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Keywords:

  • red blood cells;
  • carboxyfluorescein diacetate succinimidyl ester;
  • cell differentiation;
  • cell division;
  • erythropoiesis;
  • cell division;
  • CFSE

Abstract

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results<
  5. Discussion
  6. Acknowledgements
  7. Literature Cited
  8. Supporting Information

Herein, we describe an experimental and computational approach to perform quantitative carboxyfluorescein diacetate succinimidyl ester (CFSE) cell-division tracking in cultures of primary colony-forming unit-erythroid (CFU-E) cells, a hematopoietic progenitor cell type, which is an important target for the treatment of blood disorders and for the manufacture of red blood cells. CFSE labeling of CFU-Es isolated from mouse fetal livers was performed to examine the effects of stem cell factor (SCF) and erythropoietin (EPO) in culture. We used a dynamic model of proliferation based on the Smith-Martin representation of the cell cycle to extract proliferation rates and death rates from CFSE time-series. However, we found that to accurately represent the cell population dynamics in differentiation cultures of CFU-Es, it was necessary to develop a model with generation-specific rate parameters. The generation-specific rates of proliferation and death were extracted for six generations (G0G5) and they revealed that, although SCF alone or EPO alone supported similar total cell outputs in culture, stimulation with EPO resulted in significantly higher proliferation rates from G2 to G5 and higher death rates in G2, G3, and G5 compared with SCF. In addition, proliferation rates tended to increase from G1 to G5 in cultures supplemented with EPO and EPO + SCF, while they remained lower and more constant across generations with SCF. The results are consistent with the notion that SCF promotes CFU-E self-renewal while EPO promotes CFU-E differentiation in culture. © 2012 International Society for Advancement of Cytometry

Carboxyfluorescein diacetate succinimidyl ester (CFSE) cell-division tracking is widely used to determine the number of divisions cells have undergone in cultures or in vivo. This flow cytometric assay is based on the redistribution and dilution of the CFSE fluorescent dye between mother and daughter cells during cell division, resulting in distinct fluorescence intensity for each cell generation (1–3). Originally developed for homogenous lymphocyte populations (1), Nordon et al. (4) extended this approach to track the divisions of primary hematopoietic progenitor cell populations that are composed of multiple cell subsets (5–7). Qualitative examination of flow cytometric histograms of CFSE fluorescence is useful but does not allow a complete interpretation of time-series experiments. However, quantitative CFSE cell-division tracking consists of using computational tools and a working model of the dynamics of cell division to extract parameters that characterize the rates of cell activation, proliferation, and death from CFSE labeling experiments (8–13).

The “transition probability” model of the cell cycle developed by Smith and Martin (14) has been useful to develop mathematical models to extract proliferation rates from CFSE data (8–10, 13, 15, 16) since it has made it possible to conceptualize the observed heterogeneity of intermitotic times within a cell population. The Smith-Martin model divides the cell cycling process into two fundamentally different stages: the A-phase which length is a random variable and a B-phase which length is fixed (deterministic). The A-phase corresponds approximately to the Go/G1 stage of the cell cycle (i.e., where the cells grow) and the B-phase approximately represents the S, G2, and M stages (i.e., where the cells actively divide). When stimulated to proliferate, the cells exit the A-state and enter the B-phase. In the original Smith-Martin model, the duration of the A-phase was modeled with an exponential distribution (analogous to an exponential decay process; 17). Nordon et al. (8) developed the first Smith-Martin-based mathematical model for quantitative CFSE cell-division tracking. Their model describes the rates at which the cells exit the A compartment and enter the B compartment or undergo death. The time spent in the B compartment is constant in every generation; therefore, the rate at which cells enter and exit any given B compartment is the same with an exception of a delay. By fitting the CFSE data to this model, the authors were able to describe the population dynamics of a lymphocyte cell line (8). More recently, they developed multi-type branching models based on the Smith-Martin representation of the cell cycle that take into account cell proliferation, death, and differentiation and demonstrated the usefulness of this approach to describe the expansion of human cord blood CD34+ cells in culture (13).

In this study, we used quantitative CFSE cell-division tracking to examine, for the first time, the effects of hematopoietic growth factors on the fate of a type of primary erythroid progenitor cells, referred to as colony-forming unit-erythroid (CFU-E), in vitro. CFU-Es are responsive to both stem cell factor (SCF) and erythropoietin (EPO) and are an important cell target for the treatments for blood disorders (18) and for the manufacture of red blood cells (19). We were able to obtain a highly enriched population of CFU-Es, which progeny could be tracked for up to 7–8 generations; this was achieved by sorting primary mouse fetal liver cells using a combination of three cell surface markers (c-Kit, Ter119, and CD71) and by selecting a subset of cells of homogeneous CFSE fluorescence intensity (4). We used a mathematical model based on the Smith-Martin representation of the cell cycle, as initially proposed by Nordon et al. (8). However, we found that to accurately represent the cell population dynamics in differentiation cultures of fetal liver CFU-Es, it was necessary to develop a model with generation-specific rate parameters. The generation-specific rates of proliferation and death were extracted for six generations (GoG5) and they revealed that, although SCF and EPO alone supported similar total cell outputs in culture, stimulation with EPO resulted in significantly higher proliferation rates in four out of six generations and higher death rates in, at least, three out of six generations compared with SCF. In addition, proliferation rates tended to increase from G1 to G5 in cultures supplemented with EPO and EPO + SCF, while they remained more similar with SCF. The results agree with the notion that SCF promotes CFU-E self-renewal while EPO promotes differentiation in cultures of mouse fetal liver CFU-Es.

Materials and Methods

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results<
  5. Discussion
  6. Acknowledgements
  7. Literature Cited
  8. Supporting Information

Mice

Untimed pregnant (days 13 and 14) female CD-1 mice were purchased from Charles River Laboratories (Wilmington, MA) and kept in the Division of Comparative Medicine animal facility in the Faculty of Medicine. Animal use and experimental protocols were approved by the University of Toronto Animal Care Committee in accordance with the Guidelines of the Canadian Council on Animal Care.

Isolation of Ter119 Mouse Fetal Liver Cells

Fetal livers were isolated from the decapitated mouse embryos (days 14 and 15) using surgical forceps. The fetal livers were placed in Hank's Balanced Salt Solution (HBSS; Invitrogen, Carlsbad, CA) containing 2% fetal bovine serum (FBS; Invitrogen), collectively referred to as HF hereafter, and disrupted by using a 16-gauge blunt-end needle. To obtain single cell suspension, cells were gently passed through a 21-gauge needle three times and then a 40 μm cell strainer (BD Biosciences, San Jose, CA). Cells were spun down at 400 g for 5 min at 4°C and washed twice with HF. Subsequently, cells were subjected to Ter119 depletion by EasySep™ magnetic sorting (Stem Cell Technologies, Vancouver, BC, Canada) according to the manufacturer's instructions.

CFSE Labeling

Ter119 cells were resuspended in phosphate-buffered saline (Invitrogen) at 2 × 107 cells/mL. CFSE (Invitrogen catalog no. C34554) was added to the cell suspension to reach a final concentration of 8 μM (unless mentioned otherwise). Subsequently, the cells were incubated for 15 min at 37°C and further CFSE uptake was quenched by the addition of a third volume of cold FBS. Cells were then washed twice in HF and cultured overnight at 5 × 105 cells/mL in StemPro-34 medium (Invitrogen) supplemented with 1% BSA (Stem Cell Technologies), 75 μg/mL human transferrin (Sigma-Aldrich, St Louis, MO), 10 μg/mL insulin (Invitrogen), 0.1 mM β-mercaptoethanol (Invitrogen), and 100 ng/mL mouse SCF (BioSource, Carlsbad, CA).

Flow Cytometric Isolation of c-Kit+CD71highTer119 Fetal Liver Cells of Homogeneous CFSE Fluorescence

Ter119 CFSE-labeled cells were collected following a 8 h culture period and stained with phycoerythrin (PE)-conjugated anti-CD71 (clone C2, catalog no. 553267), PE-Cy7-conjugated anti-Ter119 (clone TER-119, catalog no. 557853), and allophycocyanin (APC)-conjugated anti-c-Kit/CD117 (clone 2B8, catalog no. 553356) antibodies for 20 min on ice. All the antibodies were purchased from BD Biosciences and used at 1:100 dilution. Cells were washed twice and resuspended in HF containing 2 μg/mL 7-aminoactinomycin D (7-AAD; Invitrogen), which was used to discriminate dead cells from live cells.

7-AAD c-Kit+CD71highTer119 cells of homogenous CFSE fluorescence intensity were sorted using an unmodified BD FACSAria flow cytometer (BD Biosciences) that was set up according to published guidelines (20). Ter119 cells cultured overnight in the same conditions (but not exposed to CFSE) were used as unstained control, as well as in the preparation of single color stain controls (for PE, PE-Cy7, and APC). CFSE-labeled cells served as the single-stain control for the CFSE fluorescence (excited at 488 nm and the band pass filter for light emission was 530/30). Fluorescence minus one controls were used to set the threshold gate so that 99.9% of the cell population was below the gate for the corresponding color that was missing. For cell-division tracking, cell-to-cell variation in CFSE fluorescence intensity in the inoculum should not be more than two fold (4, 8). In this study, the width of the sorting gate for CFSE fluorescence intensity which achieved the best compromise between cell yield and resolution of cell generations was found to satisfy the relationship represented by Eq. (1):

  • equation image(1)

The gating strategy is illustrated in Supporting Information Figs. 1A and 1B. The highly purified population obtained allows for tracking up to seven divisions (Supporting Information Fig. 1C).

Flow Cytometric Analysis of Cell Generations in Serum-Free Cultures of CFSE-Labeled c-Kit+CD71highTer119 Cells

Sorted CFSE-labeled c-Kit+CD71highTer119 cells were cultured at an initial cell density of 1 × 104 − 1 × 105 cells/mL in serum-free StemPro-34 medium (Invitrogen) supplemented with 2.5 U/mL mouse EPO (R&D systems, Minneapolis, MN), 100 ng/mL mouse SCF, 75 μg/mL human transferrin, 1% BSA, 10 μg/mL insulin, and 0.1 mM β-mercaptoethanol. At 24 h, the culture media were exchanged. Cells were analyzed every 4 h during a total period of 48 h. Sampled cells were stained with PE-anti-CD71, PE-Cy7-anti-Ter119, and APC-anti-c-Kit. 7-ADD was added prior to sample acquisition on an unmodified BD FACSCanto flow cytometer that was set up according to published guidelines (20). Compensation was performed using the BD FACSDiVa software (Version 5.0.3). A total of 30,000 live cell events were acquired per sample. Data were then analyzed and presented using FlowJo 7.4 (Tree Star, San Carlos, CA). The generational Ni (the number of live cells in generation i at a specific time point) was obtained using the proliferation analysis toolbox in FlowJo software package, which assumed a lognormal distribution of the fluorescence intensities within a specific generation. The cytometer performance was checked daily using SPHERO™ Rainbow Fluorescent Particles (catalog no. RFP-30-5A, Spherotech, Libertyville, IL).

Colony-Forming Cell (CFC) Assays

To determine the number of hematopoietic progenitors, c-Kit+CD71highTer119 cells from 0 and 48 h cultures were plated in 35-mm tissue culture dishes (Stem Cell Technologies) containing 1.1 mL of methylcellulose-based semisolid culture media supplemented with SCF, Interleukin(IL)-3, IL-6 and EPO (MethoCult® M3434, Stem Cell Technologies; 21). Each test was performed in duplicate. After 7 days of incubation, colonies derived from granulocyte-macrophage progenitors [colony forming unit-granulocyte/macrophage (CFU-GM, CFU-G, and CFU-M)], early erythroid progenitors [burst forming unit-erythroid (BFU-E)], and multipotential progenitors [(colony forming unit-granulocyte, erythroid, macrophage, and megakaryocyte (CFU-GEMM)] were enumerated using an inverted microscope. Benzidine (Sigma) staining of hemoglobin was used to discriminate progenitors with erythroid lineage potential, BFU-E and CFU-GEMM, (22). To quantify late erythroid progenitors CFU-E, cells were incubated for 48 h before the colonies were stained with benzidine and enumerated. The statistical significance of the data was determined by one-way ANOVA and post hoc Tukey's multiple comparison analyses using JMPIN 8 software (SAS Institute, Cary, NC).

Computational Approach to Determine the Generational Times to Divisions (Δi) and Death Rates (di)

A schematic of the mathematical model used to analyse the CFSE data is presented in Figure 1. The model contains generation-dependent rate parameters, as the subscript i represents the generation number. Cell division was defined as an event in which a “mother cell” in the generation i (Gi) exits the A phase of the cell cycle based on the “activation” rate parameter (λi), spends a fixed period of time in the B phase (Δi) and gives rise to two “daughter cells” in the A phase of the next generation (Gi + 1); ai and bi represent the number of cells in the A and B phases of Gi, respectively. Cells can also die in the A phase of any generation, according to a death rate di. A dead cell is defined as a cell that neither undergoes division nor gives rise to any daughter cells and is not considered a member of any live population.

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Figure 1. Schematic representation of the dynamics of cell division based on the Smith-Martin model of the cell cycle and with generation-dependent rate parameters. Cell division was defined as an event in which a “mother cell” in the generation i (Gi) exits the A phase of the cell cycle based on the “activation” rate parameter (λi), spends a fixed period of time (Δi) in the B phase and gives rise to two “daughter cells” in the A phase of the next generation (Gi + 1); ai and bi represent the number of cells in the A and B phases of Gi, respectively. Cells can also die in the A phase of any generation, according to a death rate di. The final model used for this study included a single activation rate parameter (λ0) and assumed that λi = 1 for i > 0, for all culture conditions.

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As described in the Introduction section, the model is based on the classic Smith-Martin representation of the cell cycle (14) with the general biological assumptions: (i) death occurs only in the A phase; (ii) the rates of cell division, the duration of cell division and the rates of cell death are independent of one another; (iii) the rate of cell division, the duration of cell division and the rate of cell death are dependent on the generation number only; and (iv) the system is closed (i.e., new cells are only created through the division of live cells and cells are removed from the system only through death). The resulting model can be represented as the following set of delay differential equations [Eqs. (2)–(9)] where τ represents the integration delay. The total number of live cells Ni(t) was measured experimentally (Supporting Information Table S1) and Ni(t) = ai(t) + bi(t).

  • equation image(2)
  • equation image(3)
  • equation image(4)
  • equation image(5)
  • equation image(6)
  • equation image(7)
  • equation image(8)
  • equation image(9)

Laplace transforms were used to solve these delay differential equations. Mathematica 7.0 built in function inverse Laplace transform [F(s),s,t] was then used to transform the solution back into time domain. Model parameter (λi, Δi, and di) fitting was performed using minimization of sum of square of residuals (SSR) between the average Ni obtained from two independent experiments (Supporting Information Table S1) and the model predictions. The minimization was carried out using the Minimize function found in Mathematica 7.0 toolbox. It is used for nonlinear, global, and exact optimizations. It is uses cylindrical algebraic decomposition for the optimization process (23). It is not an iterative process therefore it can give exact solutions. The residuals were approximately normally distributed. The 95% confidence limits for each fitted parameters were estimated by bootstrapping (24) with 500 simulations.

Results<

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results<
  5. Discussion
  6. Acknowledgements
  7. Literature Cited
  8. Supporting Information

Cultures Supplemented with SCF or EPO Alone Support a Similar Increase in Total Cells but the Presence of SCF is Necessary to Increase the Number of CFU-Es

The cell-surface markers c-Kit (SCF receptor), CD71 (transferrin receptor), and Ter119 (mature erythroid cell marker) can be used to purify different subsets of erythroid progenitors (25). Here, primitive erythroid progenitor populations were obtained by first removing the more mature erythroid Ter119+ cells by magnetic cell sorting followed by further selecting the cells expressing c-Kit and high levels of CD71 markers in the Ter119 subset by fluorescence-activated cell sorting (FACS; see Supporting Information Fig. 1). When tested with a standard erythroid colony-forming cell assay (21), 73 ± 21% (±SD) of c-Kit+CD71highTer-119 cells gave rise to CFU-Es colonies (Supporting Information Fig. 2). No other types of colonies were detected. Considering that the cloning (or plating) efficiency of previously isolated mouse CFU-Es using different strategies ranges from 40 to 70% (18, 26, 27), these results suggest that the c-Kit+CD71highTer-119 cell population obtained is highly enriched in CFU-Es.

To determine if the c-Kit+CD71highTer119 cell subset responds to stimulation with EPO and SCF, 1.2 × 104 cells/mL of these cells (∼ 8400 CFU-Es/mL) were cultured for 48 h with saturating concentration of EPO (10 U/mL) and SCF (100 ng/mL), individually and in combination. In these experiments, the changes in the number of total cells (Fig. 2A) and in the number of CFU-Es (Fig. 2B) were assessed after 48 h of culture. First, c-Kit+CD71highTer119 cells cultured without cytokines survived <24 h. Cells cultured with either SCF or EPO alone supported a similar total cell output at 48 h (∼10-fold increase in cell number) but there were at least four times more CFU-Es in cultures supplemented with SCF. Cultures supplemented with EPO alone did not support the expansion or the maintenance of CFU-Es; therefore, the presence of SCF was necessary to increase the number of CFU-Es. Cultures supplemented with SCF or SCF + EPO supported similar CFU-E expansions but the total cell output differed by almost two-fold. Consequently, after culture with SCF + EPO for 48 h, only 15% of the cells were CFU-Es compared with ∼32% of the cells with SCF alone. Taken together this data raised questions about the respective contribution of proliferation versus survival of c-Kit+CD71highTer119 cells and their progeny, to the variations observed in total cell, and CFU-E outputs in these cultures.

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Figure 2. Output of total cells and CFU-E expansion in cultures of mouse fetal liver c-Kit+CD71highTer119 cells in the presence of EPO, SCF, and EPO + SCF. Sorted c-Kit+CD71highTer119 cells with homogenous CFSE fluorescence intensity were cultured in serum-free media with EPO (10 U/mL), SCF (100 ng/mL), or both for a total period of 48 h. A: Viable cells were enumerated every 4 h. Plotted values are mean ± SD (standard deviation) from four independent experiments (n = 4 for 12, 24, 36, and 48-h time points). *: denotes statistical significance between EPO + SCF and EPO alone or SCF alone at 36 and 48 h of culture (no statistical significance between EPO and SCF), using ANOVA and post hoc Tukey's multiple comparison analysis (P < 0.01). B: Numbers of CFU-Es after 48 h of culture in each condition (n = 2). *: denotes statistical significance using ANOVA and post hoc Tukey's multiple comparison test (P < 0.01).

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Cell Division Profiles Obtained with SCF, EPO, and SCF + EPO Are Similar During the First 24 h and Then Begin to Differ Increasingly

We next used CFSE cell-division tracking to better understand how SCF and EPO affected total cell and CFU-E outputs in cultures of c-Kit+CD71highTer119 cells. A CFSE concentrations of 8 μM was chosen for cell-division tracking of mouse fetal liver c-Kit+CD71highTer119 cells and their progeny since we found that this concentration was high enough to allow the resolution of at least seven generations without negatively affecting cell viability (Supporting Information Fig. 3) and colony-forming activity (Supporting Information Fig. 4). In addition, CFSE has significant spectral overlap with PE, PE-Cy7, and 7-AAD, which were used simultaneously to FACS-sort c-Kit+CD71highTer119 cells and analyze cell viability; above 8 μM CFSE, the level of spill over of CFSE fluorescence into the PE and 7-AAD channels increased dramatically (Supporting Information Fig. 5) and produced undesirable effects due to the high level of compensation that was required.

C-Kit+CD71highTer119 cells of homogeneous CFSE fluorescence were sorted and placed in culture in the presence of SCF and/or EPO and analyzed every 4 h, for 48 h. As shown in Figure 3, our protocol allowed the resolution of several, distinct cell generations in different culture conditions. We also observed that these cells divided rapidly, that is, 8–10 h per division, which is expected for murine fetal hematopoietic cells. The cells cultured in the absence of cytokine underwent apoptosis within a few hours and lost their CFSE resolution. As a result, it was not possible to obtain any cell division tracking data on these cells. Qualitative observations of the cell division histograms presented in Figure 3 suggested that the cytokine conditions affected the rate of cell proliferation and that the highest average proliferation rates were obtained in cultures supplemented with SCF + EPO. However, the differences were not immediately visible at the beginning of the cultures but they became increasingly pronounced from 24 h.

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Figure 3. CFSE time-series obtained from mouse fetal liver c-Kit+CD71highTer119 cells cultured with SCF and EPO for 48 h. C-Kit+CD71highTer119 cells with similar CFSE fluorescence intensity were cultured in the presence of EPO, SCF, or EPO + SCF. Cells were harvested and data for flow cytometry histograms of CFSE intensities was collected every 4 h. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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Stimulation with EPO Results in Higher Proliferation Rates in G0, G2, to G5 and Higher Death Rates from G2 to G5 Compared with SCF Alone

The generation-dependent rate parameter model (Fig. 1) was used for the quantitative analysis of the CFSE time-series data presented in Figure 3. This model is characterized by the parameters di, Δi, and λi which are estimated by fitting Ni using the system of equations represented by Eqs. (2)–(9), see Methods section. These model parameters allowed us to quantify the rates of erythroid progenitor cell survival and proliferation in culture. Evaluation of different version of the model and its optimization was first performed by visually comparing the model predictions for Ni and the experimental data (e.g., Supporting Information Figs. 8A–8C and Supporting Information Table S1).

The activation rate λ0 for cells stimulated with EPO (λ0 = 0.1692–0.1695 h−1) was significantly lower than for cells stimulated with SCF alone (λ0 = 0.182 – 0.183 h−1) or with EPO + SCF (λ0 = 0.1803 – 0.1804 h−1), Supporting Information Table S2. Interestingly, cell-to-cell variations in the time to activation (time to exit from A into B) for each generation was nearly normally distributed (Supporting Information Fig. 6); the standard deviation (σi) characterizing the fitted normal distribution (Supporting Information Fig. 7) for each cytokine condition did not vary significantly from G1 to G5 and cells moved from one generation to the next in a homogeneous manner. These observations make it possible to simplify the model since they supported the use of a single activation rate parameter (λ0) and the assumption that λi = 1 for i > 0, for all culture conditions.

Therefore, the CFSE time-series data was fitted using a model that contained a single entry into first cell division parameter (λ0); however, the values of the death parameter (di) and time-to-cell-division parameter (Δi) were specific to each generation. The comparison between the model prediction and the experimental data (Ni) for that model is presented for each generation in Supporting Information Figures 8A–8C. The rates extracted through the minimization of SSR algorithm for the three culture conditions are presented with their 95% confidence intervals in Supporting Information Table S2. The values of the death rate parameter (di) and time to division parameter (Δi) were found to vary significantly between generations. Figure 4 compares the progression and average duration of each cell generation for the three culture conditions. The plot for the corresponding extracted time to division parameter Δi is presented in Supporting Information Figure 9 (note that the generation-specific proliferation rates referred to in the text correspond to 1/Δi). The average time to division taken by CD71highc-kit+Ter119 cells increased from G1 to G4 and then reached a plateau from G4 to G5, except in cultures supplemented with SCF alone where the plateau had already been reached by G3 (Supporting Information Fig. 9). Moreover, from G0 to G3, the time to division changed in a similar manner in all cytokine conditions; however, in G4 and G5, cells cultured with SCF had a markedly greater Δi and, therefore, a much lower proliferation rate. From G2, cells stimulated by EPO and EPO + SCF took 1.5 h less time to divide per generation than the cells stimulated with SCF only (Fig. 4). The cells stimulated with EPO and EPO + SCF completed their fifth division on average at 37.9 ± 0.2 h and 37.5 ± 0.6 h, respectively, following the initial stimulation; however, cells cultured in the presence of SCF alone took 42.3 ± 0.1 h to complete five divisions (Fig. 4).

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Figure 4. Average time spent in five successive generations by mouse fetal liver c-Kit+CD71highTer119 cells cultured with SCF and EPO for 48 h. The CFSE time-series data were fitted into the model with generation-dependent rate parameters. Generation-specific values of the parameter Δi values were determined by minimizing the SSR between experimental data and model prediction. Error bars represent 95% confidence intervals obtained through 500 iterations of bootstrapped parameter values.

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The death rate parameter (di) takes into account the nonviable cells that are unable to move to the subsequent division. For all cell culture conditions, d0 and d1 were found to be low and equal to, respectively, ∼0.04 h−1 and ∼0 h−1, that is, below the detection threshold, (Fig. 5A). Following their second division, the death rates (d2) varied dramatically as a function of the culture conditions; the EPO-stimulated cells had the highest d2 value at 0.48 h−1, followed by SCF-stimulated cells with d2 = 0.20 h−1; d2 in cultures supplemented with EPO + SCF remained negligible (Fig. 5A). Interestingly, the d3 values for all culture conditions were negligible (d3 < 0.06 h−1). The high death rates followed by a dramatic increase in viability in the subsequent generations in cultures supplemented with EPO suggest that a phenotypic change and a cell selection process took place between G2 and G3. The model predictions with regard to cell death in G2 were independently verified by using 7-AAD viability staining (Fig. 5B). In cultures supplemented with EPO alone, the proportion of viable cells was 91 ± 3%, which is significantly lower than in cultures supplemented with EPO + SCF (96 ± 1%; P < 0.05) but not significantly different than cultures supplemented with SCF (93 ± 1%; P > 0.05). At G4, the death rates increased again in cultures supplemented with SCF alone or EPO alone (Fig. 5A). At G5, in all culture conditions, death rates were at their highest point, suggesting that the culture conditions had deteriorated due to the accumulation of inhibitory factors or lack of necessary factors to support the survival of more differentiated progeny.

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Figure 5. Generation-specific death during the culture of mouse fetal liver c-Kit+CD71highTer119 cells in the presence of SCF and EPO. A: Death rates (di) for each generation were determined by fitting the CFSE data to the model with generation-dependent rate parameters. Error bars represent 95% confidence intervals obtained through 500 iterations of bootstrapped parameter values. B: Percentage of live cells in the second generation (G2) of CFSE-labeled c-Kit+CD71highTer119 cells cultured for 12–32 h determined by 7-AAD staining and flow cytometry. *: denotes statistical significance using ANOVA and post hoc Tukey's multiple comparison analysis (P < 0.05). Values shown are mean ± SD from six independent experiments.

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In Vitro Erythropoiesis is Characterized by Generation-Specific Proliferation Rates and Death Rates

The CFSE time-series data were reanalyzed using a simpler fixed-rate parameter model similar to those used previously for studying lymphocyte proliferation (28, 29) or cell lines (30) and the goodness of fit was compared with that of the more complex generation-dependent model. The simple fixed-rate model examined contained only a single entry into cell division parameter (λ), two cell death parameters (d0 and d), and two time-to-cell-division parameters (Δ0, Δ). As expected, the discrepancies between the experimental data and the model predictions for the simpler fixed-rate model (Supporting Information Figs. 10A–10C) are substantially greater than that obtained with the generation-dependent model (Supporting Information Figs. 8A–8C). The parameter values calculated as well as commonly used metrics to evaluate the goodness of fit are represented in Supporting Information Table S3 for the simpler fixed-rate model (and Supporting Information Table S2 for the generation-dependent model). The Adjusted R2 (31) values for the generation-dependent model used in the previous sections compared with the simpler fixed-rate model were 0.97 versus 0.45 for EPO, 0.92 versus 0.48 for SCF and 0.96 versus 0.65 for SCF + EPO. Therefore, despite its additional complexity, the generation-dependent model represents a significant improvement over the simple fixed-rate model for accurately representing the transition of differentiating erythroid cells from one generation to the next.

Discussion

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results<
  5. Discussion
  6. Acknowledgements
  7. Literature Cited
  8. Supporting Information

CD71highc-Kit+Ter119 cells were chosen for this study on the cell population dynamics during red blood cell development because they are enriched in erythroid progenitors (CFU-Es), which have the ability to expand and differentiate when stimulated with SCF and EPO. We obtained generation-specific measurements of proliferation rates and death rates using quantitative CFSE cell division tracking and this revealed that the greater cell output obtained in the presence of SCF + EPO, compared with SCF or EPO alone, was the result of greater proliferation and survival in most generations following the first cell division. Cell divisions in the presence of SCF generally occurred at a slower and more constant rate from one generation to the other, which is consistent with the fact that SCF alone supported CFU-E self-renewal and a modest production of differentiated progeny compared with EPO and EPO + SCF. However, cells stimulated with EPO and EPO+SCF have a markedly faster proliferation rate from the third generation, which is consistent with a change in cell phenotype. The maximum proliferation rate is approximately one division every 7 h in conditions that favored CFU-E expansion (with SCF alone) and one division every 5 h in conditions that favored erythroid differentiation (with EPO alone).

After 48 h in culture, cells stimulated with EPO underwent, on average, one more division than cells stimulated with SCF; the overall greater rate of division with EPO counterbalanced the greater survival rate due to SCF stimulation and the outputs in total cells in both cultures were similar, although they had different proportions of CFU-Es versus differentiated progeny. Toward the fifth generation (G5), in all culture conditions there was a dramatic increase in death rates. A possible explanation for the increased cell death at 48 h is that, as erythroid cells mature, their environmental requirements progressively change and adhesion molecules such as fibronectin (32) and cell-cell interactions with other hematopoietic cell types (33) may need to be present to maintain cell survival.

The incorporation of a differentiation rate parameter into the model would make it possible to gain a more complete understanding on the effects of cytokines or drug candidates on erythroid progenitor cell fate decisions. However, the complexity of the delay differential equation system involved in creating this revised model would be an order of magnitude greater than the model described in the present study (Fig. 1), mainly because of the number of discontinuities in the solution domain for SSR minimization. However, discontinuities could be avoided by solving lag-differential equations by numerical convolution (34). Moreover, alternative computational strategies such as the multitype branching models presented by Nordon et al. 2011 (13) may be more appropriate when additional parameters such as differentiation rates need to be taken into account. It is also important to note that there are still some basic technical issues that may need to be addressed to improve the accuracy of parameter estimates in CFSE cell-division tracking. For instance, the assignment of the cell generation number from the CFSE histogram with most softwares, including the Proliferation tool in FlowJo, is based on fitting a sequence of lognormal distributions. This is a relatively subjective process partly due to CFSE degradation and cell auto-fluorescence and this can potentially introduce some error in the estimation of the proliferation rates and death rates. Ko et al. (7) have addressed this issue by adopting a clustering and nearest neighbour algorithm to assign a generation number to each CFSE labeled cells. Nonetheless, the authors concluded that the lognormal distribution provided a relatively good approximation of the generation numbers when examining the divisional recruitment of CD34+ umbilical cord blood cells.

In summary, the development of a model with cell generation-dependent rate parameters was necessary for analyzing CFSE time-series data in primary erythroid differentiation cultures. This allowed for a better representation of the erythroid cell population dynamics compared with traditional Smith-Martin-inspired models that had been used previously. The high cell-sampling rate (every 4 h) that was used in this study also allowed for accurate measurement of the beginning and ending of every generation.

Population aging is expected to increase the incidence of cancer-related anemia and blood-disorders in general while decreasing dramatically the number of healthy blood donors (35) and the results of this study demonstrate the usefulness of CFSE cell division tracking in the development of new erythropoiesis-stimulating agents for in vitro and in vivo use.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results<
  5. Discussion
  6. Acknowledgements
  7. Literature Cited
  8. Supporting Information

The authors thank Dr. Geoff Clarke for advice on the mathematical model development and Dionne White and Sherry Zhao for FACS sorting.

Literature Cited

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results<
  5. Discussion
  6. Acknowledgements
  7. Literature Cited
  8. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results<
  5. Discussion
  6. Acknowledgements
  7. Literature Cited
  8. Supporting Information

Additional Supporting Information may be found in the online version of this article.

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