Model

Due to the small of amount of key molecules in this system, e.g. $\sigma ^{32}$ has only less than 30 copies at non-stress situation, and DnaK and some other gene have only one copy inside the cell, stochastic simulation method must be used to model this system reliably. In this work, I used an improved Gillespie algorithm, Next Reaction Method, invented by Gibson.

I modeled the E.coli heat shock from a temperature shift from 30c to 43c. E.coli is selected for two reasons: 1. It has the most quantitative data; 2. Experimental results from E.coli are similar to most of the other bacteria species. Compared with ordinary differential l equations (ODE), stochastic simulation, first represented by Gillepie (, ), is more suitable for system with small number of copies of molecules, and it is currently the most reliable tool to analyze system with fluctuations and noises (, ).