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Statistical Mechanics of Pluripotency
Ben D. MacArthur1,* and Ihor R. Lemischka21Centre for HumanDevelopment, StemCells andRegeneration, Institute of Developmental Sciences, School ofMathematics, and Institute forLife Sciences, University of Southampton, SO17 1BJ, UK2Department of Developmental and Regenerative Biology, Department of Pharmacology and Systems Therapeutics, Black Family Stem Cell
Institute, Mount Sinai School of Medicine, New York, NY 10029, USA
*Correspondence: [email protected]
http://dx.doi.org/10.1016/j.cell.2013.07.024
Recent reports using single-cell profiling have indicated a remarkably dynamic view of pluripotentstem cell identity. Here, we argue that the pluripotent state is not well defined at the single-cell levelbut rather is a statistical property of stem cell populations, amenable to analysis using the tools ofstatistical mechanics and information theory.
Pluripotent stem cells (PSCs) are able to
self-renew indefinitely in culture and pro-
duce all embryonic cell lineages in vivo.
Experimentally, pluripotency is assessed
using a variety of functional criteria
including the ability to differentiate to all
three germ layers in vitro and form tera-
tomas in vivo and, in mice, the ability to
contribute substantially to development
when introduced into embryos (Martı
et al., 2013). These assays reliably dis-
tinguish functionally pluripotent from
nonpluripotent cell populations and are
essential to stem cell research. However,
it is notable that they do not generally
assess the potency of individual stem
cells, but rather the regenerative potential
of stem cell derived populations. For
homogeneous populations, in which all
cells are qualitatively the same, the infer-
ence of single-cell identity from popu-
lation behavior is reasonable. However,
for heterogeneous populations in which
qualitatively different subpopulations of
cells coexist, the validity of this inference
is not clear. Here, we will argue that this
distinction is critical and that appropri-
ately defined variability is an essential
feature of pluripotent cell populations,
reflective of the latent potential of individ-
ual PSCs to rapidly increase cellular diver-
sity during early development in vivo.
Recent studies using high-throughput
single-cell gene expression profiling
have uncovered a surprising degree of
cell-to-cell variability within apparently
functionally homogeneous PSC popula-
tions. In particular, a number PSC identity
regulators including key transcription
factors such as Nanog, Rex1, and Klf4
have been found to exhibit significant
484 Cell 154, August 1, 2013 ª2013 Elsevier
expression level variability within single
cells (Canham et al., 2010; Chambers
et al., 2007; Hayashi et al., 2008; Kalmar
et al., 2009; Kobayashi et al., 2009;
MacArthur et al., 2012; Macfarlan et al.,
2012; Niwa et al., 2009; Singh et al., 2007;
Toyooka et al., 2008; Trott et al., 2012;
Zalzman et al., 2010). Interestingly, these
variations do not simply define distinct
static subpopulations. Rather, intracel-
lular expression fluctuations appear to
give rise to a state of ‘‘dynamic equilib-
rium’’ in which individual cells transit sto-
chastically between distinct metastable
states yet the overall structure of the
population remains stable (Hayashi
et al., 2008). Because individual cells
interconvert between distinct metastable
states, this extraordinary dynamic vari-
ability can endow stem cell populations
with remarkable robustness to perturba-
tion—for instance, temporary deletion of
any particular subpopulation—and may
therefore be a significant functional prop-
erty of PSC communities (Chambers
et al., 2007; Silva and Smith, 2008).
Although PSC population variability
may be decreased in vitro using defined
culture conditions (for instance, in which
Mek and Gsk3b activity are selectively
inhibited; conditions thought to more
faithfully mimic the in vivo environment
of the inner cell mass) (Macfarlan et al.,
2012; Marks et al., 2012; Miyanari and
Torres-Padilla, 2012), it is nevertheless
thought to have physiological importance
in the in vivo developmental program
(Hayashi et al., 2008). For example,
the homeodomain transcription factor
Nanog, one of the most widely studied
yet still incompletely understood regula-
Inc.
tors of pluripotency (Chambers et al.,
2003; Chambers et al., 2007; Mitsui
et al., 2003; Silva et al., 2009), has been
observed to exhibit large, apparently
stochastic, temporal fluctuations in
expression within individual Oct4 positive
embryonic stem cells (ESCs) (Chambers
et al., 2007; Kalmar et al., 2009; Miyanari
and Torres-Padilla, 2012). These fluctua-
tions apparently temporarily sensitize in-
dividual ESCs to differentiation-inducing
signals, transiently priming them for
differentiation without marking definitive
commitment. Expression variations of
other pluripotency markers such as
Rex1 (Toyooka et al., 2008) and Stella
(Hayashi et al., 2008) as well as lineage
regulators such as Hex (Canham et al.,
2010) and Hes1 (Kobayashi et al., 2009)
have similarly been observed to confer
transient lineage biases to PSC subpopu-
lations. These fluctuations may be impor-
tant because collectively they combine
to allow the entire population to respond
appropriately to a wide variety of persis-
tent environmental signals while avoid-
ing premature lineage commitment in
response to transitory stimuli (Graf and
Stadtfeld, 2008). However, the origin and
ultimate biological significance of such
fluctuations are currently unclear (see
Note Added in Proof).
Taken together, these reports indicate
a remarkably dynamic view in which indi-
vidual stem cells are apparently not
closely regulated, yet well-defined and
robust population-level behavior emerges
from stochastic dynamics at the single-
cell level (Silva and Smith, 2008). This
interdependence of the population and
the individual cell levels is reminiscent of
statistical mechanics, one of the most
successful and powerful theories in mod-
ern physics.
Statistical MechanicsStatistical mechanics was largely devel-
oped around the turn of the 20th century
by some of the great physicists of that
time (Maxwell, Boltzmann, Planck, etc.).
It provides a formal framework that relates
macroscopic bulk properties of matter,
or macrostates (such as temperature,
pressure, etc.), to the stochastic kinetics
of the microscopic elements (atoms and
molecules) of which matter is composed
(Pathria, 1996). For instance, an early
result from the kinetic theory of gasses
(a forerunner of modern statistical me-
chanics) demonstrated that the pressure
of an ideal gas in a closed container is
due to the collective impact of its con-
stitutive molecules with the walls of the
container, depending on the average
kinetic energy of the molecules. By
contrast, the detailed description of all
the molecules in the gas at any instant
(i.e., their instantaneous positions and
momenta) is an example of a microstate.
Because pressure only depends upon
average properties of the collection of
gas molecules, there are clearly very
many different molecular arrangements
that give rise to the same pressure and,
in general, numerous different inter-
changeable microstates may realize the
same macrostate.
This distinction between microstates
and macrostates is informative when
considering pluripotency. The standard
(albeit often implicit) view, based upon
population expression profiling, is that
pluripotency can, in principle, be associ-
ated with a unique, static, molecular pro-
file (Ivanova et al., 2002; Ramalho-Santos
et al., 2002). This approach has proven to
be remarkably successful at dissecting
the molecular circuitry of pluripotency
(Jaenisch and Young, 2008). However,
recent observations of dynamic variability
of single cells within PSC populations
indicate that a more nuanced per-
spective, which distinguishes between
pluripotency as a molecular state and
pluripotency as a function, is required
(Blau et al., 2001; Cahan and Daley,
2013). These reports indicate that the
pluripotent state is not unique but rather
appears to be analogous to a cellular
macrostate, compatible with a wide
variety of interchangeable molecular
microstates (patterns of gene/protein
expression). In this view, individual cells
within the population independently
explore a variety of different expression
states, in a manner regulated both by
genetic regulatory and signaling networks
and intrinsic gene/protein expression
noise (Paulsson, 2004). This continual
dynamic exploration transiently primes
each individual cell to respond to range
of different differentiation-inducing stim-
uli, depending upon its instantaneous
molecular state. Such dynamic variability
at the single-cell level naturally gives rise
to a diverse population that is continually
able to rapidly respond to a range of
environmental signals. Thus, in this
perspective, while population structure is
robustly maintained, there is no unique
pluripotent state at the single-cell level.
Rather, functional pluripotency emerges
spontaneously from the dynamic vari-
ability intrinsic to the pluripotent state.
Here, we will explore this idea, and its
consequences, further and consider the
ways in which tools from statistical
mechanics, as well as related methods
from information theory, may be used to
better understand the molecular and
cellular basis of pluripotency.
Connecting Dynamic Variabilitywith Population DiversityProtein and mRNA expression are inher-
ently stochastic processes regulated by
complex transcriptional, epigenetic, and
signaling networks (Paulsson, 2004).
The collective action of these multiple
interacting mechanisms can give rise to
robust cell-cell variability within a popu-
lation in complex ways that are difficult
to understand using experiment and
intuition alone. However, mathematical
models and methods can help dissect
this complexity (Liberali and Pelkmans,
2012).
In order to investigate cell-cell vari-
ability quantitatively it is useful to consider
the probability mass function p(x), which
denotes the likelihood of finding a cell at
position x = [x1, x2, . xn] at equilibrium,
where the vector x enumerates the copy
numbers of all the mRNAs/proteins of
interest (estimating p(x) from single-cell
data and extensions to the nonequilibrium
case present challenges that we will not
Cell 1
consider here; we assume for simplicity
that p(x) is accurately known). We will
refer to the set of all possible mRNA/pro-
tein expression patterns as the state
space. Theoretically, if there exists a
unique equilibrium distribution p(x), to
which every initial condition converges
sufficiently rapidly, then the underlying
stochastic process is said to be ergodic
and each cell in the population will inde-
pendently explore the same patterns of
expression within the state space in
accordance with p(x). In this case the
population is intrinsically robust to tar-
geted removal of any particular subpopu-
lation because the remaining cells in the
population will eventually ‘‘recolonize’’
(in state space) the removed subpopula-
tion and reconstitute the equilibrium dis-
tribution p(x). Similar reconstitution has
been experimentally observed with
respect to a number of key PSC markers,
including Nanog (Chambers et al., 2007;
Kalmar et al., 2009), Rex1 (Toyooka
et al., 2008), and Stella (Hayashi et al.,
2008) as well as with respect to the
stem cell surface marker Sca-1 in he-
matopoietic progenitor cells (Chang
et al., 2008) and between distinct pheno-
typic states within cancer cell populations
(Gupta et al., 2011), suggesting that
that the underlying stochastic processes
that regulate expression variation are
‘‘ergodic-like.’’ It remains to be seen
how widespread this property is. Howev-
er, it may be important because it con-
nects dynamic variability at the single-
cell level with diversity at the population
level. Indeed, this connection may
be central to functional pluripotency
because it theoretically endows every
individual cell with the latent ability to
reproduce the entire diverse population
through self-renewal divisions.
Statistical Mechanics andInformation TheoryClearly, not all patterns of mRNA/protein
expression will be equally likely and p(x)
may exhibit rich heterogeneity according
to the various expression patterns present
within the population. But how should
such ‘‘heterogeneity’’ actually be quanti-
fied? For complex multivariate distri-
butions a full description of variation
cannot be captured in a single number;
therefore, it depends on precisely how
‘‘heterogeneity’’ is defined. For example,
54, August 1, 2013 ª2013 Elsevier Inc. 485
if heterogeneity is taken to be synony-
mous with variability we might examine
the covariance structure of p(x), while if
heterogeneity is taken to mean ‘‘the num-
ber of qualitatively different subpopula-
tions’’ then we might examine the number
of distinct modes (or ‘‘peaks’’) in p(x) and
so forth. Each such method is useful and
each sheds light on different aspects of
what is meant by ‘‘heterogeneity.’’ A num-
ber of authors have considered such ap-
proaches (Buganim et al., 2012; Guo
et al., 2010; MacArthur et al., 2012). We
suggest that, in addition to such statistical
methods, another measure, the entropy,
may also be useful for assessing vari-
ability in stem cell populations.
Informally, entropy is used in statistical
mechanics and information theory as a
measure of ‘‘disorder’’ or ‘‘uncertainty’’
(Cover and Thomas, 2006; Pathria, 1996).
Formally, the entropy H(q) of a discrete
probabilitymass functionq(x) isdefinedas:
HðqÞ= � kX
x
qðxÞ log qðxÞ;
where the sum is taken over the entire
state space. In physical applications, k is
Boltzmann’s constant and natural loga-
rithms are used, whereas in information
theory k = 1, and the logarithm is usually
to the base 2 (in which case, entropy is
measured in bits). Clausius introduced
the modern notion of entropy in the mid
19th century to quantify the loss of useful
energy to heat in mechanical engines.
The statistical form given above was
derived by Gibbs in the 1870s and was
argued to be a general measure of uncer-
tainty by Shannon in the 1940s (Cover
and Thomas, 2006; Pathria, 1996). The
connection between entropy and uncer-
tainty is not immediately apparent from
the mathematical definition above but
can be understood using a simple
example. Consider flipping a (possibly
biased) coin, which has probability q of
obtaining a head and probability (1 � q)
of obtaining a tail. Applying the above for-
mula (and adopting the information-theo-
retic definition) the entropy of the coin
flip is H = � q log2q�ð1� qÞ log2ð1� qÞbits, which is zero when q = 0 or q = 1
(the coin is completely biased) and rea-
ches its maximum H = 1 bit, when q =
1/2 (the coin is completely fair). In other
words, the entropy increases as the
outcome of the coin flip becomes more
486 Cell 154, August 1, 2013 ª2013 Elsevier
uncertain. For our purposes, the entropy
H(p) of a cell population is the amount of
uncertainty concerning the molecular
state of a cell drawn at random from the
population. If the population has high
entropy then there is a large amount of
uncertainty concerning the identity of a
randomly selected cell, whereas if the
population has low entropy then there is
less uncertainty. Thus, entropy is a useful
measure of ‘‘variability’’: populations with
low entropy exhibit well-defined patterns
of mRNA/protein expression, whereas
those with high entropy exhibit diverse
patterns of expression.
Entropy is also an extremely useful tool
for analyzing the behavior of stochastic
processes, such as those defined by the
genetic regulatory networks that control
the mRNA and protein expression pat-
terns that ultimately define cell population
heterogeneity (Paulsson, 2004). In clas-
sical statistical mechanics the second
law of thermodynamics states that the
entropy of an isolated system increases
over time toward the maximum entropy
uniform distribution (in which all states
are equally likely). However, for biologi-
cally plausible systems, which interact
with their environment and are likely to
be subject to numerous complex regula-
tory constraints, the second law is not
directly applicable. Rather, subject to
certain reasonable assumptions, a related
quantity known as the relative entropy or
Kullback-Leibler divergence (with respect
to the equilibrium distribution) decreases
with time (Cover and Thomas, 2006;
Gardiner, 2009). For biologically relevant
dynamics, the entropy may not always
increase, and the equilibrium distribution
is not expected to be uniform except
in certain very specific circumstances
(Cover and Thomas, 2006; Gardiner,
2009). Rather, in general, regulatory inter-
actions between genes and proteins
introduce correlations in expression that
reduce uncertainty in expression patterns
and therefore reduce the entropy of the
population at equilibrium. Informally, the
equilibrium distribution maximizes en-
tropy subject to satisfying any imposed
regulatory constraints. This connection
suggests a broad principle: at equilibrium,
cell populations that are subject to
strict regulatory constraints should exhibit
well-defined and low entropy expression
patterns, whereas those that are subject
Inc.
to weaker regulatory constraints should
exhibit more diverse, higher entropy
expression patterns. Viewing variability
in this light indicates that PSC populations
may be more diverse than differentiated
populations because they are subject to
weaker regulatory constraints.
Statistical Mechanics ofPluripotencyThis reasoning above is in agreement with
recent reports that PSCs have a remark-
ably permissive and dynamic chromatin
structure that is globally enriched for
histone marks indicative of active tran-
scription, such as H3K4me3 (Meshorer
and Misteli, 2006). Although widespread
activation of gene expression is moder-
ated by numerous mechanisms, including
coexpression of repressive marks such
as H3K27me3 (at so-called bivalent
domains) and repression by polycomb
group complex proteins, this globally
hyperdynamic chromatin provides a
uniquely open regulatory environment in
which lineage markers are sporadically
expressed at low levels, allowing PSCs
to remain poised for differentiation while
keeping ‘‘all options open’’ (Efroni et al.,
2008; Gaspar-Maia et al., 2011). Although
this gene expression ‘‘noise’’ is buffered,
for instance by targeting of preinitiation
complexes for proteasomal degradation
(Szutorisz et al., 2006), it may naturally
give rise to variation in expression pat-
terns within the population (Efroni et al.,
2009). However, upon differentiation, this
transcriptionally hyperactive poised state
is gradually lost. Increasingly numerous
regions of heterochromatin form and
chromatin architectural proteins, such as
linker histone H1 and the heterochromatin
component HP1, become more tightly
bound, resulting in less expression noise
and more closely regulated patterns of
gene expression (Efroni et al., 2008).
Taken together, these results suggest
that the characteristically loose regulatory
architecture of PSCs imposes only weak
constraints on mRNA/protein expression,
which in turn naturally results in high-
entropy expression patterns within the
population. However, as differentiation
progresses and chromatin condenses,
expression patterns become more tightly
constrained and population entropy
decreases. Thus, this model predicts
that cell population entropy is positively
Figure 1. Entropy and Developmental PotencyThe permissive regulatory architecture of PSCs imposes weak constraints onmRNA/protein expression, giving rise to high-entropy expression patternswithin the population. As differentiation progresses expression patternsbecome more tightly constrained and population entropy decreases.
related to developmental po-
tency (see Figure 1).
ConclusionsHere, we have argued that it is
useful to think of pluripotency
as a statistical property,
similar to a macrostate in
statistical physics. In this
view, although individual
PSCs may have the potential
to produce pluripotent popu-
lations through self-renewal
divisions, the pluripotent state
is not well defined at the sin-
gle-cell level. Rather, func-
tional pluripotency emerges
spontaneously from the dy-
namic variability intrinsic to
the pluripotent state. During
normal development in vivo, this dynamic
variability is strictly spatiotemporally
regulated (Soriano and Jaenisch, 1986).
However, in vitro these restrictions are
largely released and, dependent upon
culture conditions, the intrinsic variability
in the population becomes apparent.
Intuitively, this view is quite simple: highly
variable expression patterns are equiva-
lent to, and responsible for, the neces-
sarily large number of developmental
‘‘choices’’ characteristic of PSCs. Indeed,
from this perspective, diverse expression
patterns may be the defining property of
PSC populations. In contrast, differenti-
ated cells have defined fates and limited
choices and therefore well-defined, less
diverse, expression patterns.
Despite recent advances in single-cell
profiling, a number of important issues
remain to be addressed. Foremost among
these is the extent to which observed
in vitro expression variability in PSC pop-
ulations reflects genuinely important as-
pects of development rather than the ef-
fects of poorly defined culture conditions
or artifacts due to the use of reporter cell
lines (Marks et al., 2012). Refinement of
PSC culture protocols, development of
procedures to reliably and robustly
assess the developmental potency of
individual cells, and generation of tech-
niques to profile the entire transcrip-
tome/proteome of large numbers of indi-
vidual cells will clarify these issues
(Newman et al., 2006; Schubert, 2011;
Tang et al., 2009; Ying et al., 2008). It will
be particularly interesting to use such
technical advances to compare patterns
of variability in different stem populations
in a range of physiologically relevant cul-
ture conditions and thereby determine
the extent to which quantitative mea-
sures of population diversity, such as
the expression entropy, relate to devel-
opmental potency. We anticipate that
the use of high-throughput screening
technologies, such as RNA interference
screens (Boutros and Ahringer, 2008),
for factors that regulate population vari-
ability in different stem cell populations
will also greatly improve our understand-
ing in this area. Similarly, advances
in recently developed techniques that
are able to noninvasively track multi-
dimensional expression changes over
time in large numbers of individual
cells will be particularly important to
dissect the molecular mechanisms, and
ultimate functional significance, of dy-
namic expression variability in single
cells (Schroeder, 2008; Sigal et al.,
2006; Spiller et al., 2010). Such experi-
mental advances will produce large
amounts of complex data. Therefore
concurrent with these experimental de-
velopments, new bioinformatic and
mathematical tools for analyzing and in-
terpreting high-throughput single-cell
expression data will also be required
(Tang et al., 2011). Ultimately, such com-
bined experimental and theoretical de-
velopments will advance our understand-
ing of how the intracellular molecular
circuitry of pluripotency not only controls
the behavior of individual cells but also
Cell 154, August 1
regulates variability within
PSC populations.
The notion that the function
of a stem cell population may
be controlled by the interplay
between deterministic and
stochastic mechanisms at
the single-cell level is concor-
dant with the extensive body
of work on the role of stochas-
ticity in regulating hematopoi-
etic stem cell fate decisions
(particularly the pioneering
work of McCulloch, Till and
Siminovitch in the 1960s and
Suda, Ogawa, and coworkers
in the 1980s) and recent ob-
servations of dynamic vari-
ability in cancer cell popula-
tions (Gupta et al., 2011;
MacArthur et al., 2009). This suggests
that a statistical view of cell identity and
function may also be appropriate in a
wide variety of different systems (Pelk-
mans, 2012). It remains to be seen if this
is the case. However, a more rigorous
evaluation of population variability and
its underlying causes and consequences,
as well as the development of methods to
dissect and control variability, will be crit-
ical to understand the molecular mecha-
nisms of pluripotency and early develop-
ment. Such an understanding will, in
turn, be necessary to take pluripotent
stem cells from the lab to the clinic.
ACKNOWLEDGMENTS
We thank Tom Fleming and Tim Sluckin for useful
feedback on earlier versions of this article.
REFERENCES
Blau, H.M., Brazelton, T.R., and Weimann, J.M.
(2001). The evolving concept of a stem cell: entity
or function? Cell 105, 829–841.
Boutros, M., and Ahringer, J. (2008). The art and
design of genetic screens: RNA interference. Nat.
Rev. Genet. 9, 554–566.
Buganim, Y., Faddah, D.A., Cheng, A.W., Itsko-
vich, E., Markoulaki, S., Ganz, K., Klemm, S.L.,
van Oudenaarden, A., and Jaenisch, R. (2012).
Single-cell expression analyses during cellular
reprogramming reveal an early stochastic and a
late hierarchic phase. Cell 150, 1209–1222.
Cahan, P., and Daley, G.Q. (2013). Origins and
implications of pluripotent stem cell variability
and heterogeneity. Nat. Rev. Mol. Cell Biol. 14,
357–368.
, 2013 ª2013 Elsevier Inc. 487
Canham, M.A., Sharov, A.A., Ko, M.S.H., and
Brickman, J.M. (2010). Functional heterogeneity
of embryonic stem cells revealed through transla-
tional amplification of an early endodermal tran-
script. PLoS Biol. 8, e1000379.
Chambers, I., Colby, D., Robertson, M., Nichols, J.,
Lee, S., Tweedie, S., and Smith, A. (2003). Func-
tional expression cloning of Nanog, a pluripotency
sustaining factor in embryonic stem cells. Cell 113,
643–655.
Chambers, I., Silva, J., Colby, D., Nichols, J., Nij-
meijer, B., Robertson, M., Vrana, J., Jones, K.,
Grotewold, L., and Smith, A. (2007). Nanog safe-
guards pluripotency and mediates germline devel-
opment. Nature 450, 1230–1234.
Chang, H.H., Hemberg, M., Barahona, M., Ingber,
D.E., and Huang, S. (2008). Transcriptome-wide
noise controls lineage choice in mammalian pro-
genitor cells. Nature 453, 544–547.
Cover, T.M., and Thomas, J.A. (2006). Elements of
information theory (Hoboken, NJ: Wiley-inter-
science).
Efroni, S., Duttagupta, R., Cheng, J., Dehghani, H.,
Hoeppner, D.J., Dash, C., Bazett-Jones, D.P., Le
Grice, S., McKay, R.D.G., Buetow, K.H., et al.
(2008). Global transcription in pluripotent embry-
onic stem cells. Cell Stem Cell 2, 437–447.
Efroni, S., Melcer, S., Nissim-Rafinia, M., and
Meshorer, E. (2009). Stem cells do play with dice:
a statistical physics view of transcription. Cell
Cycle 8, 43–48.
Gardiner, C.W. (2009). Stochastic methods (Berlin:
Springer).
Gaspar-Maia, A., Alajem, A., Meshorer, E., and
Ramalho-Santos, M. (2011). Open chromatin in
pluripotency and reprogramming. Nat. Rev. Mol.
Cell Biol. 12, 36–47.
Graf, T., and Stadtfeld, M. (2008). Heterogeneity of
embryonic and adult stem cells. Cell Stem Cell 3,
480–483.
Guo, G.J., Huss, M., Tong, G.Q., Wang, C.Y., Li
Sun, L., Clarke, N.D., and Robson, P. (2010).
Resolution of cell fate decisions revealed by
single-cell gene expression analysis from zygote
to blastocyst. Dev. Cell 18, 675–685.
Gupta, P.B., Fillmore, C.M., Jiang, G.Z., Shapira,
S.D., Tao, K., Kuperwasser, C., and Lander, E.S.
(2011). Stochastic state transitions give rise to
phenotypic equilibrium in populations of cancer
cells. Cell 146, 633–644.
Hayashi, K., Lopes, S.M.C.D., Tang, F., and Surani,
M.A. (2008). Dynamic equilibrium and heterogene-
ity of mouse pluripotent stem cells with distinct
functional and epigenetic states. Cell Stem Cell 3,
391–401.
Ivanova, N.B., Dimos, J.T., Schaniel, C., Hackney,
J.A., Moore, K.A., and Lemischka, I.R. (2002).
A stem cell molecular signature. Science 298,
601–604.
Jaenisch, R., and Young, R. (2008). Stem cells, the
molecular circuitry of pluripotency and nuclear re-
programming. Cell 132, 567–582.
488 Cell 154, August 1, 2013 ª2013 Elsevier
Kalmar, T., Lim, C., Hayward, P., Munoz-Descalzo,
S., Nichols, J., Garcia-Ojalvo, J., and Martinez
Arias, A. (2009). Regulated fluctuations in nanog
expression mediate cell fate decisions in embry-
onic stem cells. PLoS Biol. 7, e1000149.
Kobayashi, T., Mizuno, H., Imayoshi, I., Furusawa,
C., Shirahige, K., and Kageyama, R. (2009). The
cyclic gene Hes1 contributes to diverse differen-
tiation responses of embryonic stem cells. Genes
Dev. 23, 1870–1875.
Liberali, P., and Pelkmans, L. (2012). Towards
quantitative cell biology. Nat. Cell Biol. 14, 1233.
MacArthur, B.D., Ma’ayan, A., and Lemischka, I.R.
(2009). Systems biology of stem cell fate and
cellular reprogramming. Nat. Rev. Mol. Cell Biol.
10, 672–681.
MacArthur, B.D., Sevilla, A., Lenz, M., Muller, F.J.,
Schuldt, B.M., Schuppert, A.A., Ridden, S.J.,
Stumpf, P.S., Fidalgo, M., Ma’ayan, A., et al.
(2012). Nanog-dependent feedback loops regulate
murine embryonic stem cell heterogeneity. Nat.
Cell Biol. 14, 1139–1147.
Macfarlan, T.S., Gifford, W.D., Driscoll, S., Lettieri,
K., Rowe, H.M., Bonanomi, D., Firth, A., Singer, O.,
Trono, D., and Pfaff, S.L. (2012). Embryonic stem
cell potency fluctuates with endogenous retrovirus
activity. Nature 487, 57–63.
Marks, H., Kalkan, T., Menafra, R., Denissov, S.,
Jones, K., Hofemeister, H., Nichols, J., Kranz, A.,
Stewart, A.F., Smith, A., and Stunnenberg, H.G.
(2012). The transcriptional and epigenomic foun-
dations of ground state pluripotency. Cell 149,
590–604.
Martı, M., Mulero, L., Pardo, C., Morera, C., Car-
rio, M., Laricchia-Robbio, L., Esteban, C.R., and
Izpisua Belmonte, J.C. (2013). Characterization
of pluripotent stem cells. Nat. Protoc. 8,
223–253.
Meshorer, E., and Misteli, T. (2006). Chromatin in
pluripotent embryonic stem cells and differentia-
tion. Nat. Rev. Mol. Cell Biol. 7, 540–546.
Mitsui, K., Tokuzawa, Y., Itoh, H., Segawa, K.,
Murakami, M., Takahashi, K., Maruyama, M.,
Maeda, M., and Yamanaka, S. (2003). The home-
oprotein Nanog is required for maintenance of
pluripotency in mouse epiblast and ES cells. Cell
113, 631–642.
Miyanari, Y., and Torres-Padilla, M.E. (2012).
Control of ground-state pluripotency by allelic
regulation of Nanog. Nature 483, 470–473.
Newman, J.R.S., Ghaemmaghami, S., Ihmels, J.,
Breslow, D.K., Noble, M., DeRisi, J.L., and Weiss-
man, J.S. (2006). Single-cell proteomic analysis of
S. cerevisiae reveals the architecture of biological
noise. Nature 441, 840–846.
Niwa, H., Ogawa, K., Shimosato, D., and Adachi,
K. (2009). A parallel circuit of LIF signalling path-
ways maintains pluripotency of mouse ES cells.
Nature 460, 118–122.
Pathria, R. (1996). Statistical mechanics (Oxford,
UK: Butterworth Heinemann).
Paulsson, J. (2004). Summing up the noise in gene
networks. Nature 427, 415–418.
Inc.
Pelkmans, L. (2012). Cell Biology. Using cell-to-cell
variability—a new era in molecular biology. Sci-
ence 336, 425–426.
Ramalho-Santos, M., Yoon, S., Matsuzaki, Y., Mul-
ligan, R.C., and Melton, D.A. (2002). ‘‘Stemness’’:
transcriptional profiling of embryonic and adult
stem cells. Science 298, 597–600.
Schroeder, T. (2008). Imaging stem-cell-driven
regeneration in mammals. Nature 453, 345–351.
Schubert, C. (2011). Single-cell analysis: The
deepest differences. Nature 480, 133–137.
Sigal, A., Milo, R., Cohen, A., Geva-Zatorsky, N.,
Klein, Y., Liron, Y., Rosenfeld, N., Danon, T.,
Perzov, N., and Alon, U. (2006). Variability and
memory of protein levels in human cells. Nature
444, 643–646.
Silva, J., and Smith, A. (2008). Capturing pluripo-
tency. Cell 132, 532–536.
Silva, J., Nichols, J., Theunissen, T.W., Guo, G.,
van Oosten, A.L., Barrandon, O., Wray, J., Yama-
naka, S., Chambers, I., and Smith, A. (2009).
Nanog is the gateway to the pluripotent ground
state. Cell 138, 722–737.
Singh, A.M., Hamazaki, T., Hankowski, K.E., and
Terada, N. (2007). A heterogeneous expression
pattern for Nanog in embryonic stem cells. Stem
Cells 25, 2534–2542.
Soriano, P., and Jaenisch, R. (1986). Retroviruses
as probes for mammalian development: allocation
of cells to the somatic and germ cell lineages. Cell
46, 19–29.
Spiller, D.G., Wood, C.D., Rand, D.A., and White,
M.R.H. (2010). Measurement of single-cell dy-
namics. Nature 465, 736–745.
Szutorisz, H., Georgiou, A., Tora, L., and Dillon, N.
(2006). The proteasome restricts permissive tran-
scription at tissue-specific gene loci in embryonic
stem cells. Cell 127, 1375–1388.
Tang, F.C., Barbacioru, C., Wang, Y.Z., Nordman,
E., Lee, C., Xu, N.L., Wang, X.H., Bodeau, J.,
Tuch, B.B., Siddiqui, A., et al. (2009). mRNA-Seq
whole-transcriptome analysis of a single cell. Nat.
Methods 6, 377–382.
Tang, F., Lao, K., and Surani, M.A. (2011). Devel-
opment and applications of single-cell transcrip-
tome analysis. Nat. Methods 8(4, Suppl),
S6–S11.
Toyooka, Y., Shimosato, D., Murakami, K., Taka-
hashi, K., and Niwa, H. (2008). Identification
and characterization of subpopulations in undif-
ferentiated ES cell culture. Development 135,
909–918.
Trott, J., Hayashi, K., Surani, A., Babu, M.M., and
Martinez-Arias, A. (2012). Dissecting ensemble
networks in ES cell populations reveals micro-het-
erogeneity underlying pluripotency. Mol. Biosyst.
8, 744–752.
Ying, Q.L., Wray, J., Nichols, J., Batlle-Morera, L.,
Doble, B., Woodgett, J., Cohen, P., and Smith, A.
(2008). The ground state of embryonic stem cell
self-renewal. Nature 453, 519–523.
Zalzman, M., Falco, G., Sharova, L.V., Nishiyama,
A., Thomas, M., Lee, S.L., Stagg, C.A., Hoang,
H.G., Yang, H.T., Indig, F.E., et al. (2010). Zscan4
regulates telomere elongation and genomic stabil-
ity in ES cells. Nature 464, 858–863.
Note Added in Proof
Since the submission of this manuscript, several
reports have been published which question the
biological significance of previously reported
heterogeneity in Nanog expression. Using single-
molecule mRNA-FISH to quantify transcript
expression in single cells Faddah et al. observed
that coexpression patterns of a range of pluripo-
tency factors, including Nanog, are more uniformly
distributed within embryonic stem cell populations
than has previously been reported using heterozy-
gous loss-of-function knockin reporters. They
attribute previously described heterogeneity to
artifacts associated with reporter disruption of
endogenous gene expression. Because entropy
measures how uniformly expression probability is
spread over the available state space, these new
results are in accordance with the entropic classi-
fication of PSC diversity that we suggest, and
highlight the need to properly quantify, and distin-
guish between, ‘‘diversity’’ and ‘‘heterogeneity’’ of
expression patterns.
Cell 1
Additional references include the following:
Faddah, D.A., Wang, H., Cheng, A.W., Katz, Y.,
Buganim, Y., Jaenisch, R. (2013). Single-Cell Anal-
ysis Reveals that Expression of Nanog Is Biallelic
and Equally Variable as that of Other Pluripotency
Factors in Mouse ESCs. Cell Stem Cell 13, 23–29.
Filipczyk, A., Gkatzis, K., Fu, J., Hoppe, P.S.,
Lickert, H., Anastassiadis, K., and Schroeder, T.
(2013). Biallelic Expression of Nanog Protein in
Mouse Embryonic Stem Cells. Cell Stem Cell 13,
12–13.
Smith, A. (2013). Nanog Heterogeneity: Tilting at
Windmills? Cell Stem Cell 13, 6–7.
54, August 1, 2013 ª2013 Elsevier Inc. 489
