Modeling and analysis of cell differentiation using hybrid systems

The capacity of cells to differentiate into specialized types is fundamental to the development of organisms. However, the underlying cell differentiation process is not yet well understood. In this work, we consider cell differentiation resulting from interactions of the Delta and Notch proteins. We model the protein concentration dynamics using switched affine hybrid automata. Applying tools from monotone dynamical system theory, we prove steady-state properties of the model. We also find, by exploiting symmetries in the system, conditions on the model parameters to ensure that the steady-state reached is consistent with biological observations. We conclude that the piecewise affine hybrid model is a good framework for modeling the cell differentiation process because the consistency of the model with biological observations can be analyzed theoretically for cellular networks of arbitrary size.