Germ-band extension in Drosophila embryos as a learning process

During Drosophila development, tissues undergo significant morphological transformations. A key process is germ-band extension, where tissues elongate and narrow to drive large-scale movements, facilitated by the tissue’s ability to tune cell-scale properties through signaling pathways. Previous experimental work has quantified changes in tensions on cell-cell interfaces during germ-band extension. Our goal is to use the framework of physical learning to test hypotheses for how tension changes are coordinated, and characterize their effectiveness in achieving a global morphological task. We extend the well-vetted vertex model for epithelial tissues to include edge tensions as “adaptive” degrees of freedom (DOF), and identify a global cost function as the difference between the current tissue aspect ratio and the desired elongated aspect ratio. We compute tension changes that optimize the global gradient of this cost function, which requires information about all the edges. We compare this result to local rules that only require information about neighbors, rules that have been proposed as fits to experimental data, and external shear forces. We find that a specific local rule, based on edge length and orientation, successfully captures observed average cell shape and edge alignment, while external shear and global gradient descent methods do not. We also examine task efficiency and robustness. This learning framework provides valuable insights into distinguishing potential mechanisms driving tissue flow during germ-band extension.