Active T1 Transitions in Dynamic Tissues

A fundamental question in Biology is to understand the collective organisation of many cells during morphogenesis. Morphogenesis often results from the dynamic remodeling of tissues, which involves cell rearrangements, cell divisions and cell flows. Tissues are amorphous solids, where neighbour exchanges can relax local stresses and allow the material to flow. Such neighbor exchanges are associated with T1 transitions of the polygonal network that describes cell shapes. We use a vertex model for tissue mechanics and dynamics to study T1 rearrangements in anisotropic cellular networks. We consider two different physical realizations of the active anisotropic stresses: (i) anisotropic cell bond tension and (ii) anisotropic cell body stress. Interestingly, the two types of active stress lead to patterns of oriented T1 transitions that are different. We describe and explain these findings using cell based arguments and through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the tissue and express the energy balance in terms of tissue elastic energy, mechanical work, chemical work dur to active processes and heat. This allows us to define active T1 transitions that can perform mechanical work while consuming chemical energy. We apply these concepts to fly morphogenesis: the developing pupal wing and germ band extension in the embryo and show that in these systems different types of active T1 processes are at work.