The purpose of this course is to give a mathematical introduction to the working mathematical models (mainly stochastic), the analysis tools and simulation methods in chemical reaction kinetics. The students are required to have basic knowledge on stochastic ordinary differential equations. |

**Lect1 Introduction**

**Lect2 ODE modeling for cellular systems: I**

**
Biochemical Reactions (Chapter1 of Mathematical Physiology by Keener and Sneyd)**

**
History on Michaelis-Menten kinetics**

**
QSSA paper by Briggs and Haldane**

**Lect3 ODE modeling for cellular systems: II**

**Lect4 Stochastic modeling and SSA**

**
Bortz-Kalos-Lebowitz 1975 paper**

**
Gibson-Bruck's Next-Reaction method**

**Lect5 Tau-leaping algorithm**

**Lect6 Multilevel Monte Carlo for diffusion process**

**Lect7 Multilevel Monte Carlo for CKS**

**Lect8 Large volume limit and fluctuations**

**Lect9 Multiscale analysis framework**

**E. Vanden-Eijnden's HMM strategy**

**Lect10 Multiscale analysis for CKS**

**Lect11 Rare events for diffusion processes**

**String method for Cahn-Hilliard**

**Lect12 Path integral for CKS**

**Two-scale LDT via path integral**

**Lect13 Rare events for CKS**

**Lect14 Solvable models**

**Lect15 Fluctuation-Dissipation relation**

**Lect16 Protein and transcriptional bursting**

**Science paper on protein bursting 1**

**Science paper on protein bursting 2**

**Cell paper on transcriptional bursting 2**

**Lect17 Subdiffusion of protein molecule**

**Lect18 Single molecule Michaelis-Menton law**

**Lect19 Non-equilibrium steady state theory: I**

**Lect20 Non-equilibrium steady state theory: II**

**Lect21 Turing pattern dynamics**