 6 0.1 �6.1 6 0.02

COOH-SAM 295 17 6 1.6 �5.1 6 0.06

Transferrin (80) bare gold 504 4.5 6 0.2 �5.9 6 0.02

COOH-SAM 295 10.3 6 0.1 �5.4 6 0.01

Albumin (76) bare gold 117 5.0 6 0.7 �5.9 6 0.09

COOH-SAM 80 12.9 6 0.6 �5.3 6 0.03

Lysozyme (14.7) bare gold 87 8.8 6 0.5 �5.5 6 0.04

COOH-SAM 80 17.4 6 0.4 �5.1 6 0.01

aMW is the molecular weight.

FIG. 2. Sensitivity characterization (a) SPR angle shifts from ten surface

features (6 replications for each sample) (b) Four groups of six data points

on three most significant discriminant functions obtained from LDA.

TABLE II. Classification resultsa,b for sensitivity characterization.

Predicted group membership

Total

Tg (ng/ml)

Categories Control (serum) 100 10 2

Original Control 5 0 0 1 6

100 0 6 0 0 6

10 0 0 6 0 6

2 1 0 0 5 6

Cross-validatedc Control 2 0 0 4 6

100 0 6 0 0 6

10 0 0 6 0 6

2 4 0 0 2 6

a91.7% of original grouped cases correctly classified.b66.7% of cross-validated grouped cases correctly classified.cCross validation is done only for those cases in the analysis. In cross valida-

tion, each case is classified by the functions derived from all cases other

than that case.

FIG. 3. Selectivity characterization (a) SPR angle shifts from eight surface

features (6 replications for each sample). (b) Five groups of six data points

on three most significant discriminant functions obtained from LDA.

143703-4 Wang et al. Appl. Phys. Lett. 105, 143703 (2014)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.219.25.29 On: Wed, 25 Feb 2015 17:45:00

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(KD, 1.0� 10�5 M, and DGo, �6.8 kcal/mol) is similar to

that of Tg (KD, 0.7� 10�5 M, and DGo, �7.0 kcal/mol).

Eight surface features produce the patterns for the 100 ng/ml

IgM-spiked serum sample, as shown in Fig. 3(a). LDA is

then performed to analyze these samples. Four functions are

generated (84.6%, 11.9%, 3.1%, and 0.4%) and the three

most significant functions are used to build the three dimen-

sional plot in Fig. 3(b). The plot shows that the IgM-spiked

serum is clearly separated from other samples, except for a

little overlap with the 100 ng/ml Tg-spiked serum. The origi-

nal classification result and the cross-validation result are

90.0% and 63.3%, respectively, as listed in Table III.

In this work, a SPR biosensor using the competitive

adsorption of proteins and pattern recognition is demon-

strated to detect Tg in undiluted human serum. Based on

cross-responses, the biosensor bypasses the need of specific

capture of the target analyte, Tg, and enhances the selectivity

to discriminate the tiny discrepancies among multiple sam-

ples. Through the analysis of LDA, explicit plots and quanti-

tative indices are generated from the composite patterns. At

last, we detect Tg with 100, 10, and 2 ng/ml in undiluted

human serum, and estimate the possibility to predict the clas-

sification of a Tg sample with an unknown concentration.

This work was partly funded by National Science

Foundation, ECCS-0846961.

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TABLE III. Classification resultsa,b for selectivity characterization.

Predicted group membership

Tg (ng/ml)

Categories

Control

(serum) 100 10 2

IgM

(ng/ml) 100 Total

Original Control 4 0 0 2 0 6

100 0 6 0 0 0 6

10 0 0 6 0 0 6

2 1 0 0 5 0 6

IgM 0 0 0 0 6 6

Cross-validatedc Control 2 0 0 4 0 6

100 0 5 0 0 1 6

10 0 0 6 0 0 6

2 4 0 0 2 0 6

IgM 0 2 0 0 4 6

a90.0% of original grouped cases correctly classified.b63.3% of cross-validated grouped cases correctly classified.cCross validation is done only for those cases in the analysis. In cross valida-

tion, each case is classified by the functions derived from all cases other

than that case.

143703-5 Wang et al. Appl. Phys. Lett. 105, 143703 (2014)

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