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February 15, 2003 / Vol. 28, No. 4 / OPTICS LET TERS 272

Shift of whispering-gallery modes in microspheres by

protein adsorption

S. Arnold, M. Khoshsima, and I. Teraoka

Microparticle Photophysics Lab (MP3L), Polytechnic University, Brooklyn, New York 11201

S. Holler*

Los Gatos Research, Mountain View, California 94041

F. Vollmer

Center for Studies in Physics and Biology, Rockefeller University, New York, New York 10021

Received July 16, 2002

Biosensors based on the shift of whispering-gallery modes in microspheres accompanying protein adsorption

are described by use of a perturbation theory.For random spatial adsorption, theory predicts that the shift

should be inversely proportional to micorsphere radius R and proportional to protein surface density and

excess polarizability. Measurements are found to be consistent with the theory, and the correspondence

enables the average surface area occupied by a single protein to be estimated.

with crystallographic data for bovine serum albumin.

is found to be extremely sensitive to the target region, with adsorption in the most sensitive region varying

as 1?R5?2.Specific parameters for single protein or virus particle detection are predicted.

Society of America

OCIS codes:

170.4520, 300.6490.

T hese results are consistent

T he theoretical shift for adsorption of a single protein

© 2003 Optical

In therecent past, theneed for miniaturebiosensors for

the detection of infectious agents, toxins, protein, and

DNA has taken on added urgency as the world antici-

pates further bioterrorism.

reported specific detection of unlabeled biomolecules

on a spherical surface (radius R ?0.15 mm) from the

frequency shift of whispering-gallery modes (WGMs).

The modes were stimulated in a dielectric sphere

immersed in an aqueous environment by means of cou-

pling light evanescently from an optical fiber.2

authors claimed unprecendented sensitivity for the

adsorption of protein molecules with spatial unifor-

mity.In what follows, we (1) introduce an optical

theory that describes this effect in an asymptotic

limit ?2pR?l . .1?, (2) compare the predicted size

dependence with that from new experiments, and

(3) calculate the effect of reducing the size while

placing protein molecules at specific locations on

the sphere surface.We show that, for particular

locations, the sensitivity to single-protein adsorption

can be enhanced by orders of magnitude.

Figure 1 illustrates the basic configuration of inter-

est.Light from a tunable distributed feedback laser

is coupled into a WGM of the sphere from an eroded

optical fiber3and circulates about the equator.

nant modes are detected from dips in the transmis-

sion through the fiber.A protein molecule diffuses

to the sphere’s surface from the surrounding aqueous

medium and is adsorbed at position ri, where it in-

teracts with the evanescent field of the WGM.

index i distinguishes each adsorbed protein molecule.

This interaction polarizes the molecule, shifting the

frequency of the mode.

To evaluate the shift dv in angular frequency v of

a single protein molecule, it is useful to consider the

Recently Vollmer et al.1

The

Reso-

The

energy of interaction as a first-order perturbation to

a single-photon resonant state, with semiclassical field

E0?r?eivt. The evanescent tail of the field induces a

dipole moment in the protein in excess of the displaced

water, dpeivt, causing a shift in the photon energy

of the resonant state, ¯ hdv ? 2dp ? E0??ri??2. The

excess dipole moment can be represented in terms of

the real part of an excess polarizability aex, i.e., dp ?

aexE0?ri?.The fractional frequency shift for a protein

positioned at riis given by the result of dividing the

perturbation by the energy of the mode (i.e., ¯ hv), as

represented by integrating over the energy density in

the interior:

Fig. 1.

surface of a sphere near an eroded optical fiber core.

sphere and fiber are surrounded by an aqueous solution.

Nanoscopic protein molecule at position ri on the

T he

0146-9592/03/040-03$15.00/0© 2003 Optical Society of America (ms #16351a(tmp))

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273 OPTICS LET TERS / Vol. 28, No. 4 / February 15, 2003

µdv

v

∂

i?

2aexjE0?ri?2j

2ResjE0?r?j2dV

.

(1)

The integral in the denominator is taken over the

interior of the sphere, which contains the overwhelm-

ing majority of the mode energy ?.94%?.4

approximation simplifies the analysis by allowing

the homogeneous permittivity, es, of the sphere to be

pulled through the integral.

this integral results from adding equal electric and

magnetic contributions.

It should be noted that for protein molecules, which

arecomposed of a variety of aminoacids, aexis roughly

proportional tothe mass of the molecule,5and the shift

in frequency in accordance with relation (1) should be-

have in the same way.

Relation (1) represents the shift that is due to an

individual molecule at an arbitrary position on the

sphere, a point we will return to in calculating the op-

timal effect.However, in Ref. 1 it was reported that a

large number of protein molecules are distributed over

random locations on the sphere’s surface.

for all these molecules we sum the singular contribu-

tion in relation (1) over N randomly located molecules

and then turn this discrete sum into an integral over

surface differentials,

PN

where sp, the protein surface density, is N??4pR2?.

With this transformation from a discrete tocontinuous

sum, relation (1) becomes

This

The factor of 2 preceding

To account

ijE0?ri?j2?sp

RjE0?r?j2dA,

dv

v

? 2aexsp

2e0ers

RjE0?r?j2dA

RjE0?r?j2dV

,

(2)

where esis written in terms of a relative permittivity,

es? e0ers.

We now evaluate relation (2) for a general TE mode

for which the interior field at distance r from the

sphere center is given as E0? Ainjl?k0rpers?ˆLYlm,6

where Ainis the amplitude, jl?z? is a spherical Bessel

function, ˆL is a dimensionless angular momentum

operator ?ˆL ? 2ir 3 =?, k0? v?c with c being the

speed of light in vacuum, and Ylm is a spherical

harmonic function.Fortunately both the surface and

volume integrals in relation (2) contain precisely the

same angular integrands.Consequently,

dv

v

? 2aexss

2e0ers

?jl?k0Rpers??2R2

RR

0?jl?k0rpers??2r2dr

,

(3)

where R is the radius of the sphere.

nance, the volume integral in the denominator of

relation (3) may be asymptotically ?2pR?l ..1?

relatedtothe surface

RR

ers?, where erm is the relative permittivity of the

surrounding medium.7

Inserting this expression into

relation (3), we find that the fractional frequency shift

is given by a surprisingly simple formula:

On reso-

value of

jl2

through

0?jl?k0rpers??2r2dr ?R3/2?jl?k0Rpers??2??ers2 erm??

dv

v? 2

aexsp

e0?ers2 erm?R? 2

aexsp

e0?ns22 nm2?R

,

(4)

wherensand nmaretherefractiveindices of thesphere

and the aqueous medium, respectively.

of dv?v for TM modes involves changing the field in

relation (2). Theresult produced by a similar analysis

has the same aexsp?R dependence with numerically

calculated shifts that only differ from the TE shifts by

a few percent for our silica–water interface.

The 1?R size dependence in relation (4) is expected

for a homogeneous sphere.

a layer that is dR thick, it must preserve the prod-

uct k0R for a given resonance, and consequently

dk0?k0 ? dv?v ? 2dR?R. However, the formula

becomes more complicated when the sphere is optically

heterogeneous, as revealed in relation (4).

less, when the surface is saturated with protein,

as revealed by no additional shift regardless of the

external concentration, a plot of 2dv?v versus 1?R

will have slope dReff, the effective thickness of the

layer.It should be noted that dReffas defined can be

negative, if the absorbed material has a polarizability

less than that of an equal volume of water.

circumstance is not the case for protein adsorption,

since the optical permittivity of proteins is higher than

that of water.In fact, proteins have permittivities

close to that of quartz.

We have performed experiments on the adsorption

of bovine serum albumin (BSA) protein on quartz

microspheres.The silica glass surface is sensitized

for protein adsorption by chemical modification with

vapor-phase 3-aminopropyltriethoxysilane following

oxygenplasmacleaning.8

2dv?v measured for complete saturation by use of

a current-tuned distributed feedback laser9operating

at a nominal wavelength of 1.34 mm, are shown as

a function of 1?R in Fig. 2.

implemented only after equilibrium was reached at

23±C.The system was verified to have returned to

this temperature when wavelength-shift measure-

ment was taken.The spheres ranged in radius from

88 to 232 mm ?412 , 2pR?l , 1087?.

scatter in the data over this size range, a 1?R size

dependence appears reasonable.

is dReff? 3.6 nm.

An effective thickness of 3.6 nm is very close to the

smallest dimension of BSA as revealed through x-ray

The analysis

If such a sphere accretes

Nonethe-

This odd

The resonanceshifts

Protein injection was

Within the

The slope of the fit

Fig. 2.

BSA protein adsorption versus 1?R.

based on relation (4), which gives a surface density sp?

2.9 3 1012cm22.

Saturation shifts of WGM resonances measured for

T he solid line is a fit

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February 15, 2003 / Vol. 28, No. 4 / OPTICS LET TERS 274

crystallography.10

with a heart-shaped profile.

sion is the height of the pancake.

from the effective thickness and relation (4), it is

possible to estimate the molecular surface density,

sp? dReffe0?ns22 nm2??aex.

face density by use of the excess polarizability arrived

at from differential refractive-index measurements1

?aex ? 4pe0?3.85 3 10221cm3??, and the usual re-

fractive indices for quartz and water, with the result

sp ? 2.9 3 1012cm22.So a BSA molecule occupies

an area sp21? 3.4 3 10213cm2.

again with crystallographic data, for which the area

of the heart-shaped projection is 3.7 3 10213cm2.

appears that BSA forms an extremely compact layer

on the microsphere surface.

Finally, we are interested in the possibility for

single-proteindetection.

would be possible by looking at steps in the change

of dv?v with time, and this in turn provides a

possible means for separately measuring aex.

the light within a WGM circumnavigates the equator

?u ? p?2? in an orbit that is confined to a thin ring,

molecules at polar angles outside the ring cannot

influence the mode frequency.

comes from molecules that stick at

TE mode that circulates at the equator l ? m, and

the angular intensity is proportional to jˆLYllj2, which

for large l is proportional to jYllj2.11

the frequency shift for a protein at the equator to

that averaged over random positions on the surface

is enhanced by a factor EF ? 4pjYll?p?2, w?j2.

spatial enhancement EF

the average size particle used in Fig. 2, l ? 1000

and EF ?36. To obtain the average shift for an

individual protein at a random position, we set the

surface density in relation (4) to s ? 1??4pR2? with

the result ?dv?v?r? 2aex??4pe0?ns22 nm2?R3?.

shift that is due to a single protein at the equator is

?dv?v?e? EF 3 ?dv?v?r, or

BSA resembles a thick pancake

The smallest dimen-

Furthermore,

We calculate this sur-

This agrees well

It

Single-proteindetection

Since

The greatest signal

u ? p?2.For a

So the ratio of

This

Forcan be significant.

The

?dv?v?e? 2aexjYll?p?2,w?j2

e0?ns22 nm2?R3.

(5)

This single-protein shift has a large size dependence.

Since jYll?p?2, w?j2increases roughly in proportion to

l1?2or R1?2, the single-protein shift should goas R25?2.

Currently, we can detect a fractional frequency change

as small as 1028.Since we can see a shift of one

fiftieth of a linewidth, this requires that Q be 2 3 106.

This value of Q is controlled by overtone vibrational

absorption of water at 1.34 mm and the size of the

microsphere. Leakage at the quartz–water interface

limits the smallest radius for which this sensitiv-

ity is reasonable to approximately 50 mm.

first-order TE mode within such a particle, and for

For a

a wavelength of 1.34 mm, 4pjYll?p?2, w?j2? 20.8.

Under these conditions, the smallest detectable single-

protein polarizability is asd? 4pe0?2.4 3 10217cm3?,

or 6230 times the polarizability of BSA.

masses seldom exceed 106Da, which is only 15 times

the mass of BSA.Thus single-protein measurements

are unrealistic from the resonance shift at 1.34 mm.

We may overcome the problem by working in the

blue, where water absorption is reduce by more than

a factor of 100, and by choosing a material for the

microsphere with a larger refractive index.

As an example, a microsphere of amorphous sap-

phire has a refractive index of 1.7 at a wavelength of

400 nm (blue diode laser with external cavity), which

enables the radius to be reduced to approximately

3.6 mm for Q of 2 3 107in water.

we are able to see a shift of a fiftieth of a linewidth

as before, the least measurable fractional shift would

be 1029.The minimum detectable polarizability pro-

jected from Eq. (5) is now approximately three times

the polarizability of BSA, a number that is consistent

with large protein molecules such as thyroglobulin,

ferritin, and virus particles (e.g., lambda phage).

Adsorption onto the equator may be promoted by

selective silanization of the equator.

Protein

Assuming that

Research at the Polytechnic was supported by a

National Science Foundation grant (BES-0119273).

F. Vollmer was supported by a fellowship of the

Boehringer IngelheimFonds.

address is arnold@photon.poly.edu.

*Present address, Sandia National Laboratories, Al-

buquerque, New Mexico 87185.

S.Arnold’se-mail

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(ms #16351a(tmp))