Reconstructing Waddington Landscape from Cell Migration and Proliferation

Abstract

The Waddington landscape was initially proposed to depict cell differentiation, and has been extended to explain phenomena such as reprogramming. The landscape serves as a concrete representation of cellular differentiation potential, yet the precise representation of this potential remains an unsolved problem, posing significant challenges to reconstructing the Waddington landscape. The characterization of cellular differentiation potential relies on transcriptomic signatures of known markers typically. Numerous computational models based on various energy indicators, such as Shannon entropy, have been proposed. While these models can effectively characterize cellular differentiation potential, most of them lack corresponding dynamical interpretations, which are crucial for enhancing our understanding of cell fate transitions. Therefore, from the perspective of cell migration and proliferation, a feasible framework was developed for calculating the dynamically interpretable energy indicator to reconstruct Waddington landscape based on sparse autoencoders and the reaction diffusion advection equation. Within this framework, typical cellular developmental processes, such as hematopoiesis and reprogramming processes, were dynamically simulated and their corresponding Waddington landscapes were reconstructed. Furthermore, dynamic simulation and reconstruction were also conducted for special developmental processes, such as embryogenesis and Epithelial-Mesenchymal Transition process. Ultimately, these diverse cell fate transitions were amalgamated into a unified Waddington landscape.

Keywords: Cell migration and proliferation; Energy indicator; Reaction diffusion advection equation; Sparse autoencoder; Waddington landscape.