Efficient co-programming of intercellular mechanics and signaling for complex developmental patterns

Intercellular ligand-receptor signaling is fundamental for producing diverse cell types and complex developmental patterns, yet design strategies — particularly regarding spatial structure, timing, cell lineage, and molecular resources — remain unclear. With public literature and data, we outline the cell-cell contact maps and signaling during embryogenesis in nematode Caenorhabditis elegans. We devise a multi-phase field model incorporating crosstalk and memory to simulate how neighboring cells interact through mechanics and signaling, driving complex developmental patterns with diverse cell types. Our model reproduces the 1- to 12-cell-stage spatial structures and demonstrates the C. elegans program's efficiency in enhancing pattern complexity. While signaling-regulated cell division directions ensure fidelity of spatial structures and signaling, resultant patterns prove robust against variations in cell division timing and noise in cell movement and adhesion. Finally, we develop an optimization algorithm to automatically design signaling programs on top of mechanical architectures, exemplified by C. elegans embryos and synthetic synNotch spheroids.