Mechanical Instabilities in Growing Biological Systems: Wrinkling and Branching

Morphological shape transformations in biological systems often arise from patterned biochemical processes, which can produce mechanical forces either directly via molecular motors or indirectly via differential growth of connected tissues. The growth mismatch produces internal stresses, which can be released via shape transformations and mechanical instabilities. In this talk I will focus on mechanical instabilities that cause the wrinkling of Vibrio cholerae bacterial biofilms and branching in developing lungs. Biofilms grown on agar substrates form wrinkled patterns, which are radial in the outer region and zig-zag herringbone in the inner region. We demonstrate that the wavelength of wrinkles as well as their spatiotemporal pattern can be predicted by a chemo-mechanical model that takes into account the diffusion of nutrients and their uptake by bacteria, growth of the biofilm, mechanical deformation of the biofilm and the agar substrate, and the friction between them. In the second part I will discuss the branching morphogenesis of lungs. We investigate how patterned differential growth between the inner epithelium and the outer mesenchyme tissue as well as the spatial pattern of smooth muscles lead to formation of new branches and their subsequent development. Experiments and mathematical model suggest that the patterned formation of stiff smooth muscles is very important for the proper development of new branches. In the absence of smooth muscles, the wrinkling instability of growing epithelium on the soft mesenchyme produces several ectopic branches. However, when stiff smooth muscles are formed, they suppress the wrinkling instability and new branches are formed only between the gaps of smooth muscles.