Molecular Scale Origin of Surface Plasmon Resonance BiosensorsHui Yu,† Xiaonan Shan,‡ Shaopeng Wang,‡ Hongyuan Chen,*,† and Nongjian Tao*,†,‡

†State Key Laboratory of Analytical Chemistry for Life Science, School of Chemistry and Chemical Engineering, Nanjing University,Nanjing 210093, China‡Center for Bioelectronics and Biosensors, Biodesign Institute, Arizona State University, Tempe, Arizona 85287, United States

*S Supporting Information

ABSTRACT: Surface plasmon resonance (SPR) has become an indispensabletool for label-free detection and quantification of molecular binding. Traditionally,the principle of SPR biosensors is described with a stratified medium model, inwhich discrete molecules are approximated with a uniform thin film. With therecent technical advances, SPR can now detect extremely low coverage ofmolecules, which raises the question of the validity of the traditional model. Here,we present combined theoretical, numerical and experimental analysis of SPRdetection principle by considering the discrete nature of the molecules (particles).Our results show that the stratified medium model can provide reasonabledescription of SPR biosensors for relatively high coverage and weakly scatteringsamples. However, interference between the SPR images of individual particles needs to be considered for high spatial resolutionimages and for strong scattering samples at certain incident angles of light.

Surface plasmon resonance (SPR) has emerged as an icon oflabel-free detection technologies for quantification of

molecular interactions because of its high sensitivity,throughput, simplicity and imaging capability.1−9 It measuresthe coverage of molecules bound on a sensor surface, andbinding kinetics from the time profile of the coverage.Traditionally, the principle of SPR is described with a stratifiedmedium model, in which molecules bound on the sensorsurface are treated as a thin uniform film with an effectivethickness and refractive index.10−14 This view may bereasonable when the coverage of the molecules is high suchthat the average distance between the molecules is muchsmaller than the wavelength (approximately a few hundrednanometers) and propagation length (a few microns for goldfilm) of the surface plasmonic waves.15−17

With recent advances in SPR detection technology,commercially available SPR instruments can reach a detectionlimit of 0.1 RU or better (www.biosensingusa.com), corre-sponding to 0.001% coverage of a medium sized protein (∼5nm in diameter), or an average distance of 0.5−1 μm betweentwo proteins. The stratified model of SPR is thus questionable,and one may need to consider the discrete nature of moleculesin the interpretation of SPR data. This is especially the casewhen applying SPR to study long DNA molecules,18 nano-particles,19−22 viruses,23 bacteria and cells.24 In addition, recenthigh-resolution SPR microscopy can image individual nanoscaleobjects,18,19,23 as distinct parabolic fringe patterns, whichcannot be understood with the traditional stratified mediumtheory. These advances call for the development of a SPRtheory that takes in account the discrete nature of molecules orother nano- and micron-scaled objects. Here, we present such atheory and compare it with the traditional stratified mediummodel of SPR. We also present simulations and experimental

data in order to examine how the discrete nature of molecules,nanoparticles, viruses, and cells affects the accuracy of thetraditional stratified medium model.

■ EXPERIMENTAL SECTION

Experimental Setup. The experiment was carried on aninverted microscope (Olympus IX-81) with a 60× highnumerical aperture (NA 1.49) oil immersion objective.Wavelength 680 nm of light sources were used to excitesurface plasmons and the plasmonic images were recorded by aCCD camera (AVT Pike F-032B) at a frame rate of 106 framesper second. All the images were processed by Matlab program.

Plasmonic Image Intensity of Nanoparticle. Onehundred nanometer polystyrene nanoparticles were addedinto 150 mM phosphate buffer and the nanoparticles will bindonto the Au surface. The entire binding process was recordedand the background has been removed by subtracting the firstframe. Nanoparticles’ intensity was averaged over a fixed area(20 by 40 pixel rectangular, and 123.3 nm per pixel).

Simulation of Particle Images. The simulation isperformed in an area of 513 × 513 pixels, with a pixel size of100 nm. The refractive indexes of polystyrene nanoparticles,water, gold and prism are set 1.58, 1.33, (0.163 + 3.4633i), and1.515, respectively. The thickness of gold film is 50 nm. Thepropagation length of surface plasmons is 2.58 μm (calculatedby 1/2κ).

Received: April 15, 2014Accepted: August 26, 2014Published: August 26, 2014

Article

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© 2014 American Chemical Society 8992 dx.doi.org/10.1021/ac501363z | Anal. Chem. 2014, 86, 8992−8997

■ RESULTS AND DISCUSSION

We start with a brief summary of the main results of thestratified medium theory of SPR and then present the theorythat includes the discrete nature of molecules, which will bereferred to as particle-scattering theory. After presentingsimulated SPR based on the theory and experimental SPRthat validates the theory, we compare the predictions by thestratified medium theory and the particle scattering theory.Stratified Medium Model. SPR can be excited optically

with different configurations, but the most popular one is theKretschmann configuration25 (Figure 1A). In the Kretschmannconfiguration, light is incident onto a metal thin film via aprism, and the reflected beam is detected with a photodiode or

imaged with a CCD camera. When the incident angle is tunedto the so-called resonant angle, light energy is transferred intothe surface plasmons, and the reflective light intensity drops toa minimum. Figure 1B shows a SPR reflectivity vs incidentangle profile based on the stratified medium model, where theresonant angle is denoted as θR. Upon adsorption of moleculesonto the metal film, the stratified medium model furtherpredicts a shift in the resonant angle (or SPR reflectivity vsangle profile) to a higher angle.The major task of SPR biosensors based on the traditional

stratified medium model is to detect the shift in the resonantangle. A simple and widely used method to detect the resonantangle shift is to measure the reflectivity change associated withthe shift in the SPR reflectivity profile at a fixed incident anglenear the resonant angle. The change in the reflectivity, ΔR, isrelated to the shift in the resonant angle, Δθ, by12,13

θ θθ

θΔ = − ΔRR

( )d ( )

d (1)

where (dR(θ)/dθ) is the slope of the reflectivity vs angleprofile, thus the sensitivity of SPR (Figure 1C). The basicpredictions of the stratified medium SPR model are as follows:(1) When the angle is smaller than the resonant angle, theslope is negative, such that the measured reflectivity increaseswith the coverage of molecules on the SPR sensor surface. Incontrast, when the angle is greater than the resonant angle, theslope is positive, such that the measured reflectivity decreases.At the resonant angle, the slope is zero, and the reflectivitychanges little. (2) There exist maximum negative and positiveslopes at certain incident angles below and above the resonantangle, respectively. (3) The resonant angle or reflectivitychanges smoothly and linearly with the coverage of adsorbedparticles. Figure 1D plots the reflectivity change vs coverage fora 5 nm-diameter protein, showing a linear dependence. Notethat in the stratified medium model, the effective thickness ofthe protein layer is taken to be deff = (N/Nmax)d, where N is thecoverage, Nmax is the full monolayer coverage, and d is thediameter of the molecule. For a given size of the molecule, thereflectivity change is proportional to the number of moleculesper unit area. These predictions are the working principle ofSPR sensors, which have been used to quantify molecularbinding.

Particle-Scattering Model. How will these basic pre-dictions change when the discrete nature of molecules isconsidered? In order to address this question, we consider atheory that includes individual particles to model discretemolecules, nanostructures, viruses or cells. As shown in Figure2A, the main point of the theory is that the SPR image contrastof a particle is originated from the scattering of the plasmonicwave propagating along the metal film by the particle. Moreexactly, p-polarized incident light is partially reflected (Er) atthe interface of prism/gold and partially transmitted into thegold film as an evanescent wave, which excites surface plasmons(Esp). The total reflected light intensity recorded by the camera(I) is given by the superposition of the partially reflected fieldand scattered plasmonic field in the direction of reflec-tion11,15,16,26,27

β= | + |I E Er sp2

(2)

where β is a constant that describes the fraction of the scatteredplasmonic wave in the direction of the reflected light. Note thatEr can be precisely calculated at different incident angles with

Figure 1. Stratified medium model of surface plasmon resonance. (A)Schematics of the stratified medium model; (B) SPR reflectivity curveswithout (blue line) and with (red line) 10 nm thick polystyrene film,calculated with Fresnel’s equations; (C) Slope of the reflectivity curve;(D) Reflectivity change by different coverage of 5 nm proteinmolecules.

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Fresnel’s equations based on the stratified medium model,11,14

producing a SPR image with uniform intensity. However, thesecond term in eq 2 describes the particle on the surface, whichresults in a distinct parabolic pattern in SPR image, shown inFigure 2B, based on the following considerations.Surface plasmon scattering by a particle can be described by

the elastic scattering theory.28−31 When the particle is muchsmaller than the surface plasmon wavelength, we may expressthe scattered field by a decaying cylindrical plasmonic wave,

α′ = ′ κ− | − ′| − | − ′|E r r E r e( , ) ( ) er r ik r rs sp (3)

where r′ is the location of particle, α is a scattering coefficientrelated to the polarizability of each nanoparticle, Esp(r′) is thesurface plasmon field at the location of the particle, κ is thedecaying constant of surface plasmons, and k is the wave-number of surface plasmons. The total surface plasmon field(Esp)

28,29 based on the Born Approximation is given by

α′ = ′ + ′ κ− | − ′| − | − ′|E r r E r E r e( , ) ( ) ( ) er r ik r rsp sp

0sp0

(4)

where Esp0 (r) is the surface plasmon field in the absence of the

particle. The SPR image contrast of the particle is described by

α′ = | + + ′ |

− | + |

κ− | − ′| − | − ′|I r r E r E r E r e

E r E r

( , ) ( ) ( ) ( ) e

( ) ( )

rr r ik r r

r

sp0

sp0 2

sp0 2

(5)

Note that the background image in the absence of the particle issubtracted out in eq 5. In the case of multiple particles, eq 5 canbe generalized as

∑ α= | + + ′ |

− | + |

κ

=

− | − ′| − | − ′|I r E r E r E r e

E r E r

( ) ( ) ( ) ( ) e

( ) ( )

ri

N

i ir r ik r r

r

sp0

1sp0 2

sp0 2

i i

(6)

where i stands for ith particle and N is the total number ofparticles.

Single Particle. Using eqs 3 and 5, and Fresnel’s equations,we have simulated the SPR image of a single particle as afunction of the incident angle. The image contrast is highlysensitive to the incident angle, as shown in Figure 2B. Whenthe angle is smaller than the resonant angle, the image contrastis positive. When the angle is greater than the resonant angle,the image contrast is negative. At the resonant angle, the imagecontrast is smallest. The inversion of the SPR image contrast ofthe particle around the resonant angle is due to the phaseinversion of the reflected field at the resonant angle.To confirm the theoretical calculations based on the particle-

scattering model, we have imaged 100 nm polystyrene particleswith the high resolution SPR microscope. Figure 2C showsseveral experimental SPR images of the particle at angles lowerthan, near and higher than the resonant angle, which are inexcellent agreement with the calculated SPR images of theparticle at different incident angles.The average reflectivity change vs incident angle was also

obtained from the experimental SPR images, and plotted inFigure 2D. The experimental data are consistent with thecalculated reflectivity change. Note that the error bars of theexperimental data are the standard deviations from 50individual particles. By comparing the calculated andexperimental image contrasts, the polarizability, α, in theparticle-scattering model for 100 nm polystyrene nanoparticle isabout 0.027 (Supporting Information). The excellent agree-ment between the calculated and experimental images andreflectivity changes validates the particle-scattering model.The basic findings of the particle-scattering model are

qualitatively similar to those of the stratified medium model,except that the image contrast of the particle at the resonantangle is finite, instead of zero, due to the formation of theparabolic pattern. The average reflectivity change associatedwith binding of the particle vs incident angle (solid blue line) iscompared with the reflectivity change associated with thebinding of a molecular layer (dashed line) calculated with thestratified medium model in Figure 2D. The results from theparticle-scattering model and stratified medium model are notidentical both they do share similar characteristics, includingthe crossover from reflectivity increase to reflectivity decreasenear the resonant angle, and maximum reflectivity increase anddecrease at certain angles (marked by arrows) on both sides ofthe resonant angle.

Two-Particle Interference. Figure 2A and 2B show thedistinct parabolic fringe pattern of the SPR image of a singleparticle originated from the scattering of the surface plasmonwaves by the particle. When two particles bind to the sensorsurface within a distance smaller than the surface plasmonpropagation length, the overlap between the parabolic fringe

Figure 2. Particle-scattering model of SPR imaging. (A) Schematics ofthe particle-scattering model by destructive interference of scatteredsurface plasmon with partially reflected light. Simulated (B) andexperimental (C) SPR images of single particle at incident angles. (D)Reflectivity change vs resonant angle simulated by particle-scatteringmodel (blue solid line) and stratified medium model (dashed line),and by experiments (red dots). The arrows indicate the incident angleswith maximum positive or negative responses.

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patterns of the two particles leads to constructive anddestructive interferences. Consequently, the total averagereflectivity of the two particles fluctuates depending on therelative positions of the two particles. In other words, thereflectivity change based on the particle-scattering model is notnecessarily proportional to the number of particles, which isdifferent from the prediction of the stratified medium model.To illustrate this point, we have calculated and measured

SPR images of two particles at different locations (Figure 3A).The corresponding total average reflectivity as a function of therelative positions of the two particles is shown in Figure 3B,which reveals bright and dark fringes due to the interferencediscussed above. Note that the calculation was performed byfixing one particle at the center and moving the other to

different locations. Figure 3B shows that fringes fade awaywhen the two particles are separated with a distance greaterthan the propagation length of surface plasmons, indicating thatwe may neglect the interference effect when the coverage isdilute such that the average separation between particles aremuch larger than the propagation length of surface plasmons.The reflectivity fluctuations can be quantified with the

standard deviation (Supporting Information):

σα φ φ

=| − + |

+=

| || | −+

I I II I

E EI I

( ) 2 cos( )1 2

1 2

2s1 s2 1 2

1 2 (7)

where I is the average reflectivity of two particles, I1 and I2 arethe average reflectivity of each of the particles, Es1 and Es2 arethe scattered fields of the two particles defined in eq 3 for α = 1,and φ1 − φ2 is the relative phase between the two particles,which depends on the relative locations of the two particles.Figures 3C and D show the oscillation of σ with differentdistances between two particles along horizontal and verticaldirections for different α at incident angle of 70°. Thereflectivity change fluctuates with the relative positions of thetwo particles. Note also that the horizontal and vertical profilesare not identical because of the propagation of the surfaceplasmons in vertical direction.The reflectivity fluctuations as described by σ is dependent

on both the incident angle θ and α (Supporting Information).Figure 4A shows σ of two particles with a separation of 100 nmalong the horizontal direction at different incident angles.When the incident angle is smaller than the resonant angle, σshows a sigmoidal dependence on α, which saturates at bothsmall and large α. However, when the incident angle is greaterthan the resonant angle, the reflectivity fluctuation dependenceon α is strikingly different. As shown in Figure 4B, for eachincident angle, a singular point is observed in σ at a specific α.The singular point occurs when the average reflectivity changeby a single particle is zero, such that the average reflectivitychange of two particles purely arises from the interference ofSPR images of the two particles. The incident angle, θ0, atwhich the singularity occurs depends on α as shown in Figure4C. For small α, θ0 is close to the resonant angle, but itincreases with α and reaches 0.9° above the resonant angle at α= 0.1. We thus conclude that two-particle interference can leadto effect that is significantly different from the traditionalstratified medium model, especially for particles with large α atangles where the singularity occurs.

Multiple-Particle Interference. When multiple particlesbind to the sensor surface, interference between multipleparticles needs to consider. For weak scattering particles (α issmall), we can describe multiple (N) particle interference as asum of N(N − 1)/2 pairs of two particle interference, andinterference of three or more particles simultaneously is givenby high order of α terms, which can be neglected. In this case,the standard deviation by N nanoparticles (SupportingInformation) is

∑ ∑σ α φ φ=| − ∑ |

∑≈

∑| || | −=

= = = =≠

I I

I IE E

2cos( )i

Nl

iN

l iN

l i

N

j

N

i j i j1

1

2

1 1 1s s

j i

(8)

where Esi and Esj are the scattered fields of two particles definedin eq 3, and φi − φj is the relative phase difference between thetwo particles, which depends on the relative locations of thetwo particles. For randomly distributed particles, the phase

Figure 3. Two-particle interference in SPR imaging. (A) Comparisonbetween simulated (i) and experimental (ii) SPR images of twoparticles with different distances; (B) Distribution of average intensityof SPR image of two particles with different relative locations; (C)Horizontal cross sectional profile of fluctuation of SPR intensity inrelation to the scattering constant; (D) Vertical cross sectional profileof fluctuation of SPR intensity in relation to the scattering constant.

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difference for each pair of the particles is random. Therefore, σshould decrease with increasing N, which indicates theinterference corrections to the prediction of the traditionalstratified medium model diminish when the coverage is high.The particle scattering and interference effect of surface

plasmons play a great role in practical SPR imaging of biologicalsamples, especially with high spatial resolution where individualobjects (e.g., molecules, viruses and cells) are resolved. Forexample, we have successfully imaged single DNA moleculeswith high spatial resolution SPR. The image is highlydependent on the orientation of the DNA molecules relativeto the prorogation direction of SPR, which cannot be describedwith the stratified medium model.18

■ CONCLUSIONSWe have developed a theory of SPR biosensors by consideringthe discrete nature of particles (e.g., molecules, nanoparticles,viruses, and cells), and carried out experiments to validate thetheory. The essence of the theory is that the SPR biosensorsdetect the scattering of the surface plasmonic waves by theindividual particles. The interference of the scattered field in thedirection of the reflection with the reflected field is detected orimaged by SPR biosensors. Using the theory, we have

calculated SPR images of single and multiple particles as afunction of the incident light angle. When the incident angle isbelow the resonant angle, the image contrast is positive. Whenthe incident is above the resonant angle, the image contrast isnegative. At the resonant angle, the image contrast is minimum.These results are in excellent agreement with the experimentalSPR images of polystyrene particles and also match well withthe prediction of the stratified medium model. Our analysisfurther show that for weak scattering samples, such asmolecules, randomly adsorbed on the sensor surface, themeasured reflectivity increases approximately proportionallywith the coverage of the particles, which also validates thetraditional stratified medium model. However, for relativelylarge particles, such as viruses and cells, interference betweenimages of the individual particles leads to deviation of the linearrelationship between the reflectivity change and coverage,especially at certain incident angles, because of the interference.The scattering model provides theoretical guidance to optimizethe sensitivity and resolution of SPR sensing and imaging.

■ ASSOCIATED CONTENT*S Supporting InformationEstimation of scattering coefficient and analysis of intensitydisturbance by interference. This material is available free ofcharge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: hychen@nju.edu.cn. Phone: +86-25-83594862.*E-mail: njtao@asu.edu. Phone: +1-(480)-965-4456NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank Gordon and Betty Moore Foundation, and NationalNatural Science Foundation of China (Grant No. 21327008)for financial support.

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