Cytometry 12:234-241 (1991)
1991 Wiley-Liss, Inc.
Evaluation of Flow Cytometric Methods for Determining Population Potential Doubling Times Using Cultured Cells’ Nicholas H.A. Terry: R. Allen White, Marvin L. Meistrich, and Dennise P. Calkins Departments of Experimental Radiotherapy (N.H.A.T.,M.L.M., D.P.C.) and Biomathematics (R.A.W.),The University of Texas M. D. Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030 Received for publication June 12, 1990; accepted November 6, 1990
Various methods have been proposed for determining the potential doubling times (Tpot) of mammalian cell populations by using flow cytometric techniques after labeling the cells with bromodeoxyuridine (BrdUrd). We show here that, in a well-defined in vitro system where multiple time measurements are possible, all the methods give similar results that are close to the true population doubling time. Of ultimate interest, however, is the accuracy of determination of Tpot from a single time point. In this paper we compare the accuracy and precision of the methods in making such determinations at different times after labeling. The relative movement (RM) of BrdUrdlabeled cells that have not divided at the time of assay allows for computation of
A major purpose of the present work is to provide a test of methods for determining the potential doubling times (Tpot) of mammalian cell populations by using flow cytometric techniques. Of ultimate interest is the rapid evaluation of the parameters required to measure the growth kinetics of cells in human tumors. Of the possible measures of growth kinetics, the one that seems to be the most predictive of therapeutic response is the potential doubling time, Tpot of Steel (12), which is a measure of the time that would be required by a tumor to double in cell number if there were no cell loss and if quiescent cells were included. Several new procedures have been proposed (2,13-17) which allow, in principle, the calculation of Tpot from flow cytometric data obtained on the single biopsy or surgical specimen that is typically available from human tumors. To evaluate these procedures quantitatively, it is necessary to have multiple replicates of samples a t numerous time points. Therefore, we have chosen to compare several
the length of S phase (T,). The precision of estimation of T, was enhanced when a quantity, v (a function of the fraction of BrdUrd-labeled divided and the fraction of BrdUrd-labeled undivided cells), was used to estimate the initial intercept of RM. Furthermore, calculation of Tpot from the formula, Tpot = Pn(2)T,lu, gave values closest to the observed population doubling time. It is suggested that the use of RM with v be the analytical method of choice for the calculation of Tpot from single time-point observations, preferably made at times between the length of the G, and M phases (TG,M) and T,. Key terms: Cell kinetics, bromodeoxyuridine, mathematical models, v function, flow cytometry
different techniques for the computation of the potential doubling time in a well-defined in vitro system in which multiple time measurements are possible and to compare the overall data set directly with the individual time-point measurements. The experimental basis of these methods has been made possible by the development of monoclonal antibodies specific for bromodeoxyuridine (BrdUrd) that has been incorporated into DNA (6). Human tumor cells can be labeled by in vivo administration of a nontoxic amount of BrdUrd (7,9,18). The cells in the S
‘Supported by grants CA-06294 and CA-11430 from the National Cancer Institute, and by the Katherine Unsworth Fund. ‘Address reprint requests to N.H.A. Terry, Department of Experimental Radiotherapy, The University of Texas M. D. Anderson Cancer Center, 1515 Holcombe Blvd., Box 066, Houston, TX 77030.
COMPARISON OF MEASURES O F POTENTIAL DOUBLING TIME
phase of the cell cycle incorporate BrdUrd and continue normally through the cell cycle ( 2 ) ; a single sample is taken several hours later. Flow cytometry is then used to measure, simultaneously, total DNA content and BrdUrd uptake (5). In this way the DNA of all cells, BrdUrd-labeled and -unlabeled, can be measured at the time of biopsy. A single sample at a given time after administration of BrdUrd provides information regarding the progression of cells through the cell cycle, and this information can be applied to calculate Tpot. The basis for calculating Tpot from a single point was the elegant relative movement (RM) technique of Begg et al. (21, by which the mean fluorescence of the DNA stain of the BrdUrd-labeled cells that have not divided as of a given time point is measured. RM(t),the relative movement of these BrdUrd-labeled cells a t time t. is the ratio of the difference between the mean DNA content of the labeled cells and the G, DNA content to the difference between G,M and G, DNA contents. Immediately after labeling with a BrdUrd pulse, the labeled cells will have a n average DNA content approximately halfway between GI and G,M. As the cells progress through the cell cycle, with increasing time after BrdUrd labeling, the DNA content of the BrdUrd-labeled cells increases nearly linearly until the BrdUrd-labeled undivided cells have the mean DNA content of the G,M cells at a time equal to the duration of S phase (TJ. The attraction of this methodology for use with human tumors is that because RM(0) can be estimated without knowledge of the kinetics and because RM(t) is nearly a linear function of time, a single measurement of RM(t) may be used to compute a value for T, by extrapolation to RM(T,) = 1. The value of T,, together with a n estimate of the labeling index (LI), allows estimation of Tpot from Tpot=AT,/LI, where A is a constant related to the relative durations of the phases of the cell cycle (12).This methodology will be referred to as RM85 throughout this paper. It should be noted that LI and A can be estimated, but not calculated exactly, from the data made available from a flow cytometric histogram. For instance, the apparent LI is the percentage of BrdUrd-labeled cells a t any given time. This apparent LI differs from the true LI (i.e., a t time = zero) first, because of division of unlabeled G, cells and secondly, because of division of labeled S phase cells. Whereas Begg et al. (2) based the method for establishing the initial intercepts of the relative movement curve on experimental observations, White and Meistrich (15) derived analytical expressions for RM(t) in terms of the cycle parameters of the cell populations. They also derived a n explicit value for the initial point to which the nearly linear portion back-extrapolates, i.e., RM"(0). These authors demonstrated that T, may be estimated from the slope of the line connecting this initial value for RM with the value determined from a single measurement a t time t; the slope equals 1/2T,. Calculation of Tpot still required a n assumed value for A and a n estimate of LI. This method, which will be
235
referred to as RM86, theoretically gave more accurate measurements for T, than did the use of the extrapolation method, RM85. Exact calculation of Tpot from T, is made possible by the development of a new function ( v ) (17), which may be computed from the fractions of cells that are BrdUrd-labeled and either have divided or remain undivided at the time of measurement. Tpot can be found directly from v, using the formula Tpot = tn(2)T,/v, without the need to estimate LI or A. In addition, v may be used to compute RM"(0) and may yield a more accurate value than that described above (15). This methodology will be designated RM90. Relative movement methods are based on the DNA content of the labeled cells. Alternative methods involve the calculation of the fractions of labeled and unlabeled cells in different cell cycle compartments. White (14) has described a novel method, designated the depletion function (DF), which was shown theoretically to give a direct determination of the population doubling time (Tpot) from a sample a t a single time point. Other expressions describing the fractions of cells in various cell cycle compartments can also be used to calculate Tpot (16) but these methods require measurements of multiple time points. In this paper we present data from in vitro experiments using cultured Chinese hamster ovary (CHO) cells to test the application of the relative movement and depletion function methods to flow cytometric measurements of a population of cells and t o compare the values of Tpot obtained by these methods with each other and with doubling times obtained from the cell growth curves. Moreover, the precision of each of the various methods for estimating Tpot from single timepoint measurements is evaluated.
MATERIALS AND METHODS Cell Culture and Staining Exponentially growing CHO, clone AA8 cells were pulse labeled and chased as follows, care being taken to minimize perturbation. One micromolar BrdUrd was added directly to the culture medium for 20 min before washing the cells twice with warmed serum-free medium. Fresh, warmed, pre-gassed serum-containing medium was added for the chase period. Replicate dishes were sampled immediately and a t intervals from 15 min to 14 h thereafter. Trypsinized cell samples were prepared, and after resuspension in cold phosphate-buffered saline (PBS), they were fixed by addition of cold ethanol, while vortexing, until a final concentration of 60% was reached. Samples were stored a t 4°C. The experiment was performed three times and the data pooled. Single nuclei suspensions were prepared by incubation of the fixed cells a t room temperature, while rocking, for 20 min with 0.04% pepsin (EM Science, Cherry Hill, NJ) in 0.1 N HC1. The initial concentration a t the start of denaturation was standardized to 4 x 10' cells per 5 ml. Nuclei in suspension were stained using a
236
TERRY ET AL
variation of Schutte et al.'s (11)modification of Dolbeare's method (5). Nuclei were incubated with 2N HC1 for 20 min a t 37"C, and then sodium borate (0.1M twice the original sample volume) was added. The sample was washed with PBS containing 0.5% Tween-20 and 0.5% bovine serum albumin (PBTB) before resuspension in 0.2 ml of PBS 0.5% Tween-20 (PBT) containing 0.2 pL of the anti-BrdUrd monoclonal antibody IU4 (courtesy of F.A. Dolbeare, M. Vanderlaan and colleagues, Lawrence Livermore National Laboratory) and incubated for 1h a t room temperature in the dark. After washing again in PBTB, the nuclei were further incubated with PBT and 1%normal goat serum, together with FITC-conjugated goat-antimouse IgG (Sigma Chemical Co., St. Louis, MO), for 45 min. After washing once more in PBTB the nuclei were resuspended a t a concentration of 106/ml in PBTB containing 10 pgirnl propidium iodide (PI) (Sigma) before determining the fluorescence by flow cytometry.
RMT(t)=
+
Flow Cytometry Bivariate distributions of BrdUrd content (green fluorescence) vs. DNA content (red fluorescence) were measured using a n EPICS 751 flow cytometer (Coulter Corp., Hialeah, FL) equipped with narrow beam (5 pm) excitation optics and a quartz flow cell. Excitation was a t 488 nM using a 5W argon-ion laser operating a t 200 mW. BrdUrd content was measured using a logarithmic amplifier with a 530 nm short-pass filter, and DNA content (PI) collected after a 610 nm long-pass filter. Doublets and clumps were excluded from the analysis by gating on a bivariate distribution of the red peak vs. integral signal. Fifty thousand events were collected in the final gated histogram. The mean CV for the G, peak was 3%. Data Analysis The method of Begg et al. (2) was used to calculate the (RM) of BrdUrd-labeled undivided cells between the G, and G, peaks, as measured on a one-dimensional DNA projection of the bivariate histogram; RM(t) =
Fl"(t) - FGI FGZM - FG1
where FG, = G, mean red fluorescence channel; FG,M = G,M mean red fluorescence channel; and F'"(t) = the mean red fluorescence of the BrdUrd-labled cells which have not yet divided a t time (t).Cytologic analytical software (EPICS Division of Coulter Corp.) was used to model the DNA distributions of the total cell population and of the BrdUrd-labeled cells and to determine the values of these variables. The increase in relative movement with time [RM(t)l has been previously described based on basic principles of cell kinetics (15; Eq IS]). The equations used for RM(t) were made up of two different curves, RM'(t) and RM"(t), given by the following formulae:
1 + ct
e cTs(ec'i cTJ
cT,(1
=
0
if
=
TGzM 5 t
t
5
c-'~s)
(2)
TGzM, and
if
5
-
5
T,
where c, the growth rate of the population, is tn(2)/ Tpot; tn(2) is the natural logarithm of 2. Proprietary software developed by one of us (R.A.W.) was used to model the fit of these equations to the individual data points (16). This software is based on a non-linear fitting procedure developed by Marquardt (8) and implemented by Chandler (4). In the clinical setting where one or only a very few time points are available for analysis, the goal is to obtain a n estimate of T, from the RM a t only one time point. In this situation, the assumed initial value of RM(0) is critical to the estimation of T,. White and Meistrich (15) derived a n expression for the initial value a t times greater than TG,M by substituting the values of the fractions of cells (fl in each phase of the cell population into RM(0): (4)
where 2
=
Pn
L
1
+ fS + fGzM 1 + P;zM
The values of fs and fi2M can, in theory, be derived from the steady-state distributions of cells in the DNA histograms. v Function. The derivation of the v function is given in full elsewhere (17). Briefly, v is defined a s follows: (6)
where f'"(t) = fraction of cells that are labeled and remain undivided a t time t, and f I d ( t ) = fraction of cells that are labeled and have divided by time t. It can be shown that Tpot = tn(2)T,/v and c = v/T,. Furthermore, v is constant for times from TG,M to TG,M + T, and changes only slowly for longer and shorter times. An additional utility of u is that it allows computation of the initial values of RM'(0) and RM"(0) by substituting v for cT, in Equations 2 and 3. A review of the literature (12) and our experience (16) shows that for mammalian cell populations TG,M is approximately 0.3 T,. Hence, Equations 2 and 3 reduce to the following: 7)
COMPARISON OF MEASURES OF POTENTIAL DOUBLING TIME 0
Hrs
3
Hrs
237 5
Hrs
FIG 1. Bivariate histograms (upper panels) and DNA distributions (lower panels) for Chinese hamster ovary cells cultured in vitro and assayed at three different times after BrdUrd exposure. In the upper panels, the slanting lines separate the BrdUrd-labeled cell populations from unlabeled populations, and the vertical lines above the
slanting lines separate the divided from undivided labeled cells. The filled histograms in the lower panels identify the DNA distributions of the BrdUrd-labeled cells within the total DNA distributions (open histograms).
Depletion function method. The theoretical derivation of this methodology is described in detail elsewhere (14).Briefly, the depletion function D'(t) is a transformation of the fraction of BrdUrd-labeled undivided cells [t"(t)] into a form that is a linear function of time over much of its range. Tpot can be calculated directly from D'(t).
sitive even to small errors in the evaluated fractions of cells in S and G2M.
RESULTS Representative raw data are shown in Figure 1 a s bivariate histograms of total DNA content vs. BrdUrd incorporation (upper panels) and as DNA histograms of the total cell population and BrdUrd-labeled cell popD'(t) = Yn [ l + P(t)] (9) ulation only (lower panels). Data are shown for 0, 3, The same population of labeled undivided cells used and 5 h after flash-labeling of cells with BrdUrd, and in the relative movement analyses is used here, except the movement of the BrdUrd-labeled cells towards G, that it is the fraction of these cells, t"(t), rather than can clearly be seen. The vertical lines on the upper their mean fluorescence, which is modeled. For times panels of Figure 1indicate the boundaries demarcating greater than TG,M, the depletion function has the fol- the BrdUrd-labeled cells that have not yet divided from lowing form: which the RM, i.e., the mean red fluorescence, of these cells was measured. D'(t) = Cn (2 - fG1) - Yn(2) t/Tpot 110) The values of Tpot obtained from these results will This is a linear, decreasing function of time, with a slope of -en(2)/Tpot and a n intercept with the y axis be described first by using the model equations to fit all that depends on the fraction of all cells in the popula- the data points and then by fitting single data points as tion that are in Gl(fG1). fG1 can be calculated from a is necessary, for example, in the evaluation of limited one-dimensional DNA histogram. Since fG1 = 1 - ( f s clinical data. + fGGSM)Equations 9 and 10 can be rewritten a s Results from Fitting of the Total Data Set tn(2) tiTpot
=
en(l
+ fs + fc2,q)- tn(l + f"(t),
(11)
This form makes it more apparent that Tpot is sen-
Figure 2 shows the RM of the BrdUrd-labeled cells as a function of time. Equations 2 and 3 were used to fit a
238
TERRY ET AL.
Table 1 Estimates of Tpot for Each Method of Analysis Using the Total Data Set (Over the Appropriate Ranges of Time) Method Cell counts RM:Tpot = Pn(2)ic RM:Tpot = XT,/LI, A = 1 RM:Tpot = Cn(2)TS/u
DF
Time interval range (h) 0.25-24 0 -9 0-9 0-9 0-11
Tpot (h) (* 1 S.E.M.) 13.8 1.7" 11.9 i 4.2 15.3 ? 3.3 14.2 _C 1.3 13.1 2 4.8
*
"Actually the doubling time of the population, but close in value to Tpot because cell loss is negligible.
Time
( H o u r s )
FIG 2. The relative movement of the BrdUrd-labeled undivided cells between the G , and G,M DNA fluorescence channels, as a function of time. Equations 2 and 3 were used to fit a curve to all the data points using non-linear least squares fitting techiques.
curve to all the data points. The three unknowns in these RM equations-c ( = tn(2)/Tpot),T,, and TG,Mwere all allowed t o vary in the fitting of the curve in Figure 2. The initial values of RM'(0) and RMT1(0)were found to be 0.48 and 0.57, respectively. The curve in Figure 2 saturates a t a n RM of 1.0 a t t 2 T,. The computed values of T,, TG,M, and Tpot from the total data set in Figure 2 were found to be 9.0 t 0.7 h, 2.9 t 1.4 h, and 11.9 t 4.2 h, respectively. The value of TG, was indistinguishable from 0 (+ 4h); since TG, enters into the equations for RM(t) (15) only to second order through the value of c, fitting of RM(t) is very inaccurate in determining TG,. Since the precision of calculation of T, in this manner is greater than that of Tpot, we have used alternative methods to calculate Tpot. First we used the equation Tpot = A T,/LI. Since the apparent LI varies with time the true LI [P(O)] was used. For the 5 data points a t t = 0 the LI was found to be 58%' (t5% SD). Although A cannot be calculated from a single DNA histogram, we calculate A = 1.01 using more complete information on the cell cycle parameters of these CHO cells from the full set of histograms (16). From the calculated value of Ts with A fixed equal to 1.0, and using the LI a t time 0, we calculated a Tpot of 15.3 h (f3.3 h SEMI (Table l ) . Alternatively, Tpot can be calculated from T, by use of the v function. The average value of v was found to be 0.427 (-+ 0.057 SD). Hence from Tpot = en(2) T,/v the average value of Tpot, using data gathered over the range of 0-9 h , was found to be 14.2 h (t 1.3 h SEM). Figure 3 shows the DF plotted for these same data a s a function of time. The curves were fitted by calculating the variables fG, and c for times t > TG,M and the variables TG1, T,, for c for t < TG2M (14). The curve fitted to the data in Figure 3 was computed using all
-
I
Time
(Houra)
FIG.3. The fraction of BrdUrd-labeled undivided cells as a function of time (depletion function). The potential doubling time (Tpot)can be calculated from the slope.
the data points while allowing freedom of all these variables. The values of T, and TG,M calculated from this fitting were 8.1 and 2.8 h, respectively. Tpot was found to be 13.1 h (* 4.8 h SEM) (Table 1).The initial intercept of the linear portion of the curve, DF"(O), was found to be 0.58, which corresponded to a n fGl of 30%. The estimates of Tpot derived by the RM and DF methods of analysis from complete fits to this data set are similar (Table 1).Within experimental errors these results are in reasonable agreement with the estimate of population doubling time of 13.8 h made by simply counting cells a s a function of time over a 24 h period.
Results From Data at Single Time Points In order to establish the precision of estimates of Tpot that could be obtained from measurements of a single sample using each method of analysis, three time ranges were selected and fits were made to single data points. The three time periods chosen corresponded approximately to the lengths of TG,M (2-3 h), TG,M + 0.5 (T, - TG2M)(5-6 h), andT, + TGzM (9-11 h). All parameters needed to calculate Tpot-including RM, the apparent LI, v , DF, f i , and fGzM-were cal-
COMPARISON OF MEASIJRES O F POTENTIAL DOUBLING TIME
239
Table 2 Estimates o f Tpot for Each Method of Analysis From Single Samples Averaged Over Restricted Subsets of the Data
Time Method RM85 A = 1 RM(0) = 0.5 RM85 h = 1 RM(0) = 0.6 RM86 Tpot = XTsiLI X = l RM90
Tpot
=
No. of points 7 10 8 7 10 8 7 10 8 7 7 10 8 7 10 8
(h) 2-3 5-6 9-11 2-3 5-6 9-11 2-3" 5-6" 9-11" 2-3b 2-3" 5-6" 9-11' 2-3 5-6 9-1 1
Pn(2)iTJv
DF
Median Tpot (h) 7.4 8.8 c13.8 11.5 9.2
1991 Wiley-Liss, Inc.
Evaluation of Flow Cytometric Methods for Determining Population Potential Doubling Times Using Cultured Cells’ Nicholas H.A. Terry: R. Allen White, Marvin L. Meistrich, and Dennise P. Calkins Departments of Experimental Radiotherapy (N.H.A.T.,M.L.M., D.P.C.) and Biomathematics (R.A.W.),The University of Texas M. D. Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030 Received for publication June 12, 1990; accepted November 6, 1990
Various methods have been proposed for determining the potential doubling times (Tpot) of mammalian cell populations by using flow cytometric techniques after labeling the cells with bromodeoxyuridine (BrdUrd). We show here that, in a well-defined in vitro system where multiple time measurements are possible, all the methods give similar results that are close to the true population doubling time. Of ultimate interest, however, is the accuracy of determination of Tpot from a single time point. In this paper we compare the accuracy and precision of the methods in making such determinations at different times after labeling. The relative movement (RM) of BrdUrdlabeled cells that have not divided at the time of assay allows for computation of
A major purpose of the present work is to provide a test of methods for determining the potential doubling times (Tpot) of mammalian cell populations by using flow cytometric techniques. Of ultimate interest is the rapid evaluation of the parameters required to measure the growth kinetics of cells in human tumors. Of the possible measures of growth kinetics, the one that seems to be the most predictive of therapeutic response is the potential doubling time, Tpot of Steel (12), which is a measure of the time that would be required by a tumor to double in cell number if there were no cell loss and if quiescent cells were included. Several new procedures have been proposed (2,13-17) which allow, in principle, the calculation of Tpot from flow cytometric data obtained on the single biopsy or surgical specimen that is typically available from human tumors. To evaluate these procedures quantitatively, it is necessary to have multiple replicates of samples a t numerous time points. Therefore, we have chosen to compare several
the length of S phase (T,). The precision of estimation of T, was enhanced when a quantity, v (a function of the fraction of BrdUrd-labeled divided and the fraction of BrdUrd-labeled undivided cells), was used to estimate the initial intercept of RM. Furthermore, calculation of Tpot from the formula, Tpot = Pn(2)T,lu, gave values closest to the observed population doubling time. It is suggested that the use of RM with v be the analytical method of choice for the calculation of Tpot from single time-point observations, preferably made at times between the length of the G, and M phases (TG,M) and T,. Key terms: Cell kinetics, bromodeoxyuridine, mathematical models, v function, flow cytometry
different techniques for the computation of the potential doubling time in a well-defined in vitro system in which multiple time measurements are possible and to compare the overall data set directly with the individual time-point measurements. The experimental basis of these methods has been made possible by the development of monoclonal antibodies specific for bromodeoxyuridine (BrdUrd) that has been incorporated into DNA (6). Human tumor cells can be labeled by in vivo administration of a nontoxic amount of BrdUrd (7,9,18). The cells in the S
‘Supported by grants CA-06294 and CA-11430 from the National Cancer Institute, and by the Katherine Unsworth Fund. ‘Address reprint requests to N.H.A. Terry, Department of Experimental Radiotherapy, The University of Texas M. D. Anderson Cancer Center, 1515 Holcombe Blvd., Box 066, Houston, TX 77030.
COMPARISON OF MEASURES O F POTENTIAL DOUBLING TIME
phase of the cell cycle incorporate BrdUrd and continue normally through the cell cycle ( 2 ) ; a single sample is taken several hours later. Flow cytometry is then used to measure, simultaneously, total DNA content and BrdUrd uptake (5). In this way the DNA of all cells, BrdUrd-labeled and -unlabeled, can be measured at the time of biopsy. A single sample at a given time after administration of BrdUrd provides information regarding the progression of cells through the cell cycle, and this information can be applied to calculate Tpot. The basis for calculating Tpot from a single point was the elegant relative movement (RM) technique of Begg et al. (21, by which the mean fluorescence of the DNA stain of the BrdUrd-labeled cells that have not divided as of a given time point is measured. RM(t),the relative movement of these BrdUrd-labeled cells a t time t. is the ratio of the difference between the mean DNA content of the labeled cells and the G, DNA content to the difference between G,M and G, DNA contents. Immediately after labeling with a BrdUrd pulse, the labeled cells will have a n average DNA content approximately halfway between GI and G,M. As the cells progress through the cell cycle, with increasing time after BrdUrd labeling, the DNA content of the BrdUrd-labeled cells increases nearly linearly until the BrdUrd-labeled undivided cells have the mean DNA content of the G,M cells at a time equal to the duration of S phase (TJ. The attraction of this methodology for use with human tumors is that because RM(0) can be estimated without knowledge of the kinetics and because RM(t) is nearly a linear function of time, a single measurement of RM(t) may be used to compute a value for T, by extrapolation to RM(T,) = 1. The value of T,, together with a n estimate of the labeling index (LI), allows estimation of Tpot from Tpot=AT,/LI, where A is a constant related to the relative durations of the phases of the cell cycle (12).This methodology will be referred to as RM85 throughout this paper. It should be noted that LI and A can be estimated, but not calculated exactly, from the data made available from a flow cytometric histogram. For instance, the apparent LI is the percentage of BrdUrd-labeled cells a t any given time. This apparent LI differs from the true LI (i.e., a t time = zero) first, because of division of unlabeled G, cells and secondly, because of division of labeled S phase cells. Whereas Begg et al. (2) based the method for establishing the initial intercepts of the relative movement curve on experimental observations, White and Meistrich (15) derived analytical expressions for RM(t) in terms of the cycle parameters of the cell populations. They also derived a n explicit value for the initial point to which the nearly linear portion back-extrapolates, i.e., RM"(0). These authors demonstrated that T, may be estimated from the slope of the line connecting this initial value for RM with the value determined from a single measurement a t time t; the slope equals 1/2T,. Calculation of Tpot still required a n assumed value for A and a n estimate of LI. This method, which will be
235
referred to as RM86, theoretically gave more accurate measurements for T, than did the use of the extrapolation method, RM85. Exact calculation of Tpot from T, is made possible by the development of a new function ( v ) (17), which may be computed from the fractions of cells that are BrdUrd-labeled and either have divided or remain undivided at the time of measurement. Tpot can be found directly from v, using the formula Tpot = tn(2)T,/v, without the need to estimate LI or A. In addition, v may be used to compute RM"(0) and may yield a more accurate value than that described above (15). This methodology will be designated RM90. Relative movement methods are based on the DNA content of the labeled cells. Alternative methods involve the calculation of the fractions of labeled and unlabeled cells in different cell cycle compartments. White (14) has described a novel method, designated the depletion function (DF), which was shown theoretically to give a direct determination of the population doubling time (Tpot) from a sample a t a single time point. Other expressions describing the fractions of cells in various cell cycle compartments can also be used to calculate Tpot (16) but these methods require measurements of multiple time points. In this paper we present data from in vitro experiments using cultured Chinese hamster ovary (CHO) cells to test the application of the relative movement and depletion function methods to flow cytometric measurements of a population of cells and t o compare the values of Tpot obtained by these methods with each other and with doubling times obtained from the cell growth curves. Moreover, the precision of each of the various methods for estimating Tpot from single timepoint measurements is evaluated.
MATERIALS AND METHODS Cell Culture and Staining Exponentially growing CHO, clone AA8 cells were pulse labeled and chased as follows, care being taken to minimize perturbation. One micromolar BrdUrd was added directly to the culture medium for 20 min before washing the cells twice with warmed serum-free medium. Fresh, warmed, pre-gassed serum-containing medium was added for the chase period. Replicate dishes were sampled immediately and a t intervals from 15 min to 14 h thereafter. Trypsinized cell samples were prepared, and after resuspension in cold phosphate-buffered saline (PBS), they were fixed by addition of cold ethanol, while vortexing, until a final concentration of 60% was reached. Samples were stored a t 4°C. The experiment was performed three times and the data pooled. Single nuclei suspensions were prepared by incubation of the fixed cells a t room temperature, while rocking, for 20 min with 0.04% pepsin (EM Science, Cherry Hill, NJ) in 0.1 N HC1. The initial concentration a t the start of denaturation was standardized to 4 x 10' cells per 5 ml. Nuclei in suspension were stained using a
236
TERRY ET AL
variation of Schutte et al.'s (11)modification of Dolbeare's method (5). Nuclei were incubated with 2N HC1 for 20 min a t 37"C, and then sodium borate (0.1M twice the original sample volume) was added. The sample was washed with PBS containing 0.5% Tween-20 and 0.5% bovine serum albumin (PBTB) before resuspension in 0.2 ml of PBS 0.5% Tween-20 (PBT) containing 0.2 pL of the anti-BrdUrd monoclonal antibody IU4 (courtesy of F.A. Dolbeare, M. Vanderlaan and colleagues, Lawrence Livermore National Laboratory) and incubated for 1h a t room temperature in the dark. After washing again in PBTB, the nuclei were further incubated with PBT and 1%normal goat serum, together with FITC-conjugated goat-antimouse IgG (Sigma Chemical Co., St. Louis, MO), for 45 min. After washing once more in PBTB the nuclei were resuspended a t a concentration of 106/ml in PBTB containing 10 pgirnl propidium iodide (PI) (Sigma) before determining the fluorescence by flow cytometry.
RMT(t)=
+
Flow Cytometry Bivariate distributions of BrdUrd content (green fluorescence) vs. DNA content (red fluorescence) were measured using a n EPICS 751 flow cytometer (Coulter Corp., Hialeah, FL) equipped with narrow beam (5 pm) excitation optics and a quartz flow cell. Excitation was a t 488 nM using a 5W argon-ion laser operating a t 200 mW. BrdUrd content was measured using a logarithmic amplifier with a 530 nm short-pass filter, and DNA content (PI) collected after a 610 nm long-pass filter. Doublets and clumps were excluded from the analysis by gating on a bivariate distribution of the red peak vs. integral signal. Fifty thousand events were collected in the final gated histogram. The mean CV for the G, peak was 3%. Data Analysis The method of Begg et al. (2) was used to calculate the (RM) of BrdUrd-labeled undivided cells between the G, and G, peaks, as measured on a one-dimensional DNA projection of the bivariate histogram; RM(t) =
Fl"(t) - FGI FGZM - FG1
where FG, = G, mean red fluorescence channel; FG,M = G,M mean red fluorescence channel; and F'"(t) = the mean red fluorescence of the BrdUrd-labled cells which have not yet divided a t time (t).Cytologic analytical software (EPICS Division of Coulter Corp.) was used to model the DNA distributions of the total cell population and of the BrdUrd-labeled cells and to determine the values of these variables. The increase in relative movement with time [RM(t)l has been previously described based on basic principles of cell kinetics (15; Eq IS]). The equations used for RM(t) were made up of two different curves, RM'(t) and RM"(t), given by the following formulae:
1 + ct
e cTs(ec'i cTJ
cT,(1
=
0
if
=
TGzM 5 t
t
5
c-'~s)
(2)
TGzM, and
if
5
-
5
T,
where c, the growth rate of the population, is tn(2)/ Tpot; tn(2) is the natural logarithm of 2. Proprietary software developed by one of us (R.A.W.) was used to model the fit of these equations to the individual data points (16). This software is based on a non-linear fitting procedure developed by Marquardt (8) and implemented by Chandler (4). In the clinical setting where one or only a very few time points are available for analysis, the goal is to obtain a n estimate of T, from the RM a t only one time point. In this situation, the assumed initial value of RM(0) is critical to the estimation of T,. White and Meistrich (15) derived a n expression for the initial value a t times greater than TG,M by substituting the values of the fractions of cells (fl in each phase of the cell population into RM(0): (4)
where 2
=
Pn
L
1
+ fS + fGzM 1 + P;zM
The values of fs and fi2M can, in theory, be derived from the steady-state distributions of cells in the DNA histograms. v Function. The derivation of the v function is given in full elsewhere (17). Briefly, v is defined a s follows: (6)
where f'"(t) = fraction of cells that are labeled and remain undivided a t time t, and f I d ( t ) = fraction of cells that are labeled and have divided by time t. It can be shown that Tpot = tn(2)T,/v and c = v/T,. Furthermore, v is constant for times from TG,M to TG,M + T, and changes only slowly for longer and shorter times. An additional utility of u is that it allows computation of the initial values of RM'(0) and RM"(0) by substituting v for cT, in Equations 2 and 3. A review of the literature (12) and our experience (16) shows that for mammalian cell populations TG,M is approximately 0.3 T,. Hence, Equations 2 and 3 reduce to the following: 7)
COMPARISON OF MEASURES OF POTENTIAL DOUBLING TIME 0
Hrs
3
Hrs
237 5
Hrs
FIG 1. Bivariate histograms (upper panels) and DNA distributions (lower panels) for Chinese hamster ovary cells cultured in vitro and assayed at three different times after BrdUrd exposure. In the upper panels, the slanting lines separate the BrdUrd-labeled cell populations from unlabeled populations, and the vertical lines above the
slanting lines separate the divided from undivided labeled cells. The filled histograms in the lower panels identify the DNA distributions of the BrdUrd-labeled cells within the total DNA distributions (open histograms).
Depletion function method. The theoretical derivation of this methodology is described in detail elsewhere (14).Briefly, the depletion function D'(t) is a transformation of the fraction of BrdUrd-labeled undivided cells [t"(t)] into a form that is a linear function of time over much of its range. Tpot can be calculated directly from D'(t).
sitive even to small errors in the evaluated fractions of cells in S and G2M.
RESULTS Representative raw data are shown in Figure 1 a s bivariate histograms of total DNA content vs. BrdUrd incorporation (upper panels) and as DNA histograms of the total cell population and BrdUrd-labeled cell popD'(t) = Yn [ l + P(t)] (9) ulation only (lower panels). Data are shown for 0, 3, The same population of labeled undivided cells used and 5 h after flash-labeling of cells with BrdUrd, and in the relative movement analyses is used here, except the movement of the BrdUrd-labeled cells towards G, that it is the fraction of these cells, t"(t), rather than can clearly be seen. The vertical lines on the upper their mean fluorescence, which is modeled. For times panels of Figure 1indicate the boundaries demarcating greater than TG,M, the depletion function has the fol- the BrdUrd-labeled cells that have not yet divided from lowing form: which the RM, i.e., the mean red fluorescence, of these cells was measured. D'(t) = Cn (2 - fG1) - Yn(2) t/Tpot 110) The values of Tpot obtained from these results will This is a linear, decreasing function of time, with a slope of -en(2)/Tpot and a n intercept with the y axis be described first by using the model equations to fit all that depends on the fraction of all cells in the popula- the data points and then by fitting single data points as tion that are in Gl(fG1). fG1 can be calculated from a is necessary, for example, in the evaluation of limited one-dimensional DNA histogram. Since fG1 = 1 - ( f s clinical data. + fGGSM)Equations 9 and 10 can be rewritten a s Results from Fitting of the Total Data Set tn(2) tiTpot
=
en(l
+ fs + fc2,q)- tn(l + f"(t),
(11)
This form makes it more apparent that Tpot is sen-
Figure 2 shows the RM of the BrdUrd-labeled cells as a function of time. Equations 2 and 3 were used to fit a
238
TERRY ET AL.
Table 1 Estimates of Tpot for Each Method of Analysis Using the Total Data Set (Over the Appropriate Ranges of Time) Method Cell counts RM:Tpot = Pn(2)ic RM:Tpot = XT,/LI, A = 1 RM:Tpot = Cn(2)TS/u
DF
Time interval range (h) 0.25-24 0 -9 0-9 0-9 0-11
Tpot (h) (* 1 S.E.M.) 13.8 1.7" 11.9 i 4.2 15.3 ? 3.3 14.2 _C 1.3 13.1 2 4.8
*
"Actually the doubling time of the population, but close in value to Tpot because cell loss is negligible.
Time
( H o u r s )
FIG 2. The relative movement of the BrdUrd-labeled undivided cells between the G , and G,M DNA fluorescence channels, as a function of time. Equations 2 and 3 were used to fit a curve to all the data points using non-linear least squares fitting techiques.
curve to all the data points. The three unknowns in these RM equations-c ( = tn(2)/Tpot),T,, and TG,Mwere all allowed t o vary in the fitting of the curve in Figure 2. The initial values of RM'(0) and RMT1(0)were found to be 0.48 and 0.57, respectively. The curve in Figure 2 saturates a t a n RM of 1.0 a t t 2 T,. The computed values of T,, TG,M, and Tpot from the total data set in Figure 2 were found to be 9.0 t 0.7 h, 2.9 t 1.4 h, and 11.9 t 4.2 h, respectively. The value of TG, was indistinguishable from 0 (+ 4h); since TG, enters into the equations for RM(t) (15) only to second order through the value of c, fitting of RM(t) is very inaccurate in determining TG,. Since the precision of calculation of T, in this manner is greater than that of Tpot, we have used alternative methods to calculate Tpot. First we used the equation Tpot = A T,/LI. Since the apparent LI varies with time the true LI [P(O)] was used. For the 5 data points a t t = 0 the LI was found to be 58%' (t5% SD). Although A cannot be calculated from a single DNA histogram, we calculate A = 1.01 using more complete information on the cell cycle parameters of these CHO cells from the full set of histograms (16). From the calculated value of Ts with A fixed equal to 1.0, and using the LI a t time 0, we calculated a Tpot of 15.3 h (f3.3 h SEMI (Table l ) . Alternatively, Tpot can be calculated from T, by use of the v function. The average value of v was found to be 0.427 (-+ 0.057 SD). Hence from Tpot = en(2) T,/v the average value of Tpot, using data gathered over the range of 0-9 h , was found to be 14.2 h (t 1.3 h SEM). Figure 3 shows the DF plotted for these same data a s a function of time. The curves were fitted by calculating the variables fG, and c for times t > TG,M and the variables TG1, T,, for c for t < TG2M (14). The curve fitted to the data in Figure 3 was computed using all
-
I
Time
(Houra)
FIG.3. The fraction of BrdUrd-labeled undivided cells as a function of time (depletion function). The potential doubling time (Tpot)can be calculated from the slope.
the data points while allowing freedom of all these variables. The values of T, and TG,M calculated from this fitting were 8.1 and 2.8 h, respectively. Tpot was found to be 13.1 h (* 4.8 h SEM) (Table 1).The initial intercept of the linear portion of the curve, DF"(O), was found to be 0.58, which corresponded to a n fGl of 30%. The estimates of Tpot derived by the RM and DF methods of analysis from complete fits to this data set are similar (Table 1).Within experimental errors these results are in reasonable agreement with the estimate of population doubling time of 13.8 h made by simply counting cells a s a function of time over a 24 h period.
Results From Data at Single Time Points In order to establish the precision of estimates of Tpot that could be obtained from measurements of a single sample using each method of analysis, three time ranges were selected and fits were made to single data points. The three time periods chosen corresponded approximately to the lengths of TG,M (2-3 h), TG,M + 0.5 (T, - TG2M)(5-6 h), andT, + TGzM (9-11 h). All parameters needed to calculate Tpot-including RM, the apparent LI, v , DF, f i , and fGzM-were cal-
COMPARISON OF MEASIJRES O F POTENTIAL DOUBLING TIME
239
Table 2 Estimates o f Tpot for Each Method of Analysis From Single Samples Averaged Over Restricted Subsets of the Data
Time Method RM85 A = 1 RM(0) = 0.5 RM85 h = 1 RM(0) = 0.6 RM86 Tpot = XTsiLI X = l RM90
Tpot
=
No. of points 7 10 8 7 10 8 7 10 8 7 7 10 8 7 10 8
(h) 2-3 5-6 9-11 2-3 5-6 9-11 2-3" 5-6" 9-11" 2-3b 2-3" 5-6" 9-11' 2-3 5-6 9-1 1
Pn(2)iTJv
DF
Median Tpot (h) 7.4 8.8 c13.8 11.5 9.2
