Difference between revisions of "Team:Tokyo Tech/Model"
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<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig. 5-1.Time-dependent change of the concentrations of fluorescence proteins</span> | <div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig. 5-1.Time-dependent change of the concentrations of fluorescence proteins</span> | ||
</p></div><br> | </p></div><br> | ||
| − | <div align="center"><img src="https://static.igem.org/mediawiki/2016/7/79/T--Tokyo_Tech--4koma.png" | + | <div align="center"><img src="https://static.igem.org/mediawiki/2016/7/79/T--Tokyo_Tech--4koma.png" width ="1000"class="align_right" /><br></div> |
<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig. 5-2.The story of "Snow White"</span> | <div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig. 5-2.The story of "Snow White"</span> | ||
<p class="normal_text"> In the blue area of Fig, the fluorescence intensity starts to increase. Snow White coli’s fluorescence intensity exceeds that of the Queen coli’s. It represents Snow White got fairer more and more. | <p class="normal_text"> In the blue area of Fig, the fluorescence intensity starts to increase. Snow White coli’s fluorescence intensity exceeds that of the Queen coli’s. It represents Snow White got fairer more and more. | ||
Revision as of 02:27, 18 October 2016
Model
Contents
1. Overview
To reproduce the story of ”Snow White”, we have designed the cell-cell communication system with improved or characterized parts and collected data from comprehensive experiments. Furthermore, we constructed the mathematical model in order to simulate the behavior of the whole system and to confirm the feasibility of our story. This simulation successfully contributed to give the suggestions to wet lab experiments and confirm the feasibility of our system. In addition, in order to utilize TA (Toxin-Antitoxin) system, we developed a new software in Java for adjusting the number of ACA sequences, which MazF dimer recognizes and cleaves in mRNAs.
2. Story Simulation
2-1. Mathematical Model
To simulate our gene circuits, we developed an ordinary differential equation model.
[Detailed Description for Modeling]
Differencial Equations
Snow White
\begin{equation} \frac{d[mRNA_{RFP}]}{dt} = k - d[mRNA_{RFP}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{RFP}}})[mRNA_{RFP}][DiMazF] \end{equation} \begin{equation} \frac{d[mRNA_{RhlI}]}{dt} = leak_{P_{lux}} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} - d[mRNA_{RhlI}] - F_{DiMazF}f[mRNA_{RhlI}][DiMazF] \end{equation} \begin{equation} \frac{d[RFP]}{dt} = \alpha [mRNA_{RFP}] - d_{RFP}[RFP] \end{equation} \begin{equation} \frac{d[RhlI]}{dt} = \alpha [mRNA_{RhlI}] - d_{RhlI}[RhlI] \end{equation} \begin{equation} \frac{d[C4]}{dt} = p_{C4}[RhlI]P_{Snow White} - d_{C4}[C4] \end{equation} \begin{equation} \frac{d[mRNA_{MazF}]}{dt} = leak_{P_{lux}} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}}+ [C12]^{n_{Lux}}} \\ - d[mRNA_{MazF}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazF}}})[mRNA_{MazF}][DiMazF] \end{equation} \begin{equation} \frac{d[mRNA_{MazE}]}{dt} = k - d[mRNA_{MazE}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazE}}})[mRNA_{MazE}][DiMazF] \end{equation} \begin{equation} \frac{d[MazF]}{dt} = \alpha [mRNA_{MazF}] - 2k_{Di_{MazF}}[MazF] + 2k_{-Di_{MazF}}[DiMazF] - d_{MazF}[MazF] \end{equation} \begin{equation} \frac{d[DiMazF]}{dt} = k_{Di_{MazF}}[MazF] - k_{-Di_{MazF}}[DiMazF] - 2k_{Hexa}[DiMazE][DiMazF]^2 \\ + 2k_{-Hexa}[MazHexamer] - d_{DiMazF}[DiMazF] \end{equation} \begin{equation} \frac{d[MazE]}{dt} = \alpha [mRNA_{MazE}] - 2k_{Di_{MazE}}[MazE] + 2k_{-Di_{MazE}}[DiMazE] - d_{MazE}[MazE] \end{equation} \begin{equation} \frac{d[DiMazE]}{dt} = k_{Di_{MazE}}[MazE] - k_{-Di_{MazE}}[DiMazE] - k_{Hexa}[DiMazE][DiMazF]^2 \\ + k_{-Hexa}[MazHexamer] - d_{DiMazE}[DiMazE] \end{equation} \begin{equation} \frac{d[MazHexa]}{dt} = k_{Hexa}[DiMazE][DiMazF]^2 - k_{-Hexa}[MazHexa] - d_{Hexa}[MazHexa] \end{equation} \begin{equation} \frac{dP_{Snow White}}{dt} = g \frac{E_{DiMazF}}{E_{DiMazF}+[DiMazF]}\left(1- \frac{P_{Snow White}+P_{Queen}+P_{Prince}}{P_{max}} \right) P_{Snow White} \end{equation}Queen
\begin{equation} \frac{d[mRNA_{GFP}]}{dt} = k - d[mRNA_{GFP}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{GFP}}})[mRNA_{GFP}][DiMazF] \end{equation} \begin{equation} \frac{d[mRNA_{LasI}]}{dt} = leak_{P_{rhl}} + \frac{\kappa_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} \\ - d[mRNA_{LasI}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{LasI}}})[mRNA_{LasI}][DiMazF] \end{equation} \begin{equation} \frac{d[GFP]}{dt} = \alpha [mRNA_{GFP}] - d_{GFP}[GFP] \end{equation} \begin{equation} \frac{d[LasI]}{dt} = \alpha [mRNA_{LasI}] - d_{LasI}[LasI] \end{equation} \begin{equation} \frac{d[C12]}{dt} = p_{C12}[LasI]P_{Queen} - d_{C12}[C12] - D[C12][AmiE] \end{equation} \begin{equation} \frac{d[mRNA_{MazF}]}{dt} = leak_{P_{lux}} + \frac{\kappa_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} \\ - d[mRNA_{MazF}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazF}}})[mRNA_{MazF}][DiMazF] \end{equation} \begin{equation} \frac{d[mRNA_{MazE}]}{dt} = k - d[mRNA_{MazE}] - F_{DiMazF}(1-(1-f)^{f_{mRNA_{MazE}}})[mRNA_{MazE}][DiMazF] \end{equation} \begin{equation} \frac{d[MazF]}{dt} = \alpha [mRNA_{MazF}] - 2k_{Di_{MazF}}[MazF] + 2k_{-Di_{MazF}}[DiMazF] - d_{MazF}[MazF] \end{equation} \begin{equation} \frac{d[DiMazF]}{dt} = k_{Di_{MazF}}[MazF] - k_{-Di_{MazF}}[DiMazF] - 2k_{Hexa}[DiMazE][DiMazF]^2 \\ + 2k_{-Hexa}[MazHexamer] - d_{DiMazF}[DiMazF] \end{equation} \begin{equation} \frac{d[MazE]}{dt} = \alpha [mRNA_{MazE}] - 2k_{Di_{MazE}}[MazE] + 2k_{-Di_{MazE}}[DiMazE] - d_{MazE}[MazE] \end{equation} \begin{equation} \frac{d[DiMazE]}{dt} = k_{Di_{MazE}}[MazE] - k_{-Di_{MazE}}[DiMazE] - k_{Hexa}[DiMazE][DiMazF]^2 \\ + k_{-Hexa}[MazHexamer] - d_{DiMazE}[DiMazE] \end{equation} \begin{equation} \frac{d[MazHexa]}{dt} = k_{Hexa}[DiMazE][DiMazF]^2 - k_{-Hexa}[MazHexa] - d_{Hexa}[MazHexa] \end{equation} \begin{equation} \frac{dP_{Queen}}{dt} = g \frac{E_{DiMazF}}{E_{DiMazF}+[DiMazF]}\left(1- \frac{P_{Snow White}+P_{Queen}+P_{Prince}}{P_{max}}\right) P_{Queen}\\ \end{equation}Prince
\begin{equation} \frac{d[mRNA_{AmiE}]}{dt} = leak_{P_{lux}} + \frac{\kappa_{Lux}[C12]^n}{K_{mLux}^n + [C12]^n} - d[mRNA_{AmiE}] \end{equation} \begin{equation} \frac{d[AmiE]}{dt} = \alpha [mRNA_{AmiE}]P_{Prince} - d_{AmiE}[AmiE] \end{equation} \begin{equation} \frac{dP_{Prince}}{dt} = g\left(1- \frac{P_{Snow White}+P_{Queen}+P_{Prince}}{P_{max}}\right) P_{Prince} \end{equation}Explanation about Parameters
| Parameter | Description |
| $$g$$ | Growth rate of each cells |
| $$P_{max}$$ | Carrying capacity |
| $$E_{DiMazF}$$ | Effect of MazF dimer on growth rate |
| $$k$$ | Transcription rate of mRNA under \(P_{tet}\) |
| $$leak_{P_{lux}}$$ | Leakage of \(P_{lux}\) |
| $$leak_{P_{rhl}}$$ | Leakage of \(P_{rhl}\) |
| $$\kappa_{Lux}$$ | Maximum transcription rate of mRNA under \(P_{lux}\) |
| $$\kappa_{Rhl}$$ | Maximum transcription rate of mRNA under \(P_{rhl}\) |
| $$n_{Lux}$$ | Hill coefficient for \(P_{lux}\) |
| $$n_{Rhl}$$ | Hill coefficient for \(P_{rhl}\) |
| $$K_{mLux}$$ | Lumped paremeter for the Lux System |
| $$K_{mRhl}$$ | Lumped paremeter for the Rhl System |
| $$F_{DiMazF}$$ | Cutting rate at ACA sequences on mRNA by MazF dimer |
| $$f$$ | The probability of distinction of ACA sequencess in each mRNA |
| $$f_{mRNA_{RFP}}$$ | The number of ACA sequences in \(mRNA_{RFP}\) |
| $$f_{mRNA_{GFP}}$$ | The number of ACA sequences in \(mRNA_{GFP}\) |
| $$f_{mRNA_{RhlI}}$$ | The number of ACA sequences in \(mRNA_{RhlI}\) |
| $$f_{mRNA_{LasI}}$$ | The number of ACA sequences in \(mRNA_{LasI}\) |
| $$f_{mRNA_{MazF}}$$ | The number of ACA sequences in \(mRNA_{MazF}\) |
| $$f_{mRNA_{MazE}}$$ | The number of ACA sequences in \(mRNA_{MazE}\) |
| $$\alpha$$ | Translation rate of Protein |
| $$k_{Di_{MazF}}$$ | Formation rate of MazF dimer |
| $$k_{-Di_{MazF}}$$ | Dissociation rate of MazF dimer |
| $$k_{Di_{MazE}}$$ | Formation rate of MazE dimer |
| $$k_{-Di_{MazE}}$$ | Dissociation rate of MazE dimer |
| $$k_{Hexa}$$ | Formation rate of Maz hexamer |
| $$k_{-Hexa}$$ | Dissociation rate of Maz hexamer |
| $$p_{C4}$$ | Production rate of C4HSL by RhlI |
| $$p_{C12}$$ | Production rate of 3OC12HSL by LuxI |
| $$D$$ | Decomposition rate of 3OC12HSL by AmiE |
| $$d$$ | Degradation rate of mRNA |
| $$d_{RFP}$$ | Degradation rate of RFP |
| $$d_{GFP}$$ | Degradation rate of GFP |
| $$d_{RhlI}$$ | Degradation rate of RhlI |
| $$d_{LasI}$$ | Degradation rate of LasI |
| $$d_{MazF}$$ | Degradation rate of MazF |
| $$d_{DiMazF}$$ | Degradation rate of MazF dimer |
| $$d_{MazE}$$ | Degradation rate of MazE |
| $$d_{DiMazE}$$ | Degradation rate of MazE dimer |
| $$d_{Hexa}$$ | Degradation rate of Maz Hexamer |
| $$d_{C4}$$ | Degradation rate of C4HSL |
| $$d_{C12}$$ | Degradation rate of 3OC12HSL |
| $$d_{AmiE}$$ | Degradation rate of AmiE |
2-2. Results
As a result, we obtained and confirmed the desirable behavior of the whole system by modifying and improving parts. As described below, our simulation showed appropriate transition of fluorescence for the story.
Fig. 5-1.Time-dependent change of the concentrations of fluorescence proteins
Fig. 5-2.The story of "Snow White"
In the blue area of Fig, the fluorescence intensity starts to increase. Snow White coli’s fluorescence intensity exceeds that of the Queen coli’s. It represents Snow White got fairer more and more. In the pink area of Fig, C12 is being synthetized thanks to the C4’s appearance. And the concentration of C12 increases. As a result, the toxin MazF augments inside of Snow White coli and the Queen coli, suppressing the increment of fluorescent proteins. It is as if the Mirror’s answer transformed the Queen into a Witch, so she can give Snow White a poisoned apple. In the green area of Fig, C12 increases and the MazF inside Snow White coli induced by it increases even more. So the GFP exceeds the RFP. It looks as if Snow White bit the apple, sinking into unconsciousness promptly. In the yellow area of Fig, the AmiE synthetized by the introduced Prince coli decomposes the C12 molecules so the amount of MazF inside Snow White diminishes and the amount of C4 increases. It looks as if Prince lifted Snow White and she opened her eyes.
3. Fitting
TEST
4. Analysis
TEST
5. Software
5-1. Abstract
We developed a new software named ACADwarfs. This software helps to control the sensitivity of the protein to MazF by regulating the number of ACA sequences in the mRNA sequence. ACADwarfs can increase or decrease the number of ACA sequences on mRNA without changing the amino acid sequences that the mRNA specifies or frameshifts resulted from insertion of bases without considering.
Therewith we improve the practicality of the characteristic of the mazEF system. For example you can let protein A express constantly by eliminating ACA sequences of the sequence, while letting protein B suspend to express, at the desirable timing, by expression of MazF.
This software also evades using rare codons, so you don’t have to worry about them.
5-2. Key Achievement
・Provided the tool regulating the number of ACA sequences
・Released under open-source license so everyone can use it
・Able to correspond to any base arrangements
・Rare codons are evaded
・Extend the application field of mazEF system
