Quantifying cell transitions in C. elegans with data-fitted landscape models

Increasing interest has emerged in new mathematical approaches that simplify the study of complex differentiation processes by formalizing Waddingtons landscape metaphor. However, a rational method to build these landscape models remains an open problem. Building on pioneering work by Corson and Siggia (2012, 2017) we study vulval development in C. elegans by developing a framework based on Catastrophe Theory (CT) and approximate Bayesian computation (ABC) to build data-fitted landscape models. We first identify the candidate qualitative landscapes, and then use CT to build the simplest model consistent with the data, which we quantitatively fit using ABC. The resulting model suggests that the underlying mechanism is a quantifiable two-step decision controlled by EGF and Notch-Delta signals, where a non-vulval/vulval decision is followed by a bistable transition to the two vulval states. This new model fits a broad set of data and makes several novel predictions.