Waddington landscape and pathways for stem cell differentiation, reprograming and transdifferentiation

Waddington landscape in biology gives a qualitative picture for understanding differentiation and development. However, the original Waddington landscape picture lacks physical foundations and quantifications. We developed a nonequilibrium landscape and flux theory for quantifying the Waddington landscape for differentiation, reprogramming and transdifferentiation. We found that the landscape for differentiation and development emerges from the underlying gene regulatory interactions with distinct stem cell and differentiated cell state attractors. Furthermore, the pathways for differentiation, reprogramming, and transdifferentiation among the stem cell and differentiation cell state attractors can be quantified. In addition, the kinetic speed of differentiation, reprogramming, and transdifferentiation can be quantified and associated with the landscape topography. We also show that the dynamics of the differentiation, reprogramming, and transdifferentiation processes are determined by both the landscape gradient and the rotational flux. We show that the flux can influence significantly the pathways and the kinetics of these processes. Importantly, flux may also provide a nonequilibrium driving force for the formation of different cell state attractors as the new active matter phases. We apply the landscape and flux theory to several biological differentiation processes including human stem cell development. We also identified the key genes and regulations for the differentiation and reprogramming based on the landscape topography and pathways. The relationship between development and cancer is also explored with the emergence of cancer stem cell state attractor. This study may provide useful clues for the practice of tissue engineering and cancer treatment.