Observing Secretory Granules with a Multiangle Evanescent Wave Microscope

14 Pages·2000·0.38 MB·English

BiophysicalJournal Volume78 May2000 2641–2654 2641
Observing Secretory Granules with a Multiangle Evanescent
Wave Microscope
Alexander Rohrbach
MaxPlanckInstituteforMedicalResearch,69120Heidelberg,Germany
ABSTRACT In total internal reflection fluorescence microscopy (TIRFM), fluorophores near a surface can be excited with
evanescentwaves,whichdecayexponentiallywithdistancefromtheinterface.Penetrationdepthsofevanescentwavesfrom
60 nm to 300 nm were generated by varying the angle of incidence of a laser beam. With a novel telecentric multiangle
evanescentwavemicroscope,wemonitoredandinvestigatedbothsinglesecretorygranulesandpoolsofgranulesinbovine
chromaffincells.Bymeasuringthefluorescenceintensityasafunctionofpenetrationdepth,itispossiblethroughaLaplace
transformtoobtainthefluorophoredistributionasafunctionofaxialposition.Wediscusstheextenttowhichitispossible
to determine distances and diameters of granules with this microscopy technique by modeling the fluorescent volumes of
spheres in evanescent fields. The anisotropic near-field detection of fluorophores and the influence of the detection
point-spread function are considered. The diameters of isolated granules between 70 nm and 300 nm have been recon-
structed, which is clearly beyond the resolution limit of a confocal microscope. Furthermore, the paper demonstrates how
evanescentwavespropagatealongsurfacesandscatteratobjectswithahigherrefractiveindex.TIRFMwillhavealimited
applicabilityforquantitativemeasurementswhentheparametersusedtodefineevanescentwavesarenotoptimallyselected.
INTRODUCTION
Wheneveralightwaveispreventedfrompropagatingbyan ing on the decay parameter k. To a good approximation
apertureoraninterface,theconservationofmomentumand (depending on detection optics) a Laplace transform
energy of a wave causes the generation of an evanescent (ArfkenandWeber,1995)oftheobjectdistributionC(z)in
field.Themostpopularmethodofgeneratingthesedamped thezdirectionisrecordedbysequentiallyvaryingthedecay
fields is total internal reflection (TIR) (Hecht, 1987). The constant k from zero to infinity and plotting the collected
penetration depth (i.e., the distance of 1/e decay) of the fluorescence as a function of k.
exponentiallydecayingintensityrangesbetweenl/10andl BycalculatingtheinverseLaplacetransform(Arfkenand
and varies with the incoming phase, i.e., it depends on the Weber, 1995), the distribution C(z) can be reconstructed
relative refractive index and incident angle. Total internal withanaccuracyintherangeofsomenanometers(depend-
reflection fluorescence microscopy (TIRFM) (Axelrod et ing on detection optics, z sampling, and noise). This was
al., 1992) is a method of exciting and detecting fluores- implemented for a simple (one-dimensional) geometry by
cently labeled objects near the surface by these thin light Axelrod(1981),ReichertandTruskey(1990),Burmeisteret
sections. Because hardly any background fluorescence is al. (1994), and O¨lveczky et al. (1997) to determine cell-
excited, this technique provides a significant improvement substrate distances of the whole x, y plane by assuming
in spatial resolution for nonpoint, near-surface structures, top-hat functions for the fluorophore distribution in the z
even in comparison to differential interference contrast mi- direction (fluorescence is 0 or 1). The same binary depen-
croscopy (DIC) (Inoue, 1987) and optical scanning tech- dency along z has been approximated for spherical objects
niques like confocal microscopy (Pawley, 1995), theta- by Oheim et al. (1998a). For more complicated 3D geom-
microscopy (Stelzer and Lindek, 1994), or multiphoton etries of fluorophore distributions (like spheres), including
microscopy (Denk et al., 1990), which are additionally pixelblurringbyimaging,theinverseLaplacetransformhas
limited in temporal resolution. not been applied in this way.
Illuminationofa3DfluorophoredistributionC(x,y,z)by Recently, TIRFM has been used for very interesting
an exponentially decaying evanescent wave with a decay applications in the observation of processes near the cell
constantk51/dleadstotheproductC(x,y,z) z exp(2k z z). membrane (Steyer et al., 1997; see also Oheim et al.,
Detecting (integrating) the fluorescent light with a micro- 1998b). Secretory vesicles in live chromaffin cells were
scopeobjectivelensleadstoanintegralexpressiondepend- investigated during the last steps of their exocytotic path-
way. Transport, docking, and exocytosis (Almers, 1990;
Parsonsetal.,1995;Vitaleetal.,1995;Albillosetal.,1997)
Receivedforpublication29December1998andinfinalform23December of single secretory granules and pools of granules could be
1999.
observed with high image quality at the plasma lemma
AddressreprintrequeststoDr.AlexanderRohrbach,EuropeanMolecular
because of the lack of blurring background intensity.
Biology Laboratory (EMBL), Meyerhofstrasse1, 69117 Heidelberg, Ger-
many.Tel.:[phone];Fax:[phone];E-mail:rohrbach@ We modified and extended TIRFM in the same applica-
embl-heidelberg.de. tion by illuminating dense-core granules with evanescent
© 2000bytheBiophysicalSociety waves of variable penetration depths. Therefore we devel-
0006-3495/00/05/2641/14 $2.00 oped a new excitation system, applying very fast angular
2642 Rohrbach
deflection of a laser beam beyond the critical angle to get forp-polarization,whichwasusedinoursetup.I reaches
0p
more information about diameters of granules and their 7.16timestheincidentbeamintensity,whena reachesthe
i
distancesfromthecellmembrane,aswellastheirmobility critical angle because of constructive interference on the
andexocytosis.Informationaboutthesizesofgranulesand, sidewithindexn (sapphire-watertransition).Becausek 5
i z
with that, their absolute positions is not delivered by a 2i z b, the Fresnel formulae are now complex, resulting in
single-anglemeasurement(Steyeretal.,1997).Furthermore a polarization-dependent phase shift between the incident
evanescent waves with large penetration depths loose their andreflectedfields,whichleadstoanellipticalpolarization
well-defined, exponentially decaying excitation properties of the reflected beam. Separating the transmitted field
in chromaffin cells. exp(ikr) into exp(ik x) z exp(2bz), it can be seen that an
x
Here we present a method of modeling spheres in eva- amplitude-modulated plane wave propagates parallel to the
nescentfieldsmathematically,whereadefinedfluorescence surfaceinthexdirection.Energyistransportednotinthez
volumedeliversinformationaboutthesizeandtheposition but in the x direction, with an average energy flux that is
of each granule. We reconstruct the diameters of isolated described by the real part of the Poynting vector S 5
granules and distances between vesicles inside the cell and c/4pz (E 3 H*) (Axelrod et al., 1992). The energy flux is
thecoverslip.Wediscussdisturbancesandconsequencesof alsoparalleltothesurfaceandcanbedescribedasS (a)}
x i
the interaction of the evanescent wave with the vesicles. I (a) z sina z exp(2bz).Thismeansthatanypenetration
0p i i
Furthermore, we explain how to consider the effects of ofobjectsinsidetheevanescentwaveoccursfromtheside,
anisotropicemissionofdipolesnearadielectricinterfaceas notfromthetop,asisoftenassumed.Forthisreason,ifthe
well as demands on the point spread function (PSF) of the objects have a different refractive index relative to their
fluorescencedetectionoptics.Finallyweintroducethecon- surrounding, any scattering (i.e., refraction and reflection)
ceptofthetelecentricexcitationsystemandspecialfeatures of“evanescent”photonsoccursinthepropagationdirection
of the experimental setup. of this surface wave.
This effect was demonstrated by attaching a live chro-
THEORY maffin cell to the interface, as shown in a bright-field
recordinginFig.1a.Thecellcontainedplentyofsecretory
Properties of evanescent waves granules. Surrounded with an aqueous solution (n 5 1.33)
Proceeding on the assumption that electromagnetic fields stained with fluorescein, the cell was illuminated with an
must be continuous across a dielectric interface, the exis- evanescent wave with a very short penetration depth (d 5
tenceofevanescentfieldsappearsquitelogicalinthewave 70 nm). A dark spot indicates the contact area of the cell,
representation.Intheparticlerepresentation,itissomewhat wherenodyecoulddiffusebetweenitandthesapphireplate
less obvious. It is known that a photon looses momentum (Fig. 1 b). By increasing the penetration depth to d 5 160
p 5 2pz h z k 5 2ph z (k ,k ) after refraction at an nm (Fig. 1 c) and d 5 230 nm (Fig. 1 d), scattering at the
x z
interfacewithrefractiveindicesn 5n/n ,1(t,transmit- opticallydensercell(granules)inthepropagationdirection
ted; i, incident). The transversal mtiometntuim 2pz h z k re- occurred.Thecellwithgranules(n’1.37–1.39)workslike
x
mains constant, whereas the normal momentum 2pz h z k asphericallens,focusingtheevanescentwaveinsuchaway
z
changes according to angle of incidence a and ratio of that the fluorescent light could be seen as a tail. This
i
indices n . The component k becomes complex when a scattering effect of evanescent fields has been investigated
ti z
conservation of momentum in both the transversal (x) and theoreticallywitharigorouselectromagneticcalculationby
normal (z) directions is no longer possible (Rohrbach and Chewetal.(1979)andwitharayopticsapproachbyPrieve
Singer, 1998). This is the case for incidence beyond the and Walz (1993).
criticalangle,wherenomomentumcanbetransferredtothe
optically thinner medium. The original propagating wave
Effects and demands on detection optics
changes to an evanescent one, exponentially damped in z
withthedecayconstant2ik 5b5(k 22(2pn/l)2)1/25 It is the aim here to generate a defined exponentially de-
1/d: z x t cayingintensityvolumeI(x,y,z,d)5I(x,y,0,d) z e2z/dfor
excitation and a defined volume in which fluorophore de-
d~a!5l/4pz~n2zsin2a2n2!21/2 (1)
i i i t tection takes place. In a homogeneous medium, this detec-
Thisisthepenetrationdepthoftheevanescentwave,which tion volume is defined by the point spread function PSF(x,
characterizestheintensitybehindtheinterfaceasI(z,a)5 y, z) of the microscope objective with numerical aperture
i
I(0, ai) z e-z/d(ai). The intensity I0 5 I(z 5 0, ai) directly NA5nt z sinu.(uistheanglewiththeopticalaxis,under
behind the interface is described by the Fresnel formulas, which a light beam can be captured by the objective lens.)
which lead to (Axelrod et al., 1992) Ifthereisadielectricinterface(usuallyacoverslip)closeto
thefluorophores,thisprobabilityofdetectionviatheobjec-
4zcos2az~2zsin2a2n2!
I ~a!5 i i ti (2) tivelensisalteredbythereflectionandrefractionofemitted
0p i nt2izcos2ai1sin2ai2nt2i fluorescence photons at the optically denser medium (sap-
BiophysicalJournal78(5)2641–2654
FluorescenceExcitationbyEvanescentWaves 2643
FIGURE 1 (a)Bright-fieldilluminationofalivechromaffincellinasolutioncontainingfluorescein.(b)Evanescentilluminationwithashortpenetration
depthofd570nm,whereadarkspotindicatesthecontactareaofthecell.(candd)Evanescentwaveswithlargerpenetrationdepthsofd5160nm
andd5230nmarescatteredbythegranulesofthecell,whichhaveahigherrefractiveindexthantheaqueoussolution.Thusthecellwithitsgranules
behaveslikeasphericallens.Thearrowindicatesthepropagationdirectionoftheevanescentwave.Theimagesizeis50350mm.
phire). This effect is described by the collection efficiency water and through the cell, which has a higher refractive
Q(z), which is a function of the distance z. indexandthusdeflectsrays.Inanadditionalexperimentwe
The point spread function has a clearly defined volume allowed beads to diffuse between an adherent cell and the
(whichisanellipsoidforasurfaceofconstantintensityof, coverslip (sapphire plate) and again recorded the resulting
e.g., 50%), with a finite depth of focus in the z direction.
The defined volume and, with that, its elongations are lost
when the optical path lengths of the detection light are
altered by any refractive index mismatch. This is the case
whenbiologicalmaterialwithanonhomogeneousrefractive
index (like chromaffin cells) lies between the object (e.g.,
the granule) and the objective lens.
Weinvestigatedtheinfluenceofthefinitevolumeofthe
PSFontwoofitstasks.Theoneistointegrateasuniformly
aspossibleinthezdirection;theotheristoresolveaswell
as possible in the x direction. Fig. 2 shows the sapphire
system consisting of the half-cylinder, and the plate where
theevanescentfieldarisesafterTIR.Theshapeofaadher-
ent cell is outlined. Excited fluorophores emit photons,
which are then focused on the CCD camera with a proba-
bility that is proportional to the PSF amplitude. This is
indicatedinFig.2bythedetectionvolumesofthePSF,i.e.,
the images of the granules. If we specify that all fluoro-
phores in the z direction are imaged with the same bright-
ness, we require a nearly constant detection probability of
90–100%oftheaxialPSFamplitudeofanideallens(here
NA51.2).FromRayleigh’stheory(Hecht,1987)thedepth
offocusD at90%intensityI,D (I590%),is384nmatan
z z
emission wavelength of l 5 640 nm (acridine orange).
em
The corresponding full-width half-maximum (FWHM) in
thelateraldirectionisd(I50.5)5325nmanddefinesthe
x
minimum distance at which two adjacent spheres can be
separated. For latex beads with l 5 515 nm, we expect FIGURE 2 Detection of fluorescence emission close to the sapphire
em
D (0.9)5309nmandd(0.5)5262nm.Intheexperiment, interface,wheretheevanescentfieldarisesaftertotalinternalreflection.
z x
azscanofa93-nmbead(takenasapointsource)revealed Granulesaredetectedthroughthecell,whichhasahigherrefractiveindex
aD (0.9)5360nmandd(0.5)5290nminpurewater.A thantheaqueoussolution.Thepointspreadfunction,whichisinfluenced
z x by two effects (explained in the text), has the task of integrating as
changeofthePSFdistributionisexpected(e.g.,becauseof
uniformly as possible along the z direction and of resolving as well as
coma), because the objects have to be detected through possiblealongthelateraldirections.
BiophysicalJournal78(5)2641–2654
2644 Rohrbach
PSF. We found an increase in the PSF extension of ;10% and Kunz (1977), Carniglia et al. (1972), Burghardt and
in both the lateral and axial directions. The experiments Thompson (1984), and Hellen and Axelrod (1986)
.
indicatethatnearlyallfluorophoresexcitedwithanevanes- The detected fluorescence F(x, y, d) emitted from the
cent wave with penetration depth d , 250 nm are detected three-dimensional fluorophore distribution C(x, y, z) is a
with an equal probability in z (neglecting the collection function of space (x, y) and penetration depth d after inte-
efficiency).Thusinfurthercalculationstheinfluenceofthe gration in z. For a pixel (x, y), the following signal can be
PSF in the z direction can be omitted. described as
Although the influence of the limited depth of focus is
negligible, another effect of fluorophore detection plays an F~x,y,d!
E
important role: The collection efficiency Q(z), describing
‘
the nonuniform emission of fluorophores near dielectric
5fzI ~x,y,d!z @Q~z!zPSF~z!#zC~x,y,z!ze2z/ddz
surfaces, is defined by the ratio of collected power to total 0
dissipated power of a dipole. As every dipole emits propa- 0
gatingandevanescentfieldsitself,partoftheemittedpower (3)
islostasenergyistakenoutofthedipole’snearfield,which
results in propagating waves under supercritical angles in Herefdenotesthequantumefficienciesofthefluorophores
the medium with a higher refractive index. Because a con- and of the CCD camera. fand the fraction of self-absorp-
stant-power (variable-amplitude) dipole must be assumed, tion in the probe are assumed to be constant. I (x, y, d) is
0
this near-field energy absorption is at the expense of those defined by Eq. 2. As discussed above, the detection proba-
propagatingwavesthatwouldbecollectedbytheobjective. bilityPSF(z)canbesetto1inourconfiguration,becauseit
As an additional effect, the emitted far field is partly re- is nearly constant over the extension of the evanescent
flected at the interface and interferes with light coming wave,whichis;23penetrationdepth(D (I50.9)’2d).
z
directly from the dipole. Q(z) depends strongly on the TheinfluenceofthecollectionefficiencyQ(z),whichhas
polarization of the excitation light, the orientation of the beencomputednumericallyandmultipliedwithtwodiffer-
dipoles,andtheconfigurationoftheopticalsetup(refractive ent exponentially decaying fields (excitation intensities), is
indices, NA, and detection direction of the objective lens). illustrated in Fig. 3. Up to a z distance of 150 nm, fluores-
AdetailedmathematicaldescriptioncanbefoundinLukosz cenceisdiminishedconsiderablybythenonlinearQ(z).For
FIGURE 3 (a)Theextensionsoftwospheres(horizontalbars)withdiameters2zR5200nmand2zR5400nmillustratethedimensionsofthe
evanescentfields.FluorescenceintensitiesQ(z)zexp(2z/d)areshownforcollectionefficienciesQ(z)5const.(solidlines)andforthenonconstantQ(z)
(dottedlines)withpenetrationdepthsd580nmandd5180nm.(b)TheeffectofthenonconstantQ(z)(dottedlines)onthefluorescencevolumesof
thetwospherestouchingtheinterface,comparedwithaconstantQ(z)50.3(solidlines).Theuppercurvesrepresentthefluorescencevolumeofthelarger
sphere,thelowercurvesthatofthesmallersphere,asafunctionofpenetrationdepth.
BiophysicalJournal78(5)2641–2654
FluorescenceExcitationbyEvanescentWaves 2645
distances z . 150 nm its decrease approximates an expo- tion intensity as a density function inside the sphere:
nential decay. Q(z) z exp(2z/d). This approach, in which the excitation
field inside the sphere is equal to the incoming field, is
known as the First Born Approximation. After eliminating
Fluorescence volumes of spheres in I , we write for the intensity per pixel I(x, y, d) 5 F(x, y,
0
evanescent fields d)/(I (x, y, d) z f), and after total integration over (x, y) we
0
EliminationofthesurfaceintensityI0 define Id: 5 *I(x, y, d)Edx dy. IEn cylindrical coordinates:
OuraimistoreconstructthefluorophoredistributionC(x,y, ˛R22z2 R
z), which is the only unknown function in Eq. 3. Here we I ~a,R,c!5cz2pz Q~z!ze2(z1a)/dzrzdrdz
d
have to calculate Q(z) numerically (see previous section),
0 2R
becauseitcannotbemeasured.Thetermexp(2z/d),gener- E
ated by the evanescent wave, can be adjusted by the angle R
ofincidenceofthelaser.Integrationinzisperformedbythe 5czpz Q~z!ze2(z1a)/dz~R22z2!dz (5)
objective lens, so that F(x, y, d) is measured by the CCD 2R
camera. The quantum efficiency fis assumed to be equal
for all penetration depths and can be set equal to 1. For a constant collection efficiency Q(z) 5 1, this integral
accTohredinugnktnooEwqn. 2f.unHcotiwoenveI0r(,xt,hiys,wdo)ucldounlodtbcoencsaidlceurlpatoesd- dca)nzbde3 szo[lRv/eddzacnoaslhy(tiRc/adl)ly2tosIidn(ha(,RR/,dc)])554Ipdmezs.cTzheixspi(s2aan/
sibleirregularitiesofthesetup,suchastheangle-dependent equationwiththreeunknownparametersthatcanbesolved
transmission of light through the lenses, and of the acous- ifatleastthreeequationsId1(a,R,c)5I1mes,Id2(a,R,c)5
toopticbeamdeflector(AOBD),whichbothinfluenceI0(x, I2mes,andId3(a,R,c)5I3mesareknown.Theinhomogeneity
y, d). Thus we determined I0(x, y, d) by measuring the Idmesisthemeasured(andnormalized)fluorescenceintensity
fluorescing volume I (x, y, d) of a uniform distributed ofasphereinanevanescentfieldwithpenetrationdepthd.
uni
solution of fluorescein with the concentration C(x, y, z) 5 Unfortunately, Idmes is intrinsically inaccurate, because of
c . This integrated intensity is noise and measurement uncertainty, and because the pene-
FL
E trationintothesphere(thefluorescencevolume)isnotwell
‘ known. Thus, in addition to Eq. 5, the relation between the
I ~x,y,d!5c zI ~x,y,d!z Q~z!ze2z/ddz expectedintensityI (a,R,c)andthemeasuredintensityImes
uni FL 0 d d
is described by
0
5c zI ~x,y,d!zDQ~d! (4) I ~a,R,c!5Imes1dImes<Imes (6)
FL 0 d d d d
Because it is constant for all penetration depths d, cFL was Theindexddenotestheintensitiesofthedifferentpenetra-
eaarbsiiltyrabrielydseetetrtmoi1n.eTdhbeysIu0r(fxa,cye,idn)te5nsIiutyni(Ix0,ayt,zd5)/D0Qc(adn).nFoowr mtioonrsedthepanthsth.rTeheeeaqdudaittiioonnsalacnodntthrirbeuetimoneadsIudmreesmneonwts,retqoufiirneds
an ideal collection efficiency Q(z) 5 1, we would find the thetriplet(a,R,c).TheerrordImeswillbediscussedinthe
integral DQ(d) 5 d. Equation 3 can then be normalized by Results. To estimate the dimensdions of spheres in the de-
I0(x, y, d). For a constant Q(z) 5 1, the measured (and caying field and to estimate the influence Q(z), Fig. 3 a
normalized) fluorescence F in Eq. 3 is the Laplace trans- shows the product Q(z) z exp(2z/d) with different penetra-
form in z of the spatial distribution C(z), when the decay tiondepthsd.HerethesolidlinesrepresentthecaseQ(z)5
constant k 5 1/d is varied. For a nonconstant Q(z), the constant, and the dotted lines illustrate the realistic case of
integrals must be evaluated numerically. anonlinearQ(z).Twodifferentbarsshowtheexpansionof
two spheres a 5 R 5 100 nm and a 5 R 5 200 nm,
touchingtheinterfaceatz50.Aworst-caseestimateofthe
Fluorescencevolumesofspheres
influence of Q(z) on a defined fluorescence volume can be
Forsimplicity,weassumethatsecretorygranulesarespher- found from spheres touching the interface. In Fig. 3 b, a
ical. Then the fluorophore distribution C(x, y, z) can be calculation for two spheres (with R 5 100 nm (lower
described by the following three parameters: the center curves) and R 5 200 nm (upper curves)) shows the fluo-
distance a to the interface, the radius R of the sphere, and rescenceintensitytobedependentonthepenetrationdepth
the fluorophore amount inside, described by c. In other d of the illuminating evanescent wave. According to Fig. 3
words, the concentration C(x, y, z) 5 c is assumed to be a, the dotted lines in Fig. 3 b represent the case Q(z) (cid:222)
constantif[x21y21(z2a)2]1/2#R,whereasC(x,y,z)5 const.andthesolidlinesthecaseQ(z)50.3.Thecurvesare
0 otherwise (outside the sphere). The fluorescence is de- quite similar; however, if we compute the relative error in
tected and integrated over the whole spherical volume ac- intensities,Err(d)512[I(Q50.3)/I(Q5Q(z))],wefind
cording to the product of collection efficiency and excita- that Err(d) is larger for small penetration depths and small
BiophysicalJournal78(5)2641–2654
2646 Rohrbach
spheres. For example, the relative error is ;22% for small Determiningdiametersofisolatedgranules
spheres of radius R 5 a 5 50 nm but less than 65% for a
Weassumethatisolatedgranulestouchtheinterface,sothat
medium sphere of R 5 a 5 150 nm.
thecenterdistancea5radiusR.Toeliminatetheeffectof
the varying fluorophore concentration c, we again take the
quotient of two recordings. Here all the intensities will be
Determiningdistancesofgranulesincells normalized to the intensity I (a 5 R) at a penetration
100
depth of d 5 100 nm. Because only isolated granules are
To minimize movement of granules during measurements,
treated,weareabletointegratetheintensityeasilyoverthe
experiments with only two pictures I and I of granules
1 2
wholespotarea.AccordingtothemodelpresentedinEq.5,
were performed. The corresponding penetration depths are
d and d , d . By calculating the quotient of two record- we expect the following relative intensity volume Id/100 for
1 2 1 spheres touching the interface (a 5 R):
ings, it is possible to eliminate the unknown fluorophore
concentration c:
*R ~R22z2!zQ~z1R!ze2(z1R)/ddz
I ~a5R!5 2R <Imes
I~z,d !/I~z,d !5czexp~2z/d !/czexp~2z/d ! d/100 *2RR~R22z2!zQ~z1R!ze2(z1R)/100dz d/100
1 2 1 2 (9)
5exp~2z/d !5I~z,d ! (7)
12 12 By measuring the volume Imes for different penetration
d
We now get a kind of synthetic 1/e 2 depth d 5 d z depths d and normalizing them to I1m0e0s, we can reconstruct
12 1
d /(d 2d ).Ford 580nmandd 5130nm,d 5205 the last unknown parameter R. Because our data are noisy,
2 2 1 1 2 12 we plot the relative intensity volumes Imes against the
nm, which are experimentally relevant values. Within the d/100
penetration depth d (a Laplace transform is usually plotted
uncertainty of our measurements, we take the analytical
solution I (a, R, c) for the integral in Eq. 5 with Q(z) 5 1 against k 5 1/d) and perform a best fit with x2 minimiza-
d tion. The minimum of the error E(R) 5 S(I (R) 2
(justified in Fig. 3 b). For the ratio I /I , d/100
d1 d2 Imes )2 leads to the most probable radius R of the granule.
d/100
I ~a,R,c! d3z@R/d zcosh~R/d !2sinh~R/d !# e2a/d1
d1 < 1 1 1 1 z
I ~a,R,c! d3z@R/d zcosh~R/d !2sinh~R/d !# e2a/d2
d2 2 2 2 2 INSTRUMENTATION
<f~R,d ,d !ze2az(1/d121/d2) Excitation optics
1 2
<~B6DB!ze2a/d12 (8) Fast variation of evanescent field penetration depths re-
quiresatleastoneactiveelementfordeflectionofthelaser
The term exp(2a/d ) exclusively describes the center dis- beam and, second, a configuration of passive optical com-
12
tance a, and the term f(R, d , d ) describes the radius R at ponents for coupling the beam under supercritical angles
1 2
penetrationdepthsd andd .Thetermfcanbecalculatedas onto a single point of the interface. This second task was
1 2
a function of R for different parameters a. The result is a implemented with a telecentric system (Rohrbach, 1998), a
weak descending function, allowing the approximation configurationalsousedlateronbyOheimetal.(1998a).For
f(R) ’ B 5 constant, and we accept an error of DB , the interface, we chose sapphire with index n 5 1.78 as a
s
20% z BbyassumingameangranuleradiusofR5180nm highrefractingmedium.Thisallowsustogenerateevanes-
for all vesicles. centwaveswithpenetrationdepthsfrom;40nmto300nm
ThereisbackgroundfluorescenceU(x,y)ineveryimage in aqueous solution (n 5 1.33) at an excitation wavelength
I(x,y)duetofluorescingobjectsatlargerdistancesfromthe of 488 nm from a 15-mW argon-krypton laser (643-AP-
coverslip which are excited and detected by the tails of the A01; Omnichrome). As an active deflection element we
evanescent wave and the PSF. We remove the background employed an acoustooptic beam deflector (AOBD)
U(x, y) by high-pass Gauss filtering (Appendix). (N45100–3-6.5DEG, NEOS) with a maximum deflection
Asanexample,wetooktwopicturesI andI withd 5 rangeof37mrad(52.2°)andarepositioningtimeofless
1 2 1
80 nm and d 5 130 nm (thus d 5 205 nm), where no than 0.5 ms. With two achromatic lenses (Spindler and
2 12
scattering effect could be detected. The ratio leads to the Hoyer; D 5 30 mm in diameter) with focal lengths f 5
1
dependency I 5 I z exp(2a/d ) ’ I z (1 2 a/d ) 1330mmandf 5200mm,weachievedamagnificationof
12 max 12 max 12 2
infirst-orderTaylorora95a1R’d z (12(I /I )1 thedeflectedanglesoff /f 56.65(seeFig.4).Aslongas
12 12 max 1 2
180nm.HereI isthemaximumintensityofI (x,y)that thebeamdiameterisatleastoneorderofmagnitudesmaller
max 12
leads to the minimum center distance of a granule. The than the diameter of the lenses, the two lenses need not
minimumcenterdistanceshouldbeatleastthemeanradius necessarilyformaconventionaltelecentricsystem,because
of the granules R 5 180 nm (a9 5 a 1 R). A linear thedistancebetweenthemcanbemuchsmallerthanf 1f .
1 2
approximation (first-order Taylor) is justified for a center Whentwolensesareused,thefirstcaneasilybeadjustedto
distance of up to d 1 R. the deflection range of the active element (AOBD or a
12
BiophysicalJournal78(5)2641–2654
FluorescenceExcitationbyEvanescentWaves 2647
the f 5 200 mm lens down to a diameter of 103 mm (1/e2
1
intensity), equivalent to 24 mm at 90% intensity. In the p
directionthespotdiameterincreasesby1/cos(a),according
i
to the oblique incidence angle a and decreases by the
i
focusingthroughthehalf-cylinderwithf 5(n 21)/n ’
Zyl s s
0.44 z R .Thusaplanewavewillbefocusedatadistance
Zyl
0.44 z R .Thewaveincidentonthehalf-cylindermustbe
Zyl
divergenttobefocusedatthebottomofthecoverslipatthe
distance R . This results in a spot diameter of 20–30 mm
Zyl
at 90% intensity, which is sufficient for a homogeneous
illumination of the adherent surface of a chromaffin cell.
Wecalculatedarangeofincidentanglesof0.57°overthe
diameter of the laser beam, which was focused by the
deflecting lens and the half-cylinder. This Gaussian distri-
bution of incident angles generates a mean exponential
decay with a mean penetration depth d (a) (a[ [a 2
mean 0
0.57°/2, a 1 0.57°/2]), which differs by 5% at most from
0
anunfocusedincidentbeam,generatingapenetrationdepth
FIGURE 4 The deflection angle of an acoustooptic beam deflector is
of d(a) 5 200 nm.
magnifiedbyatelecentricsystem.Togetherwithahalf-cylinder,beamsare 0
deflectedandfocusedunderdifferentsupercriticalanglesintothecenterof Inhomogeneities in the beam intensity can be caused by
theimagefieldoftheobjective.Evanescentfieldsofvariouspenetration the interference of unavoidable reflections in the optical
depthsaregeneratedwithintherangeDaofsupercriticalangles.Cellsare system. To reduce these effects, we used a transparent disc
mountedinaperfusionchamberandareobservedthroughwater.
rotatingat5500rpm.Thevaryingopticalpathlengthshifts
the phase f(x, y) by more than 2pwithin the integration
time of the CCD camera. Thus the phase f(x, y) and the
tilting mirror), and the second lens can be chosen to easily resulting intensity are averaged.
adjustthenecessaryanglemagnification(therangeDa).To
avoid longitudinal spherical aberrations that lead to differ-
Detection optics
entx,ypositionsoftheevanescentwave,weusedonly90%
ofthelensaperture.WithinarangeofanglesofDa57.7°, Illuminated objects close to the interface were detected
differentevanescentdecaysbeyondthecriticalanglea 5 throughwaterwithawaterimmersionobjectivelens(Plan-
crit
48.35° could be generated. We chose a half-cylinder Apochromat 633, NA 5 1.2; Zeiss) in an inverted micro-
(R 5 5 mm) for the transition from air to sapphire scope from Zeiss (Axiovert T135). Further magnification
Cyl
(perpendicular incidence) to avoid a change of incident with an Optovar (13, 1.63, 2.53) and by 4 with an addi-
anglesbyrefraction(Fig.4).Theheightofthehalf-cylinder tional lens guaranteed high image sampling from the CCD
was shortened by the thickness of the sapphire substrate (1 camera. A cooled slow-scan CCD camera (16-bit, back-
mm), so that every incident laser beam within Dahad the illuminated)(SI502BA;SITe,Inc.)witha5123512pixel
sameopticalpathlengthfromthedeflectinglenssurfaceto array (24 3 24 mm pixel size) was used for image record-
the focus region (region of evanescent waves). For index ing. Image acquisition at a rate of 3 s21 could be achieved
matching between half-cylinder and plate (transducer) we witha2563256pixelarrayand12-bitsamplingat100ms
used Diiodide Methane, with n 5 1.78. The half-cylinder ofilluminationtime.Forzscansandfocusstabilizationwe
s
(coated on the air/sapphire interface against internal reflec- used a piezo-scanner (P-721.10 PIFOC; Physik Instru-
tions) was fixed with a special holder, while the transducer mente) together with an external sensor (E-115.21; Physik
with attached fluorescing particles could be moved with a Instrumente).
steppermotor,sothatitcouldslideunderthethinfilmofthe The position of the totally reflected laser beam was
index matching fluid. measured with a 512-pixel CCD line (TSL 218; Texas
Instruments).Thelaserspotoftheoutgoingbeam(;1mm
in diameter) was sampled with eight values; averaging and
Beam forming
maximumdeterminationoftheseeightvaluesledtoagood
The naturally diverging laser beam converges after passing angularresolution(betterthan0.1°).Thereflectedanglea
i
the lenses and the half-cylinder. This influences the spot ( 5 incident angle) was obtained with the help of the
sizeofthelaserbeamattheinterfaceandproducesasetof tangentrelationa5arctan(Dx/(Dz1Dp)).DxandDzwere
i
incident angles, i.e., a superposition of exponential decays measuredoncewitharuler;thespotmovementDpinthez
of the evanescent field. In the s direction (perpendicular to direction was then measured electronically, using the CCD
plane of incidence) the 1.2-mm laser beam is focused with line.
BiophysicalJournal78(5)2641–2654
2648 Rohrbach
Electronic setup RESULTS
Theelectronicsetuphastwoimportanttasks:firsttocontrol Evanescent illumination of secretory granules
thedeflectionofanglesandthustheevanescentillumination
Scattering signifies a change of direction of the incident
of the probes; second, to collect the fluorescent light with
k-vectors of a wave (of a photon in the particle representa-
the CCD-camera. The latter was performed with a PC and
tion). The evanescent wave, propagating parallel to the x,y
programmedmacroroutinesestablishedandimplementedin
plane, is not only scattered (focused) in the x,y plane, but
WinView (Visitron Systems GmbH) to acquire image
alsointhezdirection.Thusexcitationlightisalsoscattered
stacksinloopswithvariabledelays.AnexternalTTLsignal
intodeeperregionsofthecellbythegranules.Thiseffectis
coinciding with the camera shutter was sent from the cam-
illustrated in three images of a chromaffin cell, where flu-
eracontroller(ST138S;PrincetonInstruments)toaseparate
orescencehadbeenexcitedbyevanescentwavesofd565
electronic setup, responsible for the evanescent illumina-
nm,d595nm,andd5155nmpenetrationdepth(Fig.5,
tion.Thisreal-timeoperatingsystem(RTOS)wastriggered
a–c). A very short penetration depth (Fig. 5 a) results in a
by the TTL signal and then read out a voltage pair from a
weak excitation of dye molecules close to the interface. In
table. This voltage pair encodes the diffraction angle and
Fig. 5 b the intensity of fluorescing granules is uniform,
efficiency of the AOBD, which yield the penetration depth
whereasinFig.5canincreaseinfluorescencecanbeseen
of the arising evanescent wave and illumination intensity
from left to right (propagation direction of the wave) be-
(betweenzeroandadefinedvalue).Becauseofthespeedof
cause of more scattering at a larger number of granules.
theRTOSandtheAOBD,theexcitationoftheprobestarts
Averagedhorizontallinescansacrossthewholecellsuchas
andstopsonlywitha0.3-msdelaytotheilluminationofthe
those in Fig. 5 c reveal an increase in additional fluores-
CCD camera. The RTOS computer also calculates, moni-
cence, which reaches up to 300% after 10 mm of propaga-
tors,andsavesincidentanglesandpenetrationdepthsmea-
tionofthewaveatapenetrationdepthof;150nm(Fig.5
sured via the CCD line. For non-time-critical applications,
d). Fluorescence intensity was normalized to an averaged
the AOBD also could be controlled by two D/A converters
linescanofarecordwithoutscattering(asinFig.5b).Even
on the PC board.
for a medium penetration depth of ;115 nm, additional
fluorescence caused by scattered light increases by more
METHODS than 100%. The strength of this effect varies from cell to
cellbutoccursinallchromaffincellsforpenetrationdepths
Weimagedbovinechromaffincells2–3daysaftertheyhadbeenplated
larger than 150 nm. Additional fluorescence is possible,
ontosapphireplates(coatedwithPDL).Cellswereincubatedin135mM
NaCl,2mMKCl,5mMCaCl ,2mMMgCl ,19mMNa-HEPESatpH because excitation energy is taken locally from the other
2 2
7.2at22–24°C.TheresultingpotentialkepttheCa21channelsclosedand side of the interface, along the extension of the incident
secretiondidnotoccur.Cellswerestimulatedbyaninfluxof60mMKCl. beam.
Influxof60mMKClwith7mMMgCl insteadofCaCl allowedvesicles
2 2 This effect destroys any defined (and desired) exponen-
todockattheplasmamembranebutpreventedexocytosis.Granuleswere
stained by incubating the cells in 3.0 mM acridine orange for 12 min at tial decay of an evanescent wave and prevents quantitative
22–24°C. analysisoffluorescencewhenlargerpenetrationdepthsare
FIGURE 5 Evanescentilluminationofsecretorygranules,withthewavepropagatingfromlefttoright.Theshortpenetrationdepthofd565nmgave
aweakexcitationoftheclosegranules(a),whereaswithd595nm,aclearandhomogeneousfluorescenceofthevesiclescouldbeobserved(b).Larger
penetrationdepthsofd$140nmcanleadtoinhomogeneousfluorescence(c),increasingwiththepropagationdistanceofthewave.(d)Averagedlinescans
acrossthewholecellalongthepropagationdirectionoftheevanescentwave.Detectedfluorescenceincreasesbecauseofscatteringofexcitationlight.The
fluorescenceintensityisnormalizedtoanaveragedlinescanofarecordingwithoutscattering(asinFig.5b).
BiophysicalJournal78(5)2641–2654
FluorescenceExcitationbyEvanescentWaves 2649
used. The increasing excitation and fluorescence can be rescence (DI # 45% z Imes), photon noise (DI #
H d R
seen clearly when the evanescent wave comes from only 12% z Imes), peak intensity (DI # 45% z Imes), error in
d A d
one side, but it is hardly noticed when a symmetrical illu- surface intensity (DI # 16% z I ), and lateral scattering of
0 0
mination from all sides is used (Stout and Axelrod, 1989; excitation light (DI 5 0–300% z Imes).
S d
Steyer et al., 1997). The strongest disturbance DI can be avoided only by
S
usingisolatedgranulesorgranulesincellswithlowvesicle
density at penetration depths of d , 150 nm. Under these
Determining fluorescence volumes of granules conditions, the background intensity can be estimated with
the help of a mean signal-to-noise ratio, which can be
Penetrationofthegranules
determined by computing the peak intensity and the local
So far it has been assumed that fluorophores are excited backgroundofagranulespot.Thephotonnoisedependson
with the same intensity inside the granules as outside. This theexposureoftheCCDcamera,andhereitissmallerthan
would occur if the protein matrix of the vesicles had the 12%.
same refractive index as their surroundings. Unfortunately The error in surface intensity DI is taken to be an
0
theyhaveanindexupto0.06higherthanthatofwater.This instrumental error, which also includes uncertainty in the
indexstepwouldleadtothesuppositionthatagranuleisno refractive index of the aqueous cell solution and the spot
longer penetrated exponentially in z, because the internal homogeneity at the interface. For the largest penetration
fields now may obtain propagating components in z or depth used inside cells (d 5 155 nm), it is at most 16%.
generateresonancesinsidethegranule(Knight,1995).Ifwe A relation between the total spot intensity and the max-
assume an approximately homogeneous density of excita- imum peak intensity of a spot has been established by
tionlightinsidethegranulewithameanintensityIfull(z)5 convolving the measured PSF of the objective lens with
exp(2a0/d) at the center distance a0 (in comparison to an modeled spheres of different sizes. This relation grows
exponential decay Iexp(z) 5 exp(2z/d)) inside, we can cal- quadratically with increasing object radius. Assuming that
culatetherelativeerrorsoftheintensitiesIexp(d)andIfull(d). the total spot intensity is always proportional to the maxi-
This relative error is small as long as the radii of the mumpeakintensity,wefindamaximumerrorDI of45%
A
granules are not larger than the penetration depth of the (ameanerrorof20%)forgranulediametersfrom150nmto
illuminating evanescent wave. For larger radii, the inte- 500 nm.
grated fluorescence intensities Iexp(d) and Ifull(d) are quite The total error dImes for the fluorescence volume is esti-
different. mated using all of the errors described above and will be
Inaddition,weperformedthefollowingexperiment.We usedinthenextsection,wheretheerrorofthereconstructed
illuminated isolated granules (close to the interface), with center distances is assessed.
increasing penetration depths of evanescent waves up to
epiillumination (d 3 ‘). From the ensuing granule spots,
we measured the diameters (FWHM). As expected, we Determining distances of granules in cells
found no significant difference between evanescent and
Fig. 3 a illustrates the dimensions of evanescent fields and
epiillumination for small granules. But for large granules,
spheres.Whathappensiftheseextendedobjectsmovealong
wemeasuredanincreasingFWHMwithanincreasingpen-
the decaying excitation fields in z and all arising fluores-
etrationdepthuptoepiillumination.Thisindicatesthatwith
cenceisintegrated/averagedinthezdirection?Assumingan
evanescentillumination,onlyacapofthespherefluoresces.
exponentialdecayofexcitationlightinsidethespheres,we
This implies that despite the higher index, spheres do not
calculated the resulting fluorescence intensities as a func-
fluoresce homogeneously, but generate a sectional fluores-
tionofthecenterdistancea.TheresultisplottedinFig.6,
cence according to the penetration depth of the exponen-
wherethedecayingbehaviorofapointsource(whichis,of
tially decaying evanescent wave. course,Q(z) z exp(2z/d))iscomparedwithspheresofR5
To summarize, the internal fields can be assumed to be 100nmandR5200nmradius.Fortwodifferentpenetra-
equal to their incident external fields (Rayleigh-Gans or
tion depths, we find a quite similar behavior. Because we
Born approximation).
take the center distance, the curves for the spheres start at
a 5 R 5 100 nm and a 5 R 5 200 nm, respectively.
These results allow us to approximate extended spheres
Measuring fluorescence volumes of
aspointsandtouseanexponentialfluorescencedecaywith
granules in cells
increasingcenterdistanceforapproximationsthataremade
Equation 6 describes the relation between the measured together with Eq. 8.
intensity volumes Imes 1 dImes on the right-hand side and As explained in the Theory section, three unknown pa-
d d
expectedvaluesI asafunctionof(a,R,c)ontheleft-hand rametersa,R,andcforcenterdistance,granuleradius,and
d
side. The error dImes can be categorized as follows, with fluorophore concentration must be determined (Eqs. 5 and
d
maximum errors as a percentage of Imes: background fluo- 6).Aproblemoccursbecauseconsiderablymorethanthree
d
BiophysicalJournal78(5)2641–2654
2650 Rohrbach
FIGURE 6 Decayoffluorescenceintensitieswithin-
creasing center distance of a point source (——), a
200-nmsphere(zzzzz),anda400-nmsphere(–––).All
curvesarenormalizedto1atz5100nm.Thelower
curvesbelongtotheshortpenetrationdepthofd570
nmandtheuppercurvestothelargepenetrationdepth
of170nm.
measurements must be made to determine a, R, and c if bleachingcorrectionofthedye(acridineorange).Eachspot
dImes . 0; but vesicles move (and bleach) during the ac- intensity was divided by I(10) with d 5 100 nm according
quisitionofaseriesofmeasurementsImes.Anotherproblem toEquation9,thenplottedasshowninFig.8.Theerrorbars
n
is the blurred images of dense granules in cells due to resultfromanassumed10%errorinpenetrationdepthdand
diffraction. Integrating the intensity spots over the whole fromthemeasuredsurfaceintensityI (x,y).Threedifferent
0
spotareaofonegranuleishardlypossible.Insteadoftrying curves with different gradients represent three different
to determine the spot area intensity, we thus take the peak granule radii. In our example of Fig. 8, x2 minimization
intensityI ,whichiseasytomeasure.Inthiscasewehave leads to diameters 2R 5 70 nm, 240 nm, and 300 nm with
A
toacceptamaximumerrorDI (describedinthepreceding a small x2 or E(R). These granule sizes cannot be deter-
A
section). mined or resolved with a traditional optical microscope.
To minimize the possible movement of granules during
measurements, we performed an experiment with just two
DISCUSSION
pictures,I andI ,ofgranules(withtwopenetrationdepths
1 2
d andd ,d ).Bycalculatingthequotient,itispossibleto The purpose of this study was to develop a technique to
1 2 1
eliminate the unknown fluorophore concentration c (see rapidlyvarythepenetrationdepthsofevanescentwavesand
Theory section). The result is shown in Fig. 7 as a pseu-
do-3D plot, where the center distances of 131 secretory
granulesareplottedinacircularregion12mmindiameter.
We estimate a relative error of up to 50%.
Determining diameters of isolated granules
It is possible to optically determine isolated granule diam-
eters by deconvolving the spots from the PSF of the objec-
tive.Withthewater-immersionlong-distanceobjectivewith
NA51.2,itispossibletodistinguishspotdiametersdown
to 300 nm (FWHM), which corresponds to granule diame-
ters of the same size.
To record a Laplace transform and to reconstruct diam-
eters of isolated vesicles, we did the following experiment: FIGURE 7 Pseudo-3D plot of 131 reconstructed center distances of
wetook20exposuresI(1)toI(20)withdifferentpenetration granulestothecoverslipinalivechromaffincellbeforestimulation.The
minimum possible center distance of granules, i.e., when they touch the
depthsofisolatedgranulesfromaburstcell,wherethefirst
surface,istheassumedmeanradiusR5180nm,andthefurthestcenter
penetration depth was equal to the last. With I(20) 5 distanceisaboutd 1R’400nm.Theinvestigatedcircularregioninthe
I(1) z e2az19 or a5 19 z ln[I(1)/I(20)], we carried out a lateraldomainhas12adiameterof12mm.
BiophysicalJournal78(5)2641–2654