Results

I analyzed the parameter sensitivity and robustness. And whether the temporarily stability of $\sigma ^{32}$ can be caused by the increasing ability of peptide and proteins to compete $\sigma ^{32}$ alone or some structural change or modification must exist to guarantee this stability. I also simulated how the system reacts when peptide ( $\sigma^{32}-Q132-Q144-C-IAANS$ is added to the steady state. To collect enough simulation data to generate reliable stochastic simulation result, the model had been run 500 times, with different random number seeds, and all the data have been collected for numerical analysis.

Some results are given here with discussion in between.

Figure 1: Distribution of DnaJ at steady state 37c from 500 runs

(a)

(b)

(a)When no stress is sensed, DnaJ varies within a relative narrow range ( $670 \pm100$) molecules within 500 runs. (b)At physiological condition, majority of $\sigma ^{32}$ stays at binary complex with DnaJ.

Figure 2: A typical evolution of $\sigma ^{32}$ at steady state 37c

(a)	(b)
(c)	(d)

This figure shows DnaJ. $\sigma ^{32}$, which is the main form of $\sigma ^{32}$, fluctuates between 2-15 molecules, with an average value around 9 molecule per E.coli. Complex between DnaK and (both ATP form and ADP form) varies frequently within a small range ( 0-3 molecules per cell). Only a small amount of $\sigma ^{32}$ can exist in chaperon-free form, which can bind with RNA polymerase core enzyme. At most of the time, the quantity of $\sigma ^{32}$ is zero.