Hierarchically Coupled Biochemical Switches for Stem Cell Differentiation

In multicellular organisms, the development of diverse cell types relies on stem cell differentiation through a hierarchy of fate decisions. Pluripotent stem cells first give rise to multipotent progenitors, which then undergo successive fate decisions to generate specialized cells within their respective lineages. Waddington used the metaphor of a marble rolling down a hill through hierarchically branching valleys that represent the various states of cell differentiation, with the final valleys at the bottom symbolizing the specialized cells. Mathematically, specialized cells are seen as stable attractors in a complex dynamical system that displays multistability. However, this framework does not necessarily describe the hierarchical branching of stem cell differentiation. In a recent study, we addressed this issue by assuming that each gene regulatory network (GRN) consists of hierarchically coupled gene subnetworks (modules) that are self-regulated due to epigenetic factors. Each module was modeled using the normal form of relevant bifurcations. Overall, this approach captures both multistability and hierarchical branching in differentiation. Here, the normal forms of bifurcations are replaced by realistic biochemical switches. Theoretical analysis and numerical simulations demonstrated that hierarchically coupled biochemical switches can depict the three fundamental aspects of Waddington’s epigenetic landscape: (a) differentiation trajectories exhibit hierarchical branching, (b) attractors are robust to perturbations (homeorhesis), and (c) the proportions of specialized cells are preserved. It was further shown that appropriate external interventions can induce either probabilistic cellular reprogramming or highly predictable reprogramming outcomes. The incorporation of biochemical switches, rather than purely abstract normal forms, can contribute to more biologically grounded mathematical models of stem cell differentiation. This work also highlights the importance of normal forms for qualitatively understanding cell state dynamics and for building realistic modular GRNs.