A dynamic model for Waddington’s landscape accounting for cell-to-cell communication

Abstract

Waddington’s landscape provides a conceptual model for developmental processes. It is the basis of various mathematical models describing cell maturation and development at cell and population levels. Yet, these mathematical models mostly disregard cell-to-cell communication, an essential process that modulates cellular decision-making and population dynamics.

In this study, we provide a dynamical model for cell maturation and development which can be seen as an extension of Waddington’s landscape. The coupled system of partial and ordinary differential equations describes cell density along the cell state together with ligand concentrations. Cell-state-dependent ligand production determines ligand availability, which controls population-level processes. We provide proof of the existence and uniqueness of solutions for our coupled differential equation system and demonstrate the model’s validity by analyzing single-cell transcriptomics data. Our results show that cell-to-cell communication is essential for accurately depicting biological recovery processes, such as the regeneration of stem cells in the intestine’s crypt and the response of immune cells upon LSP stimulation.

Our findings underscore the importance of incorporating cell-to-cell communication into mathematical models of biological development. By doing so, we unlock the potential for deeper insights into complex processes such as tissue regeneration and immune responses, offering new avenues for understanding and predicting the dynamics of biological recovery and cell activation.