Physics-Informed Deep Learning for Characterizing Perturbed Cell Growth

The morphodynamical analysis of cells can be a powerful and cost-effective way of understanding the phenotypic effects of perturbations, but current techniques often only work for stationary cell morphology. Here, we introduce a novel framework that extends behavior analysis to nonstationary morphodynamics during early stage growth of the soybean rust pathogen, P. pachyrhizi. At its core, our approach learns the 2-dimensional feature space of cell shape using variational autoencoders from deep learning, and subsequently models how populations of cells develop over this space using two simple differential equations, each capturing complementary aspects of the dynamics, and with parameters depending on the perturbations. We compared two models: a Fokker-Planck model to describe the diffusive development on a Waddington-type energy landscape, providing a global perspective on the dynamics; and a cell-mechanical model describing local growth as a persistent random walk. Informative perturbation-dependent parameters are found by fitting simulations to the shape space embeddings, representing a powerful tool for linking machine-learning and biophysical modelling.