Blood, Vol. 93 No. 9 (May 1), 1999:
pp. 3148-3149
CORRESPONDENCE
"Stochastic"
40 Years of Use and Abuse
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LETTER |
To the Editor:
The term "stochastic" has been used and abused in
connection with experimental hematology for nearly 40 years. Most
recently, it has resurfaced in the inaugural "Controversy in
Hematology" between Metcalf1 and Enver et
al.2 In view of the obvious importance of the topic, it
seems useful to revisit some of the misunderstandings that have arisen
over the years.
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ORIGINS OF THE CONTROVERSY |
Till et al3,4 showed that colonies of hematopoietic cells
developed on the spleens of irradiated mice injected with normal bone marrow cells. When these colonies were excised individually and
the cells retransplanted into a second group of irradiated recipients
they were able to observe colonies on their spleens. The numbers of
these secondary colonies were highly variable and fitted a skewed
(gamma) distribution. This skewed distribution could be explained by
stem cells having a certain probability of differentiating into one of
the maturation lineages and, therefore, either losing their
clonogenicity or, alternatively, remaining as colony-forming cells.
Computer simulations were used, because mathematical solutions are
intractable, to show that this skewed distribution could be explained
by stem cells having a probability of 0.4 of differentiating into one
of the maturation lineages, and therefore losing their clonogenicity,
or remaining as colony-forming cells, giving a self-renewal probability
of 0.6. Cell death as a possible contributary factor was not considered
at the time.
Till et al explicitly pointed out in their publications that stochastic
effects would only be observed if the spleen colonies originated
in a single or a very few cells. In fact, the highly skewed
distribution provided evidence not that the cells had some special
property, as they claimed, but rather that the spleen colonies were
initiated by single colony-forming cells. They also mention that
stochastic processes are important in relation to the size of bird
populations and even to cosmic ray events.
The conclusions of this work were that stem cells may differentiate or
not (self-renew) when they divide, but that the outcome of any
individual stem cell division cannot be predicted in advance. The
erroneous perceptions were that the probability of
self-renewal/differentiation is fixed, that it is a special property of
stem cells and that it is not a property of more mature progenitors.
The so-called "stochastic" property of stem cells was challenged
by the observation that spleen colonies forming in the splenic red pulp
consisted predominantly of red cells, while colonies found just under
the splenic capsule and along the trabeculae consisted mainly of white
blood cells.5 This indicated the response of stem cells was
subject to changes in the "hematopoietic inductive
microenvironment" (HIM), and a fierce argument developed. This
seems quite surprising because one side of the argument related to
lineage selection and the other to stem cell
self-renewal/differentiation, which should be distinguished from each
other. Nevertheless, the implied meaning of "stochastic"
(hematopoiesis engendered randomly [HER]) became even more firmly
entrenched. The coining of these acronyms, which are remembered to this
day, is witness of the intensity of the debate between the proponents
of two views.
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STOCHASTIC PROCESSES |
According to the Shorter Oxford Dictionary, stochastic processes are
"randomly determined, that follows some probability distribution or
pattern so that its behaviour may be analysed statistically but not
predicted precisely." The quintessential example of a stochastic
process is radioactive decay where the probability of an atom decaying
is known very precisely, but the time that any particular atom will
decay is completely unpredictable. For example, for radioactive carbon
(14C) with a half-life of 5,770 years, an atom may
disintegrate within a microsecond, or not until tens of thousands of
years later.
Taking a cue from Aesop, consider three people entering a
consulting room at random: it will be completely unpredictable whether there will be 3 men, or 2, or 1, or all women, but the probability of
each is precisely known based on the equal probability of 0.5 that the
person entering the room is male or female. In the same way is the
growth of a single cell in a colony-forming assay variable, and the
very wide skewed distribution is the result of such a process being
repeated many times as the cells divide.
This effect has been amply shown by experimental data: for example, by
Humphries et al6 when cells from erythroid colonies grown
in vitro were replated for the formation of secondary colonies, by
Ogawa's group7,8 in the replating of blast cell colonies, and by Kurnit et al9 who used subcolony number in
individual erythroid bursts (BFU-E) as surrogates for secondary
colony-forming cells. In all cases, the skewed distributions were
reminiscent of those found by Till and McCulloch and confirmed the
existence of stochastic events in colony formation in general.
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COMMENT |
That the misconceptions behind this controversy have remained until
today is surprising because self-renewal/differentiation and the
direction of differentiation (lineage commitment) are different
biological processes, and do not necessarily occur in the same cell
populations. Furthermore, in the 1960s and 1970s there was almost
certainly a reluctance of others to take issue with the two
"combatants" who were the leaders in this field, and there were
few experimentalists with sufficient interest/expertise in the
mathematical aspects of this process. It seems appropriate to take this
opportunity to summarize briefly the importance of taking into account
stochastic effects in interpreting results obtained with colony-forming
assays, because they may be used to study the molecular biology of
progenitor cells.
There are four principal characteristics of the growth of single cells
from a homogenous population of colony-forming cells: (1) the large
variation in number of secondary colonies, already mentioned; (2) a
similar wide variation in the total number of cells in the colony; (3)
differences in growth rate between individual colonies; (4) some
colonies will be long-lived while in other colonies all the stem cells
will differentiate leading to the demise ("extinction") of the
colony.10 These points are frequently challenged by the
argument that such results are a reflection of the heterogeneity
of the cultured cell population. However, even with a 100% pure
population, stochastic events will be evident during colony formation
whenever some cells self-renew and others differentiate.
The very wide variation in the size of colonies predicted to grow from
a uniform population of colony-forming cells means that colony size
(eg, above and below a particular scoring threshold) is not necessarily
evidence that they come from a different population or a subpopulation
of progenitor cells. The same reasoning applies to the number of
secondary colonies. Furthermore, the timing of the appearance of
colonies and their disappearance is not necessarily evidence that the
colony-forming cells are heterogenous or represent different
populations. Consequently, an apparent heterogeneity in the growth of
colonies is not in itself sufficient evidence for the existence of
heterogeneity within a given progenitor population or even of different
populations, although there is ample evidence for a hierarchy in
progenitor cell maturation from the physical separation of cells
depending on a variety of different cell properties.
Mathematical predictions cannot provide proof of the correctness of a
particular biological explanation, but they are useful in showing
whether it is consistent with a set of experimental results. One
perhaps extreme case is that a simple computer simulation shows that a
uniform population of colony-forming cells can predict the time of
appearance of the so-called "transient tiny erythroid" spleen
colonies11 and the near constant number of colonies between 7 and 10 days, resulting from the concomitant appearance of colonies and the disappearance of other colonies when appropriate size thresholds are used for scoring.
The original work of Till and colleagues indicated that the probability
of stem cell renewal was 0.6 and that it was intrinsically fixed.
However, under normal steady-state conditions, self-renewal must be 0.5 so that on average one daughter cell differentiates and one daughter
"replaces" the cell that has divided, so as to maintain the same
number of colony-forming cells. The increase in self-renewal from the
steady-state value of 0.5 to 0.6 in spleen colony-forming cells is
consistent with the rapid regeneration of hematopoiesis in
irradiated mice and should have been sufficient to refute the
conclusion that self-renewal of spleen colony-forming cells is
determined "intrinsically" and so not subject to change.
There is other ample evidence12,13 that
spleen colony-forming cells are subject to external control by feedback
regulation. There is some evidence that self-renewal can be regulated
in vitro from the demonstration by Metcalf14 that
granulocyte colony-stimulating factor reduces the secondary
colony-forming ability of WEHI-3B cells, while Lewis et
al15,16 have shown that for erythroid cells the BFU-E
subcolony number distribution, and for granulopoiesis secondary colony
formation, are altered by cytokines.
To conclude, stochastic effects are the consequence of the uncertainty
of the response of individual cells, and are not a property of the
cells themselves. However, the effects only become significant when the
population comprises a single or a few cells, as in colony-forming
assays, and do not provide any information as to whether or not cells
respond to the physiological environment in which they are growing.
Therefore, de facto, they are not relevant to discussions about whether
or not cells respond to extrinsic regulators.
As molecular biology unravels the interior "workings" of
progenitor cells, a better understanding of the stochastic effects inherent in the use of colony-forming assays is important. Computer simulations can provide a useful guide as to the magnitude of these
effects for different values of the various cell kinetic parameters.
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ACKNOWLEDGMENT |
M.G. is supported by the Leukaemia Research Fund of Great Britain.
Nicolas Blackett
Myrtle Gordon
LRF
Centre for Adult Leukaemia
Imperial College School of
Medicine
Hammersmith Campus
London, UK
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