Applying Waddington Landscape To Model Cellular Development

The development process of metazoan was once regarded as an irreversible process. This perspective was largely reshaped due to the emergence of iPSCs and cellular fate conversion between different cell types, which meanwhile calls for novel mechanistic understandings of development and reprogramming. Although a bunch of mathematical models based on Boolean network and ordinary equations provide some general mechanistic explanations, the theoretical modeling over reprogramming experiments remains scanty. On the other hand, the emergences of reprogramming lead to a renaissance of the development landscape proposed by embryologist Waddington50th of last century. Though it is merely a metaphor, the developmental landscape vividly describes the autonomous hierarchical bifurcation of cellular differentiation and implies the possibility of conversions between different cell types. Therefore, recently it is used extensively as a universal framework to explain both of the development and reprogramming. Inspired by the landscape idea, there emerges a few pioneering theoretical researches for development landscape. Previous work on landscape construction merely assumes a systematical change of a parameter to represent the development process, but does not demonstrate its validity. In addition to this, it also deals with one step development. This paper extends recent theoretical modeling of cell development, and most of all, the studies on two-gene landscape initiated by previous works. Based on Boolean network (BN), stochastic differential equations (SDEs) and developmental landscape, these three layers of modeling systematically explain the development of central nervous system development and provide insights about the optimal reprogramming strategies. In contrary to previous works, we unify the BN and SDEs studies. For the development landscape, we find that some parameters change can be related to a development process if the associated entropy production rate increases monotonically. We further construct the two-step landscape for central nervous system development. Specially, this paper demonstrates that the cellular transdifferentiation can be accomplished directly under certain conditions without passing the medial stage of stem cells. Moreover, this paper predicts that the conversion between astrocyte or oligodendrocyte and neuron cells is influenced by the genes of reprogramming induction and the order for which the genes applied. These conclusions are supported partially by recent reprogramming practices and will guide future reprogramming experiments designs.