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HEMATOPOIESIS
The kinetics of clonal dominance in myeloproliferative disorders
Sandra N. Catlin, Peter Guttorp, and Janis L. Abkowitz
To study clonal evolution in myeloproliferative disorders, we used stochastic models
of hematopoiesis for mouse and cat, species for which the in vivo kinetics of hematopoietic stem cells (HSCs) have been experimentally defined. We determined the
consequence if 1 HSC became able to survive without the support of a microenvironmental niche while the rest of its behavior
did not change. Neoplastic cells persisted
and dominated hematopoiesis in 14% of
mice and 17% of cats, requiring mean times
of 2.5 ⴞ 0.5 and 7.0 ⴞ 1.2 years, respectively
(n ⴝ 1000 simulations/species). In both species, when the number of neoplastic HSCs
exceeded 0.5% of all HSCs, clonal dominance was inevitable. Our results can explain the absence of clonal myeloproliferative disorders in mice (lifetime, 2 years), are
consistent with clinical observations in cats,
and provide insight into the progression of
chronic myelogenous leukemia (CML) in
humans. They also demonstrate that competition for microenvironmental support can
lead to the suppression of normal hematopoiesis as neoplasia evolves. Toxic or immunologic suppression of normal HSCs is not
required. (Blood. 2005;106:2688-2692)
© 2005 by The American Society of Hematology
Introduction
The human myeloproliferative disorders are a family of diseases
that include chronic myelogenous leukemia (CML), polycythemia
vera, essential thrombocytosis, and idiopathic myelofibrosis. Although each family member is characterized by increased numbers
of specific blood cells, such as granulocytes in CML and red cells in
polycythemia vera, all share clinical features, including basophilia,
hyperproliferative marrow, slow progression, active hematopoiesis
in liver and spleen, and propensity for evolution to acute leukemia.1
These multilineage abnormalities, plus the presence of cytogenetic
defects (eg, Philadelphia [Ph] chromosome [bcr-abl translocation]
in CML, 20q in polycythemia vera) and skewed X-chromosome
inactivation patterns, demonstrate that the diseases result from the
neoplastic transformation and clonal expansion of a single hematopoietic stem cell (HSC) or its immediate progeny.1,2 Recent studies
showing the presence of a somatic Val617Phe Janus kinase 2
(JAK2) mutation in patients with polycythemia vera, essential
thrombocytosis, and idiopathic myelofibrosis document an overlapping molecular pathogenesis (for a review, see Kaushansky3).
Although the exact mechanism remains unclear by which
neoplastic HSC numbers increase, clonal dominance develops, and
normal hematopoiesis is suppressed4-6, clinical data imply that
neoplastic HSCs can survive at geographic sites (ie, liver and
spleen) that cannot support normal adult blood cell development.
This has led to the presumption that myeloproliferative HSCs
ignore the environmental cues that control HSC compartment size
during homeostasis.7 It, therefore, seems likely that HSCs in
myeloproliferative disorders do not require a marrow microenvironmental niche for survival.
To gain understanding of the progression of the myeloproliferative disorders and the interactions of normal and neoplastic HSCs,
we studied this physiology in mouse and cat using simulation and
mathematic calculation based on a stochastic model of hematopoiesis. The concept of stochastic differentiation is diagrammed in
Figure 1A. Each HSC decides to replicate (self-renew), differentiate, or die (undergo apoptosis) based on its unique intrinsic
programming (eg, expression of GATA-2, Hox family proteins,
Bmi-1, cell surface receptors, and adhesion determinants) and
unique extrinsic (microenvironmental) influences (eg, Wnt, bone
morphogenic protein [BMP], sonic hedgehog, notch family members, physical cell-cell interactions).8-11 These interactions are too
complex to completely define or quantitate. In addition, the low
frequencies and location of the HSCs within the marrow space
make direct observation of these cells impossible. Stochastic
modeling is an effective method for studying events that cannot be
directly observed or quantified. Our approach provides a novel
application of stochastic modeling to disease pathogenesis.
Even though the specific fate of individual HSCs cannot be
determined, the decisions can be expressed in terms of intensities
(Figure 1B). For example, there is a mean time interval (intensity) at
which HSCs replicate (termed ␭), an intensity of apoptosis (␣), and an
intensity of differentiation (␯). The hematopoietic system can be
completely described with 2 additional parameters, K, the total number
of HSCs, and ␮, the mean length of time that a clone contributes to
blood cell production.Average rates for specified outcomes do not imply
or require a particular biologic mechanism (eg, symmetric division,
asymmetric division, feedback loop, or age/replication history–
dependent decision12-14) but rather are properties of the system. This
stochastic description of normal hematopoiesis is thus inclusive of all
potential molecular and cellular mechanisms.
Data from mice suggest that the size of the HSC compartment (K) is
genetically determined,15,16 relatively constant with aging,17,18 and likely
reflects the number of supportive microenvironmental niches.9,19 Therefore, when simulating steady state blood cell production, we insert the
single assumption that if an HSC replicates when N (the number of
HSCs) is greater than or equal to K, one replicant dies. In this report, we
determine the consequence should a single neoplastic HSC (and any
From the Department of Mathematical Sciences, University of Nevada, Las
Vegas, NV; and the Departments of Statistics and Medicine, University of
Washington, Seattle, WA.
Reprints: Janis L. Abkowitz, Division of Hematology, University of Washington,
Box 357710, Seattle, WA 98195-7710; e-mail: [email protected].
Submitted March 25, 2005; accepted June 8, 2005. Prepublished online as
Blood First Edition Paper, July 7, 2005; DOI 10.1182/blood-2005-03-1240.
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.
Supported by National Institutes of Health grant R01 HL46598.
© 2005 by The American Society of Hematology
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BLOOD, 15 OCTOBER 2005 䡠 VOLUME 106, NUMBER 8
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BLOOD, 15 OCTOBER 2005 䡠 VOLUME 106, NUMBER 8
KINETICS OF CLONAL DOMINANCE
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6.9 weeks.20 For cat, these values were ␭ ⫽ 1 per 8.3, ␣ ⫽ 1 per 50, ␯ ⫽ 1
per 12.5, and ␮ ⫽ 1 per 6.7 weeks.21 K was limited to 10 000 total HSCs
(for computational convenience; values as high as 50 000 HSCs minimally
affected outcomes [data not shown]).
Simulations
The consequence of HSC transformation was determined in repeated simulations
of cat and mouse (n ⫽ 8000 per species). Simulations were performed using the
C programming language on a Mac OS X operating system and according to the
methods of Abkowitz et al.21 Because of the large numbers of neoplastic HSCs,
simulations were bounded at total HSC numbers of 200 000 (mouse) and
300 000 (cat) for computational convenience and to ensure that all normal HSCs
were exhausted during the time frame of the observations. However, in a few
murine simulations, not all normal contributing clones were exhausted by this
point, and their subsequent demise was simulated using a pure death process with
the parameters described.
Calculating the probabilities of neoplastic HSC survival
Figure 1. Modeling clonal dominance in myeloproliferative disorders. (A) The
stem cell microenvironment is a complex cellular network consisting of many cell
types, including macrophages, T cells, osteoblasts, endothelial cells, and fibroblasts.
These cells modulate stem cell behavior through direct cell-cell interactions and
through the secretion of cytokines. In addition, cytokines, chemokines, and other
substances transit the marrow sinuses and may concentrate in certain regions (by
adherence to extracellular matrix). (B) Depicted is a 2-compartment model for
hematopoiesis. The first compartment represents a quiescent pool, or reserve, of
stem cells. A cell in the reserve may self-replicate (with intensity, or conditional
probability per unit time, ␭), die (with intensity ␣), or initiate differentiation (with
intensity ␯) by entering the contributing compartment (compartment 2), at which stage
cells actively divide and differentiate to contribute progenitor cells (and then mature
cells) to marrow (and blood). A clone departing from the contributing compartment is
considered to be “exhausted” (which occurs with intensity ␮).
Transformed HSCs operate independently of normal HSCs because they are
unconstrained by the upper limit on the size of the reserve. Therefore, the
probability of transformed HSCs remaining in cat and mouse after the
initial transformation event occurred can be estimated by 1 ⫺ p0(t), where
p0(t) is the probability of extinction in a linear birth-immigration-death
process at time t—that is,
(1)
p 0(t) ⫽ 关␣⫹␯⫺(␣⫹␯)e(⫺␭⫹␣⫹␯)t]/关␭⫺(␣⫹␯)e(⫺␭⫹␣⫹␯)t].
The probability of transformed HSCs surviving in the long term is
approximated by 1 ⫺ p0(⬁), where p0(⬁) is the probability of ultimate
extinction in a linear birth-immigration-death process starting with N0
initial cells—that is,
(2)
p 0共⬁兲 ⫽ [(␣⫹␯)/␭兴N0.
future progeny of the cell) ignore this constraint. The results provide
insight into potential mechanisms of clonal progression and dominance
in the myeloproliferative disorders.
Materials and methods
Transformation of an HSC
In our study of myeloproliferative disorders, we assume that a single HSC
“transforms” (at time t ⫽ 0). Transformed HSCs (and progeny derived by
replication events) are insensitive to the environmental cues that limit compartment size to K cells. Therefore, if a transformed HSC replicates when the total
number of HSCs (N) is greater than or equal to K, both offspring survive. The
intrinsic probabilities (intensities) of HSC replication, apoptosis, differentiation,
and (in most analyses) lifespans of differentiating clones are unaffected.
Model parameters
Values for the rate parameters and for the numbers of HSCs per nucleated
marrow cells have been estimated by the analysis of limiting dilution
competitive repopulation studies in mouse20 and cat,21 and the values for ␭,
␮, and HSC frequency in mice have been independently confirmed with
unrelated methodologies.22-26 K has been estimated by multiplying HSC
frequency by the total number of nucleated marrow cells (derived by 59Fe
distribution studies), and the value for mouse (11 000-24 000 total HSCs)
overlaps the estimate for cat.27
For mouse, the mean lengths of time until each normal and neoplastic
HSC replicated, underwent apoptosis, or differentiated were ␭ ⫽ 1 per 2.5,
␣ ⫽ 1 per 20, and ␯ ⫽ 1 per 3.4 weeks, respectively, whereas each
contributing clone contributed to hematopoiesis for an average of ␮ ⫽ 1 per
Figure 2. Evolution of neoplasia after initial transformation event. (A) Sixteen
simulations of mice and (B) 16 simulations of cats.
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CATLIN et al
Table 1. Estimated probabilities of transformed HSCs remaining in mouse and cat after first appearance
Probability, %, by time after transformation event
1 wk
2 wk
4 wk
3 mo
6 mo
9 mo
1y
2y
3y
Mouse
75
61
45
24
17
15
15
14
14
Cat
91
84
72
47
33
27
24
19
17
Results
Survival of neoplastic HSCs
Using simulation and mathematic calculation, we determined the consequence if a single (neoplastic) HSC were able to survive without
microenvironmental support and whether this change in HSC behavior
was sufficient to explain the clonal progression of myeloproliferative
disorders. We assumed that cumulative mutational events resulted in HSC
“transformation” (at time t ⫽ 0) and caused this HSC and its offspring
(derived by replication/self-renewal) to become insensitive to the environmental cues that limit compartment size to K cells. Thus, if a normal HSC
replicated when the total number of HSCs was K or larger, one replicant
died. However, if a neoplastic HSC replicated when the total number of
HSCs was greater than or equal to K, both offspring survived. Conceptually, the extra (neoplastic) HSCs could occupy a niche in spleen or liver
that could not support normal HSCs. Other behaviors, including the
intrinsic probabilities of HSC replication, apoptosis, and differentiation
and the lifespans of differentiating clones, were unaffected.
We simulated this physiology in 8000 virtual mice and 8000
virtual cats. Percentages of neoplastic cells remaining in mouse and
cat for a period of 5 (mouse) and 15 (cat) years after the initial
transformation event for 16 representative outcomes of mouse and
cat are shown in Figure 2A-B. Despite each animal having an
identical initial state (1 neoplastic HSC among 10 000 total HSCs),
clinical outcomes vastly differed. The neoplastic clone dominated
in some animals, yet only small and brief clonal contributions were
observed in most virtual mice and cats. In approximately 86% of
mice and 83% of cats, the single transformed HSC and its progeny
disappeared (refer to equation 1). The time at which the neoplastic
clone was exhausted varied between animals and between species
(Table 1). In mice, 25% of neoplastic clones were exhausted during
the first week after appearance. In cats, 9% were exhausted. These
results indicate that transformation events may occur frequently,
yet they have no clinical significance should the abnormal clone
(by chance) fail to survive or clonally expand.
The results also show that the probability of survival of a
neoplastic clone increases as the number of neoplastic HSCs
increases. Once the number of neoplastic HSCs increases to 4 (cat)
or 5 (mouse), the probability that the neoplastic clone survives is
greater than 50% (refer to equation 2). If the number of neoplastic
HSCs reaches 0.5% (50 of 10 000) of total HSCs, survival is
virtually certain. Estimated probabilities of survival once different
proportions of neoplastic HSCs are reached are given in Table 2.
Clonal progression and dominance
Simulated outcomes (the percentages of differentiating cells derived from the neoplastic clone over time) for 4 randomly selected
mice and cats in which the percentage of neoplastic HSCs reaches
1% of total HSCs are shown in Figure 3A-B. As can be seen from
these simulations, the rate of disease progression also varies
considerably between animals.
To assess the pace of the disease, the first 1000 simulations in
which the neoplastic clone eventually dominates (surpassing a
level of 50%) were used to estimate means and standard deviations
of the time needed to reach various clinical end points (Table 3). In
both species, the pace dramatically accelerated when the number of
neoplastic HSCs reached 10% of total HSCs. Mean times to clonal
dominance were 2.5 ⫾ 0.5 and 7.0 ⫾ 1.2 years in mouse and cat,
respectively. Clonal dominance developed more quickly in the
virtual mice but required 2 to 3 years from first appearance (Figure
3A), a period longer than a mouse’s lifetime.
Effects of compartment 2 kinetics on clinical
observations in animals
The preceding calculations determined the numbers and phenotype
of neoplastic HSCs within the stem cell reserve (compartment 1).
In clinical settings, however, where one is making inferences about
stem cell reserve, the contributions of the contributing clones
(compartment 2), not the genotype of stem cells, are observed
(Figure 1B). There is a minor delay from the time clonal dominance
occurs in the reserve until it occurs in the contributing compartment
(4-7 weeks in mouse and 3-8 weeks in cat). Typically, there is a
wider lag from the time all normal HSCs are exhausted from the
reserve until they are exhausted from the contributing compartment. In murine simulations, this lag is an average of 50 ⫾ 21
weeks. In cat simulations, the average lag is 2 ⫾ 16 weeks. This
calculation, however, is sensitive to the degree of uncertainty
associated with the parameters ␣ and ␮.21 Other measurements
given in this report are not similarly affected.
More important, contributing clones derived from neoplastic HSCs
might have different properties than contributing clones derived from
normal HSCs. To determine how this could affect lag time, we considered
2 additional theoretical scenarios and asked what the percentage of
neoplastic HSCs (compartment 1 cells) would be at the time that
dominance (greater than 50% neoplastic cells) was observed in compartment 2 in these conditions. In simulations in which neoplastic clones
behaved normally, on average 71.3% ⫾ 1.9% of murine HSCs were
neoplastic when 50% of compartment 2 cells were neoplastic. If neoplastic clones contributed blood cells for 10 times longer than normal clones,
on average 37.2% ⫾ 1.9% of murine HSCs were neoplastic when
dominance occurred in compartment 2. If neoplastic clones contributed 10
times more blood cells per clone than normal clones (and blood cells, such
as granulocytes, were observed as a surrogate measure of compartment 2),
on average only 13.0% ⫾ 0.8% of murine HSCs were neoplastic when
dominance was clinically observed. In cat, the percentages of neoplastic
Table 2. Estimated probabilities of neoplastic HSCs surviving once various levels are reached
Neoplastic HSCs, n (%)
1 (0.01)
2 (0.02)
3 (0.03)
4 (0.04)
5 (0.05)
10 (0.1)
20 (0.2)
50 (0.5)
100 (1)
Mouse, %
14
26
36
45
53
78
95
100
100
Cat, %
17
31
42
52
60
84
97
100
100
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BLOOD, 15 OCTOBER 2005 䡠 VOLUME 106, NUMBER 8
KINETICS OF CLONAL DOMINANCE
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clone might dominate. Specifically, we assumed that neoplastic cells
never occupy designated niches but persist within the marrow (and other
spaces) without perturbing the survival of normal HSCs. Normal HSCs
remain near the upper limit of K, but the neoplastic clone, provided it
survives, grows undeterred by resources. Overall results were similar
under this alternative hypothesis, indicating that direct competition for
limited resources between normal and neoplastic HSCs is not required
for neoplastic cells to dominate. This competition is required, however,
for the exhaustion of normal HSCs (Figure 4A-B).
In final studies, we evaluated the effect of different constraints
on neoplastic HSC growth. We determined outcomes if neoplastic
cells could not survive without limitation but could only survive at
geographic sites available to all HSCs during fetal development
(eg, liver and spleen) and arbitrarily created 10 000 additional sites
accessible to neoplastic, but not normal, HSCs. We tested 2
possibilities. The first was that neoplastic HSCs preferentially
home to marrow but, when the total number of HSCs reaches K,
migrate to spleen or liver. The second was that neoplastic HSCs
randomly occupy the available niches in marrow or elsewhere.
Under both conditions, results were virtually identical to those
shown in Tables 1, 2, and 3. Clonal dominance occurred at similar
incidences and within a similar time frame. Thus, normal HSCs are
exhausted even when the growth of neoplastic HSCs is constrained.
Figure 3. Evolution of neoplasia where the percentage of neoplastic HSCs
reaches 1% or higher. (A) Four murine simulations and (B) 4 cat simulations.
HSCs when dominance was observed in compartment 2 were
57.3% ⫾ 1.2%, 19.6% ⫾ 1.0%, and 10.4% ⫾ 0.6% in the initial and the
2 additional conditions, respectively. The average lapse between the time
dominance occurred in the contributing compartment to the time it
occurred among HSCs was 5.9 ⫾ 1.1 weeks (range, 3-11 weeks) in
mouse and 47.6 ⫾ 4.0 weeks (range, 37-62 weeks) in cat when contributions of neoplastic clones were 10 times longer than those of normal
clones, and they were 24.7 ⫾ 1.9 weeks (range, 19-33 weeks) in mouse
and 79.4 ⫾ 5.2 weeks (range, 66-97 weeks) in cat when neoplastic clones
contributed 10 times more blood cells than did normal clones. Thus, under
the latter 2 scenarios, dominance occurred more quickly among observed
cells than among stem cells and would forecast events destined to occur in
the HSC compartment.
Discussion
Simulation is a novel approach for understanding the pathogenesis
of myeloproliferative diseases. Using stochastic models for mouse
and cat hematopoiesis in which one HSC becomes able to survive
without the support of a microenvironmental niche, we demonstrated that transformation events can occur often yet have no
clinical significance should the neoplastic clone fail to survive. The
probability of survival increases as the neoplastic clone expands,
Fate of normal HSCs
In our initial calculations, we assumed that normal (but not neoplastic)
HSCs required microenvironmental support for their survival. This led
to the exhaustion of normal HSCs because of excess malignant cells that
outcompeted for supportive marrow niches (Figure 4A-B). In additional
studies, we explored an alternative mechanism by which the malignant
Table 3. Estimated time from first appearance until various levels of
neoplastic HSCs were reached in simulations in which the
neoplastic clone eventually dominated
Mouse
% of total
Cat
Mean time, y
95% CI
Mean time, y
95% CI
1
1.1
0.2, 2.0
3.2
1.0, 5.5
10
1.9
1.0, 2.9
5.5
3.2, 7.8
25
2.2
1.3, 3.2
6.4
4.0, 8.7
50
2.5
1.5, 3.4
7.1
4.7, 9.4
95
2.7
1.8, 3.7
7.8
5.4, 10.1
100
3.1
2.2, 4.1
9.1
6.7, 11.4
Neoplastic clone domination was defined as greater than 50% neoplastic cells.
Figure 4. Evolution of neoplasia where the neoplastic clone eventually dominates. (A) Four murine simulations and (B) 4 cat simulations. (solid lines) Neoplastic
HSCs. (dashed lines) Normal HSCs.
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BLOOD, 15 OCTOBER 2005 䡠 VOLUME 106, NUMBER 8
CATLIN et al
and if the number of neoplastic HSCs reaches 0.5% of total HSCs,
survival (and eventual clonal dominance) is assured. Still, clonal
dominance is predicted in only 14% of mice and 17% of cats.
Interestingly, the time from neoplastic transformation until
clonal dominance differs in mouse and cat. In virtual cats, clonal
dominance took 7.0 ⫾ 1.2 years, a time course of disease progression consistent with observations in clinical veterinary practice.28-30
That clonal dominance in mice required 2 to 3 years, longer than a
mouse’s lifetime, may explain the absence of experimental murine
models in which myeloproliferative disorders develop from a
single transformed cell.
Our results prove that clonal dominance (greater than 50%
neoplastic), even in large animals such as cats, does not require a
direct (or toxic) interaction of neoplastic and normal cells or
immune response but can reflect competition for microenvironmental support. Dominance might also develop if the malignant stem
cells have an intrinsic advantage in terms of replication, apoptosis,
or differentiation intensities.31
Because human HSC parameters have not been determined, the
foregoing analyses cannot be extended to humans. However, the
results may have conceptual relevance to the development and
progression of CML. Others32 have detected low frequencies of
bcr-abl translocations in up to 30% of healthy persons using
polymerase chain reaction (PCR) assays. Given that the incidence
of CML is 1 per 100 000 healthy persons per year, bcr-abl
translocations must occur far more frequently than clinical disease
does. We hypothesize that competition for geographic niche or
microenvironmental support could also explain the disappearance
of normal HSCs in these disorders4,5 and could define the long, but
not indefinite, window in which therapeutic interventions could
restore normal hematopoiesis.
Recent findings of Jamieson et al6 argue that the clinical
manifestations of CML progression, such as blast crisis and
imatinib mesylate resistance, result from the malignant expansion
of granulocyte macrophage–colony-forming unit (CFU-GM)–like
subclones, not from relatively quiescent HSCs. Their data suggest
that the HSCs present in patients with CML (defined as CD34⫹,
CD38⫺, CD90⫹, Thyl⫹, lineage⫺ cells) are indeed neoplastic (all
contain the bcr-abl translocation) yet occur at frequencies similar to
the frequencies of HSCs in the marrow of healthy persons. Thus,
these results are consistent with the hypothesis that normal and
neoplastic HSCs compete for K marrow niches. With the identification of the somatic JAK23 mutation, it is likely that similar data
may emerge from comparable studies of the other myeloproliferative disorders.
Stochastic modeling is a powerful and versatile method to study
the in vivo behavior of HSCs and the differentiating clones that
derive from HSCs. Our data from mathematic calculations and
virtual mice and cats argue that the ability of neoplastic HSCs to
survive without niche support is sufficient to explain both the
clonal progression of myeloproliferative disorders and the disappearance of normal HSCs.
Acknowledgments
This work was partially completed while S.N.C. was on sabbatical
at the Department of Statistics and Modelling Science at the
University of Strathclyde (Glasgow, Scotland).
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From www.bloodjournal.org by guest on June 12, 2017. For personal use only.
2005 106: 2688-2692
doi:10.1182/blood-2005-03-1240 originally published online
July 7, 2005
The kinetics of clonal dominance in myeloproliferative disorders
Sandra N. Catlin, Peter Guttorp and Janis L. Abkowitz
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