Mathematical Cell Biology: insight into the dynamics of in silico models of cellular systems

The aim of the lesson is to show how mathematical analysis of models of cellular biology can provide insight beyond simulations using the pancreatic beta-cells as a motivating example. These cells exhibit complex bursting electrical activity, which has been reproduced by a range of models over the last four decades. Bursting can be explained from the fact that the cells have processes operating on different time-scales, using methods from the theory of slow-fast dynamical systems. However, early models were eventually found to be flawed, and I will show how subsequent improvements to the models were inspired by the insight gained from mathematical analyses of their ancestors. The role of cell coupling will be highlighted to explain differences between isolated cells and cells in situ. Finally, I will treat the difference between mouse and human beta-cells, and show that the analysis of human cells must be done with more advanced methods such as geometrical singular perturbation theory.