Difference between revisions of "Team:OUC-China/miniToe"
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Revision as of 03:46, 11 October 2018
Design
Reactions
We can describe our miniToe system to be followings:
\[\rightarrow [𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[\rightarrow [𝑚𝑅𝑁𝐴_{Csy4}]\]
\[[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\rightarrow [𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}]\]
\[[Protein_{𝐶𝑠𝑦4}]+[crRNA-RBS-mRNA_{gfp}]\leftrightarrow [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[[Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{gfp}]\rightarrow [𝑚𝑅𝑁𝐴_{gfp}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\]
\[[𝑚𝑅𝑁𝐴_{gfp}]\rightarrow [𝑚𝑅𝑁𝐴_{gfp}] + [𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{gfp}]\]
\[[crRNA-RBS-mRNA_{gfp}]\rightarrow \emptyset\]
\[[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\rightarrow \emptyset\]
\[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}]\rightarrow \emptyset\]
\[[Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{gfp}]\rightarrow \emptyset\]
\[[𝑚𝑅𝑁𝐴_{gfp}]\rightarrow \emptyset\]
\[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\rightarrow \emptyset\]
\[[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{gfp}]\rightarrow \emptyset\]
Two equations, describing the functional binding and cleavage of Csy4 protein in biology, and three parameters kon koff kobs describing the same things in mathematics, are the core of our model.
ODEs
To simulate the dynamics of GFP, we use ordinary differential equations to model the reactions above. And ODEs are given as follows:
\[\frac{d[𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]}{dt}=𝑘_{1}-𝑘_{d1}[𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[\frac{d[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]}{dt}=𝑘_{2}-𝑘_{d2}[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]\]
\[\frac{d[Protein_{𝐶𝑠𝑦4}]}{dt}=𝑘_{p2}[𝑚𝑅𝑁𝐴_{𝐶𝑠𝑦4}]-𝑘_{dp2}[Protein_{𝐶𝑠𝑦4}]\]
\[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[\frac{d[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]}{dt}=𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[-𝑘_{of}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{gfp}]\]
\[-𝑘_{d1}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{gfp}]\]
\[-𝑘_{obs}[Protein_{𝐶𝑠𝑦4}][Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{gfp}]\]
\[\frac{d[𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]}{dt}=𝑘_{obs}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]-𝑘_{d3}[𝑚𝑅𝑁𝐴_{gfp}]\]
\[\frac{d[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA]}{dt}=𝑘_{obs}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-crRNA-RBS-𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]-𝑘_{dc2}[𝑃𝑟𝑜𝑡𝑒𝑖𝑛_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴]\]
\[-𝑘_{on}[Protein_{𝐶𝑠𝑦4}][𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[+𝑘_{off}[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]\]
\[\frac{d[Protein_{gfp}]}{dt}=𝑘_{p1}[𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}]-𝑘_{dp1}[Protein_{gfp}]\]
For the readability, the complex symbol is simplified as:
\[\frac{d[A]}{dt}=𝑘_{1}-𝑘_{d1}[A]-𝑘_{on}[C][A]+𝑘_{off}[D]\]
\[\frac{d[B]}{dt}=𝑘_{2}-𝑘_{d2}[B]\]
\[\frac{d[C]}{dt}=𝑘_{p2}[B]-𝑘_{dp2}[C]-𝑘_{on}[C][A]+𝑘_{off}[D]\]
\[\frac{d[D]}{dt}=𝑘_{on}[C][A]-𝑘_{dp2}[C]-𝑘_{off}[D]-𝑘_{dc1}[D]-𝑘_{obs}[D]\]
\[\frac{d[E]}{dt}=𝑘_{obs}[D]-𝑘_{d3}[E]\]
\[\frac{d[F]}{dt}=𝑘_{obs}[D]-𝑘_{d3}[F]\]
\[\frac{d[G]}{dt}=𝑘_{p1}[E]-𝑘_{dp1}[G]\]
Data Processing
The leak in the experiment is an big problem in estimating parameters in our ODEs model, so we processing the data by following formula； \[Data(without leak)=Data(+IPTG)-Data(-IPTG)\]
By doing this, we can reduce some factor which may be influence estimation not just the leak, but also some background noise. So we can get more precise parameters of the Csy4.
Species, symbols and parameters
| Species | Symbol | Initial value | Units |
|---|---|---|---|
| \[𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴_{𝑔𝑓𝑝}\] | A | 15 | \[mol/L\] |
| \[𝑚𝑅𝑁𝐴_{Csy4}\] | B | 0 | \[mol/L\] |
| \[Protein_{𝐶𝑠𝑦4}\] | C | 0 | \[mol/L\] |
| \[Protein_{𝐶𝑠𝑦4}-crRNA-RBS-mRNA_{𝑔𝑓𝑝}\] | D | 0 | \[mol/L\] |
| \[𝑚𝑅𝑁𝐴_{gfp}\] | E | 0 | \[mol/L\] |
| \[Protein_{𝐶𝑠𝑦4}-𝑐𝑟𝑅𝑁𝐴\] | F | 0 | \[mol/L\] |
| \[Protein_{gfp}\] | G | 0 | \[mol/L\] |
Because the [𝑐𝑟𝑅𝑁𝐴 − 𝑅𝐵𝑆 − 𝑚𝑅𝑁𝐴𝑔𝑓𝑝] is under controlled by a constitutive promoter, so we set the initial concentration to 15mol/L .
The other parament we used in the ODEs is listed in the following table:
| Parameters | Definition | Units | Value |
|---|---|---|---|
| \[𝑘_{1}\] | 1.955 | ||
| \[𝑘_{d1}\] | 0.002 | ||
| \[𝑘_{2}\] | 1.116 | ||
| \[𝑘_{d2}\] | 0.241 | ||
| \[𝑘_{p2}\] | 1.134 | ||
| \[𝑘_{dp2}\] | 6.547 | ||
| \[𝑘_{on}\] | 23995.469 | ||
| \[𝑘_{off}\] | 2.703 | ||
| \[𝑘_{dc1}\] | 0.024 | ||
| \[𝑘_{obs}\] | 0.327 | ||
| \[𝑘_{d3}\] | 0.472 | ||
| \[𝑘_{dc2}\] | 0.024 | ||
| \[𝑘_{p1}\] | 1.711 | ||
| \[𝑘_{dp1}\]/th> | \[h^{-1}\]/ | 0.479 |
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