Topics in the Stochastic Modeling and Simulations (2015)

Instructor: Tiejun Li (PKU Math)
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)

Michaelis-Menten 1913 paper

History on Michaelis-Menten kinetics

QSSA paper by Briggs and Haldane

Goldbeter-Koshland kinetics

Lect3 ODE modeling for cellular systems: II

Lect4 Stochastic modeling and SSA

Elowitz 2002 paper

Gillespie 1976 paper

Bortz-Kalos-Lebowitz 1975 paper

Gibson-Bruck's Next-Reaction method

Constant Time KMC

Lect5 Tau-leaping algorithm

Gillespie 2001 paper

Stability analysis

Binomial tau-leaping paper

Postleap checking

Chernoff tau-leaping

Convergence analysis

Lect6 Multilevel Monte Carlo for diffusion process

Giles 2008 paper

Giles Review

Lect7 Multilevel Monte Carlo for CKS


Lect8 Large volume limit and fluctuations

Semigroup methods

Martingale methods

Specification in CKS

Lect9 Multiscale analysis framework

Papanicolaou Review

E. Vanden-Eijnden's HMM strategy

E-Engquist's HMM paper

HMM for SDEs

Lect10 Multiscale analysis for CKS

Nested SSA 1

Nested SSA 2

Lect11 Rare events for diffusion processes

LDT and StatPhys


String method

TPT for diffusion process

String method for Cahn-Hilliard

Lect12 Path integral for CKS

Doi paper 1

Doi paper 2

Peliti paper

Spin-Boson formulation

Two-scale LDT via path integral

Lect13 Rare events for CKS


Two-scale LDT

TPT for jump process

Lect14 Solvable models

Alexander's PNAS paper

Oshea paper

Lect15 Fluctuation-Dissipation relation

Paulsson Nature paper

Lect16 Protein and transcriptional bursting

Single molecule review paper

PRL paper on protein bursting

Science paper on protein bursting 1

Science paper on protein bursting 2

Cell paper on transcriptional bursting 2

Lect17 Subdiffusion of protein molecule

Science paper

PRL paper

Lect18 Single molecule Michaelis-Menton law

Science paper

Nature Chem. Bio. paper

JPCB theoretical paper

Lect19 Non-equilibrium steady state theory: I

Phys. Rep. paper 1

Phys. Rep. paper 2

Review paper

Lect20 Non-equilibrium steady state theory: II

Lect21 Turing pattern dynamics

Turing's 1952 paper

Murray Scientific American paper

Murray's Book chapter on Turing pattern