Difference between revisions of "Team:OUC-China/miniToe"

Revision as of 00:07, 11 October 2018

Team OUC-China: Main

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,𝑘_on ,𝑘_off ,𝑘_obs , 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 a 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 influenced 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	\[mol/L\]

The leak in the experiment is a 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 influenced estimation, not just the leak, but also some background noise. So we can get more precise parameters of the Csy4.

@@ Line 217: / Line 217: @@
 <h3>Data Processing</h3>
-<br /> The leak in the experiment is an big problem in estimating parameters in our ODEs model, so we processing the data by following formula；
+<br /> The leak in the experiment is a big problem in estimating parameters in our ODEs model, so we processing the data by following formula；
 		                     \[Data(without leak)=Data(+IPTG)-Data(-IPTG)\]
-<br />  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.
+<br />  By doing this, we can reduce some factor which may be influenced estimation, not just the leak, but also some background noise. So we can get more precise parameters of the Csy4.
 </p>
@@ Line 281: / Line 281: @@
 </table>
-<br /> The leak in the experiment is an big problem in estimating parameters in our ODEs model, so we processing the data by following formula；
+<br /> The leak in the experiment is a big problem in estimating parameters in our ODEs model, so we processing the data by following formula；
 		                     \[Data(without leak)=Data(+IPTG)-Data(-IPTG)\]
-<br />  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.
+<br />  By doing this, we can reduce some factor which may be influenced estimation, not just the leak, but also some background noise. So we can get more precise parameters of the Csy4.
 </p>