Growth dynamics of mammalian cells monitored with automated cell cycle staining and flow cytometry


  • Greg Sitton,

    1. Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455-0312
    2. BioTechnology Institute, University of Minnesota, St. Paul, Minnesota 55108
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  • Friedrich Srienc

    Corresponding author
    1. Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455-0312
    2. BioTechnology Institute, University of Minnesota, St. Paul, Minnesota 55108
    • BioTechnology Institute, University of Minnesota, 240 Gortner Laboratory, 1479 Gortner Avenue, St. Paul, MN 55108, USA
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To accurately observe high-frequency events during transient cell cycle kinetics, we have implemented a single step 15-min DNA staining protocol using automated flow cytometry. This protocol was used to sample and to analyze a Chinese hamster ovary cell culture for the DNA distribution, viable cell concentration, apoptotic cell concentration, and light scattering properties every 25 min over 4.5 days in response to a nutrient deprivation and a nutrient upshift. After the nutrient deprivation and exposure to fresh growth medium, two populations of cells started proliferating at different times likely corresponding to cells leaving the G0 and G1 cell cycle phases. After a nutrient upshift in late exponential growth, a cell cycle arrest occurred at the G1/S and G2/M boundary. The resulting cell cycle and proliferation kinetics followed damped oscillations that directly reveal the average time cells spend in each cell cycle phase. The observed detailed dynamics of the cell cycle progression is made possible through the high-frequency sampling enabled by automated flow cytometry. The approach should be useful in studying cell cycle perturbations in response to different environmental conditions resulting from exposure to specific nutrients or to drugs. © 2008 International Society for Advancement of Cytometry

Determination of the cell cycle distribution is one of the most basic and most widely used applications of flow cytometry in basic biological research and in diagnostic applications. It traditionally involves cell fixation and permeabilization and cell staining with nucleic acid specific dyes, often after enzymatic removal of RNA. Variations of this methodology have been well documented in many reports, review articles and textbooks (1). The cell preparation and staining steps typically involve several manual operations, and their careful execution determines the reproducibility and the quality of the cell cycle distribution that can be obtained. However, in many cases a large fraction of cells may be lost during fixation and staining steps which introduces the additional problem that the remaining cells may not be representative of the entire sample.

Traditional cell cycle staining protocols use either cell membrane permeable or impermeable dyes. Staining protocols using membrane permeable dyes are typically simple and short involving only addition of the dye to the cells. However, membrane permeable dyes often are more expensive in comparison to membrane impermeable dyes [Vybrant, DRAQ5 (2)] or limited to a UV excitation source (Hoechst, DAPI). In contrast, membrane impermeable dyes such as PI or Acridine Orange are inexpensive and can be excited by common 488 nm light sources. Cell cycle staining protocols using membrane impermeable dyes are usually long, multistep procedures.

Time dependent changes in the cell cycle distribution of a growing cell population reflect transient growth conditions. The perturbations can be caused by changing nutritional conditions or by exposure to inhibitory substances. Transient growth conditions are also characteristic of synchronized cultures. The accuracy of the experimentally measured cell cycle kinetics is fundamentally limited by the sampling frequency from the culture. This fundamental limitation stems from the Nyquist–Shannon sampling theorem (3) which states that, at best, one can only make accurate statements about a process that occur at a frequency half the sampling frequency. Thus, to observe the cell cycle kinetics with maximum detail, one must sample as frequently as experimentally feasible.

Because flow cytometry has traditionally been an offline technique, samples have to be manually taken and then subjected to the staining operations. Thus, frequent sampling involves significant labor. Also, if cell staining is performed manually, the chance for error can be significant. To overcome these problems, we have previously developed automated flow cytometry (4, 5) that can automatically sample and stain cells online. Its utility has been demonstrated in initial examples involving the monitoring of microbial (6, 7) and mammalian cell cultures (8, 9).

We demonstrate here that this approach can also be applied for automated cell cycle staining that affords the detailed evaluation of the cell cycle kinetics of growing cultures based on frequent sampling. To implement an online cell cycle stain, we first shortened the length of a traditional PI staining protocol to a single 15-min step. This modified protocol was then implemented with the automated flow cytometry device and used to monitor the cell cycle kinetics of a CHO culture using 10-min sampling intervals over 4.5 days. During that time, the culture was subjected to recovery from nutrient deprivation and a nutrient upshift. The observed kinetics directly reveal the cell cycle and proliferation kinetics of the culture during both transient and balanced growth. Knowledge of the kinetics can be useful for instance in elucidating the effects of nutrients and drugs on the underlying mechanisms governing cell cycle progression.


Cell Line and Growth Medium

Serum-free CHO cells of the strain CHO-S (Cat. # 11619-012; Invitrogen, Carlsbad, CA) were used in this study. CHO-S cells are a clonal isolate of CHO-K1 and adapted for serum free and suspension growth, and are frequently used in biotechnology for the production of proteins for diagnostic or therapeutic applications. Cells from a working cell bank, stored in liquid nitrogen, were thawed at 37°C and placed in a T-flask (75 cm2, Corning, Corning, NY) containing 25 ml of CHO-S-SFM II medium (Invitrogen) at a concentration of 1 × 105 cells per milliliter. The cells were incubated at 37°C in air containing 7.5% carbon dioxide. After being passed once into 50 ml of medium in the same size T-flask, the cells were passed a third time into a total volume of 300 ml in a 500 ml-spinner flask, Corning, Corning, NY).

Bioreactor Operation

A 2-l bioreactor (LH Fermentation) with a working volume of one liter was operated at 37°C. The bioreactor was agitated at a rate of 100 rpm using a six-blade disk impeller with a 5 cm diameter. Air and CO2 were sparged to control DO and pH, respectively. The DO remained above 80% during the duration of the experiment and the pH remained at 7.2 ± 0.05. Both the initial culture volume and the fed-batch additions were CHO-S SFM-II medium supplemented with sodium penicillin G 0.17 mM (Sigma, St. Louis, MO) and streptomycin sulfate 68.6 mM (Sigma, St. Louis, MO). Inoculation was performed from the spinner flask culture.

Nutrient Upshift and Deprivation

To add fresh nutrients to the culture, medium was removed from the bioreactor until 100 ml of culture remained while agitation, pH, and DO2 control were maintained. Next 900 ml of pre-warmed, fresh medium was added to the bioreactor, thus achieving a 1:10 dilution.

To initially deprive cells of nutrients, the inoculum culture was allowed to reach stationary phase in a spinner flask. This culture was used to inoculate the bioreactor at a 1:10 dilution ratio with fresh, prewarmed medium.

Sampling and Cell Staining

The staining microchamber previously described (4), was modified to create separate pathways through the microchamber for loading and eluting cells. Also, a syringe pump was directly connected to the microchamber to inject stain. Prior to loading cells into the microchamber, the exit pathway from the microchamber and the sample loop of the device were filled with a 30 μg/ml PI solution. After a cell sample from the bioreactor was loaded into the microchamber with the peristaltic pump through the waste pathway of the microchamber, the stain syringe pump added 30 μl of staining solution to the 180 μl microchamber filled with cells using the loading pathway. The microchamber was agitated at 100 rpm and kept at room temperature. The staining solution was prepared by first placing 30 mg of crude digitonin extract in 10 ml of a PBS solution. After vortexing and waiting 5 min at room temperature, 2 ml of a 1 mg/ml PI solution and 50 mg of RNase A was added to the staining solution. The remaining undissolved crude digitonin extract was removed by filtering through a 0.2 μm syringe filter. Thus, the resulting staining solution was comprised of saturated digitonin, 170 μg/ml PI, and 0.5 mg/ml RNase. After addition to the microchamber, the concentrations of PI and RNase in the microchamber were 30 μg/ml and 80 μg/ml, respectively. Once the staining solution was added, the cells were allowed to incubate for 15 min. Then, the stained cells were eluted from the microchamber into the sample loop by the saline syringe pump containing 30 μg/ml of PI, and the contents of the sample loop were injected into the cytometer for analysis. Cell cycle distributions were analyzed using MultiCycle analysis software.

To analyze live cells, the automated cell preparation system loaded a sample directly from the bioreactor into a sample loop. The content of the sample loop was then injected into a flow cytometer for live cell analysis of the cell concentration, cell size, cell granularity, and nonviable concentration.

Flow Cytometry

A FACS Calibur (Becton-Dickinson Immunocytometry System, San Jose, CA) flow cytometer was used for the analysis of cells. A 15 mW laser (Spectra-Physics, Mountain View, CA) with a wavelength of 488 nm was used for excitation. Data from the forward scatter diode and side scatter PMT were digitized with a linear scale. PI fluorescence was analyzed at 585 nm and digitized on a linear scale. Data of the peak width, area, and height of the PI signal were acquired. Samples were analyzed with an event rate less than 200 events/s.


Staining Procedure Development

Digitonin was previously shown to permeabilize the membrane to PI and RNase (10). Unlike organic solvents, digitonin does not reduce the activity of RNase, and completely permeabilizes CHO cells to RNase and PI in under a minute (data not shown). Thus, digitonin can be combined in a single solution with PI and RNase yielding the basis for a true one-step staining procedure (11). The total length of the staining protocol is then reduced to the time required to completely digest the RNA. To determine the minimum length of the RNA digestion step, 106 CHO cells were exposed at room temperature to 1 ml of a saturated digitonin, 30 μg/ml PI, and 80 μg/ml RNase solution. PI and RNase concentrations were similar to previously published protocols (10, 12). This preparation was then incubated at room temperature and periodically sampled and analyzed with a flow cytometer. As shown in Figure 1 the RNA was completely digested by 9 min as shown by the mean and CV of the G1 peak approaching a constant value as seen in similar protocol optimization studies (13). This time can be likely further shortened by raising the temperature or increasing the RNase concentration. As seen in Figure 2A, the stained cells produce a DNA distribution where the fraction of cells in each phase of the cell cycle is readily identified.

Figure 1.

Kinetics of the RNase digestion in the online staining treatment using 80 μg/ml of RNase at room temperature. The reaction appears to go to completion at 9 min, which is a similar result shown in literature (13).

Figure 2.

Histogram showing an example online cell cycle distribution (A), cytogram depicting the isolation of mitotic cells (B), the forward scatter versus DNA content cytogram (C), and the histogram of the forward scatter distributions of individual cell cycle phases at an example time point during the culture. Mitotic cells are defined as having twice the cell width and two copies of DNA as compared with a G1 cell.

Mitotic Cell Identification

Unlike organic solvents, digitonin does not induce aggregation of cells at room temperature. Thus, single cell morphology is preserved throughout the permeabilization and staining steps as shown in Figures 3A and 3B, where the FSC mean and CV of the permeabilized versus viable populations are shown to be correlated for 45 samples of CHO cells at differing FSC values. Mitotic cells can be identified through their characteristic cellular DNA distribution that can be detected by comparing the width of the stained DNA signal versus the area of the signal as shown in Figure 2B. This type of analysis is especially applicable to suspension adapted CHO-S cells acquired with a low event rate. Microscopic examinations of CHO-S cells show that less than 0.5% of the cells are in clumps of three or more cells. Thus, the observed doublets reflect the mitotic population. A similar approach of differentiating mitotic cells based on morphology has been used for yeast (14–16) and mammalian cells (16–21). From these data, the fraction of cells in each cell cycle phase can be readily identified, as well as a measure of the cell size (FSC) as a function of cell cycle position (Figs. 2C and 2D).

Figure 3.

Mean (A) and CV (B) of the viable, FSC distribution before the cell cycle staining protocol versus the mean of the FSC distribution after treatment (N = 45 samples). The linear relationships indicate that cell morphology is maintained by the cell cycle staining protocol.

Batch Set-Up and Monitoring

The online cell cycle staining protocol was tested on a CHO culture that was grown in a bioreactor initially containing one liter of fresh medium, and inoculated at time zero with a culture in late exponential phase. The bioreactor was then monitored by alternately taking two samples from the bioreactor with the automated flow cytometer. The first sample was stained online for the cell cycle dynamics of the culture using the staining protocol as described. The second sample was directly acquired by the cytometer without any staining yielding data on the total cell concentration, the viable and nonviable cell fractions, and cell size evaluated based on light scattering properties. As a general feature of cell death through either necrosis or apoptosis cells change their morphology by decreasing in size and changing their internal structure. These morphological changes are detectable by measuring the change in light scatter using flow cytometry (22). Thus, nonviable cells can be differentiated from viable cells based on their differing forward (FSC) and side (SSC) light-scattering characteristics (22) (Fig. 4). This strategy for differentiating between viable and non-viable cells has been applied across many different mammalian cell lines (23–25) including CHO cells (26). It is assumed in well controlled batch cultures like these that apoptotic cells are the primary components of the nonviable cells (27, 28).

Figure 4.

Apoptotic population. FSC versus SSC dot plot for a sample point during bioreactor operation. Apoptotic cells are defined as having decreased FSC and increased SSC as previously described (23).

Each respective sample was taken and analyzed every 25 min with 8 min between the cell cycle staining and live cell analysis. To directly visualize the dynamics of the occurring changes, the data shown in Figure 2D, have been assembled in a movie (provided in the online supplementary material) depicting how the cell proliferation, cell cycle phases, and cell size distributions for each phase of the cell cycle changed over time.

Over the course of the culture, offline samples were taken every 8–15 h, and fixed with ice-cold 70% ethanol. At the conclusion of the online experiment the offline samples were manually stained with PI and analyzed on the cytometer as described in standard protocols (12). As shown in Figure 5, there is excellent agreement between the offline and online samples.

Figure 5.

Comparison between the fractions of cells in each cell cycle phase for online and offline samples (N = 11). Fractions were computed using Multicycle.

Recovery from Nutrient Deprivation

Because the inoculation culture was in late exponential phase, the culture started growing with a large fraction of cells in G1 with a viable fraction of 96% (Figs. 6A–6D). The cells initially appeared starved due to nutrient deprivation, because the initial mean cell size in each phase of the cell cycle was lower than the mean cell size during subsequent exponential growth (Fig. 6C). During the first 6 h, until arrow (a), the cells adjusted to the fresh medium by increasing their mean cell size across all phases of the cell cycle (Fig. 6C). During this time, cells that were already committed to division completed the cell cycle as seen by an increase in the G1 fraction, a corresponding decrease in the S and G2 fractions, and an increase in the cell concentration (Figs. 6A and 6B). From hours 0–6, the culture proliferated with a doubling time of 21 h as shown in Figure 7. Once the cells were sufficiently recovered, a large fraction of G1 cells entered S phase as seen by a decrease in the G1 fraction and a corresponding increase in the S fraction [arrow (a), Figs. 6A and 6B]. During this time, the entire culture ceased proliferating as shown in Figure 7, h 6–15, indicating little to no cells were in the G2/M phase of the cell cycle as confirmed by Figure 6A.

Figure 6.

(A) Cell cycle fractions as a function of time using the automated staining apparatus and developed staining protocol. (B) Cell number concentration as a function of time. The culture was passaged at h 61. The mitotic fraction as determined in Figure 7 as a function of time is also shown. (C) Mean cell size as a function of time for each cell cycle fraction. Arrows correspond to events described in the results section. (D) The viable cell fraction and the apoptotic cell concentration as a function of time.

Figure 7.

Proliferation rates of the culture during recovery from nutrient deprivation. The growth curve is broken into segments defined by the discontinuities. Proliferation rate μ, doubling time tD, and the R2 values for each segment are given

Thus, the culture was partially synchronized. A partially synchronized cell population contains homogeneous cell cohorts that behave like a single cell. The cell cycle progression of these cohorts causes individual cell cycle fractions to oscillate. For instance, a cell cycle fraction will start increasing from a minimum value when a homogeneous cell cohort arrives and its front starts entering the specific cell cycle phase. The cell cycle fraction then reaches a maximum value when the entire cohort is in the cell cycle phase and this value starts decreasing again when the front of the cohort starts exiting the specific cell cycle phase. Thus, the time between the occurrences of the minimum and the maximum cell cycle fraction indicates the average time it takes for a cohort to traverse the cell cycle phase. Thus, by observing when the subsequent minima and maxima of the G1, S, G2, and M fractions occurred due to the synchronized cohort, one can directly measure the lengths of the individual cell cycle phases in a culture of many cells.

For instance, the time from the S phase fraction minimum [h 6, arrow (a)] to the S phase fraction maximum [h 12, arrow (b)] indicates that it took 6 h for the cohort to complete S phase. Alternately, the time between the G2 minimum [h 12, arrow (b)] and the G2 maximum [h 15, arrow (c)] indicate that it took 3 h to complete the G2 phase. At this time [h 15, arrow (c)], the M phase maximum appears to occur at the same time as the G2 maximum. This occurs because the sampling rate from the process is insufficient to properly differentiate the M phase in relation to the other cell cycle phases. The mitotic fraction correlates with the changes in the specific growth rate as shown in Figure 6C as previously described (29).

At h 15 [arrow (c)], the cell concentration started to increase indicating that the synchronized cells have completed their passage through the cell cycle. At this time, the onset of apoptosis appears to occur as seen by an increase in the absolute apoptotic cell concentration [Fig. 6D, arrow (c)]. From h 15 to 19 [arrows (c,d)], the fraction of cells in G1 phase begin to increase until h 19 when the fraction of cells in G1 begin to decrease, indicating that the cells that have just reentered G1 at h 15 [arrow (c)] have completed G1 and entered S phase. This implies that for these cells, the length of G1 phase is 4 h. Thus, the total length of the cell cycle and the expected average doubling time of the culture is 13 h. However, immediately after the G1 peak maximum, the measured doubling time of the entire culture increased to 46 h until balanced growth was reached at h 34 [Fig. 6A, arrow (e); Fig. 7]. The discrepancy between the synchronized cohort's average cycle time and the observed doubling time of the entire culture is likely explained by a fraction of cells that are not participating in the cell cycle and remain in the G0 phase of the cell cycle.

Balanced Growth

The oscillations induced by the recovery from nutrient deprivation are damped, and the culture reaches balanced growth at h 34 [arrow (e)] characterized by time independent forward scatter and DNA distributions. During the balanced growth phase, the culture proliferated at a doubling time of 14 h (Fig. 7), which is near the expected proliferation rate as determined by the minima and maxima of the cell cycle fractions. Balanced growth continued until the fed-batch addition at h 62, arrow (f). By measuring the dividing population of cells during balanced growth, the single cell growth rates can be extracted from the distribution data using the integrated version of the population balance equation (30, 31). The single cell rates of growth are a measure of how quickly a single cell is increasing its size as a function of its current state. In this study, the single cell rate of growth is calculated using the forward scatter distribution of each phase of the cell cycle in conjunction with the equations previously described (18–20). The mitotic population is assumed to be the dividing population. It is also assumed that the cells divide symmetrically. The resulting rates of growth are shown in Figure 8. These curves are qualitatively similar to previous results for the single cell rates of production of antibodies in hybridomas cells (18–20).

Figure 8.

Single cell rates of growth in terms of forward scatter units. Data are calculated using the Collins–Richmond approach (30) using the mitotic fraction as the dividing population and the assumption of symmetric division. The data are qualitatively similar to data obtained by the same method for antibody production rates for each phase of the cell cycle (8, 18).

Nutrient Upshift

At h 62 [arrow (f)] the culture was diluted in a 1:10 ratio with fresh pre-warmed medium. Subsequently, for 2 h, the culture was temporarily arrested as the cell number did not increase [Fig. 6, arrows (f,g)]. The arrest appears to have occurred both at the G1/S restriction point and the G2/M control point. The G1/S arrest is evidenced by a decrease in the S phase fraction whereas the G1 fraction remained constant. The G2/M arrest is evidenced by an increase in the G2 fraction and the cell number ceasing to increase. When the arrest ended after 2 h, cell proliferation resumed at a temporarily decreased doubling time of 8 h. The temporarily increased proliferation rate initiated a partial synchrony of the culture. Similar to previous arguments, the average time cells spend in individual cell cycle phases is directly revealed by tracking of the subsequent oscillation amplitudes of the G1, S, G2, and M fractions.

The time between subsequent S phase minimum [h 71, arrow (h)] and maximum [h 77, arrow (i)] indicates that it took 6 h for the partially synchronized cells to complete S phase. Alternately, the time between the G2 phase minimum [h 77, arrow (i)] and the G2 maximum [h 80, arrow (j)] indicates that it took 3 h to complete G2/M phase. At h 80, arrow (j), the fraction of cells in G1 phase began to increase until h 84, arrow (k) when the fraction of cells in G1 begins to decrease. Thus, the length of G1 phase is 4 h and, the total length of the cell cycle and the expected average doubling time of the culture is 13 h, as observed during the recovery from nutrient deprivation. During the course of the synchrony induced by the nutrient upshift, it appears that the onset of apoptosis is correlated with the maximum in the G1 fraction at h 71, arrow (h).


The use of digitonin as a permeabilization reagent offers many advantages over traditional organic solvents. First, using digitonin in traditional PI staining protocols reduces the protocol to a single step (11), which eliminates the risk of losing a large fraction of cells during separate washing, fixation, and staining steps. This guarantees that the remaining sample is representative of the entire sample. Second, as this study shows, digitonin can reduce the total staining protocol to less than 10 min which is important in a high frequency, real time analysis. Fourth, the general strategy of using digitonin to rapidly permeabilize cells can potentially be applied to other stains or fluorescently labeled antibodies to quantify intracellular targets (32–34).

The developed staining protocol offers a unique way to study the cell cycle kinetics of a culture. Traditionally, individual growth perturbed cells are analyzed with time-lapsed video microscopy (35) or representative samples of a culture are analyzed with flow cytometry (36). Although time lapse video microscopy tracks individual cells over time at a very high frequency, the number of cells examined is relatively low. On the other hand, flow cytometry analyzes large numbers of cells such that infrequent events can be observed. However, because cytometry is traditionally an offline technique, the cell cycle distribution is infrequently measured leading to an incomplete picture of the time course data. Using automated flow cytometry and the developed staining protocol, the cell cycle distribution of large numbers of cells can then be frequently determined and the kinetics can be used to help determine the mechanisms underlying cell cycle progression.

The automated flow cytometry approach yields useful kinetic information during transient and balanced growth situations. During transient growth, the relative minima and maxima of the oscillations of the G1, S, and G2 fractions directly reveal the average time cells spent in each cell cycle phases. Using this analysis, our experiments indicated that the expected doubling time is 13 h. However, this value corresponds to a faster proliferation rate than indicated by the measured cell concentration increase (Fig. 7). This is likely due to cells that have exited from the cell cycle and are temporarily in the G0 state of the cell cycle and not participating in proliferation (35, 37, 38). Use of staining protocols that can separate G0 from G1 cells using stains such as acridine orange (39, 40), fluorescent antibodies such as Ki-67 (41), or staining for specific cyclins (42) would be useful in fully elucidating the G0 and G1 kinetics.

The observed cell cycle oscillations after the nutrient upshift and the recovery from nutrient deprivation are both caused by a temporary cell cycle arrest. After the nutrient upshift, the cell cycle was arrested at both the G1/S and G2/M boundary. This is likely due to the increased nutrient concentration increasing the cell size threshold for both the G1/S and G2/M checkpoints (43). This is seen in Figure 6C arrow (h) where the mean cell size for each cell fraction increases after the nutrient addition. A similar effect is seen during the recovery from nutrient deprivation.

There appears to be differences in how the two cultures coordinated cell death with the cell cycle. During the recovery from nutrient deprivation an increase in the apoptotic cell concentration, termed the onset of apoptosis, is correlated with the beginning of cell proliferation (Fig. 6D arrows (c) and (h)). During the nutrient upshift, the onset of apoptosis is correlated with cells transitioning from G1 to S. Across either treatment, the onset of apoptosis is correlated with an increase in the mean cell size of the population. These events highlight the advantage of using automated flow cytometry to analyze large numbers of cells frequently, as the increase in the apoptotic cell concentration represents only 2% of the newborn cells.

During balanced growth conditions, automated flow cytometry in conjunction with the Collins–Richmond approach (30) can be used to determine single cell rates of generation or destruction of some aspect of cell physiology (31). In this study, the single cell rate of growth was calculated using the forward scatter distribution of each phase of the cell cycle in conjunction with the equations in (18–20). Forward scatter was forced to be a conserved quantity by assuming symmetric division of the mitotic population. Although it is unclear that forward scatter is a conserved quantity during cell division, the described approach can be applied to many other conserved, fluorescently labeled aspects of cell physiology such as total protein or cyclin content.


The high frequency assessment of the cell cycle kinetics should be useful in studying cell cycle perturbations in response to different environmental conditions resulting from exposure to specific nutrients or to drugs. Knowledge of the kinetics can be useful for instance in elucidating the effects of nutrients and drugs on the underlying mechanisms governing cell cycle progression. This can then be practically applied to optimize medium and for investigating how culture variability affects culture productivity.