Engineering emergent morphogenetic properties of cell clusters with differentiable programming

Living systems have a remarkable ability to self-organize into increasingly complex structures. Due to the sheer complexity of coordinating this over large numbers of cells via local inputs, it has been challenging to learn how individual cellular decisions can orchestrate emergent behavior. In this work, we use differentiable programming to optimize over physical models of cells, learning local decision functions to drive collective behavior. In our model, cells can interact through morphogen diffusion, adhesive interactions, and mechanical stress and make internal decisions based on local inputs. These cellular decisions, such as whether to divide or not, are parametrized by neural networks and learned via gradient-based optimization. We apply this framework to learn how to program clusters of cells to (i) grow homogeneously in the presence of a growth factor, (ii) grow into elongated and v-shaped structures, and (iii) maintain chemical homeostasis between cell types. The learned decision functions exhibit characteristics not specifically trained for and are robust to perturbations. Our work opens new avenues for learning how to engineer synthetic systems such as organoids, as well as for inferring mechanisms from experimental observations.