Fig. 1. Cell-fate changes through the lens of the complex dynamics of molecular networks.
a Cell-fate changes in the epigenetic landscape. Waddington’s landscape is widely recognized as a conceptual framework to comprehend the transitions of pluripotent cellular states toward specific valleys that represent distinct cell fates. In the landscape metaphor, these cell fates are separated by an epigenetic barrier that restricts transitions, yet the perturbation of a specific master regulator can overcome this barrier to induce a dramatic transition between cell fates (top). Each cell fate can be regarded as the most stable state (also referred to an attractor) within the attractor landscape, which represents their transition trajectories (middle). Since each cell fate is characterized by the gene activities of the underlying molecular regulatory network, altering these complex molecular interactions by regulating a specific master regulator can reshape the attractor landscape, causing it to converge into a specific cell fate (bottom). b A mathematical model to unravel the hidden molecular regulation logic of cellular systems. A mathematical model can describe the dynamics of cellular systems in terms of gene regulatory interactions. The model can formalize cellular phenotypes such as proliferation, cell cycle arrest, and apoptosis, by assembling molecular components into the network. For example, a logical dynamic model is composed of n genes, whose state at time t, defined by , corresponds to a point in a n-dimensional gene expression state space represented by the attractor landscape. The state of each molecule is influenced by its dynamic regulations, where the future state of each molecule can be determined by a logical equation (e.g., AND gate) of its upstream molecules. A cellular state evolves through the logical equations of all molecules in the network, eventually converging on a specific attractor at time t = M.