Team:OUC-China/Modeling/NoiseAnalysis

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Noise analysis-model

Aim:To analysis the noise in the ternary system .

Steps:
1. Use the Gillespie algorithm to perform the stochastic analysis;
2. Draw probability distribution figures (pdf);
3. Computing 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 use 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) > 5 times the 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:





Table 4: From the table, We can conclude that the noise is also very small .


Then we calculate the noise value From the table 4 ,we can observe that the mean of mRNA>>difference value between as1:as2=1 and 0.5.At the same time, the mean of mRNA>>difference value between as1:as2=1 and 2. So when as1:as2 is equal to 1:1,the equilibrium concentration isn’t drown the noise.

Conclusion


By using the noise analysis, we can conclude that the mRNA isn’t drawn the noise,. that’s by simulating the real organism, our model also meets the requirements to design the experiment.