Method for the quantitative evaluation of data from flow microfluorometry

COMPUTERS

AND

BIOMEDICAL

Method

RESEARCH

9,263-276

(1976)

for the Quantitative Evaluation from Flow Microfluorometry*

of Data

JERROLD FRIED Memorial

Sloan-Kettering

Cancer

Center,

1275

York Avenue,

New

York,

New

York

10021

Received July 21, 1975 A new method is proposed for estimating the distribution of cells among the phases of the mitotic cycle using data from a flow microfluorometer. The method can be applied to asynchronous or synchronous cell populations, and is not limited to systems with very low coefficients of variation of fluorescence intensity. It is based on a mathematical model of the cell population having the following properties: (i) the population is separated into compartments, one consisting of G, cells, another of G, and M cells, and several of S phase cells which have synthesized different specified fractions of their DNA; (ii) the fluorescence intensity of cells in each compartment is normally distributed with the mean of the Gz + M compartment having a channel location twice that of G, ; the S phase compartments have means at intermediate values. Coefficients of variation are the same for all compartments. The sizes of the compartments are determined by a least squares fitting procedure utilizing the observed data. The method and some of its limitations are illustrated by selected examples of simulated data from asynchronous and partially synchronized cell populations.

INTRODUCTION Flow microfluorometry has attracted considerable interest within the past few years becauseof its potential for rapidly measuring selectedcharacteristics in individual cells of a population in suspension.Several thousand cells can usually be measuredwithin a few minutes. With the recent advent of commercial instruments for flow microfluorometry, the field is no longer restricted to those having the resourcesand expertise to construct their own instruments. The original version of the flow microfluorometer (FMF) was developed by Kamentsky and his associates(6, 8), and is similar to the instrument built at Los Alamos (7). Depending on the specific application, viable or fixed cells are prepared and stained with an appropriate fluorescent dye. The suspensionis placed in the FMF and the cells are made to flow through a focused light beam, usually from an argon ion laser at 488 rnp. Scattered and emitted light are detected by appropriate sensorsand photomultiplier tubes, and the signals may be displayed on a cathode * Presented in part at the Ninth Annual Meeting of the Association for the Advancement of Medical Instrumentation, New Orleans, April 20,1974, and at the XI International Cancer Congress, Florence October 25, 1974, and at the Workshop on Mathematical Models in Cell Kinetics, Copenhagen, May 2,1975. Copyright 0 1976 by Academic Press, Inc. 263 All rights of reproduction in any form reserved. Printed

in Great

Britain

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ray tube and passed through a multichannel pulse-height analyzer for quantitative determination of the distribution of fluorescenceintensity. We have been primarily concerned with the quantitative estimation of DNA content of cell populations, and have employed a fluorescent Feulgen technique using acriflavine (II’). A microfluorogram typical of those we obtain from log phase populations is shown in Fig. I (dots). This wasobtained from a human hematopoietic cell line (SK-L7) growing in suspensionculture. Although peaks in fluorescence intensity corresponding to the DNA content of G, and G, phasecells are present.

40-

FIG. 1. Microfluorogram obtained from log phase cells following fixation, acid hydrolysis, and staining with acriflavine according to the method of Yataganas (12). The abscissa corresponds to channel number of the multichannel pulse-height analyzer (Northern Model NS-602), which is proportional to fluorescence intensity and to DNA content. Dots represent the observed data. Dashed lines show extrapolations of the two peaks, which would correspond to G, and C, + M cells, respectively, if there were no S phase cells in these regions. This is usually not the case, however. See text for further discussion.

from the diagram how one can obtain quantitative estimatesof the fractions of cells in the G,, S, and G2(+ M) phasesof the cycle from these data. If one simply extrapolates the two peaksasshown by the dashedline in the figure, and assumesthat the sizesof the G, and G2 + M components are proportional to the relative areasunder them, this would overestimate the fractions ofcells in G, and G2. and would correspondingly underestimate the fraction in the Sphase.This is because the fluorescence intensities of G, and of early S phasecells overlap, as do those in late S and G,. In the example shown, the tritiated thymidine ( [3H]-TdR) labeling index was53 y;,, while the fraction of the total area not included within the extrapolated G, and G2 + M components is only 117:. In addition, we obtained estimatesof the fractions of cells in the different phasesby more conventional methods based on use of

it is not obvious

ANALYSIS OF FLOW MICROFLUOROMETRIC DATA

265

[3H]-TdR and autoradiography (3), and found in one experiment that the percentages of cells in the different phaseswere: G, = 41”/:, S = 52T,, and G, + M = 7 “/o. This paper proposes a new method for estimating the proportion of cells in the phasesof the cycle from FMF data. This method resemblesthat of Dean and Jett (2) in certain respects, but differs from theirs in significant ways. Perhaps the most important difference between the utility of the two methods is that theirs is limited to populations in which the regions between the two peaks can be representedby a seconddegreepolynomial. While this is possiblefor many asynchronous populations and certain others with well-defined G, and G, + M components, there are obviously many synchronous and drug-treated populations to which the method cannot be applied. The method proposed here is not limited to such cases,but can be applied to partially or completely synchronous populations as well asthose in log phase. The present paper will describe the mathematical model and the algorithms employed to analyze the data. The accuracy of the method will also be tested in an idealized case using simulated data from asynchronous and synchronous cell populations. A companion paper (4) will apply the method to data from experimental cell populations either growing exponentially or partially synchronized by exposure to a cytotoxic drug or to cyclic AMP.

DESCRIPTION OF THE MODEL

The mathematical model upon which the proposed method is basedis described with reference to Figs. 2 and 3. The properties and assumptionsof the model are as follows. Subohases

Relalw

cell age 01 ImaturIty

FIG. 2. Diagram of the model of a growing cell population upon which the proposed method for analysis of microfluorometric data is based. Cells within phases or subphases of the cell cycle having similar DNA contents are considered to constitute separate compartments. Thus, Gr cells are considered to form a single compartment, as do G, + M phase cells. S phase cells are divided into several compartments, each consisting of cells which have synthesized approximately the same specified fraction of their total DNA. Thus, for example, all S phase cells which have duplicated between 30% and 40% of their genome may be included within one of the S phase compartments. This definition is similar to the “maturity time” concept of Rubinow (9).

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I. The population is separated into compartments. each consisting ol‘ cells 111 the same phase or subphase of the cell cycle. Figure 2 showsa hypothetical population in which one compartment consists of cells in the G, phahe. another contain3 cell\ in the CZ and M phases. and the remainder consist of cells which have syntheht& different specified fractions of their total DNA. Determination of the acutal numbetof S phase compartments present in a specitic case vbill be discussed belo\\,

Fir;. 3. Simulated microfluorogram (dots) synthesized (using [l]) from the G,, S, and G, + M compartments whose fluorescence intensity distributions are shown. In this example, 39% of the cells are in G,, 4.5 :/, are in each of the 10 S phase compartments, and 167; are in G2 + M. The coefficient of variation of fluorescence intensity is 9.24%. The mean channel numbers of the G, and G, + M components are 22 and 44, respectively, with the S phase compartments at equally spaced intervals between them (refer to first column of Table 1). (Reproduced from “Mathematical Models in Cell Kinetics” (A.-j. Valleron, Ed.), 1975, p. 69, with permission of European Press, Ghent, Belgium).

2. The fluorescence intensity of cells in each compartment is assumed to be normally distributed with the mean intensity of the Gz + M compartment equal to twice that of G,. Means of the S phase compartments are proportional to their average DNA contents. Coefficients of variation (CV) of fluorescence intensity are

assumedto be the samefor all compartments. This isillustrated in Fig. 3, which shows the distribution of fluorescenceintensity of the various compartments, together with the corresponding microfluorogram for the total population. The method for estimating the numbers of cells in the different compartments comprising the population consists essentially of solving a set of simultaneous linear algebraic equations relating the unknown number of cells in each compartment to the experimentally observed number of cells in each channel.

ANALYSISOFFLOWMlCROFLUOROMETRICDATA

267

Thus, if the probability that a cell in compartment j will have a fluorescence intensity detected in channel i is defined as p(i,j), then the total number of cells observed in channel i is

Ai) = j-1 5 AM-G),

i= I. . . . M

Dl

where -u(j) is the number of cells present in compartmentj, A4 is the total number of channels in which cells are detected, and N is the total number of compartments assumed to comprise the system. In these equations, v(i) is determined experimentally and p(i,j), the probability density function expressed in discrete form, can be computed from the mean and standard deviation (SD) of fluorescence intensity of cells in each compartment j. The mean is specified as explained below, and the SD is either supplied as input to the computer program, or is computed from the data (see below). The only remaining unspecified quantities are the x(j) values. Since M > N, the system can be solved by a least squares procedure; we use the packaged version supplied by IBM (5). Using the resulting least squares values of -u(j), the right hand expression in [I] is then used to compute the corresponding number of cells in each channel. The results are printed and plotted to facilitate comparison of the theoretical microfluorograms with the data. COMPUTATIONOF~NPUT

PARAMETERS

Computer programs currently operational permit the option of either supplying as input the values for the mean and CV of the fluorescence intensity of the G, compartment, or computing them from the data. This option permits the analysis of partially synchronous populations in which the channel number of the maximum of the observed microfluorogram may not coincide with that of either the G, or GZ components. Since such a case would require that the CV and location of the mean of the G, component be supplied to the program, a control population containing a well-defined G, peak must be analyzed concurrently. This will be illustrated later with examples. Mean fluorescence intensities of the several S phase compartments are specified as being located 1,2, or 3 channels apart between the G1 and Gz + M means. We generally choose the initial interval to be 2 channels. If, following the least squares analysis, this choice results in one or more compartments having negative x(j) values, those compartments are automatically deleted and the x(j)‘s are recomputed. The process is repeated until a set of nonnegative x(j) values is obtained. Location of the G1 mean. The mean fluorescence intensity of the G1 cells is assumed to be located at the same channel number as the left hand peak on the 10

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microfluorogram representing the total population. Using simulated data. it \\;I\ found that this is a realistic assumption: only when the CV was very large and or the ratio of cells in G, to early S phase was small was the peak shifted. Even in such a case, the shift was usually only one channel to the right. The right hand peak on the microfluorogram, containing most of the G2 cells, ih significantly affected by the presenceof S phasecells. In virtually all casesexamined in which a significant fraction of S phasecells was present, the peak on the microfluorogram was shifted several channels to the left. Thus, although the G2 + M component has a mean at twice the channel location of the G, cells, the observed peaks on the microfiuorogram of the total population generally differ by lessthan a factor of two. This is illustrated by the example shown in Fig. 3. Estimation qf the CV-from the data. The assumption that the fluorescence intensities of individual compartments are normally distributed i!, consistent with our data as well as that of others (2). Figure 4 illustrates this using cells from the peripheral blood of a patient with chronic lymphocytic leukemia. The method employed here for obtaining an initial estimate of the CV utilizes the property of the normal distribution that the ordinate decreasesto 0.606 of its peak

FIG. 4. Flow microfluorogram of peripheral blood cells from a patient with chronic lymphocytic leukemia. The data are shown as dots joined by the sold line. The dashed line shows a normal distribution fit to these data. Although the channel number of each point of the experimental distribution must be an integer, the normal distribution, a continuous curve, is not subject to this constraint. In the present example, the peak of the latter distribution is located 0.3 channels below that of the data.

ANALYSIS

OF FLOW

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269

value at distances of one SD from the mean. If the experimental data were in fact normal, (such as in the case of a highly synchronous population), the SD could be computed as half the distance between the 0.606 points on either side of the peak. The presence of early S phase cells, however, causes a broadening of the peak, and the estimate of SD by this method would then be too large (Fig. 5). If the SD were estimated as the distance from the peak to the left hand 0.606 point, it would generally be too small. If, however, one takes the mean of the preceding two estimates of SD, the resulting SD (and CV) estimate is fairly accurate over a broad range of CV values. provided that the ratio of cells in Cl, to S (N,;,/N, ratio) is not too small (see below 1.

FIG. 5. Illustration of method used to estimate the standard deviation of the G, component from experimental peak containing some S phase cells. The example shown is the same as that in Fig. 3, with CV = 0.0924. In terms of aL and aR, the method estimates the SD as 0..5[aL + 0..5(uL + oR)] = 0.75~~ + 0.25~~. In the example, this yields CV = 0.0940. Refer to text for additional details of the method.

To obtain the CV, the estimated SD is divided by the meanof the channel numbers of the two 0.606 points. The latter is closeto but not usually identical with the channel number corresponding to the maximum data point. For example, in Fig. 5, the abscissavalues corresponding to 17 000 cellsare 20.1 and 24.7 channels(obtained by linear interpolation between the “data” points), with a mean of 22.4 channels. The accuracy of this method was tested using a simulated population whose S phase compartments were assumed equal. Figure 6 shows the resulting CV estimatesas a function of the No,/N, ratio, for several specified CV values. More important than the No,/N, ratio itself is the size of the earliest Sphasecompartments relative to G,, sincethesewould have the greatest peak-broadening effects. Because this information is not usually known prior to analysis, the graph of Fig. 6 cannot ordinarily be used to correct inaccuracy in the CV estimate. An alternative method for this purpose is described in (4)

270

FIG. 6. The latter illustrated aid of [l],

JtiRROLD

FRIED

Relationship between the N,,/Ns ratio and the estimated CV of fluorescence intensity. was computed from the microfluorogram of the total population using the method in Fig. 5. The microfluorograms used in these computations were synthesized with the employing a model having equally sized S phase compartments, and CV’s as indicated.

TABLE SIMULATION

AND ANALYSIS

1 OF Lot

PHASE DATA

Results of analysis

cv %GI %S %Gr+M Channel ~ __-~22(Gd 24 26 28 30 I

Parameters of simulated population

Using estimated CV

Using actual CV

0.0924 39.0 45.0 16.0

0.0940 38.6 46.1 14.7

0.0924 39.0 45.0 16.0

Number of cells

--.-.130000 15000

15 000 15000 15000 15 000 15000 15000 15 000 15000 15000 53 330

128 900 23 000 _31 800 28 300 32 800 18 100 21 800 49 100

130 000 15000 15 000 15000 15001 14 997 15004 14 994 15007 14 994 15003 53 329

ANALYSIS OF FLOW MICROFLUOROMETRIC DATA EXAMPLE:

271

SIMULATLON AND ANALYSIS OF LOG PHASE DATA

To illustrate the applicability and potential accuracy of the proposed method, an idealized population is first examined. Figure 3 shows the microfluorogram synthesized according to [I 1, using parameters listed in Table 1, Fig. 7 and Table I show the results of analysis of these data by the method described above. In this

FIG. 7. Analysis of simulated data from example shown in Fig. 3. Only the numbers of cells per channel were used in the analysis; other parameters were computed from these data by the methods described. Data input to the program are shown as dots; solid lines correspond to the resulting least squares estimates of distributions of fluorescent intensities for the total population, the Gr and G, + M compartments, and the sum of the S phase compartments. The latter distribution is equal, at each channel, to the difference in cell numbers between the curves representing the total population and the G, and GZ + M components.

analysis, only the data corresponding to the total population were input to the computer program; the other parameters were estimated from these data as discussed previously. To determine the extent to which the discrepancy between the derived and the actual compartment sizes was attributable to the fact that the estimated CV used in the least squares analysis was slightly too large, the program was rerun using the correct CV of 0.0924. As seen in the right hand column of Table I, the results were in complete agreement with the original model.

273

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SIMULATION

A&II

ANALYSIS

ASSUMED

NUMBER

FRIEII

OF SYNCHRONOUS OF S PHASE

POPULATIONS:

EFFECT

ot

COMPARTMENTS

The number of S phase compartments and the relative (channel) locations of their mean fluorescence intensities are to some degree arbitrary, and must be specified to solve the system in accordance with [I]. In its present form, the computer program carrying out the analysis assumes an initially equidistant set of compartments. The distance (number of channels) between compartments is input to the program, and must be an integer. In practice, we prefer a separation of two channels between compartments, although because of computer storage limitations on our machine, the initial separation may sometimes be set at three. l3ecause the distribution of DNA content in the population is for all practical purposes continuous, it appears reasonable to think that the smaller the separation between compartments, the better. The following examples were designed to determine whether this is true. at least for an idealized case with no data error. Since an important application of the method described in this report is the analysis of synchronous or partially synchronous data, the examples analyzed were of this type. Since it cannot be assumed that the maximum point in the microfluorogram of a synchronous population corresponds to the G, compartment, the channel location of the G, mean and its CV must in that case be supplied as input. To obtain these parameters, an asynchronous population (or at least one known to have a prominent G, component) is employed as a control. These parameters must of course be the same in the control as in the synchronous population. Four simulated systems were analyzed. All were based on the asynchronous control shown in Fig. 3, whose parameters are listed in Table I, first data column. The four simulations differ essentially in the number of S phase compartments used to synthesize the histograms representing the total population, although all have the same total numbers of cells in corresponding phases. Within a single population, the sizes of the different S phase compartments are equal. The simulated data were based on an assumed separation between S phase compartments of 1, 2, 3, or 4 channels. Table 2 lists the assumed parameter values and compartment sizes for each of these cases. Analysis of each of these four data sets was then carried out using these same four separation intervals to specify the locations of the S phase compartments. Thus, a total of sixteen analyses were performed with these data. Results of these analyses are listed in Table 3 as the percentage of cells in the G,. S, and Gz. + M phases in each of the sixteen cases. and corresponding distributions of fluorescence intensities are shown in Fig. 8. In this figure, the dots correspond to the simulated data, and the lines to the microfluorograms representing the solutions for the different assumed separations of S phase compartments, as indicated. It is evident from Table 3 and Fig. 8 that the solutions are quite accurate if the assumed separation interval between S phase compartments is not greater than the

ANALYSIS

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DATA

TABLE 2 SIMULAT~ONOFSYNCHRONOUSCELLPOPULATIONS Number ofcells Separation of S phase compartments (Channels)

Channel

-.. _-

-

22 (G, = 1.9%) 23 24 25 ‘6 27 28 29 30 31 32 33 (S = 98.1%) 34 3.5 36 37 38 39 40 41 42 43 I 44(G,=O)

1 5 000 65 000 65 000 30 000 30 000 12 500 12 500 10000 10000 5000 5000 2 500 2 500 1 500 1 500 1 000 1 000 500 500 0 0 0 0

2

5000 130 000 60 000 25 000 20 000 10 000 5000

TABLE

3 5000

4 5 000

190 000 208 750 35 000 33 750 20 000 6 500

3 000 2 000 1 000 0

3 500

0

0

9 750 -

3 750 1000

-

0

3

RESULT~OFANALYSISOFSIMULATEDSYNCHRONOUSPOPULATIONS: PERCENTAGEOFCELLSING,,S,AND Gr+ M PHASES' S (98.1%)

G, (1.9%)*

Gz+ M (0%)

3’

1

3

3

4

1

2

3

4

I

2

3

1 2 3 4

1.9 7.9 21.5 33.1

1.9 1.9 12.0 23.7

1.9 0 1.9 14.7

1.9 1.9 0 1.9

98.1 92.0 78.1 66.9

98.1 98.1 87.8 76.3

98.1 100.0 98.1 85.2

98.1 98.1 100.0 98.1

0 0.1 0.5 0

0 0 0.2 0

0 0 0 0.1

4 0 0 0 0

’ Simulation and analysis programs assumed S phase compartment spacing of 1, 2, 3 and 4 channels, in all combinations. h Cell cycle distributions used in simulations. c Number of channels between S phase compartments in simulating program (across) or in analyzing program (down).

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!!

. L 9

Id1:’rti ‘“; 11

3oc

1 i i

1 10

/ -1 ,\ 20

’ 30

40

50

Fluorescence

10 mtensity

(channel

20

30

40

50

no )

Fro. 8. Effect of separation of S phase compartments on synthesized microfluorograms and on computer analysis of simulated data from a synchronous cell population. Simulated data, shown by dots, were obtained using [I], under the assumptions that the mean fluorescence intensities of successive S phase compartments were spaced (a) 1, (b) 2, (c) 3, or (d) 4 channels apart, respectively. Curves represent the corresponding least squares solutions under the respective assumptions that the S phase compartments are spaced (at least) A = 1,2,3, or 4 channels apart, as indicated. In cases where a curve or a portion thereof is not shown, it is identical in that region to the curve corresponding to A = 1 channel. In a few cases, the least squares solution yielded nonzero values for the G, + M compartment (Table 3): these were very small, however, and are not shown in the figure.

interval employed in the original synthesis.While in a specific case,the result may be quite satisfactory even when this rule is violated, it would appear that the separation interval (d) should be as small as possible.For reasonsthat will be discussedbelow, however, it may be preferable to usea separation interval of 2 rather than 1 channel in most cases. DISCUSSION

The method described in this report was designed to permit the determination of the distribution of cells among the phasesand subphasesof the cell cycle, utilizing data obtained from flow microfluorometry. The method obviously requires that a fluorescent dye be usedwhich binds quantitatively to DNA. There is evidence that the acriflavine-Feulgen technique satisfiesthis requirement (I, 7, f2). The method proposed here does not require that significant G, or G2 + M components be present. However, if these are absent, a control population containing them must be analyzed concurrently. Since the control is used to determine the

ANALYSIS

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locations of the means of the G,and Gz + M components as well as their CV, these must be the same for the test sample as for the control. This assumption is probably valid for populations synchronized by a relatively mild method such as mitotic selection, but it may not always be valid for cells exposed to cytotoxic drugs. It would be prudent to ascertain whether the binding of the fluorescent dye to DNA may be altered in the test sample as compared with the control. This point is discussed further in (4). The examples analyzed in this paper, although limited for the most part to simulated data from idealized systems, provide some insight into the potential applicability and limitations of the method. In the following paper (4), the method will be applied to real data from both asynchronous log phase populations and drugperturbed cells. The data presented in Table 1 and Fig. 7, which present the analysis of the data of Fig. 3, show that the predicted fractions of cells in the G1, S, and G, + M phases are in excellent agreement with the actual values. The distributions within the S phase compartments (column 2 of Table 1) are somewhat less accurate, however, even allowing for the fact that pairs of adjacent S phase compartments were combined by the analysis routine. These results were greatly improved when the correct CV (0.0924) was employed in the analysis (column 3). While Fig. 6 cannot always be used to correct the original CV estimate, an alternative method is described in (4). The effects of spacing between the S phase compartments on both simulated data and on their analysis were illustrated in Fig. 8 and Table 3 for an assumed synchronous cell population. In these examples, in which most of the cells were in very early S phase, the proposed method of analysis was accurate so long as the assumed spacing of S phase compartments in the analysis program was less than or equal to that in the synthesis program. Exceptions were the two examples in which the simulated data with spacing of three or four channels were analyzed under the assumptions that the spacing was two or three respectively. The errors in these cases were probably caused by the assumption in the analysis that there were no compartments corresponding to channel 25 in the former case or 26 in the latter, whereas these were in fact the largest single compartments in the population. Although the results suggest that assumed S phase compartment spacings of 3 or 4 channels are likely to be inaccurate when analyzing real data, it should be noted that this example, having a small G, component but a very large early S phase, was intended to provide a difficult test of the model. It is likely that in most asynchronous populations and some synchronous ones, these spacings would yield acceptable results. In situations in which cells may be arrested in early S phase, such as when exposed to cytosine arabinoside (IO, /I). intercompartmental S phase spacing of one or two channels is probably best. An argument against the use of single channel spacing is that with such a small distance between the G, and earliest S phase compartments (as well as between the Gz + M and last S phase compartments), it is likely that the least squares estimate of

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the relative number ofcells in these compartments will be very sensitive to data error. For this reason it may be preferable to employ a spacing of two for the analysis. Ot course, the program could be modified to prohibit the occurrence of an S phase compartment within one channel of the C, or Gz + M compartments, but to permit this spacing between adjacent S phase compartments. ACKNOWLEDGMENTS I wish to thank Mr. Harvey Friedman for expert programming assistance during the early phases of this work, and Miss Lana Hart for competent assistance in preparing this manuscript. This project wassupported by grants from the National Cancer Institute, CA 08748 and CA 16757, American Cancer Society, ACS-ET-2C and Cl 67A, and the Hearst Fund, the Lloyd Craver Fund. the United Leukemia Fund, the Grossinger Foundation Fund. and the Huntington Leukemia Research Fund. REFERENCES 1. B~HM, N. Fluorescence cytophotometric determination of DNA. Techn. Biochem. and Biophys Morphof. 1,89 (I 972). 2. DEAN, P. N. AND JETT, J. H. Mathematical analysis of DNA distributions derived from How microfluorometry. J. Cell Biol. 60, 523 (1974). 3. FRIED, J., FRIEDMAN, H., ZIETZ, S., Tooo, A., STRIFE,A., AND CLARKSON, B. Computer analysis of tracer kinetic data from a human hematopoietic cell line during different phases of growth. Comput. Biomed. Res. 7, 333 (1974). 4. FRIED, J., YATAGANAS. X., KITAHARA, T., PEREZ, A. G.. FERGUSON,R., SULLIVAN, S.. ANI) CLARKSON, B. Quantitative analysis of flow microfluorometric data from asynchronous and drug-treated cell populations. Comput. Biomed. Rex 9, 277-290 (1976). 5. INTERNATIONAL BUSINESSMACHINES COMPANY. System 360 Scientific Subroutine Package. Version 111, Program No. 360A-CM-03X, pp. 160-164 (1970). 6. KAMENTSKY, L. A., MELAMED, M. R., AND DERMAN, H., Spectrophotometer : new instrument for ultrarapid cell analysis. Science 150, 630 (1965). 7. KRAEMER, P. M., DEAVEN, L. L., CRISSMAN, H. A., ANU VAN DILLA, M.A. DNA constancy despite variability in chromosome number. Adu. CeN Molec. Biol. 2,47 (1972). 8. MELAMED, M. R., KAMENTSKY, L. A., AND BOYSE,E. A. Cytotoxic test automation: a live-dead cell differential counter. Science 163,285 (1969). Y. RUBINOW, S. I. A maturity-time representation for cell populations. Biophysical J. 8. 1055 (I 968). 10. T’OE~EY,R. A. AND CRISSMAN,H. A. Use of flow microfluorometry in detailed analysis of effects of chemical agents on cell cycle progression. Cancer Res. 32,2726 (1972). II. YATAGANAS, X., STRIFE, A., PEREZ, A., ANU CLARKSON, B. Microfluorometric evaluation of cell kill kinetics with l-b-D-arabinofuranosylcytosine. Cancer Res. 34,279s (1974). 12. YATAGANAS, X., MITOMO, Y., TRAGANOS, F., STRIFE, A.. ANU CLARKSON. B. Evaluation of a Feulgen-typereactioninsuspensionusingflow microfluorometryandacellseparationtechnique. Actu Cytologica, 19,71 (1975).