Pattern Formation in Biological Systems via Mechanical Instabilities and Phase Separation

Pattern formation is ubiquitous in biological systems. While pattern formations are often associated with Turing-like reaction-diffusion systems, biology also exploits many other mechanisms such as mechanical instabilities and phase separation. In this talk, I will discuss how mechanical instabilities cause the wrinkling of bacterial biofilms and branching in developing lungs, and how phase separation is exploited to achieve the target morphology of intracellular condensates. Bacterial biofilms grown on substrates form wrinkled patterns that can be manipulated by modifying the substrate stiffness. We showed that the wavelength of wrinkles is consistent with the mechanical stability of compressed films on soft substrates. Furthermore, we demonstrated that the spatiotemporal pattern of wrinkles can be predicted by a continuum chemo-mechanical model that incorporates diffusion of nutrients and their uptake by bacteria, growth of the biofilm, surface friction, and the ensuing mechanical stresses and deformations of the biofilm. In the second part, I will discuss the branching morphogenesis of lungs. By combining experiments and modeling we showed that the patterned formation of stiff smooth muscles and their contractions physically sculpt new branches of growing epithelium. I will also comment on how we are going to use these insights to design an optogenetic system to engineer artificial lung organoids. In the last part, I will discuss, how interfacial energies between separated phases in multicomponent liquid mixtures regulate the morphology of intracellular condensates. We developed a graph theory approach to predict the morphology of coexisting phases from a given set of interfacial energies (forward problem), enumerate all topologically distinct morphologies, and reverse engineer conditions for interfacial energies that produce the target morphology (inverse problem).