A landscape model for cell fate decisions during mesoendoderm differentiation in C. elegans based on Wnt dynamics

Geometric models allow us to quantify topography of the Waddington landscape and gain quantitative insights of gene interaction in cell fate differentiation. Often mutant phenotypes show partial penetrance and there is a dearth of quantitative models that can exploit this data and make predictions about new allelic combinations with no additional parameters. C. elegans with its invariant cell lineages has been a key model system for discovering the genes controlling development. Here we focus on the differentiation of the endoderm founder cell named E from its mother, the EMS cell. Mutants that convert E to its sister MS fate have figured prominently in deciphering the Wnt pathway in worm. We construct a bi-valued Waddington landscape model that predicts the effect on POP-1/TCF and SYS-1/beta-catenin levels based on the penetrance of mutant alleles and RNAi, and relates the levels to fate choice decisions. A subset of the available data is used to fit the model and remaining data is then correctly predicted. Simple kinetic arguments show that contrary to current belief the ratio of these two proteins alone is not indicative of fate outcomes. Furthermore, double mutants within a background reduction of POP-1 levels are predicted with no adjustable parameters and their relative penetrance can differ from the same mutants with the wild-type POP-1 level, which calls for further experimental investigations. Our model refines the content of existing gene networks and invites extensions to other manifestations of the Wnt pathway in worm.