A stochastic model of epigenetic dynamics in somatic cell reprogramming

Abstract

Somatic cell reprogramming has dramatically changed stem cell research in recent years. The high pace of new findings in the field and an ever increasing amount of data from new high throughput techniques make it challenging to isolate core principles of the process. In order to analyze such mechanisms, we developed an abstract mechanistic model of a subset of the known regulatory processes during cell differentiation and production of induced pluripotent stem cells. This probabilistic Boolean network describes the interplay between gene expression, chromatin modifications, and DNA methylation. The model incorporates recent findings in epigenetics and partially reproduces experimentally observed reprogramming efficiencies and changes in methylation and chromatin remodeling. It enables us to investigate, how the temporal progression of the process is regulated. It also explicitly includes the transduction of factors using viral vectors and their silencing in reprogrammed cells, since this is still a standard procedure in somatic cell reprogramming. Based on the model we calculate an epigenetic landscape for probabilities of cell states. Simulation results show good reproduction of experimental observations during reprogramming, despite the simple structure of the model. An extensive analysis and introduced variations hint toward possible optimizations of the process that could push the technique closer to clinical applications. Faster changes in DNA methylation increase the speed of reprogramming at the expense of efficiency, while accelerated chromatin modifications moderately improve efficiency.

Keywords: differentiation and reprogramming; epigenetic landscape; induced pluripotent stem cells; mathematical modeling; probabilistic Boolean network.

Figure 1

General model structure. Transcriptional regulators that account for the activation of a certain cell state are combined into a module. We have four modules in the complete model: Two different differentiation modules A and B, the Pluripotency Module P for the main pluripotency network, and the exogenous reprogramming genes E. Each module is governed by the activity of the other modules as well as its epigenetic states.

Figure 2

The epigenetic landscape. The x-axis shows all possible states of the model, sorted by similarity ${\Sigma }_i^{123}$ (Section 2.4) to the distinguished states, i.e., differentiated state A, differentiated state B, or pluripotent state P. The y-axis corresponds to simulation time steps, and the z-axis to state probabilities. (A) Reprogramming starting from one clearly defined state where A is active and the reprogramming factors are present. (B) Differentiation by the activation of module A through a weak signal.

Figure 3

State space of the combined model of reprogramming. Time evolution of the model starting with an active differentiation network and active reprogramming genes. The Figure only shows the states that are reached with a probability of p ≥ 10⁻⁴. The model has 2073 possible state transitions between these 149 states. Different phases can clearly be separated in the reprogramming process. In the beginning (yellow area) the epigenetic factors of the different modules are modified, but there is no change in gene expression yet. The second phase (dark yellow) represents the down-regulation of the differentiation module followed by the activation of the pluripotency module (blue area). The last step consists of the silencing of exogenous factors, that produces stable iPS cells (red area). There are some states that can lead to non-viable cells, in which no regulators are expressed at all (gray area). The bold blue arrows represent the shortest path to the main pluripotent state.

Figure 4

A schematic representation of the processes described by our model. (A) Shows the connection between DNA methylation, histone modifications and the pluripotency master regulators. Pluripotency transcription factors activate their own expression and can be suppressed by factors regulating differentiation. The pluripotency factors themselves increase the expression of DNMT3 which enables de novo methylation of DNA preferably in combination with repressive histone modifications such as methylation or deacetylation (right nucleosome). On the other hand activation of pluripotency genes also leads to a higher cell division rate, a suppression of methylation maintenance and probably active demethylation, which also increases the chances of euchromatin formation. (B) Without external influences (e.g., retroviral genes or signaling molecules), the structure of our model consists of three gene modules (P, A, B) inhibiting each other and each governed by their specific epigenetic states. The pluripotency (P) module regulates the activation of methylation and demethylation.

Figure 5

Dynamics (A) and state space (B) of the pluripotency module during overexpression of differentiation factors. The network quickly leaves the pluripotent state and passes across a number of transient states into two different attractors. The node in blue (lower right) is a point attractor in the completely differentiated state and the nodes in brown are part of a cyclic attractor consisting of the unmethylated state in either a euchromatin or heterochromatin structure.

Figure 6

Dynamics and state space of single modules of differentiation regulators. (A) Time course of a differentiation module with the constant activation of the pluripotency genes included. Methylation and demethylation are activated, the module’s genes are silenced and the model reaches an equilibrium in a hyperdynamic state switching between open and closed chromatin and varying DNA methylation. (B) Overexpression of another differentiation module leads to silencing of the gene, but does not enable methylation changes.

Figure 7

Epigenetic landscapes of start distributions (64 states). (A) Distribution around the differentiated state B without reprogramming factors. The start states converge into just a few remaining states. The differentiated states and the non-expressing states being the highest. (B) A distribution around the pluripotent state. (C) A simulation starting from a distribution around the differentiated state B with active reprogramming factors.

Figure 8

Reprogramming efficiencies of the model variants. Efficiency is plotted as the sum of probabilities of all states that are closely connected to pluripotency.