VC and CP conceived and designed the experiments. VC, CT, and CP analyzed the data. VC, CT, HMS, and CP contributed reagents/materials/analysis tools. CV, CT, UAN, HMS, and CP wrote the paper.
The authors have declared that no competing interests exist.
Recent ChIP experiments of human and mouse embryonic stem cells have elucidated the architecture of the transcriptional regulatory circuitry responsible for cell determination, which involves the transcription factors OCT4, SOX2, and NANOG. In addition to regulating each other through feedback loops, these genes also regulate downstream target genes involved in the maintenance and differentiation of embryonic stem cells. A search for the OCT4–SOX2–NANOG network motif in other species reveals that it is unique to mammals. With a kinetic modeling approach, we ascribe function to the observed OCT4–SOX2–NANOG network by making plausible assumptions about the interactions between the transcription factors at the gene promoter binding sites and RNA polymerase (RNAP), at each of the three genes as well as at the target genes. We identify a bistable switch in the network, which arises due to several positive feedback loops, and is switched
One key issue in developmental biology is how embryonic stem cells are regulated at the genetic level. Recent high throughput experiments have elucidated the architecture of the gene regulatory network responsible for embryonic stem cell fate decisions in human and mouse. In this work the authors develop a computational model to describe the mutual regulation of the genes involved in these networks and their subsequent effects on downstream target genes. They find that the core genetic network incorporates the functionality of a bistable switch, which arises due to positive feedback loops in the system. Also, this switch behaviour is very robust with respect to model parameters. The switch and architecture by which the genetic network regulates the downstream genes, is responsible for either maintaining the genes responsible for self-renewal
Embryonic stem (ES) cells possess the unique property of being able to retain their capacity for self-renewal and potential to form cells of all three embryonic germ layers (endoderm, mesoderm, ectoderm). Understanding the factors that determine the ability of ES cells to maintain their self-renewal and pluripotency, and the interplay of these factors, is of utmost relevance for both developmental biology and stem cell research. Over the last two years, a trio of transcription factors (TFs) have emerged—OCT4, SOX2, and NANOG—which play a key role in determining the fate of ES cells [
Recently, two genome-wide studies [
The three TFs OCT4, SOX2, and NANOG thus regulate genes with two distinct and opposing functions: self-renewal and differentiation. The TGs are regulated both by OCT4 and NANOG individually, and by the combined effects of OCT4–SOX2 and NANOG [
The core transcriptional network that emerges from [
Genes and proteins are represented as single entities. Each outgoing arrow represents a protein (the outgoing merging arrows from OCT4 and SOX2 represent complex formation). Each ingoing arrow represents a protein with a role as a TF. Signals
We will discuss the dynamics of the transcriptional network as a function of the inputs
We use the Shea–Ackers approach [
The transcriptional network of
Our system naturally divides into two parts: 1) The “stem cell box” with the tightly interacting OCT4, SOX2, and NANOG genes; and 2) their downstream targets—the stem cell and differentiation genes. After modeling each of these subsystems individually, the integrated model is described.
In
Prior to exploring the dynamics of the stem cell box, we examine whether its architecture occurs in the gene regulatory networks of other species. Such a search may lead to a better understanding of the network, if one could compare its functionality across different organisms. Our network motif searches are described in detail in Materials and Methods. The network in
The motif in (A) captures the regulatory interactions of the system at the gene–gene level. Because (A) was not observed in any of the databases for lower organisms (see text), we searched for the same subgraph without autoregulations (B), followed by its two-gene counterpart with positive regulation (C). Finally, one of the activations was replaced with two repressions in series, yielding (D). A small number of instances of (C) and (D) were found in the databases (see text).
A search for switch-like modules of only two genes produced the mutually activating genes CAT5 and CAT8 in yeast, and achaete and scute in
From the nature of the connections as described earlier in the Architecture section, we know that the heterodimer OCT4–SOX2 on its own serves as an activator for all three genes (OCT4, SOX2, and NANOG), and we surmise that it also works as an activator when in complex with NANOG. The model (see
As explained in the Introduction, we also assume that the signals
Furthermore, signal
With the assumptions above, a set of differential equations emerge, which describe the behavior of OCT4, SOX2, NANOG, and OCT4–SOX2, with concentration levels [
Here
Logic Underlying
Logic Underlying
In
There are two turning points (saddle-node bifurcations are marked as SN, and the dotted line connecting the SNs indicate unstable states) leading to a hysteretic curve. The arrows indicate how to interpret the hysteresis curve. As
Activating the signal
The system is a bistable switch with respect to the
The concept of bistability in a genetic regulatory network has long been hypothesized to have a role in differentiation [
We have examined the robustness of switch-like behavior of the stem cell box to changes in parameter values (see
In conclusion, the stem cell box has the interesting dynamics of being turned
As mentioned before, the TGs of the stem cell box considered here are either regulated individually by OCT4–SOX2 and NANOG or by their joint actions [
The OCT4–SOX2 heterodimer regulates NANOG, and together OCT4–SOX2 and NANOG then regulate the TGs. This is a realization of the feedforward loop motif [
(A) Coherent.
(B) Incoherent.
Whether the feedforward mechanisms governing the stem cell and differentiation genes are coherent or incoherent is not known. Here we explore the steady state properties of two different alternatives: I) stem cell genes: OCT4–SOX2 activator, NANOG a weak repressor; differentiation genes: OCT4–SOX2 activator, NANOG repressor; II) stem cell genes: OCT4–SOX2 activator, NANOG activator; differentiation genes: OCT4–SOX2 repressor, NANOG repressor.
The first case, which has the same architecture for regulating both types of TGs, is explored in some detail here. The second case will be commented upon in the next section.
To focus on the dynamics of the feedforward regulation of TGs, we will here assume a fixed OCT4–SOX2 concentration, i.e., exclude the effects of the feedback of NANOG to OCT4 and SOX2. In the next section we integrate the stem cell box of the previous section with the feedforward regulation.
We assume the following regulatory mechanism at the TGs: OCT4–SOX2 binds to the TGs as an activator and recruits NANOG. Together the OCT4–SOX2, NANOG complex then acts as a repressor for the TGs. For low OCT4–SOX2 concentrations, the TGs are activated. As the level is increased, the NANOG concentration grows, thereby enabling OCT4–SOX2 and NANOG to repress the TGs. The steady state response of this circuit is therefore maximal at an intermediate OCT4–SOX2 concentration, giving rise to a behavior of an “amplitude filter” [
With constant input concentration [
(A) NANOG.
(B) TGs.
(C) Concentrations of the stem cell and differentiation TGs as a function of [
NANOG is recruited weakly by OCT4–SOX2, causing only minor repression of the stem cell gene, so that it is expressed at a significant level. The binding strengths and the concentration of [
NANOG binds with higher affinity to OCT4–SOX2, so that the OCT4–SOX2, and NANOG complex are very effective at repressing the differentiation genes. When the [
We next integrate the stem cell box with the feedforward regulation of the TGs by closing the loop, i.e., NANOG feeds back to the OCT4 and SOX2 genes. The OCT4–SOX2 input to the feedforward motif is now a variable determined by its interaction with the signals
(A) Differentiation TG expression.
(B) Stem cell TG expression.
Once the stem cell box is
Next we consider case II for the regulation of the TGs. Here the stem cell genes are regulated with both OCT4–SOX2 and NANOG being activators, and differentiation genes are regulated with both OCT4–SOX2 and NANOG being repressors. In
(A) Stem cell genes.
(B) Differentiation genes.
Logic for the TG with the Same Notation as in
Both cases I and II comply with the fact that the stem cell genes are expressed and differentiation genes are repressed when the switch is
We now turn to the effects of reducing the feedback from NANOG to OCT4 and SOX2 on the regulation of the TGs. This is illustrated using the incoherent feedforward architecture (case I). If the binding strengths of NANOG to OCT4 and SOX2 are decreased, the positive feedback is reduced and the bistable behavior is lost, which affects the expression levels of the TGs.
(A) The effects of weak feedback of NANOG to the OCT4 and SOX2 genes. The inefficient binding of NANOG to these genes leads to a loss of the switch-like behavior.
(B) The consequence of weak NANOG binding on the TG expression. With weak feedback, the expression level does not fall off sharply as compared with the case with strong feedback, thereby demonstrating that strong feedback is essential to prevent the differentiation TGs from being expressed.
The ES cell transcriptional network architecture appears to be unique. Our data analysis has shown that the transcriptional subnetwork between OCT4, SOX2, and NANOG has no counterparts in available information from non-mammalian genomes. Hence, one cannot rely on phylogenetics to confirm and deduce the function of the architecture. Instead, dynamical modeling of the system is called for [
We have identified a bistable switch in the network consisting of the OCT4, SOX2, and NANOG genes, which arises due to positive feedback loops: OCT4 and SOX2 regulate each other through the formation of a heterodimer. This heterodimer regulates NANOG, which feeds back to OCT4 and SOX2. NANOG also binds to its own promoter region as an activator, and this autoregulation acts to further strengthen the positive feedback loop. The two states of the stem cell box switch, where the trio of TFs are all
Next we considered the regulation of TGs by OCT4, SOX2, and NANOG, pointing out that if the TGs are regulated individually by OCT4, SOX2, and NANOG, then the stem cell box dynamics takes care of keeping the stem cell genes
Two options for the regulation of TGs were modeled, and we found that both were consistent with the requirement that stem cell genes are
We now discuss several predictions that emerge from this model.
1) We have explored the parameter space of the model (see
There is only one turning point leading to an irreversible bistable switch. At the threshold
At the threshold
2) Overexpression of NANOG has recently been shown to propagate the self-renewal of human ES cells over several generations [
(A) Shows the OCT4–SOX2 and NANOG concentration showing irreversible bistability, when NANOG is overexpressed through a high value for the basal rate of transcription (i.e.,
(B) Shows OCT4–SOX2 and NANOG concentrations (the same as in
3) The architecture of the feedforward loop governing the TGs is consistent with the loss of expression of stem cell TGs and expression of differentiation TGs on suppression of OCT4–SOX2, e.g., by reducing the signal
4) Analogous to the above case, decreasing OCT4–SOX2 has different effects on the differentiation TGs, depending on the type of architecture which applies: with option I, decreasing OCT4–SOX2, from a high level, at which the differentiation genes are repressed, first leads to an increase in expression of the differentiation TGs, as the OCT4–SOX2 level passes through the maximum of the amplitude filter curve (see
The model suffers from a few deficiencies. Overexpression of OCT4 initiates differentiation [
Future work will elaborate on the effects of stochastic fluctuations in protein concentration of NANOG, OCT4, and SOX2 on the regulatory behavior of the TGs. Bistability is one way to counter chatter in input noise [
A stoichiometric map for more detailed model considerations corresponding to
All protein species are assumed to have a first-order degradation rate. The lines ending with dots could be either activating or repressing, depending on the choice of model.
We use rate equation models, which are deterministic and deal with molecular concentrations rather than with individual molecules. For small molecule numbers, one can use Monte Carlo simulations of the Master Equation [
We assume that the process of binding/unbinding of TFs and RNAP takes place over a time scale much smaller than the rate of change of the concentrations of all the proteins in the network. This corresponds to thermodynamic equilibrium at the promoter region of each gene. The transcription rate is then given by the fraction of cases when the RNAP is bound. We compute the partition function [
We model the stem cell box using the formalism defined by
For the NANOG gene, we assume that NANOG cannot bind unless recruited by the OCT4–SOX2 complex. Also, the signal
The functional form of the transcription rates used in
For the downstream TGs, which are co-regulated by OCT4–SOX2 and NANOG, we explore two different types of regulation, cases I and II, respectively (see earlier text). In case I the same incoherent architecture is shared for the stem cell and differentiation TGs. For the latter, the scheme used is that the OCT4–SOX2 complex is an activator. However, the OCT4–SOX2 complex recruits NANOG, and together this complex acts as a repressor. The other two possibilities are: for the stem cell genes both OCT4–SOX2 and NANOG are activators, and the last case, for the differentiation TGs both OCT4–SOX2 and NANOG are repressors (case II).
In
The functional form of the transcription rate used in
Finally, for the last option for the differentiation TGs, for which both OCT4–SOX2 and NANOG are repressors, we obtain from
The algorithm used to search for specific subgraphs in the model organism transcriptional networks is similar to that described in [
Reducing the network in
Widening our search by removing autoregulations (
In a further attempt to find architectural elements similar to the stem cell box, we searched for pairs of mutually activating genes, preferably also activating themselves (
Finally, since a series of two repressions in some sense amounts to a positive regulation, we expanded the search to include the motif shown in
All simulations were carried out using the Systems Biology Workbench (SBW/BioSPICE) tools [
(276 KB PDF)
We have benefitted from discussions with Patrik Edén and from the feedback by an anonymous referee.
embryonic stem cells
RNA polymerase
transcription factor
target gene