| 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