The mammalian pancreas is a branched organ that does not exhibit stereotypic branching patterns, similarly to most other glands. Inside branches, it contains a network of ducts that undergo a transition from unconnected microlumen to a mesh of interconnected ducts and finally to a treelike structure. This ductal remodeling is poorly understood, both on a microscopic and macroscopic level. In this article, we quantify the network properties at different developmental stages. We find that the pancreatic network exhibits stereotypic traits at each stage and that the network properties change with time toward the most economical and optimized delivery of exocrine products into the duodenum. Using in silico modeling, we show how steps of pancreatic network development can be deconstructed into two simple rules likely to be conserved for many other glands. The early stage of the network is explained by noisy, redundant duct connection as new microlumens form. The later transition is attributed to pruning of the network based on the flux of fluid running through the pancreatic network into the duodenum.

Organoids representing a diversity of tissues have recently been created, bridging the gap between cell culture and experiments performed in vivo. Being small and amenable to continuous monitoring, they offer the opportunity to scrutinize the dynamics of organ development, including the exciting prospect of observing aspects of human embryo development live. From a physicist's perspective, their ability to self-organize -to differentiate and organize cells in space -calls for the identification of the simple rules that underlie this capacity. Organoids provide tractable conditions to investigate the effects of the growth environment, including its molecular composition and mechanical properties, along with the initial conditions such as cell number and type(s). From a theoretical standpoint, different types of in silico modeling can complement the measurements performed in organoids to understand the role of chemical diffusion, contact signaling, differential cell adhesion and mechanical controls. Here, we discuss what it means to take a biophysical approach to understanding organogenesis in vitro and how we might expect such approaches to develop in the future.

Many organs such as the vasculature, kidney, lungs, pancreas and several other glands form ramified networks of tubes that either maximize exchange surfaces between two compartments or minimize the volume of an organ dedicated to the production and local delivery of a cell-derived product. The structure of these tubular networks can be stereotyped, as in the lungs, or stochastic with large variations between individuals, as in the pancreas. The principles driving stereotyped branching have attracted much attention and several models have been proposed and refined. Here we focus on the pancreas, as a model of non-stereotyped branching. In many ramified tubular organs, an important role of the mesenchyme as a source of branching signals has been proposed, including in the pancreas. However, our previous work has shown that in the absence of mesenchyme, epithelial cells seeded in vitro in Matrigel form heavily branched organoids. Here we experimentally show that pancreatic organoids grow primarily at the tips. Furthermore, in contrast to classical 'depletion of activator' mechanisms, organoids growing in close vicinity seem not to affect each other's growth before they get in contact. We recapitulate these observations in an in silico model of branching assuming a 'local inhibitor' is secreted by the epithelium. Remarkably this simple mechanism is sufficient to generate branched organoids similar to those observed in vitro, including their transition from filled spheres to a tree like structure. Quantifying the similarity between in silico and in vitro development through a normalized surface to volume ratio, our in silico model predicts that inhibition is likely to be cooperative and that the diffusing inhibitor decays within a length scale of 10-20 μm.