Computational Biology & Biological Physics, Lund University, Lund, Sweden

Division of Biology, California Institute of Technology, , Pasadena, USA

Lund Strategic Research Center for Stem Cell Biology and Cell Therapy, Lund University, Lund, Sweden

Abstract

Background

Embryonic stem cells (ESC) have the capacity to self-renew and remain pluripotent, while continuously providing a source of a variety of differentiated cell types. Understanding what governs these properties at the molecular level is crucial for stem cell biology and its application to regenerative medicine. Of particular relevance is to elucidate those molecular interactions which govern the reprogramming of somatic cells into ESC. A computational approach can be used as a framework to explore the dynamics of a simplified network of the ESC with the aim to understand how stem cells differentiate and also how they can be reprogrammed from somatic cells.

Results

We propose a computational model of the embryonic stem cell network, in which a core set of transcription factors (TFs) interact with each other and are induced by external factors. A stochastic treatment of the network dynamics suggests that NANOG heterogeneity is the deciding factor for the stem cell fate. In particular, our results show that the decision of staying in the ground state or commitment to a differentiated state is fundamentally stochastic, and can be modulated by the addition of external factors (2i/3i media), which have the effect of reducing fluctuations in NANOG expression. Our model also hosts reprogramming of a committed cell into an ESC by over-expressing OCT4. In this context, we recapitulate the important experimental result that reprogramming efficiency peaks when OCT4 is over-expressed within a specific range of values.

Conclusions

We have demonstrated how a stochastic computational model based upon a simplified network of TFs in ESCs can elucidate several key observed dynamical features. It accounts for (i) the observed heterogeneity of key regulators, (ii) characterizes the ESC under certain external stimuli conditions and (iii) describes the occurrence of transitions from the ESC to the differentiated state. Furthermore, the model (iv) provides a framework for reprogramming from somatic cells and conveys an understanding of reprogramming efficiency as a function of OCT4 over-expression.

Background

Understanding the molecular networks which give rise to pluripotency in embryonic stem (ES) cells is crucial for among other things developing reprogramming strategies. Recent work has shed light on several key aspects of the underlying network and its interaction with external factors, in particular the chemical media which maintain the cells

At the heart of the pluripotency network lies the triad OCT4, SOX2 and NANOG

Biochemical systems naturally exhibit stochastic fluctuations due to random interaction processes, gene transcription and translation as well as degradation. Recent studies have explored the role of stochastic fluctuations in a variety of organisms ranging from bacteria to mammalian cells

Underlying the ability of NANOG to act as a “gatekeeper” of pluripotency

It follows that a quantitative analysis of network dynamics could improve our understanding of the multiple states of the ESC. Previous purely deterministic studies have explored the dynamics of the OCT4-SOX2-NANOG regulatory network, as well as its role in determining the cell fate, i.e the final lineage: epiblast, trophectoderm and endoderm

In this work we build upon these ideas by further analyzing how fluctuations in NANOG play a role in both allowing cells to transition between ES sub-states and then to finally exit irreversibly into a differentiated state. However, this occurs in a spontaneous fashion. Key to our approach, which is different from that of refs.

Results and discussion

A simplified computational model of the ESC

Our simplified ESC network model considers a combination of positive and negative feedbacks between OCT4-SOX2 and NANOG and G. With stochastic simulations we demonstrate the permissive nature of this self-contained network – most cells retain pluripotency except for a fraction that get pushed towards differentiation. This model, is based upon an epigenetic effect by which OCT4 regulates NANOG, is also employed for reprogramming somatic cells into ESC.

The heterodimer OCT4-SOX2 is known to serve as an activator of OCT4, SOX2 and NANOG

The transcription factor interaction circuit along with external factors influences

**The transcription factor interaction circuit along with external factors influences.** The core network for the mutual and self-regulatory interactions between NANOG, OCT4-SOX2 heterodimer, FGF4 and differentiation gene G. The dashed lines indicate the effect of external factors when cells are maintained in two different media, LIF+BMP4 and the 2i/3i respectively. The dynamical model is based upon the following (see Methods): OCT4-SOX2 induces NANOG. NANOG dimerizes and regulates itself positively. NANOG represses G, which regulates itself positively. OCT4-SOX2 induces G and the latter suppresses both NANOG and OCT4-SOX2. LIF induces NANOG through Klf4. OCT4-SOX2 induces FGF4, which suppresses NANOG. The 2i/3i medium suppresses FGF4.

Exploring the ground state of the ESC

Commitment – transition from the stem cell state to a differentiated state

We first compute the steady states of the system for different values of LIF using the deterministic rate equations (Eq. 1) for the circuit in Figure

**Parameters**

**
k
**

**
c
**

**
c
**

**
c
**

**
c
**

**
c
**

**
e
**

**
e
**

**
e
**

**
a
**

**
a
**

**
a
**

**
b
**

**
b
**

**
b
**

**
b
**

**
γ
**

0.005

0.01

0.4

1

0.1

0.00135

0.01

1

1

0.01

1

5

0.005

0.005

1

1

0.01

With dynamics resulting from the interactions between G, NANOG and OCT4-SOX2, there are basically two states of the system: (i) the stem cell state, when OCT4-SOX2 and NANOG are ON and G is OFF, and (ii) vice versa for the somatic state.

In the somatic state G is high and both OCT4-SOX2 and NANOG are suppressed and hence OFF. This state remains even when increasing LIF since the model for the NANOG gene regulatory function is based upon a simplified epigenetic mechanism. For Nanog to be activated, the Nanog promoter must be bound by OCT4 along with any of its activators OCT4, NANOG (autoregulation), LIF. To be repressed, Nanog must be bound by OCT4 along with its repressors FGF4 and G.

Adding LIF, has no effect on NANOG if OCT4 is OFF, since LIF cannot access NANOG. However, if initially the cell is in a stem cell state with high OCT4-SOX2, then OCT4-SOX2 exposes NANOG, which allows LIF to induce NANOG. This in turn leads to suppression of G, which finally relieves the suppression on OCT4-SOX2. These sequential negative interactions implement a positive feedback loop between NANOG and OCT4-SOX2 (analogous to a different mechanism suggested in

Figure S1. Steady state analysis of the stem cell circuit as functions of LIF and _{I3}concentrations. The dashed lines indicate unstable states. **(A)** The steady state values of NANOG, OCT4-SOX2 and G as functions of LIF concentration. The plots display two states of the cell. (i) the stem cell state – high OCT4-SOX2/NANOG and low G and (ii) the differentiated state with low OCT4-SOX2/NANOG and high G **(B)** Similar graphs for small molecule differentiation inhibitors _{I3} concentration (here for 100). Although there are still two states, NANOG is still higher here than in the previous case. Shown also is the level of FGF4 (magenta), which is at ≃20, which is much lower than in the previous case.

Click here for file

So far we have described a deterministic approach. However, chemical reactions are necessarily stochastic, and hence protein levels fluctuate in time

Stochastic dynamics under LIF conditions

In Figure

Time series and distributions of [OS], [N] and [G] concentrations for the stochastic dynamics of the gene regulatory network with inputs from LIF-BMP4 and 2i/3i media with concentrations _{3} = 6 respectively

**Time series and distributions of [OS], [N] and [G] concentrations for the stochastic dynamics of the gene regulatory network with inputs from LIF-BMP4 and 2i/3i media with concentrations****=85**and _{3=6}**respectively.** Variation of residence time in the ES state. **(A)** Time series of NANOG (red) and OCT4-SOX2 (blue) when in LIF-BMP4 medium show significant fluctuations of NANOG expression between high and low levels. **(B)** Time series of NANOG and OCT4-SOX2 when in 2i/3i medium. **(C)** NANOG and OCT4-SOX2 distributions when in LIF-BMP4 medium. NANOG exhibits a wide distribution. **(D)** NANOG and OCT4-SOX2 distributions when in 2i/3i medium. **(E)** Time series showing the differentiation process occurring when the cells are maintained in LIF-BMP4 medium; NANOG (red), OCT4-SOX2 (blue) and G (green). The up-regulation of the differentiation gene G leads to an irreversible down-regulation of OCT4-SOX2 and NANOG. **(F)** The mean time that a stem cell remains in the ESC state increases with LIF concentration in the LIF-BMP4 stem cell medium.

It has been shown that NANOG expression fluctuations reaching very low levels lead to irreversible commitment

NANOG and OCT4 standard deviations for multiple parameter sets

**NANOG and OCT4 standard deviations for multiple parameter sets.** Each parameter set was generated by randomly sampling ±ߙ5%, 15% and 50% around each parameter in Table

The pluripotent state has high levels of OCT4-SOX2 which are less heterogeneous than those of NANOG. The continuum of NANOG values spans both, high and low NANOG values. In

Stochastic dynamics under 2i/3i conditions

Recently, it was shown that ESCs can be maintained in 2i/3i

Figure

Figure S2. NANOG mean and standard deviation as a function of the concentration of 2i/3i (

Click here for file

Reprogramming – transition from somatic to iPS cells

Ectopic expression of the pluripotency transcription factors OCT4, SOX2, KLF4 enables the transition from somatic cells to iPS cells (ES like cells)

Our minimal dynamical model elucidates the reprogramming process when only OCT4, SOX2 and KLF4 are over-expressed and identifies the obstacles to overcome: The differentiation gene G antagonizes OCT4 and NANOG, and since it feeds back positively upon itself, once ON, it ensures that OCT4-SOX2 and NANOG are OFF. When OCT4-SOX2 is OFF, NANOG cannot be induced since OCT4 is unable to fulfill its epigenetic role of exposing the NANOG promoter for transcription. Hence, NANOG stays OFF. NANOG is also repressed by FGF4, which in this case would be low, since its inducer OCT4-SOX2 is OFF. Hence, over-expression of OCT4 is the key.

Deterministic analysis

The parameter

Steady state analysis when OCT4-SOX2 over-expression is varied

**Steady state analysis when OCT4-SOX2 over-expression is varied.** Time series concentrations of NANOG (red), OCT4-SOX2 (blue) and G (green) obtained from stochastic simulation when reprogramming occurs. Reprogramming efficiency when over-expression of OCT4-SOX2 is varied. **(A)**The steady state values of NANOG, OCT4-SOX2 and G as functions of over-expression (_{3}=10 respectively. The gene regulatory circuitry is initially in the somatic state with G high and NANOG and OCT4-SOX2 low. The reprogramming occurs when G turns OFF while NANOG and OCT4-SOX2 turn ON (at **(B)** Time series of NANOG, OCT4-SOX2 and G for one case when the reprogramming was successful, G turns OFF while NANOG and OCT4-SOX2 turn ON for _{3} = 0.05 respectively. **(C)** The reprogramming efficiency for values of _{3} taking 0 and 0.4 values,

(i)

As OCT4-SOX2 over-expression is further increased and reaches

Our deterministic model analysis indicates that the stem cell circuit activation must be conditioned by OCT4-SOX2 over-expression. It is known that over-expression of OCT4 is mandatory for obtaining iPS cells in the laboratory

Stochastic simulations

In Figure

A major challenge is to increase the efficiency of the reprogramming process. We used our model to study the variation of reprogramming efficiency when the value of OCT4-SOX2 over-expression (

Our results show that the stem cell medium where the somatic cells are maintained after transduction also plays an important role in reprogramming efficiency. When reprogramming is successful, the differentiation gene G is OFF while NANOG and OCT4-SOX2 are at high values. The latter induces FGF4 which represses NANOG. The NANOG suppression by FGF4 influences negatively the reprogramming outcome. Thus, repression of FGF4 should have a positive impact on reprogramming efficiency. Indeed, when increasing 2i/3i concentration, an increase in iPS cell generation efficiency is observed (see Figure

Nevertheless, our results demonstrate that setting the degrees of over-expression and choosing the iPS cell medium should be considered for optimizing reprogramming efficiency.

For completeness we performed similar analyses for a modified network topology without the differentiation gene G (see Additional file

Figure S3. Time series of [N] and [OS] for the stochastic dynamics of the alternative architecture with no differentiation gene G for **not** lost in a differentiated cell in the model without G.

Click here for file

An architecture with no differentiation gene G.

Click here for file

Conclusions

Our computational model of the transcriptional dynamics of the embryonic stem cell suggests mechanisms in the simplified network feedback structure which allow cells to make a stochastic decision to exit from a stem cell state to a differentiated one. Such an event is random and occurs due to the internal noise of network components. In particular, we explicitly showed how NANOG heterogeneity enables such transitions. NANOG integrates several noisy signals. OCT4 both directly activates NANOG, as well as suppresses it through FGF4. When NANOG falls below a certain threshold, G gets activated, leading to shutdown of NANOG and OCT4. FGF4 can be suppressed by the 2i/3i media which leads to reduction of NANOG heterogeneity (specifically at higher levels) and hence to stability of the stem cell state, i.e the “ground state”. Our model could explain how the absence of the 2i/3i media, can result in the experimentally observed “leakage” to differentiated cells even under ideal culture conditions, since stochastic transitions of NANOG to relatively low levels can occur, in this case. The spontaneous commitment picture emerging from our model studies is consistent with the “permissive” scenarios suggested in the context of hematopoiesis

Our simplified model could be expanded as more links in this network are explored. For example, recent work

Methods

Model ingredients

NANOG is induced by OCT4-SOX2.

NANOG dimerizes and regulates itself positively

The differentiation gene G positively auto-regulates itself and is repressed by NANOG.

LIF induces NANOG, presumably through Klf4 via the Stat3 pathway.

G is induced by OCT4-SOX2 and suppresses both NANOG and OCT4-SOX2.

Even though FGF4 is a growth factor, it is induced by OCT4-SOX2

The 2i/3i medium has the effect of suppressing FGF4.

Network dynamics

For the circuit in Figure _{3}respectively.

In

We have performed Linear Noise Approximation analysis to prove the robustness of our results, as described below.

Robustness analysis for NANOG fluctuations using the LNA

A second order expansion of the master equation, obtained from the transition rates in Equation 1, is called as the linear noise approximation (LNA)

where

The bifurcation analysis was performed using JDesigner

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

VC, VO, CP conceived and developed the project. VC, VO developed the simulation and analysis programs. VC, VO, CP analyzed the data and wrote the manuscript. All authors read and approved the final manuscript.

Acknowledgements

This work was funded by the Swedish Foundation for Strategic Research Senior Individual Grant (A3 06:215) and the Swedish Research Council (Vr 621-2008-3074). VC would like to acknowledge Prof Elliot M Meyerowitz for support. We thank an anonymous reviewer for constructive comments.