Generative models of morphogenesis in developmental biology

Understanding the mechanism by which cells coordinate their differentiation and migration is critical to our understanding of many fundamental processes such as wound healing, disease progression, and developmental biology. Mathematical models have been an essential tool for testing and developing our understanding, such as models of cells as soft spherical particles, reaction-diffusion systems that couple cell movement to environmental factors, and multi-scale multi-physics simulations that combine bottom-up rule-based models with continuum laws. However, mathematical models can often be loosely related to data or have so many parameters that model behaviour is weakly constrained. Recent methods in machine learning introduce new means by which models can be derived and deployed. In this review, we discuss examples of mathematical models of aspects of devel-opmental biology, such as cell migration, and how these models can be combined with these recent machine learning methods.

Automated summary

Understanding the mechanisms of cell coordination in differentiation and migration is crucial for comprehending wound healing, disease progression, and developmental biology. Mathematical models have played an essential role in testing and improving our understanding, including the models of cells as soft spherical particles, reaction-diffusion systems linking cell movement to environmental factors, and multi-scale multi-physics simulations combining rule-based models with continuum laws. However, mathematical models often lack strong data relation or have excessive parameters, leading to weakly constrained model behavior. Recent advancements in machine learning provide new approaches for model derivation and deployment. This review explores examples of mathematical models in developmental biology, such as cell migration, and how these models can be integrated with recent machine learning methods.