Low Noise Detection of Biomolecular Interactionswith Signal-Locking Surface Plasmon Resonance

Layne D. Williams,† Tridib Ghosh,‡ and Carlos H. Mastrangelo*,†,‡

Departments of Electrical and Computer Engineering and Bioengineering, University of Utah, Salt Lake City, Utah 84112

Surface plasmon resonance (SPR) is a popular techniquefor label-free detection of biomolecular interactions at asurface. SPR yields quantitative kinetic association anddissociation constants of surface interactions such as thebinding of two molecular species, one present in the liquidphase and the other immobilized at the surface. Currentstate-of-the-art SPR systems extract kinetic constants frommeasurements of the step response of the interactionversus time. The step response measurement is subjectto the influence of noise and drift disturbances that limitits minimum-detectable mass changes. This paper pre-sents a new SPR technique that measures the biomolecu-lar interaction not in time but over a very narrow fre-quency range under periodic excitation. The measuredresponse is, thus, locked to a very specific narrow bandsignal. This narrow band spectral sensing scheme has avery high degree of rejection to uncorrelated spurioussignals. The signal-locked SPR technique was imple-mented using a chemical modulator chip connected to aset of functionalized Au sensing sites downstream. Bind-ing experiments for a model system of carbonic anhy-drase-II (CA-II) analyte and immobilized 4-(2-aminoethyl)-benzenesulfonamide (ABS) ligand display a 100-fold (20dB) improvement in the measured signal-to-noise ratio(SNR) when using the new technique compared to theSNR achieved using the conventional step responsemethod.

The measurement of interactions between biological moleculesis of fundamental importance in the life sciences. The mostcommon measured interaction is the binding of two chemicalentities. For example, one molecule (a ligand) can be immobilizedon a surface while exposed to a dissolved analyte binding partner.Detection of binding is most commonly achieved by labeling eitherentity with radioactive or fluorescent markers. Label-free opticaldetection methods have become increasingly popular in the lasttwo decades because they avoid disturbances from conjugatedmarkers or handling of radioactive materials. In particular, label-free optical techniques such as surface plasmon resonance (SPR)permit the study of biological interactions in real time, also yieldingquantitative kinetic parameters.

The most common type of SPR measurement is a singleassociation-dissociation step depicted in the sensorgram of Figure1 with corresponding association and dissociation constants ka andkd. During the cycle, the ligand-analyte complex obeys thedifferential equation

dCdt

) ka · A · (B0 - C) - kd · C (1)

where B0 is the surface concentration of the undisturbedimmobilized ligand, A is the analyte concentration, and C isthe surface concentration of the ligand-analyte complex.1 Fora sudden step change in the analyte concentration of widthTp, solutions of eq 1 obey the piecewise exponential

* To whom correspondence should be addressed. Address: University of Utah,Department of Electrical and Computer Engineering, 50 S. Central Campus Drive,Rm. 3280, Salt Lake City, UT 84112. E-mail: carlos.mastrangelo@utah.edu. Phone:801-587-7585. Fax: 801-581-5281.

† Department of Electrical and Computer Engineering.‡ Department of Bioengineering.

(1) Jonsson, U.; Fagerstam, L.; Ivarsson, B.; Johnsson, B.; Karlsson, R.; Lundh,K.; Lofås, S.; Persson, B.; Roos, H.; Ronnberg, I.; Sjolander, S.; Stenber, E.;Ståhlberg, R.; Urbaniczky, C.; Ostlin, H.; Malmqvist, M. Biotechniques1991, 11, 620–627.

Figure 1. (a) Diagram showing the association/dissociation reactionon the sensor surface. (b) Sensorgram response showing theassociation and dissociation phases.

Anal. Chem. 2010, 82, 6025–6031

10.1021/ac100504b 2010 American Chemical Society 6025Analytical Chemistry, Vol. 82, No. 14, July 15, 2010Published on Web 06/22/2010

C(t) ) ( ka · A · B0

ka · A + kd) · (1 - e-(ka·A+kd)·t) (2)

for 0 < t e Tp, and

C(t) ) ( ka · A · B0

ka · A + kd) · (1 - e-(ka·A+kd)·TP) · e-kd·(t-TP) (3)

for t > Tp. The SPR sensorgram specified by the imager intensityI(t) is proportional to the bound analyte-ligand complex C(t)by the factor GSPR.

I(t) ) GSPR · C(t) ) GSPR · ( ka · A · B0

ka · A + kd) ·

(1 - e-(ka·A+kd)·TP) · e-kd·(t-TP) (4)

Equation 4 represents the idealized SPR sensorgram response.Typically, SPR sensors are also sensitive to the bulk characteristicsof the solvent which vary slightly in the association and dissocia-tion steps, thus producing a bulk output s(t). In addition, thesensorgram signal is subject to drifts and noise originating froma variety of environmental sources (temperature, etc.) and theimaging equipment. These effects can be lumped together asdisturbance d(t) added to eq 4.

I(t) ≈ GSPR · ( ka · A · B0

ka · A + kd) · (1 - e-(ka·A+kd)·TP) ·

e-kd·(t-TP) + s(t) + d(t) (5)

The solvent bulk contribution s(t) can largely be subtracted outof eq 5 using independent measurements of sref(t) from anonreacting reference surface,2 but the disturbance d(t) gener-ally cannot be completely eliminated by referencing, as GSPR

is disturbance dependent.In a typical SPR experiment, the sensor signal is recorded as

a function of time. After the bulk solvent contribution is subtractedout, the remaining signal is fitted to the idealized exponentials ofeq 2 to determine the kinetic constants. The geometrical inter-pretation of the step response fitting procedure using conventionalmethods such as the Levenberg-Marquardt technique requiresorthogonality3 between the Jacobian of the exponential and thedisturbance d(t). This poses a problem because the exponentialpulse is not orthogonal to common nonoscillatory disturbancessuch as slow drifts. Therefore, in the presence of substantial noiseand systematic drifts, the step response fitting scheme is onlyable to accurately detect relatively coarse interactions betweenanalyte and ligand. In drug discovery applications, this is a majorlimitation, as often drug targets are large proteins with masses of104-105 Da or larger, and the interaction of interest is oftentriggered by the binding of a very small analyte (300 Da orless). In order to increase the sensitivity of these systems,commercial state of the art instruments such as the BiacoreT100 use many corrective schemes including sophisticated

referencing,2 data scrubber software,4,5 temperature control,6

and most successfully high-density binding sites on three-dimensional dextran surfaces7 (as the SPR sensor detects changesroughly within 100 nm from the metal surface). In spite of thecommercial availability of Biacore systems for many years, thesesystems have not been able to sense interactions of small analytes,presently 100 Da being the minimum detectable mass. The keyto further improvements in detection limits of SPR based systemslies in the development of more robust sensing techniques thatreject experimental noise and disturbances more efficiently.

Frequency Domain Signal-Locking Scheme. The stepresponse detection method discussed above is not optimal becauseit does not attempt to reject the influence of the disturbance on thefit. If the ordinary differential equation for the biochemical interactionis linear in A (analyte concentration), it is possible to substantiallyimprove the sensitivity of the measurement by appropriate selectionof the input test signal. In particular, an improved detection schemeis implemented if the analyte excitation and the correspondinginteraction response are highly correlated. If the analyte input signaland the corresponding sensorgram response have sharp autocorre-lations, the input signal and the response are nearly orthogonal toall other signals except themselves, hence, rejecting greatly theinfluence of uncorrelated noise and disturbances. An example of suchan approach is the signal-locking Fourier-transform SPR (SLFT-SPR)detection scheme shown in the diagram of Figure 2. In this method,the biochemical system is driven by a periodic input excitation ofanalyte or buffer of constant frequency fφ specified by digital clocksφ and φj. The corresponding periodic association and dissociationcycles produce a highly correlated sensorgram output of the samefrequency and at steady state of constant amplitude. This signalcan be easily “locked” with respect to the driving clock. Theperiodic sensorgram, thus, can be easily detected even in thepresence of high levels of additive uncorrelated disturbances andnoise. The virtues of the scheme are visibly evident when thepower spectrum of the SPR response and the disturbance areplotted as shown in the example of Figure 2. While noise anddisturbance have broad spectra, the power of the sensorgramdissociation and association response cycles is concentrated at asingle modulation frequency, thus showing as a spike in the spectrumthat can be easily discriminated from the noise using a narrow bandfilter. Most of the noise and disturbance power falls outside thisnarrow band; hence, it is greatly rejected. The improvement in thenoise rejection is quantitatively analyzed in the discussion section.

Small-Signal Biochemical Transfer Function. In order toutilize these signals effectively, we must first establish a relationbetween the excitation response and the kinetic constants. Wecan first set the clock frequency fφ and record the sensorgramresponse. By repeating this procedure at different discretemodulation frequencies, one may obtain a relation between theexcitation frequency and the sensorgram response. Since both

(2) Myszka, D. J. Mol. Recognit. 1999, 12, 279–284.(3) Moon, T.; Stirling, W. In Mathematical Methods and Algorithms for Signal

Processing; Prentice-Hall: Upper Saddle River, NJ, 2000.

(4) Khalifa, M.; Choulier, L.; Lortat-Jacob, H.; Altschuh, D.; Vernet, T. Anal.Biochem. 2001, 293, 194–203.

(5) Navratilova, I.; Papilia, G.; Rich, R.; Bedinger, D.; Brophy, S.; Condon, B.;Deng, T.; Emerick, A.; Guan, H.-W.; Hayden, T.; Heutmekers, T.; Hoorel-beke, B.; McCroskey, M,; Murphy, M.; Nakagawa, T.; Parmeggiani, F.;Qin, X.; Reve, S.; Tomasevic, N.; Tsang, T.; Waddell, M.; Zhang, F.; Leavitt,S.; Myszka, D. Anal. Biochem. 2001, 364, 67–77.

(6) Shen, B.-J.; Hage, T.; Sebald, W. Eur. J. Biochem. 1996, 240, 252–261.(7) Lofås, S.; Johnsson, B. J. Chem. Soc., Chem. Commun. 1990, 21, 1526–

1528.

6026 Analytical Chemistry, Vol. 82, No. 14, July 15, 2010

excitation and response are periodic, they can be expanded asFourier series. The relation between the fundamental termsof response and input series is the Fourier transfer function(TF) H(jω) of the biochemical system

H(jω) ) Y(jω)X(jω)

(6)

where X(jω) and Y(jω) are complex phasors8 of the input analyteexcitation and filtered sensorgram output, respectively, and ω )2πfφ is the excitation angular frequency. For small periodic inputperturbations of the type

A(t) ) A0 + ∆A · (t) ) A0 + ∑n)1

∞

∆Ansin(n · ω · t) (7)

with |∆A(t)| e 0.1 ·A0, the sensorgram response is proportionalto the analyte-ligand complex which also has the form

C(t) ) C0 + ∆C · (t) ) C0 + ∑n)1

∞

cnsin(n · ω · t + θn)

(8)

where C0 is the equilibrium analyte-ligand concentration. Ifthe biochemical interaction is determined by eq 1, the transferfunction is directly related to the kinetic constants ka and kd, andit is obtained by direct substitution of eqs 7 and 8 into eq 1,which reduces to

d∆C(t)dt

) ka · (B0 - ∆C(t)) · ∆A(t) - (ka · A0 + kd) · ∆C(t)

≈ ka · B0 · ∆A(t) - (ka · A0 + kd) · ∆C(t)

(9)

Equation 9 is valid for correspondingly small changes in theanalyte-ligand complex such that B0 . ∆C(t). The reducedsimplified eq 9 is linear in ∆A(t) and its corresponding Fourierseries components. The small-signal transfer function H(jω) iseasily obtained from eq 9 by substitution of the time derivativewith jω. The small-signal sensorgram transfer function at thefundamental component has the single pole behavior

H(jω) ) GSPR( c1

∆A1)ejθ1

) GSPR

ka · B0

(ka · A0 + kd)· 1

(1 + jω/ωp)

(10)

with characteristic pole ωp

ωp ) 2πfp ) ka · A0 + kd (11)

Therefore, we can directly measure the kinetic constants ka andkd by direct measurements of the transfer function and byfinding each TF pole for different A0 analyte concentrations.This is the basis for the SLFT-SPR methodology.

Since SLFT-SPR relies on the repetition of rapid associationand dissociation cycles, the depletion of analyte in solution is muchless severe than that for the conventional single-pulse technique;therefore, experimental flow conditions that are not subject totransport issues in the conventional single-pulse method are alsosufficient for this technique.

Sensorgram Under Large Signal Excitation. In the SLFT-SPR measurement, it is advantageous to increase the excursionof the input analyte beyond 0.10A0 because the magnitude ofthe corresponding sensorgram increases proportionally. Forlarge analyte excursions, the analysis is more complex becauseeq 1 differs for the association and dissociation cycles andinput-output linearity of the Fourier components does not hold.In the large signal analysis, we assume the analyte excitation is aperiodic square waveform of period T, amplitude A0, and clockfrequency fφ ) 1/T. At low frequencies, the sensorgram is alsosquare, but as the frequency increases, it becomes triangular,thus changing the Fourier coefficients of the response. We canaccount for the impact of the change in shape by calculatingthe Fourier series components of the sensorgram waveform.At steady state, C(0) ) C(T); hence, the characteristic solutionsof eqs 2 and 3 can be set equal to each other

(8) Giancoli, D. In Physics for Scientists and Engineers; Prentice-Hall: UpperSaddle River, NJ, 1989 .

Figure 2. (a) Diagram of SLFT-SPR detection scheme. The sensorinput excitation is a periodic stream of analyte and buffer plugscontrolled by clocks φ and φj. This produces periodic association anddissociation steps modulated at frequency fφ. (b) The power spectrumof the sensorgram contains the narrowband response and broadbandnoise and disturbances. The modulated response can be discrimi-nated from the broadband noise using a signal locking sharpbandpass filter, thus greatly rejecting the influence of out-of-bandnoise and disturbances.

6027Analytical Chemistry, Vol. 82, No. 14, July 15, 2010

a - b ) (a - b · e-1) · e-2 (12)

with a ) ((ka ·A ·B0)/(R1)), R1 ) ka ·A + kd, R2 ) kd, 1 ) (R1 ·T)/(2), and 2 ) (R2 ·T)/(2). Solving eq 12 for b, the steady statesolution can be written as

C(t) ) a(1 - [ 1 - e-1

1 - e-(1+2)] · e-R1·t), 0 e t e T2

a(1 - [(1 - e-1) · e-1

1 - e-(1+2) ]) · e-R2·(t-T/2), T2e t e T

(13)

The first component of the complex Fourier series of eq 13 fortwo limiting conditions as Tf∞ (ωf0) and Tf0 (ωf∞) aredetermined (see Supporting Information).

The amplitude of the first sine component is

c1∞ ) 2a

π(14)

while the cosine amplitude is

c10 ) -

2R1R2aT

(R1 + R2)π2 (15)

With the amplitude from these two limiting cases, an approxima-tion for the magnitude of the normalized large signal transferfunction can be written as

|T(jω)| ) |H(jω)H(0) | ≈ |c1

0(jω)

c1∞ | )

2R1R2aT

(R1 + R2)π2 · π2a

)R1R2

(R1 + R2)π · f)

2R1R2

(R1 + R2)ω

(16)

At the pole frequency f ) fp, the magnitude of the normalizedtransfer function equals 1/(2)1/2; hence, the expression for thepole for large signal excitation is approximately

fp ≈√2 · R1R2

π(R1 + R2)(17)

This can be written finally in terms of ka and kd as

fp ≈√2 · (ka · A0 + kd) · kd

π(ka · A0 + 2kd)(18)

Equation 18 provides a relation between the observed pole andthe kinetic constants under the condition of large analyte squarewave excitation. Note that this expression differs significantly fromthe small signal pole expression of eq 11. In particular, eq 18includes the effects of saturation which develop for large A0

making the pole approach (2)1/2 · kd/π.SPR System Implementation. The SLFT-SPR technique

requires sweeping of the analyte modulation frequency and thegeneration of a corresponding stream of analyte plugs over the

SPR sensing surface. In general, one may generate such plugstream using a set of valves that periodically switch equal flowsof buffer and analyte solutions over the SPR sensing sites. Thismethodology works well for low frequency plugs, but in order tocreate high frequency plugs, it is necessary to use microfluidicmodulator chips that permit the transport of time-dependentchemical signals with relatively low dispersion.9 We implementedsuch a system as discussed below.

MATERIALS AND METHODSFive kDa carboxymethyl-PEG-thiol (CM-PEG) and 2 kDa

methoxy-PEG-thiol (M-PEG) were purchased from Laysan Bio.Sulfo-N-hydroxysuccinimide (S-NHS), N-ethyl-N′-(3-dimethylami-nopropyl)carbodiimide (EDC), and phosphate buffered saline(PBS) tablets were obtained from Thermo Scientific. Carbonicanhydrase II (CA-II), 4-(2-aminoethyl)benzenesulfonamide (ABS),and 10% sodium dodecyl sulfate (SDS) solution were from Sigma.Sylgard 184 from Dow Chemicals was used to make the PDMS.SF10 glass substrates in a 2 × 2 in. square were purchased fromSchott glass. Deionized 18 MΩ water (DI) for rinsing and allbuffers used were provided by an in-house plant associated withthe University of Utah Nanofab.

Surface Plasmon Resonance System. A GWC TechnologiesSPRImagerII system was used to collect the data. The systemwas modified by the manufacturer to be used in a horizontalconfiguration, with a custom built microfluidic mounting cell. Wefurther modified the instrument with a World Star Tech TEGCIRL-100G-808 808 nm laser source, a rotating diffuser from Suss-Microoptics, a Navitar Zoom 6000 lens system, and a HamamatsuC9100-01 EMCCD camera.

Microfluidics. The microfluidic chip is fabricated using aconventional PDMS process on glass substrates. A two-layerchannel system10 is used to create valves to enable switchingbetween buffer and analyte. The PDMS is molded over photo-lithographically defined patterns using SU-8 and AZ9260 photo-resists. The two layers are cleaned and exposed to oxygen plasmafor 12 s at a pressure of 400 mTorr in a March Plasmod systemand then aligned and bonded together using an in-house builtalignment system. The system contains two sets of channels, oneto act as a reference (control) and the other for detection of theanalyte of interest (sensor). The channels are 180 µm wide and23 µm tall, with the sensing spots starting at a distance of 2 mmdownstream from the valves.

Gold/Glass Substrate. The glass substrate is cleaned bypiranha etch (3:1, H2SO4/H2O2) for 20 min, rinsed for 5 min inDI water, and dried under N2. The substrates are placed in anoven at 80 °C for 10 min before being transferred to a TMVacuum sputter deposition system. A 3 nm adhesion layer ofTi/W is deposited, followed by 40 nm of gold. The metal layerson the substrate are patterned using photolithography to makean array of 140 × 180 µm SPR sensing sites. The metals areetched, and the samples are rinsed thoroughly with DI waterafter each etch step to prevent contamination. Finally, thephotoresist is removed, and the patterned substrates are storedin a vacuum desiccator until being used.

SPR Microfluidic Chip Assembly. Before assembly with thePDMS microfluidic channels, the patterned glass substrates are

(9) Xie, Y.; Wang, Y.; Chen, L.; Mastrangelo, C. Lab Chip 2008, 8, 779–785.(10) Chen, L.; Azizi, F.; Mastrangelo, C. Lab Chip 2007, 7, 850–855.

6028 Analytical Chemistry, Vol. 82, No. 14, July 15, 2010

further cleaned by flame annealing with a butane microtorch. Thisis followed by ultrasonication in methanol for 5 min. The methanolis refreshed, and the substrate is sonicated a total of three times.The dual layer PDMS channels are drilled to make through holesfor fluid access and then cleaned with acetone, IPA, and DI water.The PDMS is dried with an air gun and then baked for 10 min ona hot plate at 100 °C, followed by a cooling step for 10 min. Atthis point, both the glass substrate and PDMS channels are placedin the oxygen plasma cleaner for 12 s at the same settingsmentioned previously. Alignment is performed to coordinate thechannels with the patterned gold surface, and then, the assembledchip is baked, again for 10 min at 100 °C.

Gold Spot Functionalization. Modification of the gold spotsis performed in situ to enable the bonding of the PDMS and glasssubstrate. The assembled chip is connected to a syringe pumpand flushed with 0.01 M HCl for 5 min to remove any contami-nants or oxide, followed by a 15 min rinse with DI water. A mixtureof long and short chain polyethylene glycol (PEG) molecules isused to provide both a capture surface and one that is proteinresistant, following the protocol described by Uchida.11 The CM-PEG molecule is introduced to the flow channels for 20 min,followed by a 0.05 M NaOH rinse. Then, the M-PEG is passedthrough the channels and rinsed similarly. The smaller PEG isapplied a total of three times to backfill any gaps in the initialPEG layer and prevent protein adsorption on the gold surface.The surface is again treated with 0.01 M HCl and rinsed with DIwater to ensure the proper chemical functionality for the next step.

Chemical modification of the CM-PEG chains is performedusing S-NHS and EDC to create an amine reactive surface. S-NHSat 100 mM and EDC at 400 mM in water are mixed 1:1 and passedthrough both the reference and sensing channels for 30 min. Thesystem is rinsed with PBS for 2 min, and then, the capturemolecule is applied. ABS is passed over the sensing surface, whileonly the buffer is passed over the reference surface, illustratingthe need for the dual channel system. Finally, both surfaces areblocked with ethanolamine in carbonate buffer at pH 9 for 30 minand rinsed with PBS.

Experiments. The microfluidic chip is placed in the SPRmounting cell, with n ) 1.72 refractive index matching fluid tocouple the prism with the glass substrate. Microfluidic connectionsare made to the valves and flow channels, and then, the valvecontrol lines are filled with water, due to the gas permeability ofPDMS. The valves are actuated by a pressure system at 30 psicontrolled by a computer. Syringes containing analyte (CA-II),buffer (PBS), and regeneration solution (0.1% SDS in PBS) arepressurized as well with a constant source at 10 psi whichcorresponds to a flow velocity of 16 cm/s, sufficiently high (>6.7cm/s, calculated) to overcome transport limiting effects.12 CA-IIsamples were prepared as follows. We first measure the dry CA-II on an analytical balance with a resolution of 0.1 mg. The dryCA-II is then added to an appropriate volume of the PBS runningbuffer to make our analyte solution; i.e., if we want a 100 µg/mLanalyte solution (or 3.4 µM at 29 kDa MW for CA-II), we measure1.0 ± 0.1 mg and add that to 10 mL of buffer. We next measurethe actual concentration in solution using a spectrophotometer

(GENSYS5, Thermo Scientific) at 280 nm. Reported values of theextinction coefficient for bovine CA-II range from 55 300 to 57 000L/mol-cm.13,14 Three different (measured) concentrations of CA-II were used, 2.3, 5.3, and 11 µM. Experiments are performed foreach CA-II concentration by collecting the response from a singlestep input first and then continuously running multiple cycles ofa square wave input at different frequencies, swept from 2 to 256mHz. The sampling rate was 4 Hz for all experiments. Wasabicamera control software from Hamamatsu is used to analyze thecollected data by selecting multiple sensing and reference spotsin the image. The mean intensity value in each spot I(t) is recordedfor all of the frames in the experiment. Fourier transform analysisof the data is performed in MATLAB. After an experiment at agiven concentration is completed, the channels are flushed withregeneration solution to clean the sensor surface.

RESULTS AND DISCUSSIONKinetic constants were obtained using both a single step

method and the large-signal SLFT-SPR scheme. In all the datasets, the fixed imager intensity offset Ioffset is first recorded atthe beginning of the measurement and subtracted from all therecorded data. Each spot analyzed comprised approximately1550 pixels on the CCD camera. In our experiments, weobserved a large discrepancy that exists between the concen-tration prepared by weight and that measured in the spectro-photometer. This discrepancy can originate from severalphenomena including differences between weighted and activeprotein12 concentration as well as various error sources of thescale and spectrophotometer. We believe our largest sourceof error originates from the uncertainty in the analyteconcentration.

Single Step Response. For each concentration, a single stepexperiment was first performed by flowing buffer for 5 min, CA-II for 5 min, and then buffer again for 5 min. After removing Ioffset

from the data, the signal from a reference spot, Iref, wassubtracted from a sensor spot, Isensor, at the same distancedownstream from the fluid control valves. This is needed tocancel the solvent bulk contribution s(t) of the analyte solutionas compared to that of the buffer. The corrected responsesfrom the single step experiments are shown in Figure 3, alongwith the fits to the exponential solution

I(t) ) I0(1 - e-kobs·t) (19)

where kobs is the observed rate constant for the associationphase,

kobs ) ka · A0 + kd (20)

The observed rate values were then plotted against the respectiveconcentration values, and a linear fit was used to determine ka

and kd according to eq 20. These values were found to be 6.5 ×103 1/M · s and 2.5 × 10-2 1/s, respectively (R2 ) 0.974), inreasonable agreement with published results.12

(11) Uchida, K.; Otsuka, H.; Kaneko, M.; Kataoka, K.; Nagasaki, Y. Anal. Chem.2005, 77, 1075–1080.

(12) Lahiri, J.; Isaacs, L.; Brzybowski, B.; Carbeck, J.; Whitesides, G. Langmuir1999, 15, 7186–7198.

(13) Krishnamurthy, V. M.; Kaufman, G. K.; Urbach, A. R.; Gitlin, I.; Gudiksen,K. L.; Weibel, D. B.; Whitesides, G. M. Chem. Rev. 2008, 108 (3), 946–1051.

(14) Nyman, P. O.; Lindskog, S. Biochim. Biophys. Acta 1964, 85, 141.

6029Analytical Chemistry, Vol. 82, No. 14, July 15, 2010

SLFT-SPR Response. The continuous cycle intensity datawas collected for each concentration at a discrete set offrequencies selected to give an even power distribution acrossthe spectrum. The input frequencies and output waveforms areshown in Figure 4. The frequencies began at 2 mHz andincreased by doubling until 256 mHz was reached, keeping thetime each frequency was applied constant. This was performedafter the single step data was collected so that the system wasnear steady state when the cycles started to avoid a longtransition during the experiment.

Fourier transform analysis is used to determine the magnitudeof the sensorgram response intensity and normalized transferfunction |T(jω)| at the excitation frequencies from the magnitudeof the measured power spectrum. |T(jω)| is next plotted versuseach excitation frequency as show in the Bode plot of Figure 5.The pole frequency for each concentration was determined at the-3 dB point. The experimental tail of the Bode plot at highfrequencies differs from the single pole behavior. We attributethis flattening of the experimental response to imperfect but notnegligible reference cancellation of bulk signals which is inde-pendent of frequency.

The ka and kd are determined from the FT-SPR analysis byfitting the pole values to eq 18. They were found to be 9.4 × 103

1/M · s and 2.7 × 10-2 1/s, respectively (R2 ) 0.968). Thesevalues match reasonably well with those determined with thesingle step method. The values determined by the FT-SPRmethod do differ slightly from reported values of ka and kd forthe same model system, but the range of these values is verylarge among the different detection methods used.12 Weattribute the difference in the values we obtained as due tothe particular surface chemistry employed in this work.

Signal to Noise Ratio, Sensitivity Analysis, and Limita-tions. The signal-to-noise ratio (SNR) in decibels (dB) for thestep response measurement was computed from the ratio of theaverage power of the exponential fitted signal to the average powerof the fit residual over the measurement period as shown below

Figure 3. (a) Plot of single step sensorgram response data for eachconcentration and the associated fit. (b) The resulting value for kobs

is plotted against the respective concentration, and a linear fit is usedto find ka and kd.

Figure 4. (a) Example input clock frequency sweep used for theSLFT-SPR measurement. (b) Resultant sensorgram waveform fromthe SPR system.

Figure 5. (a) Magnitude of the normalized transfer functionT(jω)(Bode plot) vs frequency. The poor fit at the higher tail frequen-cies originates from imperfect cancellation of the bulk response. (b)The resulting pole frequencies vs the respective CA-II inputconcentration.

6030 Analytical Chemistry, Vol. 82, No. 14, July 15, 2010

SNRstep ) 10 · log( ∫0

τIfit

2dt

∫0τ(Imeas - Ifit)

2dt) (21)

The measured SNR for the step response method was 26 dBmeaning that the average power of the fitted exponential was 400times larger than that of the noise and disturbances.

The SNR for the SLFT measurement is calculated differentlyfrom that of the step response. First, we recorded the noise anddisturbance intensity signal of the SPR system under no inputexcitation for 30 min at a sampling frequency of 4 Hz. Aftersubtraction of the initial offset, the intensity was normalized tothe full scale of the imaging camera. We next computed the powerspectral density of the normalized intensity signal measured indB-full scale/Hz (or dB-fs/Hz). Because this is a random signal,the power spectrum was averaged over 10 equal duration 180 srecording cycles. This procedure produces a reasonably well-defined estimate of the disturbance and noise spectral density.We can now readily compare the relative power of the systemnoise and disturbances to the power spectrum of the SLFT-SPRsignal (also in dB-fs/Hz) as shown in Figure 6a. Note that thepower spectrum of the SLFT-SPR interaction signal is simply|H(jω)|2 which is flat at low frequencies and displays a dualpole at fp. In contrast, the power spectrum of the noise anddisturbance seems to be largely concentrated at the lowerfrequencies flattening out at the higher frequencies. The SNRfor the SLFT-SPR measurement is equal to the ratio of the two

power spectra as shown in Figure 6b. Note that unlike the fixedSNR for the single pulse step response method the SNR of theSLFT-SPR technique increases and peaks at a specific frequencynear the TF pole. In addition, the peak SNR is much higher forthe SLFT-SPR technique than the step response method by afactor of 20 dB or 100-fold better than that of the step responsemethod. There are two reasons behind the observed SNRimprovement: (a) the measurement takes place in a region wherethe power density of the disturbances and noise is low, and (b)the power spectrum of the disturbance is broad; hence, only asmall contribution of the disturbance and noise is present at thenarrow excitation frequency. The major improvement in the SNRof the narrowband SLFT-SPR technique leads us to believe thatit may be possible to directly detect small molecule binding onthese surfaces.

Finally, we would like to state that in spite of the impressiveSNR ratios, the SLFT-SPR technique does have practical limita-tions. First, in order to make a clean measurement, the modulatorchip has to be able to produce sufficiently high frequency plugsto reach the TF pole region. Therefore, small distances betweenthe chip valves and the sensing spots are required to minimizethe plug dispersion. In addition, smaller noisier spots must beused in the chip. The technique also requires periodic excitationand a periodic response; therefore, it cannot handle irreversiblereactions with strong associations and weak dissociation, but suchreactions could be measured with the use of periodic regenerationcycles.

CONCLUSIONWe demonstrated the implementation of a signal locking

Fourier transform SPR scheme for the detection of biomolecularinteractions under periodic analyte excitation. Using this method,we obtained kinetic values of ka and kd for a CA-II binding modelexperiment similar to those obtained from SPR data analysison the given surface, with the single step determined ka ) 6.5× 103 1/M · s vs the FT value of 9.4 × 103 1/M · s, and similarlykd ) 2.7 × 10-2 1/s vs 2.5 × 10-2 1/s. When compared to thestep response methodology, the SLFT-SPR method produces100-fold improvements in the SNR of the measured signal dueto the narrowband nature of the technique which rejects verywell the uncorrelated noise and disturbances. The majorimprovement in the observed SNR leads us to believe that itmay be possible to detect very small molecule interactions withthis new technique.

ACKNOWLEDGMENTWe thank GWC Technologies for their help with the instru-

mentation and surface chemistry.

SUPPORTING INFORMATION AVAILABLECalculation of Large Signal Fourier Components. This material

is available free of charge via the Internet at http://pubs.acs.org.

Received for review February 24, 2010. Accepted June 8,2010.

AC100504B

Figure 6. (a) Comparison of the power spectrum of the sensorgramsignal (from the lowest applied concentration of CA-II) and the powerspectrum of the system noise and disturbances with no excitation.(b) Plot of the signal-to-noise ratios (SNR) for the step response andSLFT-SPR methods. The SNR of the FT method is 20 dB higher thanthat of the single step method. This translates to a 100-fold improve-ment in the SNR for the SLFT-SPR method.

6031Analytical Chemistry, Vol. 82, No. 14, July 15, 2010