Cell cycle distribution of primitive haematopoietic cells stimulated in vitro and in vivo

Abstract.

A novel approach is used to study the proliferating behaviour of primitive haematopoietic cell populations in response to different stimuli. A mathematical model based on the average proportion of apoptotic, dividing and quiescent cells in primitive haematopoietic cell populations is developed to describe the mitotic history of 5‐ (and 6‐) carboxyfluorescein diacetate succinimidyl ester‐labelled cells. The cell cycle distributions in different cytokine‐supplemented cultures of primitive human and mouse bone marrow cells are determined and compared with those found in vivo. The results indicate that a combination of flt‐3 ligand, Steel factor and interleukin‐11 or hyper‐interleukin‐6 provide a level of mitogenic stimulation similar to that existing in vivo after a myeloablative radiation dose. The comparison of the cell cycle distribution obtained for different cultures of human bone marrow CD34⁺(45RA/71)⁻ cells demonstrates that the addition of flt‐3 ligand in these cultures decreases apoptosis significantly but does not reduce quiescence. In addition, in vivo and in vitro, it was found that more than 3 days of stimulation are required to recruit a maximum number of quiescent cells into active cell cycle. These kinetics of cell cycle activation are found to be similar to those identified for the haematopoietic stem cells compartment in the same cultures. This mathematical analysis provides a useful tool for the development of haematopoietic stem cell culture processes for clinical applications.

Introduction

The implementation of cellular and gene therapies based on haematopoietic cells relies on the development of technologies permitting the isolation of the primitive cell populations and the identification of in vitro conditions that will support their survival and proliferation (Kume et al. 1999; Srour et al. 1999). Both the ex vivo expansion of primitive haematopoietic cells and their genetic modification by retroviral vector‐mediated gene transfer require in vitro conditions that induce their replicative cell cycle. Freshly isolated human haematopoietic cell populations of the CD34⁺ phenotype and murine cell populations of the lin⁻ phenotype are enriched in primitive haematopoietic cells. The vast majority of cells in these populations are quiescent. In vivo, the proliferation of primitive haematopoietic cells can be activated in response to stress, blood loss or irradiation in order to restore haematopoiesis.

The factors affecting the conservation of functional properties when primitive haematopoietic cells are stimulated in vitro are not well defined. Recent studies have demonstrated a small (2–4‐fold) increase in haematopoietic stem cell number when CD34⁺CD38⁻ cells were cultured in serum‐free medium supplemented with Steel factor (SF), flt‐3 ligand (FL), interleukin‐6 (IL‐6), granulocyte‐colony stimulating factor (G‐CSF) and IL‐3 (Bhatia et al. 1997; Conneally et al. 1997). A similar increase in stem cell number was obtained when mouse Sca‐1⁺lin⁻ cells were stimulated with SF, FL and IL‐11 or hyper‐IL‐6 (H‐IL‐6) (Miller & Eaves 1997; Oostendorp et al. 2000). In these cultures, however, the specific contribution of each cytokine to cell survival, induction of cell cycle and mitogenesis is unknown.

1997, 1999 developed a high‐resolution cell division tracking methodology to investigate the proliferation of primitive haematopoietic cells. This analysis was based on a two‐compartmental model of the cell cycle, where each generation was divided into A and B compartments. In this model, cells are assumed to leave compartment A by apoptosis or progress to compartment B before returning to A. Quiescence was not considered. In the present paper, we propose a simple modelling approach that allows us to extend this work to estimate the fractions of quiescent, dividing and apoptotic haematopoietic cells in proliferating populations. We show that this model describes the experimental data obtained by Nordon et al. (1997) and Oostendorp et al. (2000) with either human or murine haematopoietic cells stimulated with cytokines in vitro or in vivo following transplantation in myeloablated recipients. An increased understanding of the factors affecting the proliferation of primitive haematopoietic cells and the ability to distinguish effects on cell survival from effects on mitogenesis provides guidance for the optimization of culture systems for haematopoietic cell expansion.

DATA

The experimental data used in this analysis were collected from recent publications (Nordon et al. 1997; Oostendorp et al. 2000) that used a high‐resolution procedure for tracking 5‐ (and 6‐) carboxyfluorescein diacetate succinimidyl ester (CFSE)‐labelled human and murine haematopoietic cells. The precise halving of their CFSE‐fluorescence allowed the tracking of each mitosis. Data from human bone marrow cells were obtained from 3 or 4 day serum‐free cultures supplemented with a cytokine cocktail consisting of SF, IL‐3, IL‐6 and G‐CSF (Nordon et al. 1997). Data from murine bone marrow cells were obtained from 3 or 4 day cultures (Oostendorp et al. 2000). These cells were stimulated either in vitro with a combination of FL, SF, H‐IL‐6 and IL‐11 or in vivo by factors active in myeloablated recipients. Data of cell distributions according to their mitotic history were obtained either directly from Table 1 of Nordon’s paper or from scanned and digitized Figs 2, 3 and 4 of Oostendorp’s paper using the Paint software of Windows.

MATHEMATICAL ANALYSIS

At any cycle time, each haematopoietic cell can exist in one of the following three states: quiescence, division (self‐renewal or differentiation) and apoptosis. Let Q_i, D_i and A_i (Q_i + D_i + A_i = 1) represent the fractions of cells that are quiescent, dividing or undergoing apoptosis during the ith cycle time. N_{i ,j} denotes the number of progeny that have divided j times by the ith cycle time (j ≤ i, j = 0 corresponds to undivided cells, N ₀₀ stands for the initial cell number). A schematic diagram of this model is given in Fig. 1. At any cycle time m, we can write the mathematical expressions for the distributions of all subpopulations:

Figure 1.

A schematic representation of a simple model of cell proliferation. Q_i, D_i and A_i (Q_i + D_i + A_i = 1) represent, respectively, the fractions of cells remaining quiescent, dividing and undergoing apoptosis at the ith cycle time. N_{i ,j} is the number of progeny undergoing j divisions by the ith cycle time (j = 0 corresponds to undivided cells, N ₀₀ stands for the initial number of cells).

The factor 2 reflects the fact that one cell becomes two after cell division. These equations can be solved analytically to give

(1)

where the summation in the equation for N_{m ,n} includes all possible ways of picking n distinct integers out of the first m positive integers. In the simplest possible case, we assume Q_i = Q, D_i = D, A_i = A, i = 1,2, … ,m. This means that the probabilities are independent of cycle time. We then have

(2)

where C_mⁿ is the number of combinations of picking n numbers out of m. Thus the total number of progeny after m cycles can be calculated from:

(3)

Thus, the percentage of progeny undergoing n divisions after m cycles is given by

(4)

RESULTS AND DISCUSSION

Expression (4) was applied to results obtained with human 34⁺(45RA/71)⁻ cells, human 34⁺(45RA/71)⁺ cells, murine low‐density (LD) cells and murine lin⁻ cells stimulated in vitro. Murine LD and lin⁻ cells stimulated in vivo in myeloablated recipients were also analysed. The parameter values were estimated by fitting the experimental data with the model using the SLINK software (Downhill Simplex Minimization Method In Many Dimensions) in Maple (Waterloo Maple Inc.). The comparisons between the experimental and the calculated cell distributions are shown in 2, 3, 4. These results show that the simple model given in Fig. 1 can provide a satisfactory description of proliferating behaviour of different populations of human and murine bone marrow cells in response to different stimuli. The estimates for Q, D and A under the different experimental conditions are summarized in1, 2, 3.

Figure 2.

Experimental and calculated cell distributions for values of Q, D and A in Table 1 for different phenotypes of human bone marrow cells including CD34⁺(45RA/71)⁻ (a, b) and CD34⁺(45RA/71)⁺ (c) after 4 days of culture in vitro. 4GF stands for four growth factors: SF, IL‐3, IL‐6, G‐CSF, while 5GF stands for 4GF plus FL. The X axis represents the number of divisions the cells have gone through in each subpopulation. ‘Exp’ stands for experimental distribution and ‘Cal’ for calculated distribution.

Figure 3.

Experimental and calculated cell distributions for values of Q, D and A in Table 2 for low‐density murine bone marrow cells after 4 days of maintenance in culture without (a) and with (b) the stimulation of FL, SF and H‐IL‐6 or under in vivo conditions (c–e). The X axis represents the number of divisions the cells have gone through in each subpopulation. ‘Exp’ stands for experimental distribution and ‘Cal’ for calculated distribution.

Figure 4.

Experimental and calculated cell distributions for Q, D and A values in Table 3 . Cell progeny distributions for lin⁻ murine bone marrow cells after 3 (a, b) and 4 (c, d) days of maintenance in culture (a, c) with the stimulation of FL, SF and IL‐11 and in vivo (b, d). The X axis represents the number of divisions the cells have gone through in each subpopulation. ‘Exp’ stands for experimental distribution and ‘Cal’ for calculated distribution.

Table 1.

Average proportion (%) of quiescent (Q), dividing (D) and apoptotic (A) cells in 4 day cultures of CD34⁺ human bone marrow cells ( Nordon et al. 1997) . All cultures contained IL‐3, IL‐6, SF and G‐CSF

	(45RA/71)+	(45RA/71)−
	without FL	without FL	with FL
Q	32	46	49
D	46	29	35
A	22	25	16

Table 2.

Average proportion (%) of quiescent (Q), dividing (D) and apoptotic (A) cells for LD mouse bone marrow cells stimulated 4 days, in vitro or in vivo ( Oostendorp et al. 2000 )

	In vitro a		In vivo b
	no cytokine	with cytokines	marrow	spleen	blood
Q	87	40	22	40	47
D	7	38	40	32	28
A	6	22	38	28	25

^a Cells were cultured 4 days with or without H‐IL‐6, SF and FL.

^b Cells were transplanted into myeloablated recipients and retrieved 4 days later from the marrow, spleen or blood.

Table 3.

Average proportion (%) of quiescent (Q), dividing (D) and apoptotic (A) cells for lin⁻ mouse bone marrow cells stimulated 3 or 4 days, in vitro or in vivo ( Oostendorp et al. 2000 )

	In vitro a		In vivo b
	3 days	4 days	3 days	4 days
Q	48	18	66	37
D	39	50	19	34
A	13	32	15	29

^a Cells were cultured with IL‐11, SF and FL.

^b Cells were transplanted into myeloablated recipients and retrieved from the marrow.

The data presented in Table 1 compare the cell cycle distribution of human bone marrow CD34⁺(45RA/71)⁻ and CD34⁺(45RA/71)⁺ cells stimulated 4 days with SF, IL‐3, IL‐6 and G‐CSF. In cultures initiated with both populations, the calculated average proportion of apoptotic cells is similar (A = 25% versus 22%). However, the average proportion of dividing cells in cultures of CD34⁺(45RA/71)⁻ cells is smaller (D = 29% versus 46%) and the proportion of quiescent cells is greater (Q = 46% versus 32%). These results are consistent with reports that the most primitive haematopoietic cells are found in the CD34⁺(45RA/71)⁻ population (Lansdorp & Dragowska 1992; Sauvageau et al. 1994; Hogge et al. 1996) and it is therefore likely that one would find a greater proportion of quiescent cells in cultures initiated with cells of this phenotype. The relative proportions of apoptotic, quiescent and dividing cells in these two cultures support the observation that the net proliferation rate is higher in cultures of CD34⁺(45RA/71)⁺ cells than in cultures of CD34⁺(45RA/71)⁻ cells (Nordon et al. 1997).

When FL was added to the initial cytokine cocktail (composed of SF, IL‐6, IL‐3 and G‐CSF), the calculated average proportion of quiescent cells in cultures of CD34⁺(45RA/71)⁻ was not changed significantly (Q = 46% versus 49%), but the fraction of dividing cells increased from 29% to 35% and apoptosis decreased from 25% to 16%. This points to a significant effect of FL on promoting the survival of primitive haematopoietic cells. The increase in the proportion of dividing cells observed when FL is added to the cytokine cocktail is most probably associated with enhanced cell survival in these cultures since the proportion of quiescent cells was not changed. The predicted increase in the net proliferative rate when FL is added to cultures of human primitive haematopoietic cells is consistent with results obtained in expansion cultures of human bone marrow CD34⁺CD38⁻ cells (Petzer et al. 1996).

Table 2 presents the results obtained for LD mouse bone marrow cells cultured 4 days in vitro without cytokines or cultured 4 days with H‐IL‐6, SF and FL. Table 2 also summarizes the results obtained with LD cells transplanted 4 days in myeloablated mice. As expected, in the absence of cytokines, LD bone marrow cells remained quiescent (Q = 87%) during culture. When stimulated with cytokines (FL, SF and H‐IL‐6), the average proportion of quiescent cells decreased 2‐fold (Q = 87% versus 40%), the fraction of dividing cells increased 4‐fold (D = 7% versus 38%) and the proportion of apoptotic cells increased 3‐fold (A = 6% versus 22%). Thus, the cytokines added in these cultures contributed to the recruitment of quiescent cells in active cell cycle. Apparently, for a significant fraction of these cells, cycle activation led directly to apoptosis. The cell cycle distribution within the progeny of transplanted cells in the spleen and in the blood was found to be similar to that of LD cells cultured in the presence of H‐IL‐6, SF and FL. However, in the marrow, a smaller fraction of cells was quiescent compared with cells stimulated in vitro with cytokines (Q = 22% versus 40%) or compared with cells found in the spleen (Q = 40%) or blood (Q = 47%). In addition, in the bone marrow, a larger fraction was apoptotic (A = 38%). Interestingly, the highest proportion of dividing cells was found in the bone marrow (D = 40%) and this proportion was closely matched by that of cells stimulated in vitro (D = 38%). Thus, the cytokine‐supplemented cultures used to expand haematopoietic cells can closely mimic the highly mitogenic environment found in the bone marrow. However, the cell cycle distribution found in vivo is influenced not only by the stimulatory signals from the environment but also by the preferential homing of subpopulations of transplanted cells in certain organs. It is also probable that this segregation is influenced by the cell cycle status since cell cycle progression can affect engraftment of primitive haematopoietic cells in the bone marrow (Srour et al. 1999; Glimm et al. 2000).

The results presented in Table 3 indicate that important changes take place between 3 and 4 days in cultures of lin⁻ mouse bone marrow cells supplemented with IL‐11, SF and FL. From day 3 to day 4, the average proportion of quiescent cells decreased more than 2‐fold (Q = 48% versus 18%), the proportion of dividing cells increased (D = 39% versus 50%) and the proportion of apoptotic cells increased more than 2‐fold (A = 13% versus 32%). This indicates that several days of stimulation are required to recruit a maximum number of lin⁻ cells into active cell cycle. Considering that the same trend from day 3 to day 4 was observed for cells transplanted in vivo, these kinetics of activation probably reflect an intrinsic property of these cells. However, similarly to what was observed when FL was added to cultures of human bone marrow cells, the results suggest that increased cell cycle induction in lin⁻ cells is associated with increased apoptosis. This was observed in culture and in vivo. Interestingly, the majority haematopoietic stem cells in the lin⁻ cultures were found to be quiescent (undivided) at day 3 but one day later (day 4), 90% of all haematopoietic stem cells were in the divided fraction (Oostendorp et al. 2000). Although haematopoietic stem cells represent an infinitesimal fraction of the total cells in these cultures, here the calculated total cell cycle distribution was predictive of the distribution in the stem cell compartment.

In summary, the model developed can provide a satisfactory description of the proliferating behaviour of primitive haematopoietic cell populations in response to different stimuli. The calculated values of model parameters indicate that cytokine‐supplemented cultures used to expand haematopoietic cells provide a level of mitogenic stimulation similar to that existing in vivo, in the bone marrow of myeloablated recipients. The comparison of the values of the model parameters obtained for different cultures of human bone marrow CD34⁺(45RA/71)⁻ demonstrated that the increased cell expansion observed when FL is added to a combination of IL‐3, IL‐6, SF and G‐SCF is mainly the consequence of an increased cell survival. In addition, it was found that more than 3 days of stimulation are required to recruit a maximum number of quiescent lin⁻ cells into active cell cycle. Interestingly, these kinetics of cycle activation were found to be similar to those existing in the stem cells populations in the same cultures. These findings should aid in the development of haematopoietic stem cell culture processes for clinical applications.

Acknowledgements

The authors acknowledge financial support from the Mathematics of Information Technology and Complex Systems (Canadian Network of Centers of Excellence) and StemCell Technologies (Vancouver, BC) and NSERC research grants to Y.X.L. and J.M.P.