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HEMATOPOIESIS
From the Division of Hematology, Department of
Medicine, and the Department of Statistics, University of Washington,
Seattle, WA; and the Jackson Laboratory, Bar Harbor, ME.
We used stochastic modeling and computer simulation to study the
replication, apoptosis, and differentiation of murine hemopoietic stem
cells (HSCs) in vivo. This approach allows description of the behavior
of an unobserved population (ie, HSCs) on the basis of the behavior of
observed progeny cells (ie, granulocytes and lymphocytes). The results
of previous limiting-dilution, competitive-repopulation studies in 44 mice were compared with the results of simulated transplantation
studies to identify parameters that led to comparable outcomes. Using
this approach, we estimated that murine HSCs replicate (on average)
once every 2.5 weeks and that the frequency of murine HSCs is 8 per
105 nucleated marrow cells. If it is assumed that
short-term repopulating cells are distinct from HSCs, that they
contribute to hemopoiesis early after transplantation, and that they
are independently regulated, a frequency of 4 HSCs per 105
nucleated marrow cells also allows simulations that best approximate the observed data. When stochastic modeling and computer simulation were applied to limiting-dilution, autologous-transplantation studies in cats heterozygous for glucose-6-phosphate-dehydrogenase, different estimates of HSC replication rate (1 per 8.3-10 weeks) and
frequency (6 per 107 cells) were derived. Therefore, it
appears that these parameters vary inversely with increased longevity,
size, or both. An implication of these data is that human HSCs may be
less frequent and replicate more slowly. These findings on cell
kinetics have several implications.
(Blood. 2000;96:3399-3405) Hemopoietic stem cells (HSCs) give rise to all
types of mature blood cells, including granulocytes, monocytes,
lymphocytes, red cells, and platelets. They are the parent cells that
are essential for maintaining homeostasis in the blood system. Because
mammalian HSCs are infrequent and are defined functionally, information about their in vivo kinetics must be inferred from analyses of progenitors and differentiated blood cells.
Stochastic modeling is an excellent method for analyzing the
behavior of an unobserved cell population (ie, HSCs) on the basis of
observations of the behavior of derivative cells. This approach does
not require information about the outcome of individual cell divisions;
rather, it allows characterization of the behavior of a population of
cells on the basis of the assumption that the fate of an individual
member is probabilistic. The fate (replication, differentiation, or
apoptosis) of an individual HSC depends on the chance that it interacts
with specific accessory cells in the marrow microenvironment, the
presence or quantity of cytokines it uniquely encounters, its
cell-surface expression of receptors, and the integrity of its
signal-transduction pathways. A complex, yet regulated, process such as
hemopoiesis is especially amenable to stochastic analysis.
A stochastic model of HSC differentiation is diagrammed in Figure
1. A hemopoietic stem cell can replicate
(self-renew; the intensity or average rate of HSC replication is
In previous studies, we used this stochastic model and computer
simulation to determine the in vivo kinetics of HSCs in female cats
heterozygous for the x-chromosome-linked enzyme,
glucose-6-phosphate-dehydrogenase (G6PD) after transplantation of small
numbers of autologous cells (1-2 × 107 nucleated marrow
cells/kg).1 Because only a small number of HSCs were
present in the marrow inoculum, there was competition to repopulate and
maintain hemopoiesis between HSCs expressing the G6PD phenotype of the
domestic parent and HSCs expressing the G6PD phenotype of the Geoffroy parent.
The parameter values yielding simulations that best fit the
experimental observations were The aim of this study was to apply these methods to the analysis of
data generated from experiments in which small numbers of congenic
donor (Gpi-1a) and competitor (Gpi-1b) marrow
cells were transplanted in mice.2 By analyzing studies with a comparable experimental design with use of a similar analysis, we hoped to gain insight into the in vivo behavior of murine HSCs and
to define the evolutionary adaptations of HSCs to increasing animal
size and lifespan. In its lifetime (2 years), a mouse (25 g) makes the
same number of red blood cells as does a human (70 kg) in 1 day or a
cat (4 kg) in 8 days.3 Similar discrepancies exist in the
requirements for other blood-cell lineages. We wanted to determine
whether feline (and human) HSCs are more numerous than murine HSCs,
have higher proliferative potentials per cell, or are regulated by
different kinetics to satisfy this increased demand.
Data from congenic murine transplantations
Each of the 44 mice given transplants were placed into 1 of 8 categories defined by the pattern of the percentage of
Gpi-1a cells 6, 15, and 30 weeks after transplantation.
Representative studies are diagrammed in Figure
3. For category type 1, the proportion of
Gpi-1a cells was 4% or higher at 6 weeks (w6),
15 weeks (w15), and 30 weeks (w30). For type 2, it was less than 4% at w6 and 4% or higher at
w15 and w30. For type 3, it was 4% or higher
at w6 and w30 and less than 4% at
w15. For category type 4, the proportion of Gpi-1a cells was less than 4% at w6 and
w15 and 4% or higher at w30. For type 5, it
was 4% or higher at w6 and w15 and less than
4% at w30. For type 6, it was less than 4% at
w6 and w30 and 4 % or higher at
w15. For type 7, it was 4% or higher at w6 and
less than 4% at w15 and w30.
Finally, for category type 8, the proportion of Gpi-1a
cells was less than 4% at all 3 assessment times. Ten of the 44 mice
had a reconstitution pattern similar to that of type 1, whereas 3 of
the 44 mice had a type 2 pattern. The distribution of other pattern
types is shown in Figure 3.
Statistical methods for the analysis of murine studies
The 3 observations pertaining to each mouse (ie, the percentage of
"granulocytes" that expressed Gpi-1a at 6, 15, and 30 weeks after transplantation) can be seen as a random draw from a
3-dimensional distribution with a continuous range
[0-100].3 Therefore, the entire data set represents a simple random sample of size 44 from such a distribution.
We next discretized the simulated data to better understand the empiric
distribution and to simplify the comparison with experimental data. Our
discretization used a cutoff point of 4% (ie, values Given a combination of parameter values for To determine the ranges of values for the parameters that best
reproduced the experimental data, we performed a coarse lattice search
over the plausible range of values; 100 different combinations of
parameters were considered. We determined the appropriateness of each
parameter set by means of 2 criteria. The first criterion (criterion 1)
was based on the comparison between the distributions of the proportion
of Gpi-1a-type cells by week of the experimental and
simulated data. In this comparison, unique features of the experimental
data (ie, the high density of 0% Gpi-1a-positive cells at
each evaluation time and the broad distribution of observed outcomes,
including outcomes where > 30% Gpi-1a-positive
cells occurred at 15 and 30 weeks; Figure 2), needed to be maintained.
Criterion 1 was satisfied if the distributions of the simulated data
were similar to those of the experimental data. The second criterion
(criterion 2) was based on the 8 Monte Carlo tests.
A combination of parameters was considered acceptable if (1) criterion
1 was satisfied and at least 6 of the 8 Monte Carlo tests yielded
nonsignificant results simultaneously (P > .1); or (2)
criterion 1 was not satisfied but at least 7 of the 8 Monte Carlo tests
yielded nonsignificant results simultaneously. A parameterization was
considered a best fit if criterion 1 was satisfied and all 8 Monte
Carlo tests yielded nonsignificant results simultaneously. When a best
fit was found, the robustness of the parameterization was confirmed
through sensitivity analysis, ie, slightly changing some of the
parameter values, the random seed, or both and assuring that these
modifications also satisfied best-fit criteria.
Parameters generated from studies of hemopoiesis in cats could not
explain the murine data
Estimation of parameters for murine HSCs
Assumptions regarding the existence of STRCs affect estimates of HSC frequency but not other parameters An STRC can reconstitute hemopoiesis immediately after transplantation and support blood-cell production for a short period, which is operationally defined as less than 6 to 12 weeks. These characteristics are in contrast to those of a long-term repopulating cell (LTRC), which contributes to hemopoiesis from 3 to 4 months after transplantation and throughout a mouse's lifetime. Whether an STRC is a distinct cell type or a functional description of a subset of HSCs is controversial.2,5-13 With the initial analyses (Figure 5A), we assumed that C0 could be derived from the R/C mean at steady state (    + µ)/, when R0 = 35
and C0 = 50, and that only a few clones (those
transplanted from compartment 2; Figure 1) contributed to blood-cell
production immediately after transplantation. HSCs that by chance
differentiate quickly would also be considered to be STRCs, whereas
those that by chance undergo replication divisions (doubling clone size
and proliferative potential) would be considered to be LTRCs according
to the traditional definitions. Alternatively, if STRCs exist as a
distinct, independently regulated cell type, this approximation might
underestimate their numbers. The ratio of LTRCs to STRCs has been
estimated as 1:2 to 1:10.2,6,10,13 Therefore, to consider
the potential effects of contributions from STRCs at 6 weeks after
transplantation, we performed additional simulations in which values
were designated for this ratio (and not derived). If
R0:C0 was 1:2, no
parameter was affected. Values of
R0:C0 ranging from 1:4 to
1:10 affected estimates of HSC frequency but not estimates of average
HSC replication rate () or average HSC apoptosis rate (). For
example, when the ratio
R0:C0 was set equal to
1:4, HSC frequencies between 4 and 8 per 105 nucleated
marrow cells best fit the data. Figure 5B shows the results for the
combination of parameters with an R0 of 18 (HSC frequency = 4/105 nucleated marrow cells; all 8 P values were > .1 on Monte Carlo analyses). For
values of R0:C0 equal to
1:7, acceptable but not optimal (best fit) parameterizations were
achieved. For values of R0:C0
under 1:10, the simulated outcomes were not similar to the
observed data (criterion 1 was not satisfied and P values were < .1 in 3 or more of the 8 categories analyzed).
The estimated parameter values allow excellent simulations of other experimental data Data on B lymphocytes in the 44 mice given transplants were also available. There was a strong correlation between B-cell and granulocyte values at 15 and 30 weeks (but not at 6 weeks) after transplantation.2 Similarly, parameters derived from the granulocyte analysis allowed an acceptable fit of the B-lymphocyte data. To assess the validity of the estimations further, experimental data generated by transplantation of different numbers of Gpi-1a and Gpi-1b marrow cells (D.E.H., unpublished data, 1996-1999) were studied by using a comparable approach. These data were less complete (10-26 mice/experimental approach) and predominantly contained measurements of long-lived cells (red cells and total lymphocytes [eg, T and B cells]) and thus were not sufficiently powerful for independent parameter estimates or Monte Carlo analysis. Therefore, for each circumstance, 150 comparable data sets were simulated and compared with the experimental observations by using only criterion 1. An analysis was performed for lymphocytes (1, 5, and 9 months) and red cells (5 and 9 months) after 26 mice were given transplants of 1.3 × 105 Gpi-1a and 4 × 105 Gpi-1b marrow cells (0.25 ratio of donor to total cells) and for lymphocytes and granulocytes 1, 4, and 7 months after 14 mice were given transplants of 2 × 105 Gpi-1a and 2 × 105 Gpi-1b marrow cells (0.5 ratio of donor to total cells). All histograms of the distribution of simulated data were similar to the histogram of the experimental observations, confirming that the initial estimations were reasonable.
We studied the in vivo behavior of HSCs by analyzing data generated from the transplantation of small numbers of HSCs labeled by GpI-1a or GpI-1b phenotype into congenic mice. Through computer simulation and the assumption that all HSC decisions are stochastic, we estimated the average rates of HSC replication (self-renewal), differentiation, and apoptosis. Our data suggest that murine HSCs are not quiescent; rather, they replicate an average of once every 2.5 weeks. Thus, the median time to replication (ie, the time when 50% of HSCs have divided) is 1.7 weeks. Similarly, we determined that the frequency of HSCs in normal, steady-state marrow is 4 to 8 per 105 nucleated cells. These results are remarkably consistent with estimates using other approaches. For example, incorporation of bromodeoxyuridine was used to determine the rate at which murine HSCs, phenotypically defined as rhodamine 123lo and Hoechst 33342lo cells14 or c-kitbright Thy1.1lo Sca-1+ lineage-negative cells15 enter the cell cycle over time. In these 2 studies, approximately 4.3% and 7.8%, respectively, of these cells were found to enter the cell cycle each day, apparently in random fashion. Because the cell cycle was estimated to last 3 days,15 50% of HSCs should complete their cell cycle (ie, replicate) in 9 to 19 days (1.3-2.75 weeks). This approach might overestimate the replication rate of HSCs if cells that were more differentiated and less quiescent than HSCs were included among cells termed HSCs as a result of metabolic or immunologic-phenotype analyses. In the study by Bradford et al,14 for example, 1 of 12 cells termed HSCs supported long-term hematopoiesis in transplantation studies. The comparability of results achieved with 2 different experimental methods reinforces the validity of the findings and also suggests that stem-cell kinetics after transplantation are similar to that during steady-state hemopoiesis. Our estimate of murine HSC frequency At an average replication rate of 1 per 2.5 weeks, the stem-cell reserve (compartment 1; Figure 1) will not be reconstituted to steady-state values until 134 weeks (2.6 years) after limiting-dilution transplantation (R0 = 35), which exceeds the lifespan of mice. Reconstitution will not occur until 94 weeks (1.8 years) after transplantation if more typical numbers of nucleated marrow cells (R0 = 400; 5 × 106 cells/mouse) are transplanted (assuming the total number of nucleated marrow cells in a normal mouse is 2.8 × 108 (ref 21) [results obtained with simulation studies and Markov analyses]). These kinetics findings are consistent with the observation that only a few1-2 serial transplantations can be done before exhaustion of the hemopoietic reserve but that 3 to 5 transplantations can be accomplished if they are performed at intervals of more than 6 months.5,13 Table 1 shows the estimated replication rate and frequency of murine and feline HSCs. Although no studies have been done to confirm these values in other large animals, Wang et al22 transplanted subpopulations of human marrow cells into nonobese diabetic-severe combined immunodeficient mice as an indirect method for enumerating human HSCs. There is controversy about whether xenotropic transplantation assays indeed measure HSC activity or only correlate with this activity, but the value obtained for HSC frequency (3/107 nucleated marrow cells) in their study was less than estimated HSC frequencies in mice and cats. These data provide insight into the evolutionary adaptation to increased size and longevity. They suggest that in larger animals, HSCs are less frequent and divide more slowly. Therefore, the proliferative potential of each cell (ie, differentiated progeny per clone lifetime) is high. Thus, either murine and feline (and human) HSCs are biologically different in their intrinsic capacities or, if they are biologically similar, there is excess capacity in murine cells that is not needed to support hemopoiesis throughout a mouse's lifetime. An extension of this idea would be that cells that are not technically stem cells (ie, cells that derive from a differentiating stem-cell clone that has undergone 1 or 2 divisions [STRCs]) could exist in mice but perhaps not in larger species. If feline HSCs had a replicative rate equivalent to that of HSCs in mice (1 per 2.5 weeks), these cells would undergo enough replications (312 vs 42) in the longer lifetime of cats (15 years vs 2 years in mice) that they would vastly exceed cell senescence, which was approximated (but likely underestimated) as 50 divisions in diploid fibroblast cells maintained in vitro.23 Such an outcome could lead to high levels of aplastic anemia or myelodysplasia, but this has not been observed in either cats or humans. The estimated value in cats (one HSC replication every 10 weeks) would predict 78 cell divisions in a 15-year lifespan, a result that is more compatible with the hypotheses of Hayflick and Moorhead.23 Lastly, these data provide insights into the concept of clonal succession.24,25 This term was previously defined in 2 different ways. To some, clonal succession implies that the hemopoietic reserve is composed of a large number of stem cells but that only one or a few are active at any time. The experimental data do not support this idea. A second interpretation of clonal succession is that hemopoiesis is supported by a succession of clones. When transplantation is done with a few hemopoietic stem cells, only a few HSC initially support blood-cell production. However, in the steady state or when transplantation uses a large inoculum of HSCs, clones derived from many HSCs support hemopoiesis.26 Still, each clone has a discrete lifetime and is then succeeded by another.27 This interpretation of clonal succession is consistent with all murine and feline data and the stochastic model diagrammed in Figure 1. Indeed, if either the feline or the murine data are modeled with the assumption that µ is 0 (ie, that differentiating clones never become exhausted), no values for other parameters provide simulations that mimic the observed data (unpublished data). Aside from the teleologic implications of these data, there are practical consequences. In larger animals, stem cells are quite infrequent and thus more difficult to purify and manipulate. They may be more likely to lose "stem cellness" as measured by repopulating ability after in vitro manipulation, since a vast proliferative potential is required for a cell to be counted in a transplantation assay. In addition, the slow kinetics of the stem-cell cycle explains why it is difficult to label feline, canine, and primate (including human) hemopoietic stem cells with retroviral vectors that require cell division for proviral integration. Although murine cells can be labeled readily at rates (30%-50%) comparable with clinical efficacy, this is not the case in gene-transfer studies in larger animals (rates of 0.01%-10%),28-32 despite pharmacologic stimulation (ie, with granulocyte colony-stimulating factor, kit ligand, or flt3 ligand) in vivo before marrow or peripheral blood stem-cell collection or in vitro. An alternative approach, such as using lentiviral vectors, may be required. The in vivo kinetics of hemopoietic stem cells, not just their number, has major biologic implications.
We thank Allan Dimaunahan and Zeny Sisk for help with preparation of the manuscript.
Submitted February 11, 2000; accepted July 18, 2000.
Funded by a grant (R01 HL46598) from the National Institutes of Health. J.L.A. is the recipient of a Faculty Research Award from the American Cancer Society.
The publication costs of this article were defrayed in part by page charge payment. Therefore, and solely to indicate this fact, this article is hereby marked "advertisement" in accordance with 18 U.S.C. section 1734.
Reprints: Janis L. Abkowitz, Division of Hematology, University of Washington, Box 357710, Seattle, WA 98195-7710.
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© 2000 by The American Society of Hematology.
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  B. E. Shepherd, H.-P. Kiem, P. M. Lansdorp, C. E. Dunbar, G. Aubert, A. LaRochelle, R. Seggewiss, P. Guttorp, and J. L. Abkowitz Hematopoietic stem-cell behavior in nonhuman primates Blood, September 15, 2007; 110(6): 1806 - 1813. [Abstract] [Full Text] [PDF]
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Top
Abstract
Introduction
4% were
recorded as 0) for consistency with the experimental data, since
recipient mice were scored negative for donor granulocytes if less than
4% of their granulocytes had a GpI-1a
phenotype.
4 to 8 per 105
nucleated marrow cells