110 Quantitating Fluorescence Intensity From Fluorophore ... · of fluorescein labeled microspheres and Ceq is the molar concentration of soluble fluorescein which gives the same

1. Introduction

RM 8640 consists of six plastic bottles each contain-ing a 2 mL suspension of polymethyl methacrylate(PMMA) microspheres with a specified amount ofimmobilized fluorescein isothiocyanate (FITC). Themicrospheres are intended for calibrating the fluores-cence response of flow cytometers [1]. This paperdescribes the procedures used for assigning values ofMESF (molecules of equivalent soluble fluorophore) to

the microspheres with immobilized FITC. There arethree major measurements in this procedure. First, theconcentration of microspheres is measured using aMultisizer 3 (Coulter Corporation, Miami FL) particlecounter1. Second, a fluorometer is calibrated using

Volume 110, Number 2, March-April 2005Journal of Research of the National Institute of Standards and Technology

101

[J. Res. Natl. Inst. Stand. Technol. 110, 101-114 (2005)]

Quantitating Fluorescence Intensity FromFluorophore: Assignment of MESF Values

Volume 110 Number 2 March-April 2005

A. K. Gaigalas and Lili Wang

National Institute of Standards andTechnology,Gaithersburg, MD 20899-8312

Abe Schwartz

Center for Quantitative CytometryPO Box 19344,San Juan, PR 00919

Gerald E. Marti

Center for Biologics Evaluation andResearch, FDABethesda, MD 20892

and

Robert F. Vogt, Jr.

Division of Laboratory Sciences,CDCAtlanta, GA 30341

[email protected]

A procedure is presented to convert thecomparison of measured fluorescence sig-nals into a comparison of fluorescenceyields (FY). The fluorescence yield, whichis a property of a solution or a suspension,is defined as the product of the fluo-rophore concentration and the molecularquantum yield. The paper revises themeasurement model which relates themeasured fluorescence signal to the FY.The equality of FY of two solutions pro-vides an equivalence between the concen-trations of fluorophore in the two solu-tions. The equivalence is the basis forquantitation in terms of molecules ofequivalent soluble fluorophore (MESF).The quantitation procedure starts with themeasurement of fluorescence signals froma serial dilution of fluorescein solutions toobtain a calibration of a fluorometer. Thefluorometer is used to measure the fluores-cence signal of a suspension of micros-pheres with immobilized fluorescein isoth-

iocyanate (FITC). The calibration is usedto obtain the concentration of soluble fluo-rophores which gives the same fluores-cence signal as the microsphere suspen-sion. The number concentration of micros-pheres is measured and the equality of flu-orescence yields is used to obtain the num-ber of soluble fluorescein moleculesequivalent to a single microsphere.

Key words: cytometry; FITC; fluores-cein; fluorescence yield; MESF; micros-pheres.

Accepted: January 31, 2005

Available online: http://www.nist.gov/jres

1 Certain commercial equipment, instruments, or materials are iden-tified in this paper to foster understanding. Such identification doesnot imply recommendation or endorsement by NIST, nor does itimply that the materials or equipment identified are necessarily thebest available for the purpose.

SRM 1932, a fluorescein solution. Third, the fluores-cence signal is measured for each of the microspheresuspensions. Finally, the data from the three measure-ments are used to calculate the MESF values of themicrospheres.

In practice, we made serial dilutions of SRM 1932and calibrated the fluorometer response as a function offluorescein concentration. Since the concentration offluorescein varies from 10–12 mol/L to 10–9 mol/L, itwas necessary to pay special attention to contamina-tion, linearity, photodegradation, and background sub-traction. The measurements of the concentration of themicrosphere suspension constitutes the operational def-inition of particle concentration. There are at present noparticle number standards to validate the concentrationmeasurement.

A cytometer was used to measure the fluorescencesignals associated with the five microsphere popula-tions each with a different amount of immobilizedFITC. A valid assignment of MESF values should yielda linear relation between the measured fluorescencesignal in the cytometer and the assigned MESF values.A linearization procedure was used to impose a linearrelation between the cytometer response of the fivemicrosphere populations and their MESF values.

2. Revised Measurement Model and theAssignment of MESF

It was pointed out [2] that the quantum yield asdefined in Eqs. (A3) and (A14) in Ref. [3] is the ratioof fluorescent radiant flux to absorbed radiant flux.Since the radiant flux is the product of the number fluxand average spectral energy, the ratio of radiant fluxesis not the same as the ratio of number fluxes. In the fol-lowing we introduce a modification to the measurementmodel which allows a consistent use of quantum yield,a molecular property defined in terms of number flux.

In the previous paper [3] we expressed the fluores-cence spectral radiance, Lf(λm,λx), as

(1)

λm and λx are the emission and excitation wavelengths,Sf, S ′, are measured signals, L ′ is the spectral radianceof a reference source, F, l, Φi(λx), and ∆λx are instru-ment characteristics, and N, y, and ε are sample proper-ties. The quantity y(λm, λx) relates the absorbed radiantflux at wavelength λx to the fluorescent radiant flux at

wavelength λm. In other words, the radiant flux fromfluorescence is a fraction y of the absorbed radiant flux.The radiant flux can be converted to a photon numberflux by dividing the radiant flux by the energy of a sin-gle photon. Thus the quantity y(λm, λx) can be convert-ed into a relation between fluorescence photon numberflux and absorbed photon number flux by multiplying itby the ratio of the respective wavelengths.

(2)

The quantity y′(λm, λx) is conveniently separated into aquantum yield φ and a normalized relative photonemission function s′(λm, λx) (1/nm), where

(3)

Thus Eq. (1) can be rewritten as

(4)

Integrating over all emission wavelengths gives

(5)

The change in the measurement model amounts to amodification of the spectral correction function givenby the term in brackets on the left side of Eq. (5). Eq.(5) supplants a similar equation in Ref. [3]. The leftside of Eq. (5) is found experimentally by performingthe specified operation on the measured fluorescenceemission spectrum. The reference source used to cali-brate the detector wavelength response was unpolar-ized. In order to minimize the effects due to polariza-tion of the fluorescence emission, the incident laserbeam polarization was confined to the plane defined bythe incident and detected light beams. We made no esti-mate of possible artifacts due to polarization differ-ences.

Suppose that the operation in Eq. (5) is performed onthe emission spectrum from a reference solution withknown concentration of fluorophore and the emissionspectrum from a suspension of microspheres withimmobilized FITC. Furthermore, the number concen-tration of microspheres is known. In the case that thetwo numbers on the left of Eq. (5) are equal, the corre-sponding solution and suspension properties on theright side of Eq. (5) are also equal.


102

f mf m x m

m

m x x i x x

( )( , ) ( )

( )2.3 ( , ) ( ) ( )

SL LS

F Nl y

λλ λ λλ

λ λ ε λ Φ λ λ

′=′

= ∆

mm x m x

x

( , ) ( , ).y yλλ λ λ λλ

′ =

m x m( , )d 1.s λ λ λ′ =∫

f m mm

m x

m x x i x x

( )( )

( )2.3 ( , ) ( ) ( ) .

S LS

F Nl s

λ λ λλ λ

φ λ λ ε λ Φ λ λ

′′

′= ∆

m mf m m x 0

x m

( )( ) d ( ) .

( )LS N IS

λ λλ λ φε λλ λ

′ = Ω ′

∫

(6)

The subscripts “sol” and “sus” in Eq. (6) refer to solu-tion and suspension, respectively. We assume that theexperimental conditions used for the measurements onsolution and suspension are the same and that the solu-tion and suspension have equal indexes of refraction. Inthat case, I0 and Ω are the same on both sides of Eq. (6)and can be factored out.

(7)

It is known from measurements that there are shifts inthe wavelength of maximum absorption. It is likely thatthe absolute value of the extinction coefficient is alsodifferent. The extinction coefficient of fluorophoreimmobilized on a microsphere has not been measureddue to predominance of scattering. However, we makethe major assumption that the molar extinction coeffi-cient is the same for fluorophore in solution and immo-bilized on the microsphere. Thus, Eq. (7) reduces to anequality of fluorescence yields.

(8)

Based on Eq. (8) Nsol is equivalent to Nsus. The calcula-tion used to assign molecules of equivalent soluble flu-orophore (MESF) values to the microspheres is givenby

(9)

where Nsus = Nsphere (mL–1) is the number concentrationof fluorescein labeled microspheres and Ceq is the molarconcentration of soluble fluorescein which gives thesame value for the left side of Eq. (5) as the suspensionof microspheres. Avogadro’s constant, NA (6.022 ×1023), in Eq. (9) is a conversion factor between molarand number concentrations. The equivalent concentra-tion of soluble fluorescein is determined using the flu-orescein calibration curve

(10)

where “intercept” and “slope” are the linear fit param-eters describing the relationship between the logarithmof the observed fluorescence signal and the logarithmof the concentration of fluorescein. FS is the fluores-cence signal of the microsphere suspension evaluatedaccording to the left side of Eq. (5). The value FS has

to be adjusted for possible differences in illuminationintensity between the calibration measurements and themicrosphere measurements. The ratio of the average ofthe power readings taken during the calibration andmicrosphere measurements is set equal to the adjust-ment factor, Padj, which multiplies FS in Eq. (10). Thepower readings varied by less than 1 % during the cal-ibration or the microsphere measurements. However,since the two measurements were taken on differentdays, the difference in average power could be as highas several percent. Eq. (9) and Eq. (10) constitute theoperational definition of the MESF assignment.

In the following we describe the procedure used forobtaining the five factors needed in Eq. (9) and Eq.(10). As an example, the value of MESF is obtained forone specific suspension of microspheres.

3. Calibration of the Fluorometer

Figure 1 shows a schematic of the fluorometer usedin the MESF assignments. A water-cooled argon ionlaser (Lexel model 95) was the source of 488 nm light.A glass slide reflected a portion of the output beam anddirected it towards a photo diode (Newport 818 UV)whose output was processed by a power meter(Newport 1815-C). The accuracy of the power readingwas about 2 % (product specifications). The output ofthe power meter was monitored as an index of relativeillumination power which was used to determine thefactor Padj in Eq. (10). The laser beam, transmittedthrough the glass slide, passed a neutral density (ND)filter wheel which contained ND filters of nominaloptical density (OD) values 0, 1, 2, and 3. The beampassed through a laser line filter to eliminate plasmalines from the laser and then was directed via two mir-rors to the entrance aperture of a 10× microscope objec-tive. The two reflections changed the vertical polariza-tion into horizontal. The objective lens focused thelaser beam on a square capillary flow cell(WWP100375 from Polymicro Technologies) with ainner dimension of 100 µm. The portion of the capillarythat was illuminated by the laser was stripped of thepolyimide coating which normally surrounds the glasscapillary. The capillary flow cell was mounted on arotary stage which in turn was mounted on a X-Y trans-lation stage. The rotary stage was used to position thecapillary so that the incident beam was perpendicular toone of the sides. The X-Y stage was used to position thecapillary at the position of the monochromator entranceslit image.


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sol sol sol x 0 sus sus sus x 0( ) ( ) .N I N Iφ ε λ φ ε λΩ = Ω

sol sol sol x sus sus sus x( ) ( ).N Nφ ε λ φ ε λ=

sol sol sus sus .N Nφ φ=

eqA

spheres1000CNMESF

N=

intercept slopeeq adj10 ( )C FS P−= ×

The Model 270M monochromator, made by JYHoriba, was equipped with a CCD-3000 DetectorSystem. The CCD chip used in the measurements wasback illuminated with a minimum quantum efficiencyof 65 % at 550 nm. The operational temperature of thechip was 213 K with a dark current less than 4 e– pixel–1

min–1. The pixel layout was 1024 by 256, and thedynamic range of the 16 bit analog to digital converterwas 65535 digital number (DN). The measurementswere performed by binning the 256 pixels in the shortdirection of the CCD chip. The entrance slit of themonochromator was equipped with a mechanical shut-ter, the single axial Model 227MCD (JY Horiba).Appendix A describes the procedures used to validatethe performance of the fluorometer [4].

3.1 Calibration of the Fluorometer With SRM1932

SRM 1932 certifies the concentration of fluoresceinas (60.97 ± 0.88) µmol/kg. Given the density of theSRM buffer as 1.003 g/mL, the molar concentration ofthe SRM 1932 is (61.15 ± 0.88) µmol/L. This value ofthe concentration was used as the initial concentration.Serial dilutions were made by combining previouslymade solution with additional buffer. All solutions wereprepared gravimetrically using a calibrated balance(Sartorius 2024MP) with a resolution of 0.01 mg. Theerrors were obtained from the standard deviation offour weighins. The standard error in the fluorescein

concentrations was about 1.6 % and originated mostlyfrom the initial error in the SRM concentration. Theweighin errors contributed a minimal error to the finalfluorescein concentrations.

3.2 Measurement of the Fluorescence Signal

The fluorescein solution was pumped with a peri-staltic pump through a capillary flow cell [5]. The 10×objective and the capillary were mounted on appropri-ate mounts to provide the necessary adjustment. A goodadjustment was indicated by the appearance of a cleancircular beam cross section after the transit through thecapillary. Poor adjustment was characterized by com-plex interference bands from light reflected by varioussurfaces of the capillary. The capillary tube (length =0.7 m) was coupled to a plastic tube (length = 20 cm)via a stainless steel pressure “Swagelok” coupling. Theplastic tube was inserted into the pumping mechanismof a peristaltic pump (PP). A centrifuge vial (1.5 mLcapacity) contained the test solution and a small mag-netic stirring bar. The ends of the capillary or the plas-tic tube were inserted in the solution and the pumpdirection set appropriately to pump the solution to thewaste container. Neither the capillary nor the plastictube touched the waste solution. Formation and detach-ment of small droplets above the waste container wasan indicator of flow.

The spectrum was accumulated over a period of 40 sleading to appearance of sharp spikes in the CCD


104

Fig. 1. A schematic diagram of the fluorometer used for the assignment of MESFvalues to microspheres, with immobilized fluorescein isothiocyanate, in suspen-sion. The instrument is a modified Raman spectrometer. A square capillary flowcell with 100 µm inside dimension contained the flowing sample. Not shown is aperistaltic pump which pumped the sample from a 1.5 mL vial.

response. The spikes are pixels with unusually largecharge content, the spikes are confined to one or twoadjacent pixels. We removed the spikes by simplyreplacing the contents of the pixel containing a spike(attributed to cosmic ray events hitting a pixel in theCCD array) by an average of the contents of two near-by pixels. The necessary overall dynamic range wasobtained by varying the integration time from 0.5 s to40 s, and by the dynamic range of the CCD itself (about60). The ND filter was not used to modify the illumina-tion intensity.

The peristaltic pump produced a pulsating flow witha time period of approximately 1.6 s. The strong illumi-nation caused substantial photodegradation of the fluo-rescein solution in the capillary. The photodegradationand the pulsating flow produced a time variation in thefluorescence signal. This variation was averaged ade-quately during integration times longer then 5 s.However, for shorter integration times we had to takemultiple measurements and average the resulting fluo-rescence signals. The pulsating fluorescence intensityenlarged the measurement errors for the concentratedfluorescein solutions. We avoided changing the intensi-ty of the illuminating beam since that would change thephotodegradation rate for measurements performed onsolutions with different fluorescein concentrations. Theassumption is made that the photodegradation is thesame for solution and fluorescein immobilized onmicrospheres. To minimize possible systematic errorsdue to photodegradation, the flow conditions for thecalibration and microsphere measurements were madeas similar as possible. The polarization anisotropy forfluorescein solutions was approximately zero.Therefore, the measured spectra are characteristic of asolution of random emitters and systematic effects dueto polarization are small.

3.3 Background Subtraction

Figure 2a shows the measured spectra of a purephosphate buffer (solid circles) and a fluorescein solu-tion with a concentration of approximately 16 pM(open circles) in phosphate buffer. The laser line filtershown in Fig. 1 was a critical component in the fluo-rometer since without it the spectra in Fig. 2a would bean order of magnitude higher and dominated by laserplasma lines. The spectra in Fig. 2a have DN valueslarger than 2000, suggesting that CCD linearity correc-tion was not significant. Figure 2b shows the spectrumwhen the buffer response is subtracted from the fluores-cein solution response. As expected, the emission spec-trum peaks at approximately 510 nm. The integration of

the spectrum was performed by summing the DN val-ues of the subtracted spectrum in Fig. 2b. The resultingtruncation errors for wavelengths less than 595 nm andwavelengths greater than 620 nm were not evaluated.We estimate that these truncations lead to a systematicbias of less than –1 %. Similar spectra were collectedfor solutions with higher values of fluorescein concen-tration and the integration time was lowered as requiredto insure that the resulting CCD response was not satu-rated. The subtracted spectrum was corrected for thespectral response of the detector as described inAppendix A. The corrected integration times were usedto normalize all integrated fluorescence signals (FS) tothe fluorescence signal (FS) at an integration time of1 s.


105

Fig. 2. (a) The top trace is the recorded fluorescence spectrum froma solution with a fluorescein concentration of 16 pmol/L. The bottomtrace is the spectrum from a pure buffer. The dominant features inboth traces are the water Raman line at 585 nm and Raman lines fromthe capillary walls. Both traces were taken with a 40 s integrationtime. Spikes were eliminated by replacing the contents of a pixelwith a spike by the average of the contents of several adjacent pixels.(b) The fluorescence from fluorescein determined by subtracting thebottom trace from the upper trace in (a). The quality of the subtrac-tion is judged by the amount of residual Raman line. The integratedfluorescence signal (FS) was found by summing the subtracted trace.The sum is a good approximation of the integral over all wave-lengths.

Figure 3 shows a log-log plot of the integrated DNvalues on the horizontal axis and five different concen-trations of fluorescein plotted on the vertical axis. Thebest linear fit to the data in Fig. 3 is

log(concentration) = – 15.20 + 0.957 × log(FS) (11)

The errors of the fit parameters were 0.09 and 0.009 forthe intercept and slope, respectively. The errors wereobtained from a linear regression procedure inMathcad. The lowest point (for a concentration ofapproximately 7 pmol/L) was systematically lowerthan expected from the linear trend set by the higherpoints. We rationalize this as an effect of adsorption offluorescein on the capillary walls [4]. A calibration wasaccepted if the slope of the best fit fell between 0.95and 1.05. A perfectly linear relation has a slope of 1.0,however a deviation of ± 0.05 was accepted. The valuesof “intercept” and “slope” are used in Eq. (10).

4. Measurement of Fluorescence FromMicrospheres With Immobilized FITC

The measurements of fluorescence signal were car-ried out in the identical apparatus as the calibrationwith serially diluted fluorescein solutions. Since themicrosphere measurements were carried out after thefluorescein solution, great care was needed to eliminatepossible contamination. Prior to the microsphere meas-urements, the capillary flow cell was washed for sever-al hours. The washing was performed by pumping

buffer through the capillary in alternating directions.The switch in pumping direction was important to clearpossible dead spaces in the connection between thecapillary tube and the plastic tube. As a rule of thumb,the cleaning was sufficiently good when the CCD sig-nal was about 370 DN at 510 nm with an integrationtime of 10 s, and a power indicator of about 20. Thisnumber was obtained through experience. During allmeasurements the following pumping sequence wasfollowed: first the suspension was pumped through theplastic tube into the capillary (this direction filled thecapillary quickly); second the suspension was pumpedthrough the capillary into the tube and fluorescencespectra were accumulated. Normal flow was indicatedby the presence of a scattering diffraction pattern in thetransmitted light. The pattern indicated the presence ofspheres in the capillary as well as proper alignment.The intensity of the diffraction pattern fluctuated asexpected since the number of microspheres in the sens-ing volume was of the order of twenty. On occasion,small bubbles passed through the illuminated region inthe capillary. The passage of a bubble was obviousfrom the distortion of the transmitted laser beam.Clogging was obvious because flow stopped and thefluorescence signal decreased.

4.1 Fluorescence Measurement

Figure 4a shows the spectrum measured for a sus-pension of microspheres (Suspension #1, open circles)and a suspension of blank microspheres (solid circles).The suspensions were identical to those used in themicrosphere concentration measurements. The meas-urements in Fig. 4a were performed with integratingtime of 40 s, and power indicator displaying 19.2.Figure 4b shows the difference spectrum. The locationof maximum emission shifts to the red, and the spec-trum is broader. Both facts are typical of emission fromimmobilized FITC and serve as additional indicatorsthat the flow cell is clean and free of fluorescein insolution. The quality of background subtraction wasgauged by the disappearance of the water Raman linecentered at 585 nm. In further analysis, the spectra inFig. 4a were corrected for CCD non linearity (≈0.8 %effect) and normalized to an integration time of 1 s. Thespectrum was summed and the errors of the summedspectrum were estimated from multiple measurements.Spectral response corrections were made on the data inFig. 4 (≈3 % effect). The resultant summed spectrumfor Suspension #1 was (11220 ± 600) DN. The value ofthe summed spectrum was substituted for FS in Eq.(10). Taking the ratio of average power levels during


106

Fig. 3. The plot of the log of the concentration of a fluorescein solu-tion versus the log of the integrated fluorescence signal (FS) associ-ated with the known concentration. The ideally linear response has aslope of 1.0. The linear relation between the logs of the two quanti-ties constitutes a calibration of the fluorometer.

calibration and microsphere fluorescence measure-ments gave Padj = 0.92 ± 0.02.

5. Measurement of MicrosphereConcentration

The microsphere concentration was measured usinga Coulter Multisizer 3 particle counter. The instrumentdetects small changes in conductivity between tworeservoirs separated by a narrow orifice of diameter100 µm. Whenever a particle passes through the orificefrom one reservoir to the other, a transient change inconductivity is detected and recorded as a particle. In

practice, the reservoir outside the orifice is the testreservoir into which samples are placed. A volumetricsyringe withdraws fluid from the test reservoir throughthe orifice and the concentration is determined as theparticle counts divided by the preset volume of fluidwithdrawn. The fluid that was placed into the test reser-voir was obtained from the original fluid by diluting theoriginal fluid about 500 times using Isotone fluid.Isotone is a proprietary fluid which has optimal proper-ties for the performance of the Multisizer 3. The com-position of Isotone is sufficiently close to that of phos-phate buffer saline (PBS) so that microsphere suspen-sion stability is not degraded. The concentration of theparticles in the original fluid is found by multiplyingthe measured concentration by the reciprocal of thedilution.

5.1 Determination of the Dilution Factor of theTest Suspension

The microspheres were obtained from BangsLaboratories as a special order and were delivered in 5mL opaque plastic bottles. The nominal solids massfraction was about 2 %. The microspheres, as shipped,were suspended in a solvent optimized for enhancingthe stability of the suspension. For the purpose of meas-uring the fluorescence signal of the microspheres, itwas necessary to re-suspend the microspheres in pH =7.2 PBS. The first step was to take about 1 ml of themicrosphere suspension directly from the plastic bottleand centrifuge it (Marathon 13K centrifuge from FisherScientific at 2000 rpm). The pellet of microspheres wasthen re-suspended in 1 ml of PBS, pH 7.2, containing≈0.1 mg SDS. An additional advantage of bufferexchange is that possible soluble fluorescent impuritiesin the bottle are minimized. The mass of about 200 µgof the resulting suspension was placed into a containerwith a mass of Isotone equivalent to about 100 ml ofIsotone. The mass of the buffer was determined using abalance, OHaus ED4130, while the suspension wastransferred using calibrated 100 µL or 200 µL pipettesand the mass approximated as 0.1996 g using theknown density of water. A gravimetric check of theamount of solution delivered by the 100 µL pipettegave (0.10016 ± 0.0006) g using water at 23 °C and aSartorius 2024 MP balance. The error in the reciprocalof the dilution factor was estimated to be less than 1 %.The remaining suspension was used for fluorescencemeasurements as described above.


107

Fig. 4. (a) The top trace is the recorded fluorescence spectrum froma suspension of microspheres with immobilized FITC. These are themicrospheres with the smallest amount of FITC. The bottom trace isthe spectrum from a suspension of microspheres with no FITC,“blank” microspheres. The dominant features in both traces are thewater Raman line at 585 nm and Raman lines from the capillarywalls. Both traces were taken with a 40 s integration time. Spikeswere eliminated by replacing the contents of a pixel with a spike bythe average of the contents of several adjacent pixels. (b) The fluo-rescence spectrum from microspheres determined by subtracting thebottom trace from the upper trace in (a). The integrated fluorescencesignal (FS) was found by summing the subtracted trace.

5.2 Concentration Measurement

Prior to each series of measurements the operation ofthe Multisizer 3 was verified by running a suspensionof calibration microspheres. The quality of the meas-urement was evaluated by measuring the mean diame-ter of the microspheres, and the coefficient of variation(CV) of the diameter values. The diluted microspheresuspension was placed in the Multisizer 3 and stirred atan indicated rate of 13 rpm. An image of the orifice wasalways examined to verify that the orifice was freefrom debris. The instrument analytical volume was setto 500 µL or 1 ml and a dilution factor (as determinedabove) was entered as a parameter in the acquisitionsoftware. Figure 5 shows a typical result of a singleMultisizer 3 measurement. The horizontal axis givesthe inferred particle diameter, and the vertical axisgives the number of times a particle with this diameterpassed through the orifice. Using the dilution factor, thevertical axis can be converted into concentration. Theinferred concentration of Suspension 1 was (1.427 ±0.016) × 106 mL–1 for all particles with diametersbetween 6.3 µm and 8.1 µm. The peak to the right ofthe main peak corresponds to “doublets”. These areevents associated with the passage of two particles. Theconcentration of “doublets” (diameters between 8.3 µmand 9.7 µm) was calculated to be (0.077 ± 0.002) × 106

mL–1. Since the concentration of particles in the testsolution is small, it is likely that the “doublets” corre-spond to permanent associations of two microspheres.

For permanent associations, the radii of doublets andtriplets are related to the particle radius by rdoublet =21/3rsphere and rtriplets = 31/3rsphere respectively. These rela-tions are consistent with the observed size distributionsof singlets, doublets, and triplets. This measurement ofparticle associations is relevant to the proper interpreta-tion of the fluorescence signal as discussed below. Theconcentration measurement was repeated five timesand the error associated with each concentration wasfound by dividing the standard deviation by the squareroot of 5, the number of trials. It should be noted thatthe error in the concentration is about 5 % implyingthat the error due to the uncertainty of the dilution fac-tor (about 1 %) is negligible. The error of the concen-tration measurement is due mainly to the statistics ofthe particles entering the orifice. Whenever possible,the errors in the concentration measurement were min-imized by using more concentrated test suspensionsand larger sampling volumes.

5.3 Correction for Microsphere Doublets

Both the Multisizer 3 and the cytometer measure-ments show the presence of microsphere doublets- per-manent associations of two microspheres. Some aggre-gation of colloidal particles is expected and the amountdepends on previous treatments (e.g., sonication, age,and solvent). The concentration measurements wereperformed with the same suspension as the fluores-cence measurements. Furthermore the two measure-ments were performed on the same day. The simplestassumptions are that the Multisizer 3 gives the correctconcentration of doublets in the suspension used forfluorescence measurements and that the fluorescenceintensity from doublets is twice the fluorescence inten-sity from single microspheres. Therefore, in comparingthe fluorescence yield of a suspension and solution wemultiply the doublet concentration by a factor of tworelative to the singlet concentration.

NTotal = NSingle + 2 NDouble. (12)

Where NSingle is the number concentration of singlemicrospheres, NDouble is the number concentration ofdouble microspheres, and NTotal is the total concentra-tion which should be used in comparing fluorescenceyields in Eq. (9). The assumption that the fluorescenceintensity from a double microsphere is twice the fluo-rescence from a single microsphere is qualified by suchconsideration as distortion of the illuminating lightand changes in quantum yield at point of contactbetween the microspheres. The measured polarization


108

Fig. 5. The frequency distribution of microspheres of specific size asdetermined by the Coulter Multisizer 3. The data was taken for a 500µL sample of diluted suspension of the microspheres. Using theknown dilution factor and the number of particles of the appropriatesize, a concentration of microspheres was determined. The peak tothe right of the major peak corresponds to microsphere “doublets”which are permanent associations of two microspheres. The concen-tration of “doublets” was also determined.

anisotropy in microsphere suspensions was about 0.08.This small value was rationalized by the large tetherlength of the chain of seven carbon atoms that immobi-lized the FITC to the microsphere surface. A long teth-er permits considerable rotational freedom. The sys-tematic effects due to polarization differences betweensolution and microsphere suspension were neglected.

6. Assignment of MESF Values

The assignment of values of molecules of equivalentsoluble fluorophore (MESF) entails the comparison ofthe fluorescence signal from suspensions of micros-pheres with immobilized fluorophore and solutions offluorophore [3]. The comparison requires the integra-tion of the emitted fluorescence over all wavelengths.The comparison requires a correction for differences inthe molar absorption coefficient of soluble and immo-bilized fluorescein. Fluorescence excitation spectrashow that the absorption spectra of the soluble andimmobilized fluorescein are shifted relative to eachother [3]. The fluorescence excitation spectra allow usto estimate the change in absorbance at 488 nm due tothe shift. However, we were not able to measure theabsolute value of the molar absorption coefficient forthe immobilized fluorescein. This adjustment is left fora future refinement. The values of FS, “intercept”,“slope”, Padj, and Nspheres were used in Eq. (9) and Eq.(10) to calculate a value of MESF of 1667 ± 400. Thesame procedure was carried out for the other suspen-sions. Four independent series of measurements werecarried out and the resulting MESF values averaged togive the final value reported in the Certificate ofInvestigation.

7. Linearization of MESF AssignmentsWith a Cytometer

The objective of this measurement was to demon-strate that the MESF assignments obtained with the flu-orometer were self-consistent. The microspheres werepassed through a cytometer, and the response wasmeasured. Each population of microspheres produced apopulation of fluorescence pulses which are character-ized by a mean pulse area and a standard variation.Since the cytometer response is linear, the mean pulseheight of the five populations of microspheres shouldcorrelate linearly with the assigned values of MESF.The cytometer does not provide a measurement of the

absolute MESF values, however it does place a strin-gent constraint on relative MESF values. The MESFvalues obtained with the fluorometer were modified sothat they correlate linearly with the mean channelmeasured with the cytometer. Appendix B gives detailsof the procedure used for validating the performance ofthe cytometer.

7.1 Microsphere Measurements

Alignment microspheres from Spherotech Corp.were used to align the cytometer laser beam. The align-ment was sufficiently good when the fluorescencepulse mean channel was between 180 000 DN and200 000 DN, and the CV was better than 4 %. After thealignment, the six populations of the microspheres inthe reference material were mixed and pumped throughthe cytometer and the corresponding fluorescence andscattering peaks recorded. The suspensions were pre-pared by putting two drops of the suspension from eachof the six plastic bottles into 1 ml of PBS buffer. Figure6 shows typical results. Note that the single and doublemicrosphere signals are resolved. The dense groupingswith circular bounds correspond to single microspheresignals. Diagonally to the upper right of each densegrouping are less dense groupings (not enclosed byboundaries) corresponding to the passage of doublemicrospheres. The table in Fig. 6 gives the properties ofthe groups of dots enclosed by the circular bounds. TheY geometric mean gives the mean scattering pulseamplitude, while the X geometric mean gives the meanfluorescence pulse height for each population. Asexpected, the scattering is relatively constant for thefive populations, while the fluorescence signal differssubstantially.

Figure 7 shows a plot of the log of the mean fluores-cence channel (X geometric means in Fig. 6) associatedwith each microsphere as a function of the log of theassigned MESF value for each microsphere. Asdescribed above, the MESF assignments were per-formed using the fluorometer. A fit to a straight linegives a slope of 0.984, indicating that there is a smalldeviations from linearity. All points are within twostandard deviations of the best straight line fit. Sincethe cytometer is a linear device, the measured meanchannels should correlate linearly with the MESF val-ues which are proportionate to the number of fluo-rophore on the microsphere and hence to the fluores-cence signal. This fact provides a means to linearize theassigned MESF values.


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7.2 Linearization

The response of the cytometer was shown to be lin-ear over the dynamic range encompassing the responseof the five microsphere populations. Therefore, theMESF values have to correlate linearly with theobserved mean channels in the cytometer measure-

ment. The cytometer measurement provides a relativeordering of the MESF values but gives no measure ofthe absolute values. The procedure that was used toimpose a linear relation on the MESF values deter-mined by fluorometer was as follows. The solid circlesin Fig. 7 show the MESF values obtained in Series 4measurements as a function of mean cytometer chan-


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Fig. 6. Output window from FCS Express V2, a program for the analysis of cytometer data.The upper diagram shows the distribution of side scattering signals (SSC) and fluorescence sig-nals (FL1) from six populations of microspheres containing different amounts of immobilizedFITC. The broad peak closest to the SSC-A axis is the signal from the blank microspheres withno immobilized FITC. The table below the diagram contains the geometric means of the scat-tering signal (Y) and fluorescence signal (X) for each of the five populations defined by the cir-cular regions in the graph above. The row label “1” denotes the population with the highest flu-orescence signal. The row labeled “None” contains the geometric means for the entire data set.Other parameters, such as the width of the distribution, can also be obtained for each popula-tion.

nel. The data in Fig. 7 was fitted with a straight linewhose slope was constrained to 1.027, which character-izes the cytometer linearity. Next, the MESF valuegiven by the straight line was calculated for each meanchannel. This calculated value is the linearized MESFvalue obtained for that series of measurements.

8. Certification of MESF Values

The MESF values were assigned by averaging thevalues obtained in four independent measurementseach consisting of 1) calibration of the fluorometerusing SRM 1932, 2) measurement of the microspherefluorescence intensity, and 3) measurement of themicrosphere concentration. The data in each set of fourmeasurements gave an assignment of MESF values tothe five populations of microspheres. The four differentassignments provide a measure of reproducibility andan estimate of random error. The possible errorobtained from the variation of the four MESF assign-ments was consistent with the error estimate for each ofthe four MESF assignments. The average values arereproduced in the Certificate of Investigation for RM8640. The cytometer measurements were used to lin-earize the MESF values yielding values of linearizedMESF. The four values of linearized MESF were aver-aged to give the average linearized MESF values in theCertificate of Investigation. The certificate includesboth the average MESF values determined by the fluo-rometer, and the average linearized MESF values.

The MESF values were assigned under certainassumptions which are restated below in the order ofdecreasing relevance.

1. The molar extinction coefficient is the same forfluorescein in solution and fluorescein immobi-lized on the microspheres. It is known that thereare differences in the wavelength of maximumabsorption between fluorescein in solution and onthe surface of the microsphere. It is expected thatthe magnitude at maximum absorption will alsobe different, however these have not been meas-ured yet. The difference in molar extinction coef-ficient can be taken into account as soon as thevalues become available. The equality of fluores-cence yield would imply that Nsus microspheresare equivalent to a concentration of soluble fluo-rophore given by Nsol[εsol(λx)/εsus(λx)].

2. Photodegradation of fluorescein is the same insolution and at the surface of the microsphere.Systematic measurements of photodegradation inthe two environments are not available.Differences in photodegradation rate would leadto systematic differences in the fluorescence sig-nal between calibration measurements andmicrosphere measurements.

3. Residual polarization of fluorescence emission isthe same for fluorescein in solution and at the sur-face of the microsphere. The measured polariza-tion anisotropies are slightly different for fluores-cein in solution and on the surface of a micros-phere. Sensitivity of detectors to polarizationwould lead to small systematic differences in flu-orescence signal between fluorescein in solutionand on the surface of microspheres.

4. Adsorption on capillary flow cell walls is thesame. If the adsorption (and holdup in deadspaces) of fluorescein in solution and fluoresceinon microspheres is not the same, then there willbe systematic differences in the fluorescence sig-nal at low and high concentrations.

5. Illumination of FITC immobilized on micros-pheres is the same as the illumination of fluores-cein in homogeneous solution.

9. Conclusions

A method was described for comparing the fluores-cence yields of a solution of fluorescein and a suspen-sion of microspheres with immobilized fluoresceinisothiocyanate (FITC). The equality of fluorescenceyields leads to an assignment of molecules of equiva-


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Fig. 7. The plot of the log of the MESF value assigned to a givenmicrosphere population versus the log of the mean channel deter-mined by the cytometer (X in the Table in Fig. 6). The cytometermeasurements provide a relative relation between the MESF values.The MESF values determined by the fluorometer were modifiedslightly to conform to the linear relation as given by the cytometermeasurements.

lent soluble fluorophore (MESF) to a microsphere withimmobilized FITC. The MESF values may be theappropriate units for comparing fluorescence measure-ments. There is a need to investigate the validity ofsome of the assumptions that were made in carrying outthe MESF assignment as described above.

Acknowledgment

The authors are indebted to Dr. John Lu for assis-tance in the statistical analysis of data. We are indebtedto Dr. Gary Kramer for the use of a reference lightsource.

10. Appendix A. FluorometerCharacterization

10.1 Wavelength Calibration

The wavelength calibration was performed usingmercury lamp lines, and a neon lamp (Oriel 6032). Theparameters in the data acquisition software were adjust-ed so that over the wavelength range 480 nm to 700 nm,the deviation between the true and measured wave-lengths was less than 1 nm.

10.2 CCD Linearity

The output of a light emitting diode (LED) waspassed through a variable ND filter and focused on theend of a bifurcated optical fiber. One of the arms of theoptical fiber was placed at the location of the sample inthe monochromator setup (see Fig. 1), and the otherarm was placed in front of a photo diode (PD). Siliconphotodiodes are known to be linear within 0.1 % up toa photocurrent of 200 µA [6]. The LED spectrum wasrecorded by the CCD for an integration time of 0.2 s.The spectrum was taken with automatic subtraction ofthe dark current. The CCD response was characterizedby finding the average value of DN in a narrow range(518 nm to 522 nm) of wavelengths around the maxi-mum response. The integrated CCD response was com-pared to the photo diode reading.

We examined the dependence of the average signalin DN as a function of the PD response. There was asubstantial deviation from linearity at low values ofDN. The most likely source of this deviation is trappingof electrons during the readout process [7]. Duringreadout, the electrons are switched sequentially frompixel to pixel. The trapping centers prevent some of theelectrons from reaching the final register pixel. Since

the number of trapping sites is fixed, the relative impor-tance of these sites increases with decreasing number oftotal electrons. The measured deviations provide a fac-tor which can be used to linearize the CCD response.Thus the linearized DN value is given by

(DN)linear = (DN)measured(1 + f)

f = 10[0.6418–0.7181´log(DNmeasured)] (1)

where (DN)measured is the DN value that is read out dur-ing a measurement and (DN)linear is the linearized valueof the CCD response which is used in further dataanalysis. The factor f was obtained from the fit of thedeviation of the measured CCD data from the linear PDresponse. We did not assign an error to the correction.The correction was applied to background measure-ments and sample measurements prior to subtraction ofbackground. The correction is negligible for DN valuesabove 600.

10.3 Integration Time Linearity

The CCD accumulates electrons for a preset integra-tion time that is determined by a mechanical shutterlocated after the entrance slit of the monochromator. Tomeasure the correspondence between the integrationtime setting in the software and the actual time, we illu-minated the monochromator entrance slit with a con-stant light source and measured the CCD response fordifferent indicated integration times tindicated. The refer-ence light source (see Sec. 10.4) was used as the con-stant light source. The CCD response was integratedfrom 540 nm to 560 nm. The ratio of the CCD responsedivided by indicated time tindicated relative to the CCDresponse for 1 s of indicated integration time showed abias in the indicated time setting. At indicated timeslonger than 1 s, the actual integration time is shorterthan the indicted time. The difference between the actu-al integration time, tactual, and the indicated integrationtime, t

indicated, was corrected by multiplying the indicated

time by the correction factor 1.00102-0.000782 ×tindicated.

10.4 Spectral Response

The reference lamp’s output was calibrated at NISTover the range of wavelengths 340 nm to 800 nm insteps of 20 nm. The output port of the calibrated lampwas placed at the location of the sample in the fluorom-eter. The variable iris of the calibrated lamp was set sothat the CCD response was between 10 000 DN and


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40 000 DN. The CCD linearity is excellent in thisregion.

We formed the ratio of calibrated output of the refer-ence lamp to the output at 520 nm (normalized refer-ence output) and compared it to the ratio of measuredCCD response of the reference lamp to the CCDresponse at 520 nm (normalized CCD response). Thesharp decline in the response at shorter wavelengthswas due to the holographic filter which was used toreject the 488 nm excitation light. The spectral correc-tion factor was obtained by dividing the normalized ref-erence output by the normalized CCD response to thereference lamp. Multiplying the measured CCDresponse by the correction factor corrects for the vari-ability of the detector response over the wavelengthrange.

11. Appendix B. CytometerCharacterization

The cytometer was constructed to be as simple aspossible with all physical processes open to inspection.An air-cooled Argon ion laser (Omnichrome Model150) provided the source of 488 nm illumination. Thelaser beam was focused by a spherical lens with a focallength of 50 mm. The focal point was located in theflow channel of a cytometer flow cell provided byBecton Dickinson Biosciences. The sample waspumped by a syringe pump (Yale Apparatus Model YA-12), and the sheath fluid was pumped by the pressure inthe container vessel. A flow meter (Aalberg ModelTMR1-010426) in the sheath flow line gave an indica-tion of the flow rate (usually set to 90 scale units). Thelaser beam passed through a glass plate whose orienta-tion provided a sensitive adjustment of the beam posi-tion in the scattering plane. The flow cell contained thecollection optics that focused the emitted light about 25cm from the lens where photomultiplier (PMT) detec-tors (Hamamatsu Model H6780) were placed. Theusual arrangement of dichroic mirror (DM) and band-pass filters selected the fluorescence and elasticallyscattered light components. The outputs from the twoPMTs were processed by digital electronics providedby Becton Dickinson Biosciences (BD FACSDiVa sys-tem). An oscilloscope provided a visual monitor of thepulses associated with the side scattering (SSC) and thefirst fluorescence (FL1) channels of the detection elec-tronics.

11.1 Linearity and Dynamic Range

The output of a green LED was focused on a slit of achopper and then split by a glass plate reflector andpassed to the inputs of two optical fiber (FO) bundles.One of the split beams (that transmitted through theglass plate) passed through a neutral density (ND) fil-ter, and the FO routed the light to the PMT associatedwith the first fluorescence channel (FL1). The otherbeam (reflected from the glass plate) was incident onthe FO that routed the light to the PMT associated withthe side scattering channel (SSC). The chopper rotationwas adjusted to give pulses that approximated the dura-tion of the pulses from the microspheres in the flowcell. The adjustment was performed by visual inspec-tion of the oscilloscope traces. The pulse rate was about190 pulses per second. The linearity measurementswere performed by noting the mean channel of thedetected pulses in FL1 for a given OD value of the NDfilter. Six ND filters were purchased from NewportCorp., and the attenuation values were used as provid-ed by the manufacturer. The data was accumulated byrecording events for different OD values of the ND fil-ters. The six mean channels corresponding to OD val-ues of 0, 0.51, 1.05, 1.50, 1.98. and 2.49 were record-ed. The mean channels were plotted on a log-log scaleversus the OD values. The average slope was found tobe 1.027 ± 0.008. Therefore, we conclude that thecytometer response is linear. We assume that the photonpulses in the above simulation and from fluorescentmicrospheres behave in an identical fashion.

The noise properties of the cytometer are given bythe coefficient of variation (CV) defined as the standarddeviation of a pulse distribution divided by the meanpulse amplitude [8]. A linear relation between (CV)2

and the inverse of the mean pulse amplitude wasobserved, and indicated that the main source of noisewas the statistics of photon arrival at the photomultipli-er cathode.

12. References

[1] A. K. Gaigalas, L. Li, et al., “The Development of FluorescenceIntensity Standards.” J. Res. Natl. Inst. Stand. Technol. 106, 381-389 (2001).

[2] W. V. Prestwich, Unit of Medical Physics, McMaster University.Personal communication (2003).

[3] A. Schwartz, L. Wang, et al., “Quantitating FluorescenceIntensity from Fluorophore: The Definition of MESFAssignment.” J. Res. Natl. Inst. Stand. Technol. 107, 83-91(2002).


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[4] R. Mavrodineanu, J. I. Shultz, et al., eds., Accuracy inSpectrophotometry and Luminescence Measurements,Washington D.C., National Bureau of Standards (1973).

[5] L.-Q. Li and L. M. Davis, “Rapid and efficient detection of sin-gle chromophore molecules in aqueous solution.” Appl. Opt.34(18), 3208-3217 (1995).

[6] T. Kubarsepp, A. Haapalinna, et al., “Nonlinearity measurementsof silicon photodetectors.” Appl. Opt. 37(13), 2716-2722 (1998).

[7] R. M. Smith, How Linear are Typical CCDs?, ExperimentalAstronomy 8, J. W. Beletic and P. Amico, eds., Kluwer AcademicPublishers, Netherlands (1998).

[8] E. S. Chase and R. A. Hoffman, “Resolution of DimlyFluorescent Particles: Measure of Fluorescence Sensitivity.”Cytometry 33, 267-279 (1998).

About the authors: A. K. Gaigalas is a physicist andLili Wang a research chemist both in the BiotechnologyDivision of the NIST Chemical Science and TechnologyLaboratory. Abe Schwartz is a chemist at the Center forQuantitative Cytometry. Gerald E. Marti is a reviewand research officer at CBER, FDA and an attendingphysician at NCI. Robert F. Vogt is a chemist at theCenter of Disease Control and Prevention, Atlanta, GA.The National Institute of Standards and Technology isan agency of the Technology Administration, U.S.Department of Commerce.


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