Applied Physics | Inflationary embryology: Growth and size in living matter

One of the enduring mysteries of biology is how cells and organs know to stop growing at the correct size (and how those sizes are coordinated so that animals can retain their correct proportions). Here, I will discuss several studies that, in different ways, address the physics of how size is set and how precisely it can be controlled. First, I will introduce a simple phenomenological framework that allows one to consider tradeoffs between noise in the actual growth process and in a system's internal measurement of its own size. I will show how this framework places a bound on the size precision of individual bacterial cells and analyze data from recent experiments to show that, at least in some circumstances, the measured precision is very near this bound. Then, I will extend the framework to consider how sizes can be coordinated by chemical signals, for example between organs like the left and right wings of a fruit fly, and show that theory severely limits how well this can be done. Finally, I will study the noisy dynamics of growth of multi-cellular tissues in the presence of various feedback laws, finding that only certain forms of mechanical feedback can specify a unique organ size. Along the way, I will introduce a formalism to describe the elasticity of growing objects with strong connections to differential geometry and observe that growing tissues tend to show power law density correlations, reminiscent of those also observed in models of the early universe.