Long-range elastic interactions, stem-cell differentiation and development

Materials science has long been aware of the effective interactions between inclusions that are mediated by the deformations they induce in the surrounding, elastic medium.  These are long-ranged, depend on the shape of the system and can lead to phase transitions in which the inclusions attract to form macroscopic clusters.  Over the last 20 years, the new and interdisciplinary field of mechanobiology has borrowed concepts from materials physics to understand the role of mechanics in cell shape, adhesion, assembly and more recently, differentiation and development.  In contrast to passive inclusions, contractile cells are “active inclusions” in which myosin molecular motors consume energy to deform the cell, and hence the surrounding medium.  These deformations lead to active elastic interactions that can cause ordering in an intracellular or intercellular manner.  Recently, it has been shown that such mechanical properties affect not only cell structure and assembly, but also genetic expression. This talk will briefly review several examples of changes in cell function induced by mechanical and elastic perturbations. I will then present a theoretical model of how substrate rigidity modifies the elastic interactions of myosin motors, leading to their collective orientation.  This is compared with experiments on stem cells by the Discher group at the University of Pennsylvania and suggests an early-time cue for their differentiation into muscle cells.  In addition, I will discuss theoretically the coupled diffusion of a morphogen (a molecule that regulates development) and cell contractility.  The theory leads to suggestions of mechanobiology experiments to measure coupled diffusion and mechanics that may be important in development.