Noise analysis-model

Aim:To figure out whether output is robust when presented with intrinsic noise.

Steps:
1. Use the Gillespie algorithm to perform the stochastic analysis;
2. Draw probability distribution figures (pdf);
3. Compute the noise statistically.

Background:After having determined the parameter range, we would make the noise analysis.According to theoretical predictions, elementary chemical reactions involved in biochemical processes exhibit substantial stochastic fluctuations when low numbers of reactant molecules are involved within the small volume of a living cell. The existence of significant stochastic fluctuations in biochemical processes has been confirmed by numerous experiments including tracking of individual protein molecules in individual cells in gene expression processes[Zhou L, Gregori G, Blackman J,Robinson J, Wanner B (2005) Stochastic activation of the response regulator PhoB by noncognate histidine kinases.J Integrative Bioinformatics 2: 11.] We refer to the most classical Gillespie algorithm and lots of improvements have been made by later generation. For example, Sagar Indurkhya et al mentioned that Dynamic Monte Carlo methods are a common means of simulating the time-evolution of chemical systems.The Gillespie Algorithm (SSA) [1] is the standard algorithm for this process, and has inspired a variety of derivative methods that speed up computation, including the Optimized Direct Method (ODM) [2] and the Next Reaction Method (NRM) [3]. These methods, however, are still computationally costly.Now,we still use the classical algorithm.:

ηij is used to describe the noise, where：

σ ij stands for standard deviation and represents the mean value. If i=j then

The value of noise is ηi2 . If the mean([m]1:1)-mean([m]1:2) >> the value of noise, we identify the output wouldn’t be drown in noise.

Result_Ratio sensor

Fig.1 Pdf means probability distribution frequency

The statistics is given below:

Comparator

Fig.2 Pdf stands for probability distribution frequency.

The statistics is given below:

Conclusion

Both ratio sensor and comparator, the change of mRNA concentration is robust enough when presented with noise(mean([m]1:1)-mean([m]1:2) >> noise).It is rational to design our device by this parameter sets.