Evolution of robust cell differentiation under epigenetic feedback

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.