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 . The current understanding is that ESCs occupy a multiplicity of sub-states, with stochastic transitions between them. One aim is to understand the molecular interactions that maintain cells in a pluripotent state, destabilize this state leading to commitment, as well as allow a return to the pluripotent state from a committed state. Given the substantial experimental efforts currently underway to understand these mechanisms, a computational systems biology approach seems like a way forward within which such questions could be formulated [2–6]. As in many other biomedical problem areas, a computational approach would here allow diverse experimental results to be absorbed into the formulation of the model, but more importantly, could serve as a hypothesis generator to test mechanisms through further experimentation. The recognition that states of a ES cell are read out by the gene expression of key regulators, has lead to a simple hypothesis regarding the pluripotent nature of the ESC . An ES cell can be in a “ground state”, in which it is neutral to any developmental specification. However, it is possible for the cell to transition to a differentiated state. Here we explore the dynamics of a simplified network model representing key elements of ESC transcription factor and signaling regulators to suggest mechanisms for such a transition state picture.
At the heart of the pluripotency network lies the triad OCT4, SOX2 and NANOG [8–10], where OCT4 and SOX2 act together as a heterodimer regulating several genes including NANOG, OCT4 and SOX2 . There are additional TFs that also impact pluripotency. The exact regulatory mechanisms in the network with impact on pluripotency remain to be fully understood. However, it appears that self-reinforcing mechanisms through feedback of these key regulators upon themselves seem to be instrumental. Interacting with these key components in mice are external factors like Leukemia Inhibiting Factor (LIF), which can substitute for feeders by activating the transcription factor STAT3 that inhibits ES differentiation [12, 13]. Another factor, Bone Morphogenetic Protein (BMP4), has been shown to inhibit the differentiation proteins and thus can be used as a replacement for serum . There are corresponding factors active in humans. The common media for maintaining stem cells in cultures is LIF plus serum or BMP4. It has been shown that serum/BMP4 can be replaced by small molecules which inhibit FGF4 receptor tyrosine kinases and the ERK cascade (2i/3i medium) . The 2i/3i (two or three types of differentiation inhibiting molecules) medium is used successfully to maintain stem cells in vitro in combination with or without LIF.
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 [16, 17]. In ESCs, it was shown that the expression of some transcription factors important for pluripotency are heterogeneous when cells are maintained in the “classical” environment i.e. LIF plus BMP4 or serum. Stochasticity or heterogeneity has been observed in key stem cell TFs such as NANOG [18–20], REX1 , STELLA . Based upon these observations, it appears that stem cells exist in a multitude of sub-states, where each sub-state represents a certain multi-distribution of TF concentrations. In particular, NANOG shows more heterogeneity than OCT4 and SOX2 [18, 20]. Cells expressing lower levels of NANOG are more prone to differentiate [18, 23], thereby conferring a stochastic component to the ability of the cell to self-renew. Hence, the state space of ESCs is intricately woven into the heterogeneous gene expression of some of the key regulators of the network.
Underlying the ability of NANOG to act as a “gatekeeper” of pluripotency , is the fact that OCT4-SOX2 also induces FGF4, a differentiation promoting growth factor . The ES cell requires OCT4 and SOX2 to maintain it in a pluripotent state, while at the same time pushing it towards differentiation. NANOG is thought to prevent differentiation, and hence when it reaches low levels, the probability to commit increases. How FGF4 fits into this network has so far not been computationally explored. Mouse ESCs can be maintained in a pluripotent state, through introduction of small molecule inhibitors. Ying et al.  discovered two different sets of small molecule inhibitors; 3i – FGF receptor inhibitor, Mitigen activated protein (MAP) kinase/ERK kinase - MEK inhibitor and GSK3 inhibitor, 2i – MEK inhibitor and a GSK3 inhibitor. Wray et al.  established that the expressions of NANOG and REX1 within the mouse ES cultures under 2i conditions were not heterogeneous i.e. only NANOG high or REX high are present, suggesting the existence of cells in a state that is intrinsically less fluctuating. This could be denoted a true “ground” state, which they suggested is an inherent stable pluripotency network governed by OCT4, SOX2 and NANOG, but, which is perturbed by Erk signaling acting through the FGF receptors.
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 [26, 27]. However, neither of these computational studies analyzed heterogeneity in NANOG expression. Kalmar et al.  suggested by stochastic modeling of a simplified stem cell network based upon observations, how NANOG fluctuations could make the stem cell state transition between multiple states. Their model involved feedbacks, both positive and negative between OCT4 and NANOG which lead to NANOG levels cycling between high and low levels as an excitable system. Subsequently Glauche et al.  further studied the nature of such stochastic transitions with two different model scenarios. In one model NANOG, which is induced by OCT4-SOX2 can act as a bistable switch, and can transition between high and low levels. In the other model, which is based upon an activator-repressor mechanism, NANOG can oscillate on a fixed limit cycle, and can recapitulate the observed heterogeneity in NANOG levels. Hence, several types of mechanisms could lead to NANOG heterogeneity. It is also suggested how NANOG can act as a gatekeeper by suppressing any differentiation signals which would ultimately make the cell transition into a differentiated cell. However, in , the signal to differentiate is external, and cells therefore cannot differentiate spontaneously as observed.
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. [20, 28], is the development of a self-organized network, in which the pluripotent network governed primarily by OCT4-SOX2-NANOG interacts with a differentiation pathway gene denoted by “G”. Candidates for G are for example GATA6 and SOX17. It is the stochastic dynamics of this network in which several types of feedbacks give rise to the observed stochastic stem cell fate. The noise therefore is internal to the network, with external stimuli controlling the strength of the fluctuations. Hence, stem cells can spontaneously change fate in accordance with observations. This also allows us to answer the second question as to how reprogramming can be simulated in our model. In  it has been shown that over-expression of OCT4 can lead to reprogramming a somatic cell to an ESC. However, the efficiency is maximal for the levels of OCT4 within a certain window . Our model can reproduce this result, and we show how the interaction between OCT4, NANOG and the differentiation pathway gene G lead to this result.