M. Yampolskaya: Finding signatures of low-dimensional geometric landscapes in high-dimensional cell fate transitions

Many species of animals have cells that perform highly-specialized functions. These cells can broadly be categorized into cell types according to their function. From alveolar types responsible for gas exchange in the lung to proliferative crypt cells in the intestine, there is a wide range of cell types vital to an animal’s health. Cells adopt cell types, or fates, in a process known as differentiation. In development, it is critical that stem cells differentiate into the correct cell fates. After injury, some cells are able to transition from one fate to another to regenerate the injured tissue. Finding the general mathematical and physical principles that govern cell fate transitions is an essential part of understanding the complexity of living systems. In this thesis, I describe some steps towards a general theory of cell fate transitions inspired by statistical physics. This theory is built on the foundation of Hopfield models, which are networks that retrieve different stored patterns depending on their initial states.