Cytotechnology 5: 243-254, 1991. 9 1991 KluwerAcademic Publishers. Printed in the Netherlands.
Cell cycle dependency of monoclonal antibody production in asynchronous serum-free hybridoma cultures Richard A. Richieri 1, Lance S. Williams 2 and Pao C. Chau 1 Departments of (AMES) 1Chemical Engineering and 2Biology, University of California, San Diego, La Jolla, CA 92003-0310, USA Received26 April 1990; accepted in revised form 20 November 1990
Key words: hybridoma, serum-free medium, flow cytometry, cell cycle kinetics, bromodeoxyuridine labelling Abstract
The cell cycle kinetics of F3(B6) mouse hybridoma was examined by immunocytochemical staining of bromodeoxyuridine incorporated into the DNA of exponentially growing cells in three different cultures: one supplemented with 10% fetal bovine serum and two adapted to serum-free media, TABIES and BITES. The serum-free cultures, particularly the BITES, had longer cycling times and higher specific antibody production rate. Both observations were correlated to the prolongation of the G1 phase traverse time and substantiated with a starvation blocking experiment.
Introduction
The advantages and nominal ingredients required in a serum-free medium are well documented (Barnes and Sato, 1980). Immense interest is also expressed in serum-free hybridoma cultures (Glassy et al., 1988; Murakami, 1989; Schneider, 1989). A common observation during the development of serum-free culture is that while the growth rates of the hybridomas are slower in most serum-free media, the immunoglobulin secretion rates on a per cell basis (which will be referred to as the specific secretion rate, gg/106 cell.h) are in many circumstances higher (Tharakan et al., 1986). While the energy metabolism in serum-free media may for yet unknown reasons favor protein synthesis, there should be a mechanistic explanation for the phenomenon. Our work considers the possibility that immunoglobulin
synthesis is cell cycle dependent. In a study with synchronous lymphoid cell lines, Buell and Fahey (1969) found that the expression of immunoglobulins is regulated with respect to the cell cycle. Later, Lerner and Hodge (1971) showed that immunoglobulin synthesis is associated with the transition of resting cells to G 1 fractions. Subsequent inhibition of DNA synthesis does not alter the rate of Ig synthesis. In an ensuing study, Watanabe et al. (1973) showed that the immunoglobulin synthesis rate is elevated in the late G1 and early S phases and to a lesser extent in the G 2 phase, a result consistent with that of Buell and Fahey who observed a much decreased synthesis rate in the M phase. More recently, several studies have shown the cell cycle dependency of surface antigens on lymphocytes and hybridomas (Ernst et al., 1988; Gerdes et al., 1984; Takabayashi et al., 1983).
244 Most of these works used either 3H-thymidine labelling of asynchronous cultures or synchronous cultures generated by double thymidine blocking. With the addition of cell cycle blocking agents, the possibility always exists that cell cycle events are perturbed, thus affecting the interpretation of results. Hence, asynchronous cultures, in theory, are preferred to synchronous cultures. Advances in flow cytometry and nonradioactive bromodeoxyuridine (BrdUrd) labelling open up a new avenue in the study of cell cycle dependent kinetics (Dolbeare et al., 1983). This relatively new cytometry technique has been adapted to hybridoma cultures (Williams et al., 1990). Most flow cytometric studies of hybridomas have analyzed the DNA population distribution throughout a batch culture (Schliermann et al., 1987). The intention of this work is to apply BrdUrd pulse-labelling to study possible cell cycle dependent effects of antibody production in asynchronous serum-free hybridoma cultures. Our objective is to show that the variation in cell cycling time and the enhancement of specific immunoglobulin production rate in serum-free media could be caused by a prolonged G 1 phase. The two serum-free media used in this work are designated BITES and TABIES. BITES is a variation of the ITES medium developed by Murakami et al. (1982) and is a low protein lipid lean formulation which other than ethanolamine, lacks sources or precursors for fatty acids. The TABIES medium is BITES with the addition of albumin, serving as the carrier for fatty acids and lipids. TABIES, considered as lipid-rich, is expected to provide growth rates approaching that of a serum supplemented culture while BITES is expected to provide a culture with much slower growth rates. Only cultures adapted to the serumfree media are used and culture supplemented with 10% fetal bovine serum is the control. Data collection is restricted to roughly one cell cycle in the early exponential growth phase to avoid variations in the cell cycle phase traverse times. Our work should help us better understand the causeeffect relationship between growth regulation and antibody production.
Materials and methods Cell culture and media
F3(B6) hybridoma was donated by Dr. Alex Lucas (Immunology, Scripps Clinic, CA). The fusion partners were mouse myeloma X63-Ag8.653 and anti-PLA B-cell donor C3H/St mouse spleen cell. The hybridoma secretes IgG2a antibodies against phospholipase A2. Cells were stored at - 7 0 ~ and thawed prior to experimental use. The culture medium FCS was RPMI-1640 supplemented with 25 mM HEPES (Sigma Chemical, St. Louis, MO), 10% fetal bovine serum (Hyclone, Logan, UT), 2 mM glutamine, 50 btM g-mercaptoethanol, 0.5% gentamycin and 0.5% fungizone. The serum-free medium BITES consisted of RPMI1640 supplemented with 25 mM HEPES, 2 mM glutamine, 50 p,M B-mercaptoethanol, 10 btg/ml bovine insulin, 10 btg/ml human transferrin, 20 }.tM ethanolamine, 58 nM sodium selenite, with 0.5% gentamycin and 0.5% fungizone. All supplements were purchased from Sigma Chemical. TABIES had the same make up as BITES with the addition of 1 mg/ml bovine serum albumin, fraction V (BSA), All media were sterilized with 0.2 btm filters.
Bromodeoxyuridine labelling
All procedures followed the development of Williams et al. (1990). To adapt the cells in the FCS culture to serum-free media, they were washed once in RPMI-1640 and resuspended in fresh BITES or TABIES at 2 x 105 cells/ml. These cells in serum-free media were passed every two days for roughly 2 weeks until they were well adapted. The adaptation was judged by cell doubling times between passages. In later references to BITES and TABIES cultures (with the exception in the starvation blocking experiments), they are the adapted cultures. Cells in their respective media were grown to 6-8 x 105 cells/ml and resuspended in fresh media in T-150 cm 2 flasks 20-24 h before the experiment. Prior to labelling, two samples were taken as negative controls.
245 Cells in each flask were labelled with filter sterilized 10 gM bromodeoxyuridine (Sigma Chemical, St. Louis, MO) for 35 min at 37~ After incubation, the cells were washed once in warm (37~ basal medium, and resuspended in their respective fresh culture media. The cell densities were adjusted to 3 x 105 cells/ml. At two hour intervals, 11 ml samples were taken. One ml was used for cell count after which the cells were spun down and the supematant saved at 4~ for later assay of immunoglobulin concentration. The remaining 10 ml samples were washed twice with 5 ml PBS (phosphate buffered saline) buffer each and fixed in 3 ml cold 70% ethanol. Vigorous vortexing was applied during each resuspension. The fixed samples were stored at 4~ for later staining procedures.
Starvation blocking The starvation medium FCS- was essentially the FCS medium with the omission of the bovine serum. BITES and TABIES were also used in this sudden change experiment. The FCS culture was grown to mid-log phase, 6 x 105 cells/ml. A 2-ml sample was pulsed with 10 gM BrdUrd for 20 minutes and fixed for later measurement of the labelling index. The remaining cells were washed once in basal medium RPMI-1640, resuspended using either FCS (control), FCS-, BITES or TABIES, and aliquoted into T-25 cm 2 flasks. At one day intervals, cells in a selected flask were pulsed with BrdUrd as described above. The cell count was taken, the supernatant saved for antibody assay and the cells fixed accordingly for staining.
Flow cytometry The fixed cells were pelleted and washed twice with 3 ml PBS. The cell pellet was digested with 400gl pepsin (4100 units/mg, Sigma Chemical) in 0.1 N HCI for 25 min at 37~ The digestion, which was used to extract the nuclei, was stopped by washing the nuclei twice in 1 ml PBS buffer
containing 1 mg/ml BSA. The washed nuclei were resuspended in 1 ml 2N HCI and incubated at 37~ for 25 min. The nuclei were pelleted and resuspended in 1 ml borate (0.1 M Na2B407, pH 8.48). Subsequently, 20 gl anti-BrdUrd antibody (Becton-Dickinson, Mt. View, CA) was added and incubated at 37~ for 25 min. The nuclei were washed once with 1 ml PBS/Tween (PBS with 0.5% Tween 20) and resuspended in 200 gL PBS/Tween containing 1.5 gg FITC conjugated F(ab')2 goat-anti-mouse IgG (Tago Immunologicals, Burlingame, CA) and incubated at room temperature for 25 minutes. Afterward, 500 ~1 PBS was added and the nuclei were sedimented. The nuclei were washed once in PBS/Tween and resuspended in 500 gl PBS containing 10 gg/ml propidium iodide (Calbiochem, San Diego, CA). After a 15 min incubation at room temperature, the nuclei were filtered through a 62 gm nylon mesh prior to flow cytometric analysis. The dual-labelled nuclei were analyzed on an Ortho System 50-H cytofluorograph (Ortho Instruments, Westwood, MA). The 50-amp Argon laser was set at 488 nm for fluorescence activation. Green fluorescence was measured through a 515 nm bandpass filter and red fluorescence was through a 600 nm long-pass filter. Twenty thousand nuclei were analyzed for each sample at a flow rate of approximately 100 particles per second. Cellular debris and doublets were gated out by examining the forward versus orthogonal scatter, and a bivariate incorporated BrdUrd/DNA (log green/red) cytogram was constructed. The bivariate plots were circumscribed into six subpopulations representing the three phase fractions (G1,S, and Gz/M) of BrdUrd labelled and unlabelled cells. The same partitions were used to obtain the cell distributions for successive time points. For the sample immediate after BrdUrd pulsing, all labelled cells were considered as S phase cohorts. The data were analyzed with a Data General 2150 data processing system (Raritan, NJ) and further processed with a program from Pheonix Flow Systems (San Diego, CA).
246 60
Analytical methods
(a) r-cs
5o
Antibody. Enzyme linked immunosorbent assay was performed with goat anti-mouse IgG and goat anti-mouse IgG conjugated to alkaline phosphatase (gamma and light chain specific, Tago, Burlingame, CA). Standard samples were diluted from isolated anti-PLA antibody, RIA tested, courtesy of Dr. A. Lucas, Scripps. The substrate was p-nitrophenyl phosphate (1 mg/ml, Sigma) in glycine buffer. The absorbance was measured with Multiskan Plus MK II (EFLAB) at 405 nm. Cell density. Cell densities were measured with a hemacytometer, using 0.2% trypan blue in the dye exclusion test.
.~
40
30 d~ 20
I
I
10
15
I
I
25
30
35
(b) TABLES
70 60 "6
50
m=4o 3o I
1
5
10
and discussion
We first compare the cell cycle phase traverse times of the adapted cultures in the three media: FCS, TABIES and BITES. Afterward, the results on specific immunoglobulin secretion and starvation blocking are presented.
I
20 Ihrl
80
20
Results
!
S
I
I
15 20 Time [hrl
I
I
25
30
35
8O
70 so "6 g 5o
Comparison of the cell cycle traverse times
40 et
30
Cell cycling appears, on a BrdUrd/DNA bivariate distribution, as movements of different phase cohorts along the DNA axis between G] and G~VI equivalent contents (Williams et al., 1990b). The respective percentages of total G1 and S cell fractions as extracted from the corresponding bivariate distributions are illustrated in Figs. 1 and 2. The data points are scattered as the relative error from the bivariate distribution is fairly large. Therefore, a computational model is used to estimate the cell cycle parameters. The BrdUrd pulse-labelling experiment is best described with a population balance model which includes BrdUrd uptake (Yanagisawa et al., 1985). However, we are only interested in the chase period. Hence, if we take the pulse-labelled cells as the initial condition and model only the
0
I
I
5
10
I
I
15 20 Tln~ lhrl
I
I
25
30
35
Fig. 1. The time variations of percentages of G 1 phase fractions alter the cultures have been pulsed with 10 gM BrdUrd for 35 minute at 37~ (a) Serum supplemented culture, FCS and the two adapted serum-free cultures, (b) TABIES and (c) BITES. The error bar indicates the standard deviation of each data point.
total cell fractions in the chase period, a simpler compartmental model suffices (Gray, 1976). A brief description of the model is presented here; the details are provided by Gray (1976). The cell cycle is divided into k compartments with the population distributed among them. The cell movements from one compartment to another are described by simple first order terms
247 8O =
8
(1)
dnl/dt = 2~k_lnk_ 1 - ~lnl
(a) FCS
70'
co 6 0 ' "6 " 50-
which accounts for the cell division between the last compartment k, and the first compartment. In general, for the j-th compartment,
403020 5'
0
10 '
15 '
2o
2
30 '
35
dnj/dt
= ~j_lnj_l
--
~,jl'lj
with 2
Cell cycle dependency of monoclonal antibody production in asynchronous serum-free hybridoma cultures Richard A. Richieri 1, Lance S. Williams 2 and Pao C. Chau 1 Departments of (AMES) 1Chemical Engineering and 2Biology, University of California, San Diego, La Jolla, CA 92003-0310, USA Received26 April 1990; accepted in revised form 20 November 1990
Key words: hybridoma, serum-free medium, flow cytometry, cell cycle kinetics, bromodeoxyuridine labelling Abstract
The cell cycle kinetics of F3(B6) mouse hybridoma was examined by immunocytochemical staining of bromodeoxyuridine incorporated into the DNA of exponentially growing cells in three different cultures: one supplemented with 10% fetal bovine serum and two adapted to serum-free media, TABIES and BITES. The serum-free cultures, particularly the BITES, had longer cycling times and higher specific antibody production rate. Both observations were correlated to the prolongation of the G1 phase traverse time and substantiated with a starvation blocking experiment.
Introduction
The advantages and nominal ingredients required in a serum-free medium are well documented (Barnes and Sato, 1980). Immense interest is also expressed in serum-free hybridoma cultures (Glassy et al., 1988; Murakami, 1989; Schneider, 1989). A common observation during the development of serum-free culture is that while the growth rates of the hybridomas are slower in most serum-free media, the immunoglobulin secretion rates on a per cell basis (which will be referred to as the specific secretion rate, gg/106 cell.h) are in many circumstances higher (Tharakan et al., 1986). While the energy metabolism in serum-free media may for yet unknown reasons favor protein synthesis, there should be a mechanistic explanation for the phenomenon. Our work considers the possibility that immunoglobulin
synthesis is cell cycle dependent. In a study with synchronous lymphoid cell lines, Buell and Fahey (1969) found that the expression of immunoglobulins is regulated with respect to the cell cycle. Later, Lerner and Hodge (1971) showed that immunoglobulin synthesis is associated with the transition of resting cells to G 1 fractions. Subsequent inhibition of DNA synthesis does not alter the rate of Ig synthesis. In an ensuing study, Watanabe et al. (1973) showed that the immunoglobulin synthesis rate is elevated in the late G1 and early S phases and to a lesser extent in the G 2 phase, a result consistent with that of Buell and Fahey who observed a much decreased synthesis rate in the M phase. More recently, several studies have shown the cell cycle dependency of surface antigens on lymphocytes and hybridomas (Ernst et al., 1988; Gerdes et al., 1984; Takabayashi et al., 1983).
244 Most of these works used either 3H-thymidine labelling of asynchronous cultures or synchronous cultures generated by double thymidine blocking. With the addition of cell cycle blocking agents, the possibility always exists that cell cycle events are perturbed, thus affecting the interpretation of results. Hence, asynchronous cultures, in theory, are preferred to synchronous cultures. Advances in flow cytometry and nonradioactive bromodeoxyuridine (BrdUrd) labelling open up a new avenue in the study of cell cycle dependent kinetics (Dolbeare et al., 1983). This relatively new cytometry technique has been adapted to hybridoma cultures (Williams et al., 1990). Most flow cytometric studies of hybridomas have analyzed the DNA population distribution throughout a batch culture (Schliermann et al., 1987). The intention of this work is to apply BrdUrd pulse-labelling to study possible cell cycle dependent effects of antibody production in asynchronous serum-free hybridoma cultures. Our objective is to show that the variation in cell cycling time and the enhancement of specific immunoglobulin production rate in serum-free media could be caused by a prolonged G 1 phase. The two serum-free media used in this work are designated BITES and TABIES. BITES is a variation of the ITES medium developed by Murakami et al. (1982) and is a low protein lipid lean formulation which other than ethanolamine, lacks sources or precursors for fatty acids. The TABIES medium is BITES with the addition of albumin, serving as the carrier for fatty acids and lipids. TABIES, considered as lipid-rich, is expected to provide growth rates approaching that of a serum supplemented culture while BITES is expected to provide a culture with much slower growth rates. Only cultures adapted to the serumfree media are used and culture supplemented with 10% fetal bovine serum is the control. Data collection is restricted to roughly one cell cycle in the early exponential growth phase to avoid variations in the cell cycle phase traverse times. Our work should help us better understand the causeeffect relationship between growth regulation and antibody production.
Materials and methods Cell culture and media
F3(B6) hybridoma was donated by Dr. Alex Lucas (Immunology, Scripps Clinic, CA). The fusion partners were mouse myeloma X63-Ag8.653 and anti-PLA B-cell donor C3H/St mouse spleen cell. The hybridoma secretes IgG2a antibodies against phospholipase A2. Cells were stored at - 7 0 ~ and thawed prior to experimental use. The culture medium FCS was RPMI-1640 supplemented with 25 mM HEPES (Sigma Chemical, St. Louis, MO), 10% fetal bovine serum (Hyclone, Logan, UT), 2 mM glutamine, 50 btM g-mercaptoethanol, 0.5% gentamycin and 0.5% fungizone. The serum-free medium BITES consisted of RPMI1640 supplemented with 25 mM HEPES, 2 mM glutamine, 50 p,M B-mercaptoethanol, 10 btg/ml bovine insulin, 10 btg/ml human transferrin, 20 }.tM ethanolamine, 58 nM sodium selenite, with 0.5% gentamycin and 0.5% fungizone. All supplements were purchased from Sigma Chemical. TABIES had the same make up as BITES with the addition of 1 mg/ml bovine serum albumin, fraction V (BSA), All media were sterilized with 0.2 btm filters.
Bromodeoxyuridine labelling
All procedures followed the development of Williams et al. (1990). To adapt the cells in the FCS culture to serum-free media, they were washed once in RPMI-1640 and resuspended in fresh BITES or TABIES at 2 x 105 cells/ml. These cells in serum-free media were passed every two days for roughly 2 weeks until they were well adapted. The adaptation was judged by cell doubling times between passages. In later references to BITES and TABIES cultures (with the exception in the starvation blocking experiments), they are the adapted cultures. Cells in their respective media were grown to 6-8 x 105 cells/ml and resuspended in fresh media in T-150 cm 2 flasks 20-24 h before the experiment. Prior to labelling, two samples were taken as negative controls.
245 Cells in each flask were labelled with filter sterilized 10 gM bromodeoxyuridine (Sigma Chemical, St. Louis, MO) for 35 min at 37~ After incubation, the cells were washed once in warm (37~ basal medium, and resuspended in their respective fresh culture media. The cell densities were adjusted to 3 x 105 cells/ml. At two hour intervals, 11 ml samples were taken. One ml was used for cell count after which the cells were spun down and the supematant saved at 4~ for later assay of immunoglobulin concentration. The remaining 10 ml samples were washed twice with 5 ml PBS (phosphate buffered saline) buffer each and fixed in 3 ml cold 70% ethanol. Vigorous vortexing was applied during each resuspension. The fixed samples were stored at 4~ for later staining procedures.
Starvation blocking The starvation medium FCS- was essentially the FCS medium with the omission of the bovine serum. BITES and TABIES were also used in this sudden change experiment. The FCS culture was grown to mid-log phase, 6 x 105 cells/ml. A 2-ml sample was pulsed with 10 gM BrdUrd for 20 minutes and fixed for later measurement of the labelling index. The remaining cells were washed once in basal medium RPMI-1640, resuspended using either FCS (control), FCS-, BITES or TABIES, and aliquoted into T-25 cm 2 flasks. At one day intervals, cells in a selected flask were pulsed with BrdUrd as described above. The cell count was taken, the supernatant saved for antibody assay and the cells fixed accordingly for staining.
Flow cytometry The fixed cells were pelleted and washed twice with 3 ml PBS. The cell pellet was digested with 400gl pepsin (4100 units/mg, Sigma Chemical) in 0.1 N HCI for 25 min at 37~ The digestion, which was used to extract the nuclei, was stopped by washing the nuclei twice in 1 ml PBS buffer
containing 1 mg/ml BSA. The washed nuclei were resuspended in 1 ml 2N HCI and incubated at 37~ for 25 min. The nuclei were pelleted and resuspended in 1 ml borate (0.1 M Na2B407, pH 8.48). Subsequently, 20 gl anti-BrdUrd antibody (Becton-Dickinson, Mt. View, CA) was added and incubated at 37~ for 25 min. The nuclei were washed once with 1 ml PBS/Tween (PBS with 0.5% Tween 20) and resuspended in 200 gL PBS/Tween containing 1.5 gg FITC conjugated F(ab')2 goat-anti-mouse IgG (Tago Immunologicals, Burlingame, CA) and incubated at room temperature for 25 minutes. Afterward, 500 ~1 PBS was added and the nuclei were sedimented. The nuclei were washed once in PBS/Tween and resuspended in 500 gl PBS containing 10 gg/ml propidium iodide (Calbiochem, San Diego, CA). After a 15 min incubation at room temperature, the nuclei were filtered through a 62 gm nylon mesh prior to flow cytometric analysis. The dual-labelled nuclei were analyzed on an Ortho System 50-H cytofluorograph (Ortho Instruments, Westwood, MA). The 50-amp Argon laser was set at 488 nm for fluorescence activation. Green fluorescence was measured through a 515 nm bandpass filter and red fluorescence was through a 600 nm long-pass filter. Twenty thousand nuclei were analyzed for each sample at a flow rate of approximately 100 particles per second. Cellular debris and doublets were gated out by examining the forward versus orthogonal scatter, and a bivariate incorporated BrdUrd/DNA (log green/red) cytogram was constructed. The bivariate plots were circumscribed into six subpopulations representing the three phase fractions (G1,S, and Gz/M) of BrdUrd labelled and unlabelled cells. The same partitions were used to obtain the cell distributions for successive time points. For the sample immediate after BrdUrd pulsing, all labelled cells were considered as S phase cohorts. The data were analyzed with a Data General 2150 data processing system (Raritan, NJ) and further processed with a program from Pheonix Flow Systems (San Diego, CA).
246 60
Analytical methods
(a) r-cs
5o
Antibody. Enzyme linked immunosorbent assay was performed with goat anti-mouse IgG and goat anti-mouse IgG conjugated to alkaline phosphatase (gamma and light chain specific, Tago, Burlingame, CA). Standard samples were diluted from isolated anti-PLA antibody, RIA tested, courtesy of Dr. A. Lucas, Scripps. The substrate was p-nitrophenyl phosphate (1 mg/ml, Sigma) in glycine buffer. The absorbance was measured with Multiskan Plus MK II (EFLAB) at 405 nm. Cell density. Cell densities were measured with a hemacytometer, using 0.2% trypan blue in the dye exclusion test.
.~
40
30 d~ 20
I
I
10
15
I
I
25
30
35
(b) TABLES
70 60 "6
50
m=4o 3o I
1
5
10
and discussion
We first compare the cell cycle phase traverse times of the adapted cultures in the three media: FCS, TABIES and BITES. Afterward, the results on specific immunoglobulin secretion and starvation blocking are presented.
I
20 Ihrl
80
20
Results
!
S
I
I
15 20 Time [hrl
I
I
25
30
35
8O
70 so "6 g 5o
Comparison of the cell cycle traverse times
40 et
30
Cell cycling appears, on a BrdUrd/DNA bivariate distribution, as movements of different phase cohorts along the DNA axis between G] and G~VI equivalent contents (Williams et al., 1990b). The respective percentages of total G1 and S cell fractions as extracted from the corresponding bivariate distributions are illustrated in Figs. 1 and 2. The data points are scattered as the relative error from the bivariate distribution is fairly large. Therefore, a computational model is used to estimate the cell cycle parameters. The BrdUrd pulse-labelling experiment is best described with a population balance model which includes BrdUrd uptake (Yanagisawa et al., 1985). However, we are only interested in the chase period. Hence, if we take the pulse-labelled cells as the initial condition and model only the
0
I
I
5
10
I
I
15 20 Tln~ lhrl
I
I
25
30
35
Fig. 1. The time variations of percentages of G 1 phase fractions alter the cultures have been pulsed with 10 gM BrdUrd for 35 minute at 37~ (a) Serum supplemented culture, FCS and the two adapted serum-free cultures, (b) TABIES and (c) BITES. The error bar indicates the standard deviation of each data point.
total cell fractions in the chase period, a simpler compartmental model suffices (Gray, 1976). A brief description of the model is presented here; the details are provided by Gray (1976). The cell cycle is divided into k compartments with the population distributed among them. The cell movements from one compartment to another are described by simple first order terms
247 8O =
8
(1)
dnl/dt = 2~k_lnk_ 1 - ~lnl
(a) FCS
70'
co 6 0 ' "6 " 50-
which accounts for the cell division between the last compartment k, and the first compartment. In general, for the j-th compartment,
403020 5'
0
10 '
15 '
2o
2
30 '
35
dnj/dt
= ~j_lnj_l
--
~,jl'lj
with 2
