The developmental process implies precise but significant changes in the geometry and structure of the embryonic tissues. Recent results show that apparently minor changes in adhesion at the local level of cell-cell contacts trigger deep, non-linear transitions in the topological organization of the whole embryonic tissue and, in consequence, change its material properties and facilitate geometrical deformations. Open questions remain, like the potential existence of causal feedbacks between cell differentiation processes and the potential heterogeneity of topological patterns existing within the tissue. The results presented in this talk are based on the fundamental assumption that predictive frameworks in theoretical biology must explore the connection between different scales of the system. In this particular case, we use topology to establish a bridge between the system’s scales defined by i) the cell level and ii) the tissue level. This enables us to predict global, non-trivial behaviours in tissues from the empirically feasible observables related to the mechanical properties of single cells.

During development, biological systems exhibit large-scale flows coupled to patterning processes, allowing for their self-organisation. In this talk I will discuss two examples of such couplings. I will use an active matter hydrodynamic description of surface flows to explore the dynamics of spontaneous three-dimensional rotation of cell doublets, and how the shape of the cell-cell interface of these doublets can be understood from the Curie principle. I will then discuss the relative role of cellular flows and dynamics of cell fate change in the formation of the vein pattern in Drosophila pupal wings. I will propose a minimal biophysical description of the process of vein refinement to a precise width.

Molecular binding is central to cellular regulation, from ligands that bind to receptors, to transcription factors that bind DNA. In this talk I will discuss recent theoretical work on the functional capabilities of binding-based regulatory systems, motivated by the transcriptional control of the model Drosophila gene hunchback by Bicoid. On the one hand, I will discuss the capabilities of allosteric conformational ensembles to integrate information through binding cooperativity. On the other, I will describe a fundamental limit to the generation of sharp sigmoidal responses in the absence of energy expenditure. These findings reveal general regulatory principles in transcription and beyond.