Mechanobiological Induction of Long-Range Contractility and Size Scaling in Cell Assemblies

Pattern formation in developing embryos is stimulated in part by spatial gradients of “morphogens” -- locally secreted, diffusing chemical signals that trigger cellular development. Such patterns can develop proportionately in embryos of different sizes if the morphogen concentration profile scales with the embryo size as has indeed been observed to happen in some cases. Biochemical explanations for such scaling include the coupled diffusion of several species whose reaction can influence degradation of the morphogen, but the possible role of mechanics in morphogen diffusion, possibly leading to such a size scaling, has not been extensively explored. Inspired by this fundamental problem in developmental biology, we present a generic theoretical model that couples the diffusion and degradation of biomolecules to cytoskeletal elastic forces which are, by their very nature, long-ranged and boundary dependent. The theory shows that such a coupling of these biochemical “mechanogens” which induce cellular contractility and the mechanics of the cells can lead to scaling of the mechanogen concentration with the size of the cellular assembly in a manner that is robust and does not depend on the details of the interactions. We suggest model experiments on cell assemblies in vitro on substrates that can test the theory and elucidate the role of mechanics in morphogen diffusion.