2014.igem.org talk:HUST-China
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Modeling
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Modeling of a synthetic biological wastewater treatment
engineering system
Yuanxin Wang, Jianjie Zhao, Ruihao Li
Overview
Our project mainly focus on designing gene circuits to gather copper ions, degrading cyanide, detoxifying fluoride and suggesting whether the water is safety for further use. With these giant goals, the first thing we needed to do is using computational method to simulate the biological process and figure out whether our design is feasible. We established DDEs (delay differential equations) to see whether our instructors are trustable and give some further information for the detective part of our toolkit. Then we tested the robustness and sensitivity to get a broader insight of biological system both in single cell level and multicellular level. By doing this, we can get their properties for better application.
Single cell level
DDEs simulation
There are two kinds of E.Coli in the project—workers and instructors. The former ones produce some proteins binding with copper ions in the polluted water and the latter ones tell us whether the water is safe enough for further use. Since the thing we care about most is the safety of the water and the workers will be dedicated to remove the ions in the water before we decided to let them flow to the following pool, we established some equations to simulate the biological process of instructors. Considering about it will take some time for the transcription and translation process before a protein can bind with some certain promoters, we use DDEs instead of ODEs to make our simulation closer to the reality. And here are the equations:
<img src="Images/new/Modeling/images/HUST_Modeling_Equation_01.png" width="412" height="66" /> |
<img src="Images/new/Modeling/images/HUST_Modeling_Equation_02.png" width="340" height="70" /> |
<img src="Images/new/Modeling/images/HUST_Modeling_Equation_03.png" width="544" height="80" /> |
<img src="Images/new/Modeling/images/HUST_Modeling_Equation_04.png" width="531" height="74" /> |
<img src="Images/new/Modeling/images/HUST_Modeling_Equation_05.png" width="292" height="66" /> |
<img src="Images/new/Modeling/images/HUST_Modeling_Equation_06.png" width="699" height="78" /> |
<img src="Images/new/Modeling/images/HUST_Modeling_Equation_07.png" width="380" height="82" /> |
<img src="Images/new/Modeling/images/HUST_Modeling_Equation_08.png" width="580" height="89" /> |
<img src="Images/new/Modeling/images/HUST_Modeling_Equation_09.png" width="377" height="76" /> |
parameter | description | value | reference | ||
copynum | copy number of pACYDuet-1 plasmid | 18~22 | [1] | ||
trc1 | transcription rate of mCII |
|
[2] | ||
deg1 | transcription rate of mCII | 0.12 | [3] | ||
deg2 | degradation rate of CII | 0.1 | [4] | ||
deg3 | degradation rate of mCI | 0.12 | [3] | ||
deg4 | degradation rate of CI | 0.042 | [4] | ||
deg5 | degradation rate of mGFP | 0.13 | [5] | ||
deg6 | degradation rate of GFP | 0.017 | [6] | ||
deg7 | degradation rate of mRFP | 0.13 | [5] | ||
deg8 | degradation rate of RFP | 0.017 | [6] | ||
trl1 | translation rate of CII | 0.12 | [4] | ||
trl2 | translation rate of CI | 0.09 | [3] | ||
trl3 | translation rate of GFP | 5.4 | [7] | ||
trl4 | translation rate of RFP | 5.4 | [7] | ||
Vmax1 | maximum transcription rate when induced by CII protein | 0.9 | [4] | ||
Vmax2 | maximum transcription rate when induced by CI2 protein | 0.66 | [4] | ||
τ1 | time for CII transcription, translation and folding | 0.24min | estimated the same as CI2 | ||
τ2 | time for CI2 transcription, translation and folding | 0.24min | [3] | ||
km1 | apparent association constant for CII binding with pRE promoter | 0.398 | [8] | ||
km2 | apparent association constant for CI2 binding with pR promoter | 1.58*10-3<> | [3] | ||
k1 | reaction constant for CI forming CI2 | 3 | [4] | ||
k2 | reaction constant for CI2 disassociating to CI | 30 | [4] |
[1]
[2] Copper-inducible transcriptional regulation at two promoters in the Escherichia coli copper resistance determinant pco D. A. Rouch and N. L. Brown Microbiology (1997), 143, 1191-1202
[3] K噬菌体操纵基因和调控蛋白相互作用网络及溶原态/裂解态转变特性的动力学研究 丁辉,et al. Journ al of Inn er Mongolia University Sep. 2007 Vol. 38 No. 5
[4] Stochastic Kinetic Analysis of Developmental Pathway Bifurcation in Phage l-Infected Escherichiacoli Cells Adam Arkin ,et al. Genetics 149: 1633–1648(August 1998)
[5] Global analysis of mRNA decay and abundance in Escherichia coli at single-gene resolution using two-color fluorescent DNA microarrays, Jonathan A. Bernstein, et al. PNAS July23, 2002, vol.99 no.15, 9697–9702
[6] <a href="http://bionumbers.hms.harvard.edu/">http://bionumbers.hms.harvard.edu/</a>
[7] <a href="https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters">https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters</a>
[8] Kinetic analysis of mutations affecting the cII activation site at the PRE promoter of bacteriophage λ, MING-CHE SHIH, et al. Proc. Natl. Acad. Sipi. USA, Vol. 81, pp. 6432-6436, October 1984, Genetics
The results of simulation are shown in the graphs below:
<img src="Images/new/Modeling/HUST_Modeling_Result_01.png" width="1040" height="774" /> |
<img src="Images/new/Modeling/HUST_Modeling_Result_02.png" width="1039" height="775" /> |
As you can notice in the picture, the expression level of fluorescent protein is changed a lot between polluted and non-polluted water. Thus, by detecting the fluorescence intensity of each protein, we can gain the information about whether the water is safe for further use. Considering about the severe consequences about taking in too much copper ions, we should make sure that our data is credible and the information we get from it is accurate.
<img src="Images/new/Modeling/HUST_Modeling_Result_03.png" width="1040" height="773" /> |
We simulated the whole process of the water-dealing procedure. In the view of that the transcription rate of the copper sensitive promoter is related to the concentration of copper in the water, we divided the dealing process into several parts with different transcriptional rate and combine all the data eventually to make our simulation closer to the reality. The result showed below indicates that detecting one of the fluorescent intensity only is enough to get the information we want. But to detect the other fluorescent intensity redundantly can make the conclusion more trustable.