Evolution of robust cell differentiation under epigenetic feedback

TL;DR

This work investigates how robust multicellular differentiation emerges from the coupled dynamics of fast gene expression and slow epigenetic feedback within evolving gene-regulatory networks. By simulating a stochastic, slow–fast GRN model and evolving networks to maximize the number of distinct cell fates across lineages, the authors identify three canonical differentiation modes: Type A (chaotic oscillations that self-organize into fixed points via epigenetic fixation), Type B (channelled annealing with noise-driven fixed-point migration along low-dimensional channels), and Type C (rapid quenching through saddle-node/SNIC bifurcations). Types A and B reproduce a Waddington-like developmental landscape with robust differentiation under perturbations, while Type C is more sensitive to initial conditions and perturbations. The study connects dynamical-systems concepts with evolutionary processes, provides a framework for interpreting experimental gene-expression variance during differentiation, and suggests extensions to spatial patterning and morphogen-guided canalization in development.

Abstract

In multi-cellular organisms, cells differentiate into multiple types as they divide. States of these cell types, as well as their numbers, are known to be robust to external perturbations; as conceptualized by Waddington's epigenetic landscape where cells embed themselves in valleys corresponding to final cell types. How is such robustness achieved by developmental dynamics and evolution? To address this question, we consider a model of cells with gene expression dynamics and epigenetic feedback, governed by a gene regulation network. By evolving the network to achieve more cell types, we identified three major differentiation processes exhibiting different properties regarding their variance, attractors, stability, and robustness. The first of these, type A, exhibits chaos and long-lived oscillatory dynamics that slowly transition until reaching a steady state. The second, type B, follows a channeled annealing process where the epigenetic changes in combination with noise shift the cells towards varying final cell states that increase the stability. Lastly, type C exhibits a quenching process where cell fate is quickly decided by falling into pre-existing fixed points while cell trajectories are separated through periodic attractors or saddle points. We find types A and B to correspond well with Waddington's landscape while being robust. Finally, the dynamics of type B demonstrate a differentiation process that uses a directed shifting of fixed points, visualized through the dimensional reduction of gene-expression states. Correspondence with the experimental data of gene expression variance through differentiation is also discussed.

Figures (22)

• Figure 1: Schematic representation of a simplified network with M=4. All genes ($x_i$) have a positive feedback cycle with their epigenetic factor ($\theta_i$). Gene interactions are not symmetric and can promote (red) and suppress (blue) all genes, including themselves.
• Figure 2: The fitness, i.e. the distinct cell types (y-axis) plotted as a function of generation (x-axis). The black line shows the best-performing network, while the red with the blue ribbon shows the mean and standard deviation in scores. The fitness increases stepwise. It stays stable for 50-350 generations until mutation around generation 350 connects one of the target genes such that it is now able to differentiate into about twice as many types.
• Figure 3: Orbits in PC space at various stages of differentiation for a given evolved network. The color indicates the different final cell types. PCs are obtained from $x_i$'s for the developmental time $T=1$ to 2500. Orbits of $x_i(t)$'s are plotted by three PCs for the displayed ranges of developmental time. These time ranges represent the different developmental stages. This specific example finishes type A differentiation much faster ($T\approx400$) when compared to other type A processes ($T\approx1000$) but is chosen for its clearer visualization. The initial shared periodic attractors diverge and they eventually reach fixed point states. We verified these were fixed points in the 40-dimensional phase space of gene expression levels as confirmed by their time-series.
• Figure 4: The time course of the first principal component throughout differentiation for a type A network. Initial dispersion ($T\approx 10^{1.3}$) is followed by cells sharing and jumping between subcycles ($t=10^{1.5}-10^{2.5}$) to eventual fixation once these cycles have died out ($T=10^{3}$). The simulation continues until $T\approx 10^{4.3}=20000$ but no longer shows any changes. The color indicates the different final cell types.
• Figure 5: Attractors for the genes $x_i$ are displayed in PC space for fixed $\theta_i$ at the given times. The color indicates the different final cell types as defined by the target genes. By setting $\theta_i$ as a constant, we can analyze the full orbit of $x_i$ and distinguish these dynamics from the change in $\theta_i$ during development. Trajectories are generated by assigning each cell the gene expression levels $x_i$ and epigenetic factors $\theta_i$ exhibited by a cell at the given times as it goes through a differentiation simulation. (This plot shows a different example from Fig. \ref{['fig:A_Orbits']} and \ref{['fig:A_PCInTime']})