Landscape reveals critical network structures for sharpening gene expression boundaries

Chunhe Li, Lei Zhang, Qing Nie

Spatial pattern formation is a critical issue in developmental biology. Gene expression boundary sharpening has been observed from both experiments and modeling simulations. However, the mechanism to determine the sharpness of the boundary is not fully elucidated. We investigated the boundary sharpening resulted by three biological motifs, interacting with morphogens, and uncovered their probabilistic landscapes. The landscape view, along with calculated average switching time between attractors, provides a natural explanation for the boundary sharpening behavior relying on the noise induced gene state switchings. To possess boundary sharpening potential, a gene network needs to generate an asymmetric bistable state, i.e. one of the two stable states is less stable than the other. We found that the mutual repressed self-activation model displays more robust boundary sharpening ability against parameter perturbation, compared to the mutual repression or the self-activation model. This is supported by the results of switching time calculated from the landscape, which indicate that the mutual repressed self-activation model has shortest switching time, among three models. Additionally, introducing cross gradients of morphogens provides a more stable mechanism for the boundary sharpening of gene expression, due to a two-way switching mechanism. Our results reveal the underlying principle for the gene expression boundary sharpening, and pave the way for the mechanistic understanding of cell fate decisions in the pattern formation processes of development.