We will now focus on the structural modications mentioned further above and their eects on the system's eciency. Table 5.3 summarizes the results and as to which degree these modications reect known experiments from literature.
5.6.1 Spontaneous Methylation
First, we are considering spontaneous methylation which we introduced by attributing a probability for the methylation states of modules to be ac-tivated independently of all other factors except dnmt. This introduces a certain measure of stochasticity into the DNMT3A/B dependent de novo methylation process which, in fact, is still only poorly understood.
The eects of this modications are a drastic decrease of reprogramming eciency approximately by the factor 10 although half-maximal saturation occurs slightly faster than in the main model. As already mentioned above in the explanation of the reprogramming simulation of our main model, in this modication there is a strong accumulation of an undened state in which all the modules are silenced except for the exogenous one. Further discussion of this undened roadblock state will be done below further below after having discussed the other structural modications.
Section 5.6: Structural Modications of the Model 125
Figure 5.7: Epigenetic Landscapes of Reprogramming and Dierentiation (taken from Flöttmann, Scharp, and Klipp (2012))
Shown are 3-dimensional graphs of time courses simulating a dierentiation (A) and a re-programming experiment (B). On the x-axis, the 16384 states of the model are sorted according to their similarityΣ123i (see Section 2.3.5) to the 3 states that are pointed out on the x-axis.
The y-axis is the time line and shows the 500 time steps of the simulation. The z-axis shows the probability of the network to be in a state. The states are furthermore color-coded with colors transitioning from green (dierentiated state A) over blue (dierentiated state B) to red (pluripotent state). A A simulation starting from a unique state, the pluripotent state (see Table 5.2) but with the dierentiation module A activated which is needed in order to give a direction to the dierentiation is done by signaling pathways in vivo. One can see that the network quickly leaves the pluripotent state and transitions into a few states, the highest probabilities being reached by the undened state (see text) and the dierentiated state A. B A simulation starting from the dierentiated state A (see Table 5.2) but with the retroviral reprogramming genes being active. We can observe a slow transition from the dierentiated state A into states that more and more resemble the pluripotent state and a nal progressive accumulation of the latter.
5.6.2 Spontaneous Heterochromatin Formation
When DNA methylation is poorly understood, the wealth of chromatin mod-ications and their exact eects on DNA packaging and transcriptional reg-ulation add an even more complex layer to the epigenetic jungle. As for the spontaneous DNA methylation, we introduced stochasticity by spontaneous heterochromatin formation, thus partly depriving the process of any external regulation.
The eect of this modication is even stronger than for the de-regulation of DNA methylation and decreases the overall reprogramming eciency by the factor 40. However, the early rst 50 time steps of the process see a faster accumulation of reprogrammed states than the original model. Since heterochromatin formation now occurs spontaneously, there is a considerable probability that dierentiation related genes will be shut down via the epige-netic silencing, which leads the system to quickly attain this crucial step in reprogramming. This could explain the faster reprogramming at the begin-ning. However, the blocking eects of the de-regulation will become apparent rapidly afterwards. Furthermore, we again observe a strong accumulation of the undened state.
5.6.3 Spontaneous Demethylation
While a lot of epigenetic modications have been studied for many years, researchers have only recently gained more interest in DNA demethylation processes with some new ndings even suggesting that there are enzymatic processes catalysing active demethylation in contrast to cell cycle depen-dent passive demethylation by decreased DNMT1 activity (see Table 5.1) (Bhutani et al., 2011). We tried to reect this uncertainty in knowledge on passive or active processes by including a spontaneous demethylation feature as one model variant.
The latter variant reaches the highest reprogramming eciency after 500 time steps among all model modications with an eciency which is ap-proximately 3-4 times lower than in the main model. Moreover, in contrast to the other variants, the spontaneous demethylation model also shows a similar behavior as the original model which is especially characterized by a fast initial decay of the dierentiated state followed by a slower decreasing phase.
Section 5.6: Structural Modications of the Model 127 5.6.4 Stronger Interaction Between Methylation and
Hete-rochromatin
As a next model variant, we examined how a stronger synergistic eect be-tween DNA methylation and chromatin formation (described as well in Table 5.1) inuences the reprogramming eciency. The reprogramming eciency over time is very similar to the one of spontaneous demethylation described in the Section before this one as are the dynamics of the dierentiated state that also show a strong similarity to the original model. Intriguingly, when starting the experiment from cell lineage A, a state similar to the one of dierentiated cell lineage B - with the only dierence that the pluripotency module is already deprived of its epigenetic marks - is transiently reached with a high probability before it decreases again over time to be transformed steadily into more pluripotency related states. This phenomenon strongly recalls direct biological trans-dierentiation of cells during reprogramming which was thought to only work by passing the pluripotent states before the ndings of Vierbuchen et al. (2010) who were able to directly convert broblasts into functional neurons by dened factors.
5.6.5 No Methylation
In a more drastic modication, we examined the theoretical hypothesis, that DNA methylation has no inuence at all on gene expression or chromatin structures. As expected, the model shows a strongly dierent behavior than before. Leaving out the DNA methylation eects abolishes the ability of the system either to reprogram from a dierentiated state with retroviral genes or to dierentiate out of a pluripotent state upon signals. We can observe that the start states evolve into a distribution of states that are very closely related just as in the stable cell lineages experiments of the main model. Apparently, without DNA methylation, there is no full silenc-ing of transcriptionally active genes because the crosstalk with chromatin structures and thus heterochromatinization is abolished which is required for complete silencing. Hence, active modules can never be silenced and inactivated gene's expression can never be triggered, even if they are in per-missive chromatin structures and their DNA is unmethylated. Therefore, the master regulators of the cell lineage will never change and reprogramming and trans-dierentiation are thus impossible.
5.6.6 Polycomb Repressor Complexes (PRCs)
In Table 5.3, we explain the mechanism of Polycomb Repressor Complexes (PRCs). They are in fact epigenetic modifyers that are recruited to the
DNA of dierentiation associated and developmental genes upon binding of pluripotency related factors such as OCT4, SOX2 and NANOG. When bound, they modify histone marks in a way as to favour condensed, tran-scriptionally inactive chromatin. Therefore, to include this PRC mechanism into our model, transformed the equation for heterochromatin formation of the dierentiated modules in a way that it positively depends on the expres-sion of the pluriotency module. The model thus created gave a very similar result to the one of our main model (results not shown) suggesting that in our model the mutual transcriptional repression of pluripotency modules and dierentiation modules is interchangeable with this PRC mechanism, because they have the same eects. In reality, however, when the system be-comes more complex and more tightly regulated, the PRC mechanism might enhance this transcriptional repression and make it more permanent.
5.6.7 Summary of the Model Variants
In Figure 5.8, the eects on the reprogramming eciency of the dierent analyzed model variants are shown. Across all variants except for the one without methylation, the reprogramming eciency generally augments with time although after 2000 time steps it is smaller in nearly every variant than in the main model. The strength of the decrease, however, is very dierent from variant to variant. As an explanation, it should be noted that all model variants correspond to a more or less strong de-regulation of the main model.
More specically, the epigenetic processes that are tightly regulated in the original model, are rendered more prone to stochasticity which results in the expression of important genes being de-regulated as well. This phenomenon is accompanied with a strong increase of the number of potentially reach-able states during the transition. While in the main model a total of 2592 states were reached after 500 time steps in the reprogramming process, in the spontaneous methylation model for example the number increased ap-proximately 4-fold to 10240 states. At the same time the reprogramming eciency is approximately 10 times lower. It is noteworthy that the 366 pluripotency related states that are reached are the same in both models only diering by their probability after 500 time steps.