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capable of capturing concentration-dependent responses;
therefore, certain biological systems often require biological
reaction networks (BRN) and models.
Core networks, determining key self-renewal and
differentiation decisions, are transcriptional; for this reason,
BRNs describing stem cell behavior often rely on tran-
scriptional regulation. Steady-state models for transcrip-
tional regulation typically take into account a single step in
gene regulation, binding of transcription factors to their sites
in gene regulatory regions, promoters and enhancers [116] .
Such site occupancy models, or fractional occupancy models
(FOM), were successfully used in many biological systems,
including phages, bacteria, yeast and flies [26,65,117,118] ;
however, their distribution in the stem cell field is currently
limited by insufficient knowledge regarding the pluripotency
gene's control regions. Thus, binding sites for the core
pluripotency factors (Oct4, Nanog, Sox) were observed in
the upstream regions of many potential targets, but only
a single structured element, the Oct4-Sox2 sequence
element, has been identified so far. Binding sites for Oct4
and Sox2 are found in close proximity in many genes,
suggesting the formation of heterodimers between these two
critical pluripotency factors [56,119] . Potential cooperativity
between interacting factors may change their binding
properties and the responses of their target genes, thereby
producing new dynamic solutions or cell states (cell line-
ages). It is quite possible that such signal integration
contributes to the alternative lineage commitment in the case
of alternative expression of Oct4 vs. Sox2 or concentration-
dependent response of the genes to Oct4.
Mapping transcription regulatory signals and binding
sites in gene control regions essential in self-renewal or
differentiation serves (1) to establish directed and signed
GRNs, and (2) to provide additional data (along with gene
expression) for model validation. Steady-state FOMs or
dynamic models based on ordinary and stochastic differ-
ential equations (ODEs or SDEs, respectively) require
many rate constants, such as affinities of binding sites, to be
known or at least estimated in order to reduce the space of
potential solutions and the level of model ambiguity. Inte-
gration of several data types may produce highly valuable
maps for distribution of binding motifs and the binding
motif combinations in promoters and enhancers. Most
important data sources include (1) chromatin immunopre-
cipitation followed by deep sequencing or microarrays
(ChIP-chip or ChIP-seq); (2) evolutionary conservation of
DNA in the gene control regions; (3) bioinformatics anal-
yses of the control regions for the presence of binding motif
matches; and (4) finding enhancers specifically activated in
stem cells. ChIP data relevant to stem cells are widely
available in dedicated databases, such as CHEA [78] , but
the method itself suffers from high false positive rates and
its current resolution is not sufficient for mapping single
binding sites [120] . Preliminary filtering of ChIP-X data
based on data regarding chromatin structure [121,122] may
be a solution. Methods based on genome alignments, such
as the PhastCons program [123,124] , help to narrow down
the regions indicated by ChIP-seq. Mapping binding motif
matches using bioinformatics analyses of promoter and
enhancer DNA sequences is useful, but also sensitive to the
quality of the binding motif models (typically alignments
of known binding sites for a given transcription factor)
[125] . Finally, enhancer and promoter DNA sequences,
specifically activated in stem cells, may be identified in
independent genome-wide studies in vivo [126] . These
types of data have been proved to be extremely valuable in
the analysis of transcription regulatory signals [127,128] ,
but are not widely available in the stem cell field.
Dynamic Biological Reaction Model
for the Core Pluripotency Network
A deterministic dynamical model for the minimal core
pluripotency network, shown in Figure 22.6 A, has been
expressed using a system of three ordinary differential
equations
(ODE)
involving fractional
site occupancy
(BRN) under the synthesis terms (x
¼
Nanog, Oct4, Sox2):
d
dt ¼ að
½
x
1
ð
1
P Nanog Þð
1
P Oct Sox ÞÞ b½
x
(1)
Nanog may bind its target genes as a homodimer, which
can be adequately described in terms of the fractional site
occupancy (FOM model) describing cooperativity between
Nanog monomers C N-N and Nanog-DNA binding K N . The
binding constants in FOMs are sometimes expressed via
true thermodynamic terms (K
G/RT)). The same
framework may serve to describe the formation of Oct4-
Sox2 heterodimers, where the heterodimers are virtually
present only when bound to bipartite sites and heterotypic
cooperative interactions are expressed using cooperativity
C O-S between the Sox2 (S) and Oct4 (O) monomers:
¼
exp(
e D
K s ½
S
þ
K o ½
O
þ
C o s K s ½
S
K o ½
O
P Oct Sox ¼
(2)
1
þ
K s ½
S
þ
K o ½
O
þ
C o s K s ½
S
K o ½
O
Expansion of the model for the core pluripotency
network may be necessary for several reasons. For instance,
it has been suggested that negative feedback plays a critical
role in the function of the core circuit. Indeed, some core
factor target genes, such as Tcf3, encode transcriptional
repressors, which in turn target the core factors. Second, it
has been found that different concentrations (threshold
levels) of some core pluripotency factors (Oct4) may
induce alternative differentiation events. Such threshold
responses are quite common in developmental and differ-
entiation pathways. Sometimes they are mediated by
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