Probing the role of stochasticity in a model of the embryonic stem cell: heterogeneous gene expression and reprogramming efficiency

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.

Figure 1

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.

Figure 2

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 concentrationsLIF=85and I₃₌₆respectively. 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.

Figure 3

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 1 for LIF=100. In each case the NANOG standard deviation (SD) was greater than the OCT4-SOX2 SD, thereby suggesting that NANOG displays more heterogeneity. The oval A correspond to those parameter sets representing the differentiated state in which G is high and all other components are suppressed (hence low values of NANOG and OCT4). The points enclosed by the oval B represent parameter sets in which: NANOG is weakly regulated by itself; strongly suppressed by FGF4 and G. In addition OCT4 is weakly suppressed by G, which allows NANOG and G both to be expressed.

Figure 4

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 (α) of OCT4-SOX2 for LIF=100 and I₃=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 α≃0.001). At higher values of α(α≃0.2), there now exist two states of the system: the existing ES state and the differentiated state which occurs since G turns ON while OCT4-SOX2 and NANOG switch to lower levels. (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 LIF=100 and I₃ = 0.05 respectively. (C) The reprogramming efficiency for values of α varying from 0 to 0.4 and I₃ taking 0 and 0.4 values, LIF=100