The revolution of molecular biology in the early 1980s has revealed complex network of non-linear and stochastic biochemical interactions underlying biological systems. To understand this complex system, mathematical models have been widely used. In this talk, I will introduce the typical process of mathematical modelling including mathematical representation, model fitting to data, analysis and simulations, and experimental validation. Across each step of modelling process, I will also describe our efforts to develop a new mathematical tools and point to the parts of current toolbox of mathematical biology that need further mathematical development. Finally, I will present how mathematical modelling reveals the key mechanism underlying circadian clocks.
