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Microparticle Photophysics Laboratory, Polytechnic University, Brooklyn, New York 11201
Correspondence: Address reprint requests to Iwao Teraoka, E-mail: teraoka{at}poly.edu.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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–4). The amount of the surface-bound protein can be evaluated by various methods (2–11). However, methods to find the state of the adsorbed molecules are not well established, except that submolecular information can be obtained using spectroscopic methods (8–10). There are controversies about the state and orientation of adsorbed molecules, even for often studied proteins such as serum albumin (2,4,11). Their conformation may depend on the surface—whether it is hydrophobic or ionic (positively or negatively charged)—and on the pH of the immersing aqueous phase. This article proposes using resonance shifts of photonic whispering gallery modes (WGM) as a method to determine the state of adsorbed protein.
A transparent microsphere can accommodate WGM in the vicinity of the sphere surface. The light propagates near the curved surface by total internal reflection. Resonance is achieved when the light path closes upon itself in phase after one cycle. If the diameter of the sphere is sufficiently large compared with the wavelength, the resonance can have a narrow width. The Q value of a silica microsphere in water at a 1.3-µm wavelength can be as large as 2 x 106 (12). A much greater Q value, exceeding 108, is reported for a toroidal resonator at 680 nm (13).
In each reflection along the circular path of WGM, the light seeps into the surroundings as an evanescent wave. The wavelength of the sharp resonance is sensitive to small changes in dielectric property in the immediate neighborhood of the transparent microsphere (14). The changes include adsorption of molecules onto the microsphere and a change of refractive index (RI) in the surrounding medium. The shift of the wavelength upon adsorption of biomolecules onto the microsphere has been heralded as the most sensitive detector ever made possible without the necessity for fluorescent labeling (12,15–18). Detection of a single protein molecule is considered within reach (15). Recent prediction (19) and demonstration (20) of enhanced sensitivity by a high RI coating has paved the way for the difficult detection. The sensor's capability is not limited to estimating the surface density of adsorbed molecules. Independent detection of the resonance shifts for two polarization modes—transverse electric (TE) and transverse magnetic (TM)—is expected to allow us to estimate the orientation of adsorbed anisotropic molecules (21).
Each WGM is specified by l, m, 
, and polarization (22). l represents the number of waves in a circular orbit, m (= –l, –l + 1, ..., l) is the azimuthal index, and is equal to the number of peaks in the radial function of the electric field intensity, thus specifying the radial mode. The polarization is either TE or TM. The wavelength at resonance is determined by l, , and polarization. In a perfect spherical resonator, modes of different m are degenerate. The shift of resonance wavelength in response to the environmental changes depends also on l, , and polarization (23). It was recently demonstrated that the observed shifts of TE modes due to RI changes in the surroundings were in agreement with the shifts calculated using the indices evaluated for the microsphere used (24).
More than a decade ago, Folan distinguished TE and TM shifts of WGM in a small polystyrene sphere levitated electrodynamically in air (25). Folan examined the change in the scattering spectrum as water condensed onto the polymer sphere for the two polarizations, but the difference between the two shifts was insignificant within experimental error.
In this report, we use side coupling of a core-exposed single-mode fiber to induce both TE and TM polarizations in a silica microsphere and measure the wavelength shifts when proteins are added to the surrounding fluid to adsorb onto the sphere surface. We find that the shifts are different for TE and TM and the ratio of the two shifts provides information on the state of adsorbed protein. We confirmed the polarization-sensitive shifts by adding NaCl to the surroundings to cause a uniform increase of RI. The latter situation simulates adsorption of large objects such as mitochondria (17).
Recently developed dual polarization interferometry (DPI) (26–29) can provide information on the state of surface-bound proteins. DPI uses two polarizations of light transmitted through a pair of planar waveguides to find the RI and thickness of the adsorption layer, which in turn provide information on the protein conformation. To achieve a high sensitivity comparable to that of the surface plasmon resonance (SPR) instrument, DPI uses a large sensor area, 
150 mm2. Our WGM sensor has a much smaller sensor area, typically <0.005 mm2, yet easily surpasses the sensitivity of DPI and SPR in terms of adsorbed mass per unit area while retaining the capability to find the state of the adsorbate. More importantly, the WGM sensor allows easy interpretation of the resonance shift in terms of molecular parameters (21), without the need to assume an adsorption layer of uniform RI and thickness (26). Neutron reflectivity (7) is another method that macroscopically characterizes the adsorbed molecules as a whole, but its sensitivity and usefulness are limited.
Theoretical background
A plain microsphere of radius a and uniform relative permittivity 
is placed in a uniform medium of 
(n1 > n2). When the wavelength, 
, of WGM is much shorter than a, the electric field, E(r), of the WGM is mostly confined to the interior of the microsphere. However, the evanescent field extends into the surroundings to the depth of (/2
)(
)–1/2, which polarizes the molecules in the immediate neighborhood of the microsphere surface. The resonance wavelength of WGM shifts from 0 to 0 + 
, when small molecules (much smaller than /n2) adsorb onto the sphere surface to displace a part of the surrounding medium. The adsorbed molecules are polarized by E(|r| = a+), where a+ indicates the exterior side of the sphere surface.
The fractional shift /0 is equal to the ratio of the polarization energy in the adsorbed molecules to the total mode energy (12,15,21). In general, the TE and TM modes exhibit different shifts, as the TE mode has only a tangential component, Et(a) as E(a+), whereas the TM mode has also a normal component, En(a+). For uniform adsorption of Np molecules of excess polarizability, 
, at a low surface density, the fractional shift of either mode is given as (21)
 | (1) |
tt and nn are the polarizability tensor components in directions of Et and En, respectively, 
...
indicates the average on the sphere surface (for Et and En) or the average with respect to the configuration of adsorbed molecules (for tt and nn), 
0 is the vacuum permittivity, and the volume integral in the denominator covers the entire space (relative permittivity r is r1 in the sphere; r2 elsewhere).
We showed earlier that the denominator in Eq. 1 is equal to 4a30(r1 – r2) [Et(a)]2 for the TE mode (21,23). Then, the fractional shift of the TE mode is given as
 | (2) |
The shift is identical for all radial modes ( = 1, 2, ...). Since Np 
a2 for a given surface density of adsorbates, /0 a–1. There is a weak dependence of TE/0 on 0 through wavelength dispersions of tt, r1, and r2. For the TM mode, the denominator in Eq. 1 is calculated as 4a30(r1 – r2)([Et(a)]2 + (r2/r1)[En(a+)]2) (21,23). The expression for the TM shift, TM, is then obtained. The ratio TM/TE is
 | (3) |
. Here, A+ 
[Et(a)]2/[En(a+)]2 is the intensity anisotropy ratio of the evanescent field of the TM mode (right on the sphere surface). When l >> 1, the following approximation is useful (21):
 | (4) |
1 – r2/r1. The second approximation is not good except for the first-order radial modes ( = 1). The shift ratio given by Eq. 3 is insensitive to the dimension of the adsorbed molecule, as long as it is sufficiently smaller than 0/n2.
We now evaluate Eq. 3 for a molecule of volume Vp and uniform, isotropic relative permittivity 
We consider five geometries of the molecule—a sphere, a rod (cylinder) standing vertically on the surface, a rod lying on the surface, a disk standing on the surface (edge-on), and a disk lying on the surface (face-on), as illustrated in Fig. 1. For now, we assume a low surface density of adsorbed molecules. The effect of interference from the dipoles induced at nearby adsorbed molecules will be discussed toward the end of this section.
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nn is definite: nn = nn. For a sphere, a standing rod and a lying disk, tt, is also definite. For a lying rod and a standing disk, the orientation of the molecule on the surface relative to Et varies from molecule to molecule. If we assume random orientation of molecules in the directions tangential to the surface, tt is the isotropic mean of the orthogonal tensor components in the directions parallel to the surface.
Table 1 lists tt/(0Vp) and nn/(0Vp) for the five geometries. These expressions were obtained from the boundary conditions for the electric field across the surface of the adsorbate. The expressions for the sphere and the two orientations of the rod were obtained earlier (21). Our early works also showed that the image dipole induced within the sphere does not affect the polarization of the adsorbed particle (21,30). For rods lying on the surface, tt/(0Vp) is the isotropic mean of 2r2(rp + r2)–1(rp – f2) and rp – r2, which gives the listed expression. For edge-on adsorbed disks, tt/(0Vp) is the isotropic mean of (r2/rp)(rp – r2) and rp – r2. A thin uniform layer has the same tt and nn as those for isolated disks lying on the surface. The two geometries are listed in the last row of the table.
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r1 = 1.4522 (silica), r2 = 1.322 (water), a = 171 µm, 0 = 1.312 µm, l = 1170, and rp = 1.552, where Eq. 4 was used for A+. Here, the RI of protein at 1.32 µm was estimated as 1.55 from the value of 1.57 at 589 nm (31). More accurate calculation of the shift ratio employing the numerical method described earlier (21) gives the same values. The shift ratio for the sphere represents the ratio of the field intensities of the two modes on the surface and is nearly equal to 2 – r2/r1. For the other geometries, the ratio is 2 – r2/r1 = 1.18 at np = n2 and deviates from that value with an increasing np. The shift ratio >1.18 indicates nn > tt, which is likely due to molecules of an anisotropic shape standing on the surface. The ratio smaller than 1.18 indicates a geometry of the adsorbate extending parallel to the surface. The capability of the WGM sensors to provide information on the molecular orientation, independent of the size of the molecule, will be useful in studies on protein adsorption in different solutions and surface environments as well as conformational changes.
The above discussion applies to low surface coverages. With an increasing surface density, dipolar fields by nearby particles decrease [En(a+)]2 but increase [Et(a)]2 (21). Earlier (30), we used dipolar approximation to consider the effect for spherical molecules sequentially and randomly adsorbed onto the surface. Since we do not have a formula for geometries other than spheres, we adopt a formula for the spheres. Calculations for spheres of np = 1.55 show that the effect increases Et(a) by 0.9% and decreases En(a+) by 1.8% at 15% coverage of the projection of the spheres onto the surface. As a result, the TE shift is 0.9% greater than the estimate given by Eq. 2, and the TM shift is 1.3% less. The increase in A+ with an increasing surface density causes the ratio to drop to 1.07 at the highest surface coverage in random sequential adsorption (32–34). Concomitantly, the criterion of the shift ratio for the anisotopic polarizability moves to a smaller value.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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). The surface of microspheres used in BSA adsorption was modified with aminopropyltriethoxysilane. Microspheres used in NaCl experiments were washed in pyrranhia solution. The diameter of each microsphere was evaluated under an optical microscope to a reference of the optical fiber of cladding diameter 125 µm.
WGM resonance shift measurement system
The optical part in our measurement system is shown in Fig. 2. We used a pigtailed butterfly laser (distributed feedback laser; DFB) from NTT Electronics (NLK1B5E1AA; Saddle Brook, NJ) operating at 1.31 µm as a light source. The laser is linearly polarized with an extinction ratio 1000 as observed by a photodiode (PDA400; Thorlabs, Newton, NJ) at the end of the single-mode fiber. Exposing the core of the fiber by etching in hydrofluoric acid solution decreased the extinction ratio to 200. However, neither etching nor contact with the microsphere skewed the polarization. Rotation of the laser mount around the axis of the output fiber changed the polarization direction. The angle of rotation of the polarizer at the photodiode to maximize the intensity of transmitted light was measured as the laser mount was rotated in a step of 10° up to ±90° from the unstrained direction. The required polarizer rotation was nearly identical to the laser rotation. The standard deviation of the difference between the two angles of rotation was 4.8°. The extinction ratio barely changed during the rotation. Thus, we know what angles of the laser mount cause vertical and horizontal polarizations in the etched section of the fiber, which in turn will excite TE and TM modes, respectively, within the microsphere that touches the fiber at its horizontal equator.
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). For this study, the laser wavelength, , was scanned at 10 Hz by changing the laser drive current, i, linearly with time. A sawtooth function generator was used for that purpose. The scan range was 0.2 nm. The relationship between and i was evaluated using an interferometer (Agilent, Santa Clara, CA; HP3325A). In each scan, the laser intensity and wavelength increase almost linearly with time, and the two increases are nearly parallel to each other. When a microsphere is placed in contact with the core-exposed section of the fiber, destructive interference by the WGM causes dips in the light intensity at the photodetector. Each dip represents a WGM of a unique set of indices (l, m, , polarization). |
RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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0.042 nm, ascribed to splitting of the degenerate azimuthal modes (m) by a spheroidal shape of the microsphere; Lai et al. predicted polarization-independent splitting by distortion of the meridional cross section of the microspheroid (35). There is a major dip and several minor dips in each period. The major dips are for = 1. Our scan range of 0.2 nm sees just a part of a cluster of the dips having the same l but different values of m. The minor dips are ascribed to higher order radial modes ( = 2, 3; l may be different) and a tail portion of adjacent clusters with = 1 (l is different by 1).
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). We expect that the surface coverage is similar for all the microspheres. Fig. 4 shows typical changes of the TE and TM spectra. A part of the scan range is zoomed for clarity. The pair of experiments in Fig. 4 was selected so that the microsphere used for TM is slightly larger than the one used for TE. The intensity spectrum undergoes a red shift without changing the overall pattern. In either TE or TM mode, deep and shallow dips shift nearly equally. The TM shifts are greater than the TE shifts, although the sphere radius, a, is greater for TM; the shift is reciprocally proportional to a.
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/0, where k0 = 2/0 (k0a is called a size parameter). From Eq. 2, we find that k0a/0 is proportional to the product of the number density of BSA on the surface and the polarizability. A similar relationship exists for the TM modes. In our TE mode experiments, 103k0a/0 is 7.7 ± 0.1 (mean ± SD), regardless of whether the dip is deep or shallow. For the TM modes, the reduced shift is 10.3 ± 0.2. The shift's independence of the radial mode agrees with the theoretical prediction for adsorption of small particles (21). The ratio of the TM shift to the TE shift is 1.34, which is close to the ratios for standing rods and standing disks in Table 1. It is known that the BSA molecule is heart-shaped at pH = 7.4 (36). The result of our TE-TM shift study indicates adsorption of the heart-shaped molecule by one of its tips. At pH = 7.4, the protein surface has a high density of –N+H3 and COO– (4), and the microsphere surface is dense with –N+H3. It is not surprising that the protein anchors to the aminopropyl surface by facing one of the sections covered predominantly with COO– to the sphere surface. A study of protease digestion of BSA adsorbed on an unmodified silica surface at the same pH indicates a similar geometry (4), although sections predominantly covered with –N+H3 would face to –SiO– on the silica surface in the latter experiment.
The volume of a BSA molecule, Vp, is estimated from the molecular mass (1.10 x 10–19 g) and the specific volume of BSA, 0.734 g/cm3 (37), as 81.0 nm3. To estimate the surface coverage of BSA from our experimental data, we use below a picture of a standing disk with radius R and height H. First, we note that the above Vp can be equated to a disk of R = 4.1 nm, H = 1.5 nm, where the aspect ratio is close to the one proposed (38) in a phosphorescence study as consistent with x-ray crystallographic data (36). Then, from Table 1, we obtain tt/0 as 46.1 nm3, where r2 = 1.322 and rp = 1.552 were used. The surface density of the BSA molecules can be estimated using the formula
 | (5) |
Since k0 = 2/0 = 4.796 µm–1, r1 = 1.4522, and k0a(/0)TE = 7.7 x 10–3 in our measurement, 
is estimated as 1.3 x 104 µm–3. Therefore, the area fraction 
of the projection of the rectangular cross section 2RH onto the surface is estimated as 
The latter value is <1/3 of the highest possible value of by spheres, 0.55 (30,32–34).
We could assume another geometry for the BSA molecule, for instance, a standing rod. The molecular dimension of the rod that gives Vp = 81.0 nm3 is R = 1.9 nm and H = 7.1 nm, for example. Then, tt/0 = 44.9 nm3, virtually identical to the one we obtained for the disk model.
As discussed earlier, = 0.15 is too low for the dipoles induced in nearby particles to affect the estimate of or the TM/TE shift ratio. Therefore, we do not need to change our discussion for the surface density and orientation of the adsorbed BSA molecules.
Refractive index change of the surroundings
We tested our polarization-sensitive WGM sensor for a uniform change of relative permittivity, 
in the surroundings. The change mimics adsorption of particles with a linear dimension greater than the penetration depth of the evanescent field. The shift will be greater for the mode with a greater , since its evanescent field penetrates deeper into the surroundings. Numerical calculation of the resonance conditions (23) gives the reduced response, k0a/(
), of the TE mode in a microsphere with a = 174 µm at 0 = 1.312 µm as 2.507 and 2.755 for = 1 and 2, respectively. The reduced response of the TM mode will be 2.950 and 3.252 for = 1 and 2, respectively. The reduced response is insensitive to a: At a = 196 µm, the response for = 1 is 0.9% less than it is at a = 174 µm.
In adding NaCl to the surroundings three times, the shifts exhibited a complicated pattern, as each radial mode had a different shift. Two parts of Fig. 5 show 103k0a/0 for TE and TM modes as a function of NaCl concentration c in PBS buffer surrounding a plain silica microsphere (a = 174–196 µm). The data were compiled from the shifts of different dips in a few measurements. Attention was paid not to include broad dips that apparently consisted of two or more dips at any stage of NaCl addition; the shape of these dips changed as more NaCl was introduced.
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= 1 modes. The line gives 103k0a/(0c) = 0.990 L/g. With k0a/0 = 2.507 x 2n2n2, we obtain dn/dc = 0.150 mL/g, slightly less than 0.171 mL/g, the value reported for = 589 nm at 25°C (39). We believe that the difference is mostly due to RI dispersion. Likewise, most of the data run along the lower solid line in the plot for TM modes (Fig. 5 b). The ratio of the TM slope to the TE slope is 1.19, close to the theoretical value of 1.18.
In both of TE and TM plots, two sets of data are away from those for = 1. They are ascribed to the = 2 modes. The ratio of k0a/(0c) for these sets to that for = 1 is 1.11 in TE and TM. The ratio compares favorably with the theoretical values.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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45° from the TE direction, splitting the light by the polarizations right before the photodetector, and measuring the fiber transmission spectra using two photodiodes. The high sensitivity of the WGM sensor will allow such measurements at extremely low coverages of small molecules. |
ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSACKNOWLEDGEMENTSREFERENCES |
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This work was supported by the National Science Foundation through BES0522668.
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FOOTNOTES |
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Submitted on December 15, 2006; accepted for publication February 15, 2007.
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REFERENCES |
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