Development of Multicolor Flow Cytometry Calibration Standards

1. Introduction

Multicolor flow cytometers are used extensively inresearch and clinical settings [1-3]. Cells are incubatedwith labeled antibodies specific to antigens on thesurface or inside of a cell. Antibodies with spectrallydifferent labels are detected in different fluorescencechannels of the flow cytometer and are indicative of thepresence of specific surface or intracellular antigensthat are the targets of the labeled antibodies. The objec-tive of quantitative flow cytometry is to relate the

fluorescence intensities in a given fluorescence channelto the number of the labeled bound antibodies on thecell surface or within the cell [4, 5]. Each fluorescencechannel should give an estimate of the number ofbound antibodies labeled with the fluorophore assignedto that channel. In a previous publication, we proposeda method to accomplish this objective in two steps [6].

The first step is the establishment of a linear fluores-cence intensity scale for each fluorescence channel.The second step is to convert the intensity scale to ascale giving the number of labeled antibodies on the

Volume 116, Number 3, May-June 2011Journal of Research of the National Institute of Standards and Technology

671

[J. Res. Natl. Inst. Stand. Technol. 116, 671-683 (2011)]

Development of Multicolor Flow CytometryCalibration Standards: Assignment of

Equivalent Reference Fluorophores(ERF) Unit

Volume 116 Number 3 May-June 2011

Lili Wang and Adolfas K.Gaigalas

National Institute of Standardsand Technology,Gaithersburg, MD 20899

[email protected]@nist.gov

A procedure is described for assigningthe number of equivalent referencefluorophores (ERF) values to microsphereslabeled with a fluorophore designed toproduce a fluorescence response in a givenfluorescence channel of a multicolor flowcytometer. A fluorimeter was calibratedby a series of solutions of the referencefluorophores. The fluorimeter was used toobtain the microsphere fluorescenceintensity, and a multicolor flow cytometerwas used to obtain the microsphereconcentration. The microspherefluorescence intensity and theconcentration were used to obtain thevalue of ERF for each model microspherecalibration standard. The procedure isdescribed in detail only for microsphereswith allophycocyanin (APC) immobilizedon the surface. ERF values were alsodetermined for microsphere calibratorsfor three other fluorescence channels:fluorescein isothiocyanate (FITC),phycoerythrin (PE), and Pacific Blue(PB).The four model microsphere calibratorsprovide a one point calibration for the four

channels of a flow cytometer. By usingsoftware controls and changing thephotomultiplier voltages, it is possible toobtain a multipoint calibration for eachfluorescence channel using eachmicrosphere calibrator.

Key words: allophycocyanin (APC);equivalent reference fluorophores (ERF);fluorescein isothiocyanate (FITC);fluorescence; multicolor flow cytometer;Pacific Blue (PB); phycoerythrin (PE).

Accepted: April 15, 2011

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

cell. This manuscript describes a procedure to establisha linear scale in four fluorescence channels (fluoresceinisothiocyanate (FITC), phycoerythrin (PE), allophy-cocyanin (APC), and Pacific Blue (PB)) of a multi-color flow cytometer. The simplest possible procedureis a single point calibration of each fluorescencechannels. Four CompBeads1 populations from BDBiosciences were chosen as the model microspherecalibrators. These microspheres were provided with acoat of rat anti-mouse kappa light chain antibodies, andwere incubated with four mouse antibodies labeledwith either FITC, PE, APC, or PB fluorophores. Afterincubation, the number of Equivalent ReferenceFluorophores (ERF) was assigned to each microspherecalibrator. The linear scale for a flow cytometer wasestablished by passing the labeled microspheresthrough a flow cytometer and plotting the measuredfluorescence intensity in each channel versus theassigned ERF value of the calibrator. The flow cytome-ter calibration can be extended to multiple points bychanging the photomultiplier voltage. Alternately, amultipoint calibration can also be obtained by usingseveral populations of microspheres each with a differ-ent ERF value as shown in a previous work with UltraRainbow beads [6]. The development of a standard totranslate the linear scale into a scale related to the num-ber of bound antibodies will be described in a subse-quent paper.

Considering that most commercially availablemicrosphere calibrators are small in size (2-4 μm) andcontain multiple microsphere populations similar to theCompBeads, we have developed this procedure toaccurately assign the ERF value to the major micro-sphere population within the calibrator. The develop-ment of clinical multicolor flow cytometer assays iscurrently a major undertaking. Future multicolor flowcytometer assays are likely to incorporate internalcalibration standards so that comparable results can be obtained with any multicolor flow cytometer. Thewide-spread implementation of this procedure willensure the comparability of clinical assay results.

2. General Procedure for AssigningERF Values

The ERF value of a microsphere calibrator is definedas the number of equivalent reference fluorophoreswhich give the same fluorescence intensity as thatof a single microsphere calibrator [6]. A summary ofthe scheme for assigning ERF values to the fourmicrosphere calibrators is given in Fig. 1. First afluorimeter was calibrated with a set of progressivelydiluted solutions of a stock solution of each referencefluorophore shown in the left column in Fig. 1. Thefluorimeter calibrations related the fluorescence inten-sity from the solution of reference fluorophores to theconcentration of the reference fluorophores. Since thedilution factor was between 5 and 10, the concentra-tions of the reference solutions tended to group in thelower portion of the axis when plotted on a linear scale.Therefore, several methods of fitting the data wereinvestigated in order to obtain the most representativecalibration line. Next, the fluorescence intensity of themicrosphere calibrator suspensions (shown in the rightcolumn of Fig. 1) was measured. The fluorimetercalibration line was used to relate the fluorescenceintensity of the microsphere suspension to the concen-tration of the corresponding reference fluorophores(shown by the horizontal arrows in Fig. 1). Finally thenumber concentration of each microsphere suspensionwas measured using a multicolor flow cytometer and aninternal bead counting standard. The two values, theequivalent reference fluorophore concentration and thenumber microsphere concentration, enabled the assign-ment of the ERF value to each microsphere calibrator.The following contains an outline of four differentfitting procedures used to generate the fluorimetercalibration line, the procedure to find the microsphere concentration, and finally how this data is used to esti-mate the ERF values of the calibration microspheres.

2.1 Fitting Procedures for Obtaining a CalibrationLine From a Set of Reference Solutions

Let x be a set of concentrations and y a set of corre-sponding fluorescence intensities. A calibration line isobtained by a best linear fit to the pairs of data pointsdenoted by (x, y). A linear fit assumes that the datapoints are related by Eq. (1)

(1)


672

1 Certain commercial equipment, instruments, and materials areidentified in this paper in order to specify the experimental procedureas completely as possible. In no case does this identification imply arecommendation or endorsement by the National Institute ofStandards and Technology, nor does it imply that the equipment,instruments, or materials identified are necessarily the best availablefor the purpose. 0y y m x= + ⋅

where m is the slope and y0 is the y-intercept. If the datais such that the majority of points are located at lowvalues of x, then taking a log of the data results in amore uniform distribution of points along the fluores-cence intensity and concentration axes. Such a distribu-tion gives each region a similar importance in thefitting. The fitting of the transformed data has to beperformed using a more general nonlinear procedure.Performing a log transforming of Eq. (1) leads to

(2)

Equation (2) suggests that the fitting of the transformeddata should use a parameterization given by Eq. (3)

(3)

The fit parameters of the transformed data give theslope and y-intercept according to the relations:

(4)

Given noiseless data, using either Eq. (1) or Eq. (3)leads to the same result for the slope and intercept.Given data with noise (uncertainties in the values ofconcentration and fluorescence intensity), the trans-formed data is more uniformly distributed along thegeometric axis, thus the fit is not biased toward anyspecific region of data.

In practice, the log transformed data is often mod-eled with a linear relation.

(5)


673

Fig. 1. A schematic description of the procedure used to obtain ERF values of four microsphere calibrators using four different referencefluorophore solutions. A value of equivalent concentration of a reference fluorophores is obtained for each microsphere suspension using afluorimeter calibrated with a set of solutions of a reference fluorophore under a specified instrument setting. The solutions were obtained byserial dilutions of a stock solution. The number concentration of each microsphere suspension was measured using a multicolor flow cytometerand an internal bead counting standard. The two values, the equivalent reference fluorophore concentration and the number microsphereconcentration, were used to assign a ERF value to each microsphere calibrator.

0

0

log( )0

log( ) log( (1 / ))log( ) log( ) log(1 / )

log( ) log( ) log(1 / 10 ) .x

y mx y mxm x y mx

m x y m

= += + + +

= + + + ⋅

log( )log( ) log( ) log(1 /10 ) .xy a x b= + + +

0

1010 * .

a

a

my b

==

log( ) log( ) .y a d x= + ⋅

Equation (5) is a valid representation of the data ifthe intercept y0 can be neglected. In that case, theparameter d should be equal to 1 and the parameter agives the slope as before, m = 10a . However if the inter-cept can not be neglected, then Eq. (5) is equivalent torepresenting the actual data with a model given byEq. (6).

(6)

The model tries to minimize the effect of neglectingy0 by introducing a slight curvature in the representa-tion of the data, hence the presence of the parameter din Eq. (6).

2.2 Calibration of the Fluorimeter and the Estimateof Equivalent Fluorophore Concentration

The fluorimeter was calibrated using solutions of areference fluorophore. The dependence of the referenceconcentration, Cref , on the fluorescence intensity, FIref ,was represented by a calibration line given by

(7)

The measured fluorescence intensity from a suspen-sion of microspheres, FImicrospheres , was put intoEq. (7) to define an equivalent concentration of refer-ence solution, Cequivalent , which gives the same fluores-cence intensity as the microsphere suspension. Assuggested by the previous discussion, there are severalways to estimate the parameters in Eq. (7). The firstmethod is simply to fit the reference data using a linearmodel. Then Cequivalent can be evaluated using Eq. (1)

(8)

In the case of a linear fit to the log transformedreference data, Eq. (5) gives:

(9)

In the case of a nonlinear fit to the log transformedreference data, Eq. (3) gives:

(10)

In many situations, it may be possible to neglect theintercept and estimate the slope using one calibrationpoint nearest to the measured microsphere fluorescenceintensity. In that case, the equivalent concentration isgiven by

(11)

The subscript ref in Eq. (11) refers to the calibrationpoint which is nearest to the measured microspherefluorescence intensity when approached from a largervalue on the axis.

2.3 Obtaining Microsphere Concentration FromFlow Cytometer Measurements

The concentration of microspheres was obtainedusing the ARIA II flow cytometer and the TruCountbeads with a diameter of approximately 2.7 μm (BDBioscience, San Jose, CA) as an internal countingstandard. The hard dyed, single population TruCountbeads are packaged as a dry pellet in a tube. The beadsgive a fluorescence signal in multiple fluorescencechannels of the flow cytometer. The number of beadsper tube, NTruCount is given by the manufacturer.

The test microspheres with the unknown concentra-tion and the counting beads were suspended in a bufferof known volume (e.g., 0.5 mL). For simplicity, theentire content of the tube of the counting beads wassuspended in the buffer containing the test suspension.The mixture of the counting beads and test micros-pheres was passed through the flow cytometer. It wasassumed that the relative number of the test micros-pheres to the counting beads per analytical volumemeasured by flow cytometer was the same as the rela-tive total number of test microspheres to TruCountbeads in the original mixture. Based on this assump-tion, the working equation is given by Eq. (12)

(12)

where Nmicrospheres is the number of test microspheres inthe mixture, COUNTmicrospheres is the number of testmicrospheres measured by the flow cytometer, andCOUNTTruCount is the number of the counting beadsmeasured by the flow cytometer. Solving Eq. (12) for


674

.dy m x= ⋅

0 .ref refC C m FI= + ⋅

0 .equivalent microsphereC C m FI= + ⋅

( log( ))10 .microspherea d FIequivalentC + ⋅=

( log( ) log(1 ))

10 .microsphere

microsphere

ba FIFI

equivalentC+ + +

=

.refequivalent microsphere

ref

CC FI

FI=

microspheres microspheres

TruCount TruCount

N COUNTN COUNT

=

Nmicrospheres and dividing by the volume of the suspensiongives the microsphere number concentration as shownin Eq. (13)

(13)

To use Eq. (13) properly it was necessary to identifythe test microspheres and the counting beads in theflow cytometric measurement. Usually it is possible touse either scattering or fluorescence signals to distin-guish between the two populations of particles. A gate(to be described as P8 in Fig. 5a) is set in the sidescatter-forward scatter (SSC-FSC) plot of the totalparticle events. Counting the events in this gategives the number of total particles detected,COUNTmicrospheres + COUNTTruCount . Next, a gate (to bedescribed as P9 in Fig. 5c) is set on the fluorescencepeak in the histogram associated with the countingbeads’ fluorescence in the APC channel. The count inthis peak gives the total number of the countingbeads detected, COUNTTruCount . Thus the ratio of thecounts is given by Eq. (14)

(14)

where P8 and P9 stand for the total number of events inthe corresponding gates. Thus the final concentration ofthe microspheres is given by Eq. (15)

(15)

For the case where the TruCount microspheres donot have a fluorescence signal, the procedure given byEq. (15) has to be modified. In this case, it is necessaryto measure a sample of the test microspheres (withoutthe counting beads) with the same concentration of testmicrospheres as in the mixture of both test micros-pheres and TruCount beads. Let P3W be a gate aroundthe region in the SSC-FSC scatter plot which containsboth the TruCount beads and unknown microspheres.Let be P3WO the same gate for the case of the samplewith test microspheres, but without the TruCountbeads. Then, Eq. (14) is modified according to Eq. (16)

(16)

2.4. Assigning ERF Values to Microspheres

The equivalent number of reference fluorophoresper microsphere (ERF) is estimated by dividing Cequivalent

with the concentration of microspheres in the suspen-sion, Cmicrospheres. Explicitly

(17)

The constant in Eq. (17) converts the referenceconcentration from mol/L to mL–1.

Inserting one of the estimates of Cequivalent , the resultfrom each of the different models defined byEqs. (8, 9, 10, or 11) gives an estimate of the ERF valuefor that microsphere.

Equation (17) gives the measured value of ERF forthe microsphere suspension, which may have severaldistinct populations, each with the same fluorophore,but characterized by a different size and/or fluorophoreloading. The different populations are associated withidentifiable clusters in the SSC-FSC scatter plot. Mostflow cytometer analyses are performed using a single,dominant population. In the case of the APC micros-phere calibrator, there are two distinct populations ofmicrospheres (to be described as P1 and P2 gates inFig. 6a). Let Imajor represent the average fluorescencesignal of a microsphere in the major microsphere cali-brator population (as seen in P1 gate). The ERF for themajor population can be written in terms of the ERF forthe total suspension by Eq. (18)

(18)

where Iavr is the average fluorescence response of allmicrospheres. Equation (18) is justified by noting thatthe ratio of ERF values describes the relative fluores-cence response of individual microspheres and is there-fore identical to the ratio of the fluorescence intensitiesmeasured in the flow cytometer. Thus, the ratio offluorescence intensities of two distinct microspherepopulations should be identical to the ratio of theirrespective ERF values. In order to obtain a value forERFmajor (this is the population which is used in inter-preting a flow cytometer measurement), it is necessaryto evaluate the fluorescence intensity of the majormicrosphere population relative to the total micros-phere population. This can be performed on a flowcytometer, where forward and side scattering can be


675

.microspheres TruCountmicrospheres

TruCount mixture

COUNT NC

COUNT V= ⋅

8 99

microspheres

TruCount

COUNT P PCOUNT P

−=

18 9 , .9

TruCountmicrospheres

mixture

NP PC mLP V

−−= ⋅

8 ( 3 3 ).

3 3microspheres W WO

TruCount W WO

COUNT P P PCOUNT P P

− −=

−

236.0221*10 .1000

equivalent

microspheres

CERF

C=

( )major major avrERF ERF I I= ⋅

used to identify the microspheres in the major and totalpopulations, and the fluorescence signal can measure the fluorescence signal can measure the relativefluorescence intensity of the two populations (to bedescribed as Fig. 6.

3. Results

The procedures outlined in the previous section wereapplied to four microsphere preparations each with adifferent fluorophore. Detailed results will be given forthe APC microsphere calibrator; the results for theother microspheres will be different in values, but theidentical procedure was used to obtain them.

3.1 Assignment of ERF Value to APC MicrosphereCalibrator

The assignment of ERF values to APC microspherecalibrator used reference solutions of APC. The con-centration of a stock solution of APC was obtainedusing amino acid analysis as described previously [6],and its value was (3.76 ± 0.33) mg/mL. Using a molarmass of 106,610 g/mol, the molar concentration of theAPC stock solution was estimated to be 35.3 μmol/L[7, 8]. Next, a series of dilutions of the stock solutionwas performed to obtain a set of solutions with progres-sively smaller concentrations of APC. Table 1 gives theresults of weighing of the APC stock solution to makethe first dilution. First a small tube was weighed(column 1 in Table 1), followed by the weighing of thetube containing the APC stock solution (column 2 inTable 1) and finally the tube containing the APCstock solution and PBS buffer, 0.02 % (w/w) Tween20 (column 3 in Table 1). Each weighing was followedby a measure of the empty balance to determine driftsin the “zero” values, and these drifts were subtractedfrom the weighings.

The concentration of the new solution, called Sol1,was determined using Eq. (19)

(19)

The quantities gAPC and gPBS were found from theaverage of the differences between columns 2 and 1and columns 3 and 2, respectively. In all cases, thebackground value was subtracted. The symbol dil rep-resents a dilution factor and is defined by Eq. (19) as aratio of the indicated masses. Equation (19) assumesthat the densities of the APC stock solution and thebuffer are identical. This assumption introducessystematic errors, which are insignificant compared tothe measured uncertainty of the concentration of theAPC stock solution. The uncertainty in the concentra-tion of the new solution was found using the standarderror propagation expression given in Eq. (20)

(20)

The uncertainty in the dil factor was found using thedefinition in Eq. (19) and an expression similar toEq. (20). The procedure outlined above for the firstdilution of the stock solution of APC was followed toproduce additional 5 serial dilutions. The results areshown in Table 2 with the lowest concentration(Solution 6) in the first row. The third column inTable 2 gives the uncertainties, which include theuncertainty of the stock solution of APC and thesubsequent uncertainty introduced by the weighing.

3.2 Fluorescence Intensities of the ReferenceSolutions of APC

The fluorescence was measured using a JY HoribaFluorolog 3 commercial fluorescence spectrometerwhich was modified to allow excitation with an exter-nal laser. Figure 2 shows the schematic of the illumina-tion arrangement. An external laser beam (a 405 nmlaser for PB calibrator, a 488 nm laser for FITC and PEcalibrators and a 633 nm laser for APC calibrator)entered the Fluorolog 3 sample chamber through asmall aperture in the wall of the sample compartment.A laser line filter was placed in front of the aperture tominimize extraneous light. A holographic notch filterwas placed in front of the detector port inside the sam-ple compartment. Measurements were performed byscanning the detector wavelength over the emission


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Table 1. Weightings of the APC stock solution, all values in grams

Tube tube + APC tube + APC+PBS

7.87937 7.97237 17.892617.87937 7.97249 17.893207.87958 7.97345 17.89361

1 .APCSol APC APC

APC PBS

gC C C dil

g g= ⋅ = ⋅

+

1/ 2

2 21 1 ( ) ( ) .APC dil

Sol SolAPC

CC dilσ σσ

⎡ ⎤= ⋅ +⎢ ⎥

⎣ ⎦

Table 2. Concentrations of reference solutions of APC

Solution name Concentration, mol/L Uncertainty, Mol/LSolution 6 2.64e-11 1.4e-12Solution 5 1.32e-10 6.7e-12Solution 4 6.56e-10 3.4e-11Solution 3 3.29e-9 1.7e-10

region in steps of 1 nm. The detector slit width was setto 2 nm, the integration time was set to 1 s., and thephotomultiplier voltage was set to 1000 v. The solidtraces in Fig. 3 show the uncorrected fluorescenceemission spectrum from reference solutions prior tosubtraction of the medium spectrum. The dashed tracesin Fig. 3 show the uncorrected spectrum from micro-spheres assigned to FITC fluorescence channel (a),PE fluorescence channel (b), APC fluorescence channel(c), and Pacific Blue fluorescence channel (d). Prior toanalysis, the medium spectra were subtracted from allfluorescence spectra. The subtracted spectra were fur-ther corrected for spectral variation of the detector

response. The fluorescence intensity was estimated bysumming the emission spectrum from the lowest to thehighest observed wavelength. In the case of APC, thesubtracted and corrected spectrum was summed from640 nm to 800 nm (Fig. 3c). The fourth column ofTable 3 shows the result of the fluorescence measure-ments for four dilutions of APC stock solution.The concentration data are reproduced from Table 2.Table 3 constitutes the data used for calibration of thefluorescence spectrometer. Similar procedures werefollowed for the calibration of the fluorimeter with405 nm and 488 nm excitation (data not shown). Thelaser line filter and holographic filter were changed to


677

Fig. 2. A schematic of the commercial fluorimeter with an external laser, used to illuminate a sample located in the sample compart-ment. The laser entered the sample compartment through a small hole. A holographic notch filter was placed in front of the detectoraperture in the sample compartment. The data was collected using the software associated with the spectrometer.

accommodate the excitation laser. Different referencefluorophore solutions were used for calibrating thefluorimeter at the different excitation wavelengths asdescribed in Fig. 1 and in the caption of Fig. 3 [6].

Figure 4 shows the results of fitting the data inTable 3 to obtain a calibration line. The fluorescenceintensity is given on the horizontal axis, and thevertical axis shows the ratio of the deviations betweenthe concentration data and the fitted values, and theconcentration data. The solid circles give the resultsusing Eq. (1) (linear fit to data), the open circles givethe results using Eq. (5) (linear fit to log of data), andthe solid triangles give the results using Eq. (3)(non linear fit to log of data). The linear fit gives largedeviations at lower concentrations, while the fits to thelog of the data yield similar deviations across theentire range of concentrations. Similar calibrationcurves were obtained for the FITC, Nile Red, andCoumarin [30] reference solutions (results not shown).


678

Fig. 3. Unsubtracted and uncorrected fluorescence spectra of reference solutions (solid traces) and the associated microsphere calibrators in PBSbuffer, pH 7.4, 0.5 % (w/w) BSA and 0.1 % (w/w) sodium azide (dotted trace). (a) FITC in PBS buffer, pH 7.4 and FITC microsphere calibratorwith 488 nm laser excitation. (b) Nile Red fluorophores in acetonitrile (ACN) solvent and PE microsphere calibrator with 488 nm laser excitation.(c) APC in PBS buffer, pH 7.4, 0.02% (w/w) Tween 20 and APC microsphere calibrator under a 633 nm laser excitation. (d) Coumarin 30fluorophores in ACN solvent, and PB microsphere calibrator with 405 nm laser excitation.

Table 3. Spectrometer calibration with reference solutions of APC

Solution name Concentration, Uncertainty, Fluorescencemol/L mol/L Signal, AU

Solution 6 2.64e-11 1.4e-12 1.43e6Solution 5 1.32e-10 6.7e-12 6.85e6Solution 4 6.56e-10 3.4e-11 3.65e7Solution 3 3.29e-9 1.7e-10 3.07e8

3.3 Fluorescence Intensity of the APC Microspheres

Three identical suspensions of APC microsphereswere prepared according to the instructions supplied bythe manufacturer. A PBS based buffer with 0.5 %(w/w) Bovine Serum Albumin (BSA) and 0.1 % (w/w)sodium azide was provided by the manufacturer ofAPC microspheres. Each suspension was transferred toa cuvette and fluorescence measurements were per-formed in a manner identical to those performed for thecalibration solutions. An example of spectra is shownin Fig. 3c for the APC microspheres. Two measure-ments were performed in sequence to detect photo-degradation. The fluorescence intensity was obtained inthe same way as in the case of the reference solution.The average intensity value of the first fluorescencemeasurement of the three identical APC micro-sphere suspensions was (1.392 ± 0.011)*106 and theaverage value of the second measurement was(1.356 ± 0.005)*106. There appears to be some photo-degradation, but the amount in terms of percentage issmall compared to that observed for FITC micros-pheres (about 20 % reduction in fluorescence intensityin the subsequent measurement). In order to minimizeeffects of photodegradation, the first measurement was always used in the determination of the ERF value.

Using the fluorescence intensity of the APC micros-pheres in the calibration line provided by the data inTable 3, we obtained the equivalent concentration ofreference fluorophores shown in the second column in Table 4. The first column in Table 4 gives the type of fitused for the data in Table 3. The last row in Table 4gives the equivalent concentration obtained by usingthe nearest calibration point to estimate the slope andneglecting the intercept (Solution 6 in Table 3). Use ofthe slope obtained from the nearest calibration point toestimate the concentration is the easiest method since itdoes not require any fitting of the data. The valueobtained by the linear fit to data is significantly differ-ent from values by other fitting methods because of thelarger fitting deviations at lower concentrations asshown in Fig. 4.


679

Fig. 4. The deviations between the best fit and the intensity response of four solutions of APC with progressivelylarger concentrations of APC. The fit of the data with a line gives the largest deviations at smaller concentrations.Fits to logarithms of the data yield smaller deviations.

Table 4. Equivalent concentration of reference fluorophore APC*

Type of calibration Value, mol/L

Linear fit to data 1.241e-10Linear fit to log of data 2.917e-11Non linear fit to log of data 2.749e-11Nearest calibration point 2.578e-11

* The uncertainties are about 8 % of the actual values

3.4 Concentration of APC Microsphere Calibrator

Figure 5 shows the results of a flow cytometer meas-urement on a sample containing the APC microspherecalibrator and the TruCount beads. The sample wasmade by re-suspending a tube of TruCount beads in0.5 mL of the suspension of APC microsphere calibra-tor. (A portion of the same suspension of APC micro-spheres was used in the fluorescence measurementsdiscussed above). When a microsphere passes throughthe laser beams of the flow cytometer, a total of sixsignals are detected and analyzed. These signals are theforward scattering, side scattering at 90°, and the fourfluorescence channels (FITC, PE, APC and PB). Thetwo scattering signals are used to classify the micro-spheres according to size and shape. The scatter plot inFig. 5a with axes labeled SSC-A (side scatter channel)and FSC-A (forward scatter channel) shows severalmicrosphere populations. The gate P8 encloses thescattering events associated with all microspheres andthe counting beads in the sample. The gate P8 is furthersubdivided into regions associated with differentparticle populations. The gate P1 contains the majorpopulation of the APC microspheres. The gate P3contains a minor part of the APC microspheres and theentire population of TruCount beads. The gate P2contains another minor population of the APC micros-pheres. Fig. 5a does not give a graphical display of therelative intensity of the different populations; howeverit is simple matter to electronically count the number ofdots in each gate. The result box (d) at the bottom ofFig. 5 gives the number of events associated with theP8 gate as 43972. The TruCount beads, contained in theP3 gate, have a large fluorescence signal in the APCfluorescence channel. The fluorescence signal can beused to identify and select the counting beads. Figure5b shows a dot plot, labeled with axes APC-A andFSC-A, which was obtained from all events in Fig. 5a.The gate P4 in Fig. 5b gives the distribution of fluores-cence signals associated with the TruCount beads. Theevents in P3 scatter plot are further displayed in ahistogram in Fig. 5c with axis labels Count and APC-A.The gate P9 in the histogram gives the number ofTruCount beads, the value of which is 7799. The gateP7 in the histogram gives the number of APC micro-spheres in the minor population contained in gate P3.The number of events in gates P4 and P9 for TruCountbeads in Fig. 5 is within the measurement uncertainty,which was estimated from the spread of the distribution

of events. Using 48918, provided by the manufacturer,for the given number of TruCount beads in the vial,Eq. (15) gives the concentration of APC microspheresas (453800 ± 36000) mL–1. The uncertainty associatedwith this measurement is about 8 % of the total value.

3.5 Assignment of ERF Values to APCMicrosphere Calibrator

In the previous sections, procedures were describedfor obtaining the microsphere concentration and theequivalent concentration of reference fluorophores forAPC microspheres. Given these values, Eq. (17) wasused to calculate the value of equivalent referencefluorophores (ERF). The second column of Table 5gives the values of ERF obtained by using(453800 ± 36000) mL–1 for the microsphere concentra-tion and the values of the equivalent fluorophore con-centrations given in Table 4. The ERF values are for allmicrospheres. However, as mentioned in the discussionof Fig. 5, the APC calibration microspheres consist of amajor population and two minor populations. Themajor population consists of the events in gate P1 in theSSC-FSC scatter plot in Fig. 5a. The minor populationsconsist of events in the P3 and P2 gates in the samescatter plot. Figure 6 is similar to Fig. 5, except that itrepresents a sample that contains only APC calibrationmicrospheres without the TruCount beads as was thecase in Fig. 5. Note that the density of events in gate P3without the TruCount beads is much smaller in Fig. 6than in Fig. 5 with TruCount beads. The fluorescencesignals from the major and minor populations of theAPC calibration microspheres are different. This wasestablished by comparing the mean fluorescencechannel of the events associated with the three gates inFig. 6a. The resulting histogram is shown in Fig. 6cwith mean fluorescence channels 9764 for P1, and17475 for P3. Figure 6b shows the fluorescencehistogram for events associated only with gate P1 inFig. 6a. The gate P1 contains about 80 % of the eventsassociated with the APC calibration microspheres and itis the gate that defines the APC microsphere event inthe calibration of the flow cytometer and flowcytometry applications. Therefore, it is important toobtain an estimate of the ERF value associated with thismajor microsphere population in the gate P1. This canbe accomplished by multiplying the ERF values givenin column 2 of Table 5 by the ratio of mean fluores-cence signal of events in gate P1 and P8 in Fig. 6a, or


680


681

Fig. 5. (a) A scatter plot of data from a sample containing TruCount beads and APC microspheres calibrator. Thehorizontal axis is the forward scattering signal and the vertical axis is the side scattering signal. Each dot correspondsto a single particle event recorded by the flow cytometer. The gate P8 encompasses almost all of the recorded particleevents except the debris, and the regions P1, P2, and P3 represent different populations of the APC microsphereswith P1 containing the major population. The TruCount bead events are contained in the P3 gate. (b) A scatter plotof the APC fluorescence signal on the vertical axis and the forward scattering signal on the horizontal axis. Thegate P4 encloses all events associated with the TrueCount beads. (c) A histogram of the APC fluorescence signalfor all events contained in gate P3 of Fig. 5a, (d) a compilation of the number of events associated with the gates inFigs. 5 a,b,c.


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Table 5. Assigned values of equivalent reference fluorophore (ERF) APC calibration microspheres

Type of calibration All microspheres, ERF ERF of the majorpopulation of microspheres*

Linear fit to data 16470 15400Linear fit to log of data 38720 36300Non linear fit to log of data 36490 34200Nearest calibration point 34220 32100

* uncertainties are about 12 % of the values

Fig. 6. (a) A scatter plot of data from a suspension of APC microspheres calibrator. The horizontal axis is the forward scattering signal and thevertical axis is the side scattering signal. Each dot corresponds to a single APC microsphere recorded by the flow cytometer. (a) The gate P8encompasses almost all of the recorded microsphere events except the debris, and the regions P1, P2, and P3 represent different populations ofthe microspheres. (b) A histogram of the fluorescence signal in the APC channel for events in gate P1. (c) A histogram of the fluorescence signalin the APC channel for events in gate P8. Note: not all microspheres are included in the gate P6. P6 only shows the majority of microspheres. (d)A compilation of the mean fluorescence intensity values associated with the gates in Fig 6 a,b,c.

specifically by P1/P8 = 9764/10408 = 0.938(Eq. (18)).The ERF values of the major population of the APCcalibration microspheres are given in the third columnof Table 5. The uncertainties in the ERF values areabout 8 % of the actual value and were obtained fromthe uncertainties of the values of Cequivalent and Cmicrospheres.Additional systematic uncertainties are introduced bythe choice of the calibration algorithm.

4. Conclusion

The detailed procedure outlined for the APCfluorescence channel was also performed for threeother fluorescence channels: FITC, PE, and PacificBlue (PB). The resulting values of ERF for the majorcomponent of each microsphere calibrator, determinedusing the nearest calibration point method, are shownin the second column of Table 6. The third columngives the name of the reference fluorophore. The fourpopulations of microspheres would give a single pointmeasurement in the four fluorescence channels. Thecalibration could be extended to multiple points bydeveloping software controls to change the photomulti-plier voltages and collect data at each value of the volt-age. Alternately, a calibration could be obtained withmultiple populations of microspheres, each with a dif-ferent fluorescence intensity and a different ERFassignment. Once the linear ERF scale is established,another reference standard will be used to change theERF scale to a scale giving the antibodies bound tothe cell. The nature of this second reference standard isthe topic of a subsequent paper.

Acknowledgments

The authors are indebted to Dr. Kenneth D. Cole atthe Biochemical Science Division of the NIST MaterialMeasurement Laboratory for his help in the determina-tion of the concentration of the allophycocyanin stocksolution by amino acid analysis. The work performed is

a part of the NIST and ISAC (International Society forAdvancement of Cytometry) co-organized fluores-cence standardization study.

5. References

[1] H. He, A. N. Courtney, E. Wieder, and K. J. Sastry, MulticolorFlow Cytometry Analyses of Cellular Immune Response inRhesus Macaques, J. Vis. Exp. 38, 1743 (2010).

[2] J. M. Brenchley, B. J. Hill, D. R. Ambrozak, D. A. Price,F. J. Guenaga, et al., T-cell Subsets That Harbor HumanImmunodeficiency Virus (HIV) in Vivo: Implications for HIVPathogenesis, J. Virol. 78(3), 1160-1168 (2004).

[3] P. O. Krutzik and G. P. Nolan, Intracellular Phospho-proteinStaining Techniques for Flow Cytometry: Monitoring SingleCell Signaling Events, Cytometry A 55(2), 61-70 (2003).

[4] L. Wang, F. Abbasi, A. K. Gaigalas, R. F. Vogt, and G. E. Marti,Comparison of Fluorescein and Phycoerythrin Conjugates forQuantifying CD20 Expression on Normal and LeukemicB-cells. Cytometry Part B (Clin Cytometry) 70B, 410-415(2006).

[5] J. W. Gratama, J. L. D’hautcourt, F. Mandy, G. Rothe,D. Barnett, G. Janossy, S. Papa, G. Schmitz, and R. Lenkei,Cytometry 33(2), 166-178 (1998).

[6] L. Wang, A. K. Gaigalas, G. E. Marti, F. Abbasi, and R. A.Hoffman, Toward Quantitative Fluorescence Measurementswith Multicolor Flow Cytometry. Cytometry Part A 73A, 279-288 (2008).

[7] K. Brejc, R. Ficner, R. Huber, S. Steinbacher, Isolation,Crystallization, Crystal Structure Analysis and Refinement ofAllophycocyanin from the Cyanobacterium Spirulina platensisat 2.3 Å Resolution. J Mol Biol 249, 424-440 (1995).

[8] J. Y. Liu, T. Liang, J. P. Zhang, D. C. Liang, Crystal Structureof Allophycocyanin from Red Algae Porphyra yezoensis at 2.2Å Resolution. J Biol Chem 274, 16945-16952 (1999).

About the authors: Lili Wang is a research chemistand A. K. Gaigalas is a scientist emeritus in the Bio-chemical Science Division of the NIST MaterialMeasurement Laboratory. The National Institute ofStandards and Technology is an agency of theU.S. Department of Commerce.


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Table 6. Assigned values of equivalent reference fluorophore

Microsphere ERF Referencefluorophore

FITC 7.74e04 ± 9.1e03 FITC (SRM)PE 7.94e05 ± 9.1e04 Nile RedAPC 3.21e04 ± 4.0e03 APCPacific Blue (PB) 1.59e06 ± 2.0e05 Coumarin 30

Development of Multicolor Flow Cytometry Calibration Standards

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