Revision as of 21:32, 19 October 2016

Model

1. Overview

To recreate the story of ”Snow White”, we have designed a cell-cell communication system with improved or characterized parts and collected data from comprehensive experiments. Furthermore, we constructed the mathematical model 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. In addition, in order to help us utilize our Toxin-Antitoxin (TA) 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

In order to simulate our gene circuits, we developed an ordinary differential equation model.

[Model development]

▼ Differential 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}

▼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

We obtained and confirmed the desirable behavior of the whole system by modifying and improving parts. As described below, our simulation showed an appropriate transition of concentration of RFP and GFP for the story.

Fig.5-2.2. Time-dependent change of the concentrations of fluorescent proteins

In the blue area of Fig.5-2-2, the concentration of fluorescent proteins start to increase. The concentration of RFP of Snow White coli exceeds that of GFP of the Queen coli.
It is as if Snow White got fairer more and more.

In the pink area of Fig.5-2-2, the concentration of C12 increase thanks to the appearance of C4. As a result, the MazF inside Snow White coli and the Queen coli start to suppress the increment of fluorescet proteins.
It is as if the Queen, influenced by the Mirror's answer, transforming into a Witch in order to give Snow White a poisoned apple.

In the green area of Fig.5-2-2, the concentration of C12 more increases and the MazF inside Snow White coli more suppress the increment of GFP. So the concentration GFP exceeds that of RFP.
It looks as if Snow White bit the apple, sinking into unconsciousness soon.

In the yellow area of Fig.5-2-2, the AmiE synthesized by the introduced Prince coli decomposes C12 so the MazF inside Snow White coli diminishes and the concentration of GFP resumes.
It looks as if the Prince lifted Snow White and she opened her eyes.

3. Fitting

3-1. Population growth

First, we tried to model the growth curve of the system. When the number of E. coli approaches a certain value, the growth will stop. We defined this value in the culture as P_max. Then the population growth equation for our system is described as follows:
$$ \frac{dP}{dt} = g\left(1 - \frac{P}{P_{max}}\right)P$$
where g is the population growth rate.
This equation can be analytically solved as:
$$ P = \frac{P_{0} P_{max} e^{gt}}{P_{max} - P_{0} + P_{0} e^{gt}}$$
where P ₀ is the population at t = 0. We used this equation to fit the experimental data.

Fig.5-3-1. Modeled growth curve of E. coli fitted to experiment data

Using the experimental data from the Toxin assay for this fitting, we estimated the following parameters:

g = 0.0123
and
P_max =3.3

respectively.
These parameters can be used for Snow White coli, the Queen coli and the Prince coli in the same way.

3-2. Toxin-Antitoxin system

▼Read more

3-3. Promoters

▼Read more

We measured the relation between the AHL inputted and the fluorescence intensity.
Changing the AHL concentration from 10^-4 to 10⁴ by one power of 10 at a time, we measured the fluorescence intensity 4 hours after the insertion. We then performed the fitting with these data.
In our experimental data we only measured the fluorescence intensity of GFP. However, we can only do the modulation for the concentration of GFP. Therefore, we needed the relationship between the concentration of GFP by modeling and the fluorescence intensity by experiment. We assumed that the fluorescence intensity is proportional to the concentration of GFP. We determined the parameter from experimental data.

Fluorescence intensity = 31.8 [GFP]

From this parameter, we determined the parameters of the promoters.

We defined the following set of differential equations.
$$ \frac{d[GFP]}{dt} = leak_{Prhl} + \frac{\kappa_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} $$
The same holds true for Lux system.
$$ \frac{d[GFP]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} $$ We used MATLAB to fit the parameters to the experimental data and we fit them to the experimental concentrations.

Fig.5-3-3-1. Fitted to the experimental data of Rhl system

We obtained these parameters as follows:

Leak_Prhl = 0.86
κ_Rhl &=& 1.326
n_Rhl &=& 5
K_mRhl &=& 1000

Fig.5-3-3-2. Fitted to the experimental data of Lux system

Leak_Plux = 0.86
κ_Lux = 1.326
n_Lux = 5
K_mLux = 1000

3-4. More realistic model with mRNA

▼Read more

We defined the differential equations and estimated the parameters in the AHL - GFP system as described in 3-3. However, the translation from mRNA to protein was not considered in the model. To simulate the story of ‘Snow White,’ the translation is essential because the whole system includes the toxin-antitoxin system involving the cleavage of mRNA. We also had to take in account in our fitting that the AHL inputted at the beginning decreases with time.
Then, we redefined the following set of differential equations.
$$ \frac{d[mRNA_{GFP}]}{dt} = leak_{Prhl} + \frac{κ_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} - d[mRNA_{GFP}]$$
$$ \frac{d[GFP]}{dt} = α[mRNA_{GFP}] - d_{GFP}[GFP] $$
$$ \frac{d[C4]}{dt} = - d_{C4}[C4] $$
The same holds true for Lux system.
$$ \frac{d[mRNA_{GFP}]}{dt} = leak_{Plux} + \frac{κ_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} - d[mRNA_{GFP}]$$
$$ \frac{d[GFP]}{dt} = α[mRNA_{GFP}] - d_{GFP}[GFP] $$
$$ \frac{d[C12]}{dt} = - d_{C12}[C12] $$
As a result, we obtained these parameters as follows:

Leak_Prhl = 4.65
κ_Rhl = 14.95
n_Rhl = 5
K_mRhl = 1000
and
Leak_Plux = 2.26
κ_Lux = 6.98
n_Lux = 0.76
K_mLux = 116.24

Using these parameters we simulated the reproduction of the story of Snow White.

4. Analysis

4-1. The Prince coli should be put in during the process

We run simulations in order to determine whether we would get a better behavior let we introduce the Prince coli at the beginning or halfway of the story.

Fig.5-4-1-1. Number of individuals when the Prince coli is introduced from the beginning

Fig.5-4-1-2. AHL concentrations when the Prince coli is introduced from the beginning

As a result, if we introduce the Prince coli from the beginning, the number of Prince coli increases too much (Fig.5-4-1-1) so the AmiE the Prince coli produces augments and the decomposition of C12 also occurs overly. So C12 is almost inexistent in the medium (Fig.5-4-1-2).

Fig.5-4-1-3. Number of individuals when the Prince coli is introduced at t = 700

Fig.5-4-1-4. AHL concentrations when the Prince coli is introduced at t = 700

On the other hand, if we introduce the Prince coli at t = 600, the number of Prince coli does not increment much (Fig.5-4-1-3), so C12 can exist until t = 700 and then decreases thanks to the augment of AmiE (Fig.5-4-1-4).
In conclusion, if we introduce the Prince coli at t = 700, the circuit will behave accordingly.

4-2. Prhl should be changed

In order to confirm the feasibility of the story with our gene circuit by the combination of the existing promoters, we performed some simulations based on the results of our assays.

Fig.5-4-2. The intensity of Plux and Prhl promoters

The diagram above shows that the intensity of the two promoters should be in the red region of the figure.The combination of promoters which we were originally going to use is shown in the graph by the green point. To move this point into the red region, we had to improve Prhl to raise its expression level.

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.
Then 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 stop being expressed, at the desirable timing, by expression of MazF.
This software also evades the use of rare codons, so you don’t have to worry about them.

5-2. Key achievements

・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

5-3. Work flow

▼Read more

5-4. Demonstration

We created a demo to present the features of this software. Using this, we regulated the number of ACA sequences and control the sensitivity of the protein to MazF.

Gene	Pre number of ACA sequences	Post number of ACA sequences
RFP	10	30
GFP	23	39
MazF	2	1
MazE	2	1

We increased the numbers of ACA sequences of RFP and GFP decreased the numbers of ACA sequences of MazF and MazE .

Fig.5-4. Comparison between the results of simulations using original sequences and modified sequences

We can see that the concentration of expressed MazF reacts more keenly after adjusting the ACA sequences than before doing so.

5-5. Download

To download click here.

The code is available on github.

Parameter	Value
k_DiMazF	6.82 nM^-1 min^-1
k_-DiMazF	6.24 min^-1
k_DiMazE	3.46 nM^-1 min^-1
k_-DiMazE	7.25 min^-1
k_Hexa	4.51nM^-2 min^-1
k_-Hexa	4.05 min^-1
E_DiMazF	0.46 nM^-1 min^-1
d_MazF	0.7 min^-1
d_MazE	0.55 min^-1
d_DiMazF	0.17 min^-1
d_DiMazE	0.416 min^-1
d_Hexa	0.511 min^-1

Parameter	Range	Step size
D	$$ 0.0001 < D < 0.001 $$	0.0001
p_C4	$$ 0.0001 < p_{C4} < 1 $$	0.001
p_C12	$$ 0.0001 < p_{C12} < 1 $$	0.001
α	$$ 0.01 < α < 0.2 $$	0.01
d_AmiE $$	$$ 0.001 < d_{AmiE} < 1 $$	0.001

Parameter	Value
D	$$ 0.0056 < D < 0.001 $$
p_C4	$$ 0.0029 < p_{C4} < 0.778 $$
p_C12	$$ 0.001 < p_{C12} < 0.217 $$
α	$$ 0.01 < α < 0.16 $$
d_AmiE	$$ 0.001 < d_{AmiE} < 1 $$

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-			<h1 align="center">Project</h1>
+			<h1 align="center">Model</h1>
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-				<h3 class="link"><a href="#introduction">1. Introduction</a></h3>
+				<h3 class="link"><a href="#overview">1. Overview</a></h3>
-				<h3 class="link"><a href="#story">2. Our goal is to evaluate the real beauty of Snow White and the Queen</a></h3>
+				<h3 class="link"><a href="#story_simulation">2. Story simulation</a></h3>
-				<h3 class="link"><a href="#system">3. Introduction of system forming the basis</a></h3>
+				<h3 class="link"><a href="#mathematical_model"><font size="2.7">&nbsp;&nbsp;&nbsp;2-1. Mathematical model</font></a></h3>
-				<h3 class="link"><a href="#sys1"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;3.1. What is TA system?</span></a></h3>
+				<h3 class="link"><a href="#results"><font size="2.7">&nbsp;&nbsp;&nbsp;2-2. Results</font></a></h3>
-				<h3 class="link"><a href="#sys2"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;3.2. The art of MazF / MazE</span></a></h3>
+				<h3 class="link"><a href="#fitting">3. Fitting</a></h3>
-				<h3 class="link"><a href="#circuit">4. Our genetic circuit design</a></h3>
+				<h3 class="link"><a href="#population"><font size="2.7">&nbsp;&nbsp;&nbsp;3-1. Population growth</font></a></h3>
-				<h3 class="link"><a href="#sce1"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;4.1. Scene1 : The magic mirror's answer</span></a></h3>
+				<h3 class="link"><a href="#toxin"><font size="2.7">&nbsp;&nbsp;&nbsp;3-2. Toxin-Antitoxin system</font></a></h3>
-				<h3 class="link"><a href="#sce2"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;4.2. Scene2 : The Queen's trap</span></a></h3>
+				<h3 class="link"><a href="#promoters"><font size="2.7">&nbsp;&nbsp;&nbsp;3-3. Promoters</font></a></h3>
-				<h3 class="link"><a href="#sce3"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;4.3. Scene3 : Snow White's sleep </span></a></h3>
+				<h3 class="link"><a href="#more"><font size="2.7">&nbsp;&nbsp;&nbsp;3-4. More realistic model with mRNA</font></a></h3>
-				<h3 class="link"><a href="#sce4"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;4.4. Scene4 : The Prince's rescue</span></a></h3>
+				<h3 class="link"><a href="#analysis">4. Analysis</a></h3>
-				<h3 class="link"><a href="#Q.E.D.">5. Q.E.D. for the representation of Snow White</a></h3>
+				<h3 class="link"><a href="#prince_coli"><font size="2.7">&nbsp;&nbsp;&nbsp;4-1. The Prince <span style ="font-style : italic">coli</span> should be put in during the process</font></a></h3>
-				<h3 class="link"><a href="#5-sce1"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;5.1. Cold inducible promoter functions at 18°C in Scene 1</span></a></h3>
+				<h3 class="link"><a href="#prhl"><font size="2.7">&nbsp;&nbsp;&nbsp;4-2. Prhl should be changed</font></a></h3>
-				<h3 class="link"><a href="#5-sce2"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;5.2. The screening of rhl promoter with optimal strength for Scene 2</span></a></h3>
+				<h3 class="link"><a href="#requirements"><font size="2.7">&nbsp;&nbsp;&nbsp;4-3. Requirements</font></a></h3>
-				<h3 class="link"><a href="#ass"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.2.1. reporter assay</span></a></h3>
+				<h3 class="link"><a href="#production_ahl"><font size="2.7">&nbsp;&nbsp;&nbsp;4-4. Production rate of C4HSL and 3OC12HSL by RhlI and LasI</font></a></h3>
-				<h3 class="link"><a href="#sml"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.2.2. Simulation regarding Prhl strength</span></a></h3>
+				<h3 class="link"><a href="#translation"><font size="2.7">&nbsp;&nbsp;&nbsp;4-5. Translation rate of protein</font></a></h3>
-				<h3 class="link"><a href="#imp"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.2.3. Improvement of Prhl</span></a></h3>
+				<h3 class="link"><a href="#decomposition"><font size="2.7">&nbsp;&nbsp;&nbsp;4-6. Decomposition rate of 3OC12HSL by AmiE</font></a></h3>
-				<h3 class="link"><a href="#5-sce3"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;5.3. MazF-MazE system as Toxin-Antitoxin system can be controlled in Scene 3</span></a></h3>
+				<h3 class="link"><a href="#degradation_amie"><font size="2.7">&nbsp;&nbsp;&nbsp;4-6. Degradation rate of AmiE</font></a></h3>
-                                <h3 class="link"><a href="#5-sce4"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;5.4. AmiE degrades 3OC12HSl selectively and does not degrade C4HSL in Scene4</span></a></h3>
+				<h3 class="link"><a href="#degradation_protein"><font size="2.7">&nbsp;&nbsp;&nbsp;4-7. Degradation rate of RFP and GFP</font></a></h3>
-                                <h3 class="link"><a href="#5-sml"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;5.5. the simulation related to the story</span></a></h3>
+				<h3 class="link"><a href="#software">5. Software</a></h3>
-				<h3 class="link"><a href="#5-str"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.5.1. When the Prince comes?</span></a></h3>
+				<h3 class="link"><a href="#abstract"><font size="2.7">&nbsp;&nbsp;&nbsp;5-1. Abstract</font></a></h3>
-				<h3 class="link"><a href="#5-str2"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.5.2. representation of the story</span></a></h3>
+				<h3 class="link"><a href="#key_achievements"><font size="2.7">&nbsp;&nbsp;&nbsp;5-2. Key achievements</font></a></h3>
-				<h3 class="link"><a href="#hp">6. Integrated Human Practice</a></h3>
+				<h3 class="link"><a href="#work_flow"><font size="2.7">&nbsp;&nbsp;&nbsp;5-3. Work flow</font></a></h3>
-                                <h3 class="link"><a href="#cha1"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;6.1. "Snow White"</span></a></h3>
+				<h3 class="link"><a href="#demo"><font size="2.7">&nbsp;&nbsp;&nbsp;5-4. Demonstration</font></a></h3>
-                                <h3 class="link"><a href="#cha2"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;6.2. Addition of other characters</span></a></h3>
+				<h3 class="link"><a href="#download"><font size="2.7">&nbsp;&nbsp;&nbsp;5-5. Download</font></a></h3>
-                                <h3 class="link"><a href="#sof"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;6.3. The software development for future work</span></a></h3>
-				<h3 class="link"><a href="#exp"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.3.1. The dialogue with an expert</span></a></h3>
-				<h3 class="link"><a href="#ACA"><span style="font-size: 14px;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.3.2. ACA Dwarfs</span></a></h3>
-				<h3 class="link"><a href="#reference">7. Reference</a></h3>
 				</div><!-- /contents_menu -->
 			</div><!-- /contents_contents -->
 		</div><!-- /contents -->
+		<div id="overview" class="container">
+			<div id="overview_header" class="container_header">
+				<h2><span>1. Overview</span></h2>
+			</div><!-- /overview_header -->
+			<div id="overview_contents" class="container_contents">
+				<p class="normal_text">To recreate the story of ”Snow White”, we have designed a cell-cell communication system with improved or characterized parts and collected data from comprehensive experiments. Furthermore, we constructed <a href="https://2016.igem.org/Team:Tokyo_Tech/Modeling_Details">the mathematical model</a> to simulate the behavior of the whole system and to confirm the feasibility of our story. This simulation successfully contributed to give <a href="https://2016.igem.org/Team:Tokyo_Tech/Model#prince_coli">the suggestions</a> to wet lab experiments. In addition, in order to help us utilize our Toxin-Antitoxin (TA) system, we developed a new software in Java for adjusting the number of ACA sequences, which MazF dimer recognizes and cleaves in mRNAs.</p>
+			</div><!-- /overview_contents -->
+		</div><!-- /overview -->
-		<div id="introduction" class="container">
+		<div id="story_simulation" class="container">
-			<div id="introduction_header" class="container_header">
+			<div id="story_simulation_header" class="container_header">
-				<h2><span>1. Introduction</span></h2>
+				<h2><span>2. Story simulation</span></h2>
-			</div><!-- /_header -->
+			</div><!-- /story_simulation_header -->
-			<div id="introduction_contents" class="container_contents">
+			<div id="story_simulation_contents" class="container_contents">
-				<p class="normal_text">When you were little, before going to sleep, you have probably asked your mother, "Mommy, read some picture books to me, please?" Your mother may have read aloud many stories. </p>
+			<div id="mathematical_model">
-				<p class="normal_text">Most of the stories that have been told for generation have lessons in it. The lessons from Snow White story are mainly the following two points.</p>
+				<div id="mathematical_model_header">
-				<p class="normal_text">&#8544;. Do not show off or envy someone.</p>
+					<h3><span>2-1. Mathematical model</span></h3>
-				<p class="normal_text">&#8545;. Do not trust unfamiliar people blindly. </p>
+				</div><!-- /_header -->
-				<p class="normal_text">For a beautiful mind, we need not only to be kind and generous but also to keep a strong heart and control ourselves.</p>
+				<p class="normal_text">In order to simulate our gene circuits, we developed an ordinary differential equation model.</p>
-				<p class="normal_text">In our project, we will recreate Snow White story and evaluate Snow White and the Queen in terms of the beauty inside and out.</p>
+				<p style="text-align:center;" class="normal_text">[<a href="https://2016.igem.org/Team:Tokyo_Tech/Modeling_Details">Model development</a>]</p>
+<!-- 折り畳み展開ポインタ -->
+<div onclick="obj=document.getElementById('open1').style; obj.display=(obj.display=='none')?'block':'none';">
+<a style="cursor:pointer;">▼ Differential equations</a>
+</div>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open1" style="display:none;clear:both;">
+							<h3>Snow White</h3>
+							\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}
+							<h3>Queen</h3>
+							\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}
+							<h3>Prince</h3>
+							\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}
+</div>
+<!--// 折り畳まれ部分 -->
+<br>
-				</p>
+<div onclick="obj=document.getElementById('open2').style; obj.display=(obj.display=='none')?'block':'none';">
+<a style="cursor:pointer;">▼Parameters</a>
+</div>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open2" style="display:none;clear:both;">
+							<table border="1" style="margin: auto;">
+								<tbody>
+									<tr><td>Parameter </td><td> Description </td></tr>
+									<tr><td>$$g$$ </td><td> Growth rate of each cells</td></tr>
+									<tr><td>$$P_{max}$$ </td><td> Carrying capacity </td></tr>
+									<tr><td>$$E_{DiMazF}$$ </td><td> Effect of MazF dimer on growth rate</td></tr>
+									<tr><td>$$k$$ </td><td> Transcription rate of mRNA under \(P_{tet}\) </td></tr>
+									<tr><td>$$leak_{P_{lux}}$$ </td><td> Leakage of \(P_{lux}\) </td></tr>
+									<tr><td>$$leak_{P_{rhl}}$$ </td><td> Leakage of \(P_{rhl}\) </td></tr>
+									<tr><td>$$\kappa_{Lux}$$ </td><td> Maximum transcription rate of mRNA under \(P_{lux}\)</td></tr>
+									<tr><td>$$\kappa_{Rhl}$$ </td><td> Maximum transcription rate of mRNA under \(P_{rhl}\) </td></tr>
+									<tr><td>$$n_{Lux}$$ </td><td> Hill coefficient for \(P_{lux}\)</td></tr>
+									<tr><td>$$n_{Rhl}$$ </td><td> Hill coefficient for \(P_{rhl}\)</td></tr>
+									<tr><td>$$K_{mLux}$$ </td><td> Lumped paremeter for the Lux System</td></tr>
+									<tr><td>$$K_{mRhl}$$ </td><td> Lumped paremeter for the Rhl System</td></tr>
+									<tr><td>$$F_{DiMazF}$$ </td><td> Cutting rate at ACA sequences on mRNA by MazF dimer</td></tr>
+									<tr><td>$$f$$ </td><td> The probability of distinction of ACA sequencess in each mRNA</td></tr>
+									<tr><td>$$f_{mRNA_{RFP}}$$ </td><td> The number of ACA sequences in \(mRNA_{RFP}\)</td></tr>
+									<tr><td>$$f_{mRNA_{GFP}}$$ </td><td> The number of ACA sequences in \(mRNA_{GFP}\)</td></tr>
+									<tr><td>$$f_{mRNA_{RhlI}}$$ </td><td> The number of ACA sequences in \(mRNA_{RhlI}\)　</td></tr>
+									<tr><td>$$f_{mRNA_{LasI}}$$ </td><td> The number of ACA sequences in \(mRNA_{LasI}\)</td></tr>
+									<tr><td>$$f_{mRNA_{MazF}}$$ </td><td> The number of ACA sequences in \(mRNA_{MazF}\)　</td></tr>
+									<tr><td>$$f_{mRNA_{MazE}}$$ </td><td> The number of ACA sequences in \(mRNA_{MazE}\)　</td></tr>
+									<tr><td>$$\alpha$$ </td><td> Translation rate of Protein </td></tr>
+									<tr><td>$$k_{Di_{MazF}}$$ </td><td> Formation rate of MazF dimer </td></tr>
+									<tr><td>$$k_{-Di_{MazF}}$$ </td><td> Dissociation rate of MazF dimer </td></tr>
+									<tr><td>$$k_{Di_{MazE}}$$ </td><td> Formation rate of MazE dimer </td></tr>
+									<tr><td>$$k_{-Di_{MazE}}$$ </td><td> Dissociation rate of MazE dimer </td></tr>
+									<tr><td>$$k_{Hexa}$$ </td><td> Formation rate of Maz hexamer </td></tr>
+									<tr><td>$$k_{-Hexa}$$ </td><td> Dissociation rate of Maz hexamer</td></tr>
+									<tr><td>$$p_{C4}$$ </td><td> Production rate of C4HSL by RhlI</td></tr>
+									<tr><td>$$p_{C12}$$ </td><td> Production rate of 3OC12HSL by LuxI </td></tr>
+									<tr><td>$$D$$ </td><td> Decomposition rate of 3OC12HSL by AmiE </td></tr>
+									<tr><td>$$d$$ </td><td> Degradation rate of mRNA </td></tr>
+									<tr><td>$$d_{RFP}$$ </td><td> Degradation rate of RFP</td></tr>
+									<tr><td>$$d_{GFP}$$ </td><td> Degradation rate of GFP </td></tr>
+									<tr><td>$$d_{RhlI}$$ </td><td> Degradation rate of RhlI</td></tr>
+									<tr><td>$$d_{LasI}$$ </td><td> Degradation rate of LasI</td></tr>
+									<tr><td>$$d_{MazF}$$ </td><td> Degradation rate of MazF</td></tr>
+									<tr><td>$$d_{DiMazF}$$ </td><td> Degradation rate of MazF dimer</td></tr>
+									<tr><td>$$d_{MazE}$$ </td><td> Degradation rate of MazE </td></tr>
+									<tr><td>$$d_{DiMazE}$$ </td><td> Degradation rate of MazE dimer </td></tr>
+									<tr><td>$$d_{Hexa}$$ </td><td> Degradation rate of Maz Hexamer </td></tr>
+									<tr><td>$$d_{C4}$$ </td><td> Degradation rate of C4HSL </td></tr>
+									<tr><td>$$d_{C12}$$ </td><td> Degradation rate of 3OC12HSL </td></tr>
+									<tr><td>$$d_{AmiE}$$ </td><td> Degradation rate of AmiE </td></tr>
+								</tbody>
+							</table>
+</div>
+<!--// 折り畳まれ部分 -->
+</div>
-			</div><!-- /introduction_contents -->
+			<div id="results_contents" class="container_contents">
-		</div><!-- /introduction -->
+			<div id="results">
+				<div id="results_header">
-		<div id="story" class="container">
+					<h3><span>2-2. Results</span></h3>
-			<div id="story_header" class="container_header">
+				</div><!-- /_header -->
-				<h2><span>2. Our goal is to evaluate the real beauty of Snow White and the Queen</span></h2>
+				<p class="normal_text">We obtained and confirmed the desirable behavior of the whole system by modifying and improving parts. As described below, our simulation showed an appropriate transition of concentration of RFP and GFP for the story.</p>
-			</div><!-- /_header -->
+                <div align="center"><img src="https://static.igem.org/mediawiki/2016/7/7f/T--Tokyo_Tech--2-1-1.png" height ="500"><br></div>
-			<div id="story_contents" class="container_contents">
+				<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-2.2. Time-dependent change of the concentrations of fluorescent proteins</span></p></div>
-				<div id="stories">
-				                                <div align="center"><span style="font-style : italic; font-size:18px;">"Magic Mirror on the wall, who is the fairest one of all?"</span></div>
-<p class="normal_text">Once upon a time, there lived a Queen.<br>
-She was the fairest in the world and she herself also believed so.<br><br>
-Each time the Queen asked, "Magic Mirror on the wall, who is the fairest one of all?," the mirror would give the same answer.<br>
-"You are the fairest one of all."<br>
-This pleased the Queen greatly, for she knew that her Magic mirror could speak nothing but the truth and  she asked it the same question.<br><br>
-"Magic Mirror on the wall, who is the fairest one of all?"<br><br>
-One winter night, the Queen asked her mirror as usual.<br>
-"Magic mirror on the wall, who is the fairest one of all?"<br>
-The mirror answered,<br>
-"Snow White is the fairest one."</p><br><br>
-				<p class="normal_text">The Snow White was Queen's daughter&#8208;in&#8208;law.</p>
-				<p class="normal_text">She was a kind and pure girl, and just turned seven years old.</p><br>
-				<p class="normal_text">Then the Queen was shocked, and beside herself with rage. </p><br>
-				<p class="normal_text">And thought,</p>
-				<p class="normal_text">"If I kill Snow White, I would be the fairest one of all again."</p><br>
-				<p class="normal_text">The Queen prepared a poisoned apple.</p><br>
-				<p class="normal_text">She decided to transform into a Witch and give the apple to Snow White.</p>
+				    <div class="floating"><img src="https://static.igem.org/mediawiki/2016/7/79/T--Tokyo_Tech--4koma.png" width ="300"class="align_right">	</div>
-				<p class="normal_text">Snow White, who always takes people at their word , bit the apple, then sank into unconsciousness soon.</p><br>
+					<p class="normal_text"> In the blue area of Fig.5-2-2, the concentration of fluorescent proteins start to increase. The concentration of RFP of Snow White <span style ="font-style : italic">coli</span> exceeds  that of GFP of the Queen <span style ="font-style : italic">coli</span>. <br>
+					It is as if Snow White got fairer more and more.<br><br>
+					In the pink area of Fig.5-2-2, the concentration of C12 increase thanks to the appearance of C4. As a result, the MazF inside Snow White <span style ="font-style : italic">coli</span> and the Queen <span style ="font-style : italic">coli</span> start to suppress the increment of fluorescet proteins. <br>
+					It is as if the Queen, influenced by the Mirror's answer, transforming into a Witch in order to give Snow White a poisoned apple.<br><br>
+					In the green area of Fig.5-2-2, the concentration of C12 more increases and the MazF inside Snow White <span style ="font-style : italic">coli</span> more suppress the increment of GFP. So the concentration GFP exceeds that of RFP. <br>
+					It looks as if Snow White bit the apple, sinking into unconsciousness soon.<br><br>
+					In the yellow area of Fig.5-2-2, the AmiE synthesized by the introduced Prince <span style ="font-style : italic">coli</span> decomposes C12 so the MazF inside Snow White <span style ="font-style : italic">coli</span> diminishes and the concentration of GFP resumes. <br>
+					It looks as if the Prince lifted Snow White and she opened her eyes.</p>
+				</div><!-- /results_contents -->
+			</div><!-- /results -->
+			</div><!-- /story_simulation_contents -->
+		</div><!-- /story_simulation -->
-				<p class="normal_text">The Dwarfs  found Snow White and they grieved her "death," but they built a coffin and put her in it carefully.</p><br>
+		<div id="fitting" class="container">
+			<div id="fitting_header" class="container_header">
+				<h2><span>3. Fitting</span></h2>
+			</div><!-- /fitting_header -->
+			<div id="fitting_contents" class="container_contents">
+			<div id="population">
+				<div id="population_header">
+					<h3><span>3-1. Population growth</span></h3>
+				</div><!-- /_header -->
+				<div id="population_contents">
+					<p class="normal_text">First, we tried to model the growth curve of the system. When the number of <span style ="font-style : italic">E. coli</span> approaches a certain value, the growth will stop. We defined this value in the culture as P<sub>max</sub>. Then the population growth equation for our system is described as follows:<br>
+					$$ \frac{dP}{dt} = g\left(1 - \frac{P}{P_{max}}\right)P$$<br>
+					where g is the population growth rate. <br>
+					This equation can be analytically solved as:<br>
+					$$ P = \frac{P_{0} P_{max} e^{gt}}{P_{max} - P_{0} + P_{0} e^{gt}}$$<br>
+					where P <sub> 0</sub> is the population at t = 0. We used this equation to fit the experimental data.
+					</p>
-				<p class="normal_text">One day, a Price from a neighboring country passed by the Dwarfs' house.</p><br>
+					<div align="center"><img src="https://static.igem.org/mediawiki/2016/e/ed/T--Tokyo_Tech--FittingPopulation.png" height ="500"><br></div>
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-3-1. Modeled growth curve of <span style ="font-style : italic">E. coli</span> fitted to experiment data</span> </div>
-				<p class="normal_text">Although he knew her death, he couldn't help lifting her up because of her beauty.</p>
+					<p class="normal_text">Using the experimental data from the <a href="https://2016.igem.org/Team:Tokyo_Tech/Toxin_Assay/mazEF_System_Assay">Toxin assay</a> for this fitting, we estimated the following parameters:
-				<p class="normal_text">Then, she opened her eyes!</p><br>
+					<p class="normal_text" style="text-align: center;">g = 0.0123<br>
+					and<br>
-				<p class="normal_text">because this action dislodged from Snow White's throat the piece of poisoned apple that she had bitten off.</p><br><br>
+					P<sub>max</sub> =3.3<br>
+					<p class="normal_text">respectively.<br>
+					These parameters can be used for Snow White <span style ="font-style : italic">coli</span>, the Queen <span style ="font-style : italic">coli</span> and the Prince <span style ="font-style : italic">coli</span> in the same way.
+					</p>
+				</div> <!-- population_contents-->
+			</div> <!-- population-->
+			<div id="toxin">
-				<p class="normal_text">Awakened Snow White was adored by everyone and lived happily ever after. </p><br><br>
+				<div id="toxin_header">
+					<h3><span>3-2. Toxin-Antitoxin system</span></h3>
+				</div><!-- /_header -->
+				<div id="toxin_contents">
-				<p class="normal_text">THE END</p><br><br><br><br>
-				<div class="gradation_cover"><a href="javascript:void(0);" onclick="show('stories'); return false;"><img src="https://static.igem.org/mediawiki/2016/5/54/T--Tokyo_Tech--readmore.png" /></a></div><!--- /.gradation_cover -->
-				</div><!-- /stories -->
-<p class="normal_text">In our project, we evaluate the real beauty of Snow White and the Queen with the fluorescence intensities of RFP and GFP.
-  We use the graph shown below to evaluate. The vertical axis of the graph shows the beauty of Snow White and the Queen, and the horizontal axis shows the elapsed time.
-</p>
-				<p class="normal_text">The REALreal beauty is defined as the followings in this project.<br>
-<p class="normal_text">No matter how beautiful the appearance is, no one can be a real beauty without a beautiful mind. We will show you which woman has the real beauty, Snow White or the Queen.  </p>
-                                <p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Real Beauty =  beauty + inner beauty</span>
-<p class="normal_text">To evaluate the Real beauty, we will recreate Snow White story by using E.coli.</p>
-				</p><br>
+<div onclick="obj=document.getElementById('open3').style; obj.display=(obj.display=='none')?'block':'none';">
+<a style="cursor:pointer;">▼Read more</a>
+</div>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open3" style="display:none;clear:both;">
-				<div align="center"><a href="https://static.igem.org/mediawiki/2016/7/7f/T--Tokyo_Tech--2-1-1.png"><img src="https://static.igem.org/mediawiki/2016/7/7f/T--Tokyo_Tech--2-1-1.png" height ="500px"></a><br></div>
+					<p class="normal_text">Since there are only few researches that actually discussed on the kinetics of the TA system, we estimated the parameters for our TA system. We got the experimental data from <a href="https://2016.igem.org/Team:Tokyo_Tech/Toxin_Assay/mazEF_System_Assay">Toxin assay</a> for this fitting. The differential equations representing the TA system are described as follows:
-				<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig. 2-2-1. </span>
+					$$ \frac{d[MazF]}{dt} = \alpha [mRNA_{MazF}] - 2k_{Di_{MazF}}[MazF] + 2k_{-Di_{MazF}}[DiMazF] - d_{MazF}[MazF] $$<br>
-				</p></div><br>
+					$$ \frac{d[DiMazF]}{dt} = k_{Di_{MazF}}[MazF] - k_{-Di_{MazF}}[DiMazF] - 2k_{Hexa}[DiMazE][DiMazF]^2  + 2k_{-Hexa}[MazHexamer] - d_{DiMazF}[DiMazF] $$<br>
+					$$ \frac{d[MazE]}{dt} = \alpha [mRNA_{MazE}] - 2k_{Di_{MazE}}[MazE] + 2k_{-Di_{MazE}}[DiMazE] - d_{MazE}[MazE] $$<br>
+					$$ \frac{d[DiMazE]}{dt} = k_{Di_{MazE}}[MazE] - k_{-Di_{MazE}}[DiMazE] - k_{Hexa}[DiMazE][DiMazF]^2  + k_{-Hexa}[MazHexamer] - d_{DiMazE}[DiMazE] $$<br>
+					$$ \frac{d[MazHexa]}{dt} = k_{Hexa}[DiMazE][DiMazF]^2 - k_{-Hexa}[MazHexa] - d_{Hexa}[MazHexa] $$<br>
+					We used genetic algorithms to fit this data. We used ODs at 7 points and fit them to experimental ODs.
+					</p>
-				<p class="normal_text">  To evaluate the real beauty, we recreated Snow White story by using E.coli.<br>
+					<div align="center"><img src="https://static.igem.org/mediawiki/2016/8/8e/T--Tokyo_Tech--FittingTA.png" height ="400"><br></div>
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-3-2. Fitted growth curve of <span style ="font-style : italic">E.coli</span> to the experimental data of TA system</span> </div>
-								</p>
+					<p class="normal_text">As a result, we obtained the following parameters.</p>
-			</div><!-- /story_contents -->
-		</div><!-- /story -->
-		<div id="system" class="container">
+					    <table border="1" style="margin: auto;">
-			<div id="system_header" class="container_header">
+								<tbody>
-				<h2><span>3. Introduction of system forming the basis</span></h2>
+									<tr><td>Parameter </td><td> Value </td></tr>
-			</div><!-- /_header -->
+									<tr><td> k<sub>DiMazF</sub></td><td> 6.82 nM<sup>-1</sup> min<sup>-1</sup> </td></tr>
-			<div id="system_contents" class="container_contents">
+									<tr><td> k<sub>-DiMazF</sub> </td><td> 6.24 min<sup>-1</sup> </td></tr>
-				<p class="normal_text">  We will first introduce the  system that forms the basis of our project, the TA system.
+									<tr><td> k<sub>DiMazE</sub></td><td> 3.46 nM<sup>-1</sup> min<sup>-1</sup> </td></tr>
-                        	</p>
+									<tr><td> k<sub>-DiMazE</sub> </td><td> 7.25 min<sup>-1</sup> </td></tr>
-				<div id="sys1_header">
+									<tr><td> k<sub>Hexa</sub></td><td> 4.51nM<sup>-2</sup> min<sup>-1</sup> </td></tr>
-					<h3><span>3.1 What is TA system?</span></h3>
+									<tr><td> k<sub>-Hexa</sub> </td><td> 4.05 min<sup>-1</sup> </td></tr>
+									<tr><td> E<sub>DiMazF</sub></td><td> 0.46 nM<sup>-1</sup> min<sup>-1</sup> </td></tr>
+									<tr><td> d<sub>MazF</sub> </td><td> 0.7 min<sup>-1</sup> </td></tr>
+									<tr><td> d<sub>MazE</sub> </td><td> 0.55 min<sup>-1</sup> </td></tr>
+									<tr><td> d<sub>DiMazF</sub> </td><td> 0.17 min<sup>-1</sup> </td></tr>
+									<tr><td> d<sub>DiMazE</sub> </td><td> 0.416 min<sup>-1</sup> </td></tr>
+									<tr><td> d<sub>Hexa</sub> </td><td> 0.511 min<sup>-1</sup> </td></tr>
+							    </tbody>
+					    </table>
+			    </div> <!-- toxin_contents-->
+		    </div><!--toxin-->
+</div>
+			<div id="promoters">
+				<div id="promoters_header">
+					<h3><span>3-3. Promoters</span></h3>
 				</div><!-- /_header -->
-				<div id="sys1">
+				<div id="promoters_contents">
-				<div id="sys1_contents">
-					<p class="normal_text">A toxin-antitoxin system is composed of two or more cognate genes that encode toxins and antitoxins. Toxins are proteins, whereas antitoxins are either proteins or non-coding RNAs. Many prokaryotes have toxin-antitoxin systems, and organisms often have them in multiple copies. Changes in the physiological conditions, such as stress conditions or viral infection leads to the antitoxin degradation, and proteases degrade many antitoxins. Unleashed toxin proteins impede or alter cellular processes including translation, cell division, DNA replication, ATP synthesis, mRNA stability or cell wall synthesis and lead to dormancy. This dormant state probably enables the bacteria to survive in unfavorable conditions.
+<div onclick="obj=document.getElementById('open4').style; obj.display=(obj.display=='none')?'block':'none';">
-In general, toxin is more stable than antitoxin, but antitoxin is expressed to a higher level.<br><br>
+<a style="cursor:pointer;">▼Read more</a>
+</div>
-                                        <div align="center"><p class="normal_text">First toxin&#8208;antitoxin: MazF / MazE</p></div>
+<!--// 折り畳み展開ポインタ -->
-                                        <p class="normal_text">MazF is a toxin protein, and MazE is its cognate antitoxin protein. MazF is a ribosome-independent endoribonuclease. This endoribonuclease activity leads to bacterial growth arrest. MazE and MazF form homodimers, and MazF dimer cleaves mRNAs at ACA sites.  One MazE dimer binds to two MazF dimers, thereby inactivates endoribonuclease activity of MazF dimer.  MazE is labile, subjected to degradation by ClpAP protease, whereas MazF is more stable. <br>
+<!-- 折り畳まれ部分 -->
-<div align="center"><a href="https://static.igem.org/mediawiki/2016/5/5d/T--Tokyo_Tech--MazMaz.jpeg"><img src="https://static.igem.org/mediawiki/2016/5/5d/T--Tokyo_Tech--MazMaz.jpeg" height ="300"></a><br></div>
+<div id="open4" style="display:none;clear:both;">
-				<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig. 2-2-1. </span>
-				</p></div><br>
-<br>
+					<p class="normal_text">We measured the relation between the AHL inputted and the fluorescence intensity.<br>
+					Changing the AHL concentration from 10<sup>-4</sup> to 10<sup>4</sup> by one power of 10 at a time, we measured the fluorescence intensity 4 hours after the insertion. We then performed the fitting with these data.<br>
+					In our experimental data we only measured the fluorescence intensity of GFP. However, we can only do the modulation for the concentration of GFP. Therefore, we needed the relationship between the concentration of GFP by modeling and the fluorescence intensity by experiment. We assumed that the fluorescence intensity is proportional to the concentration of GFP. We determined the parameter from experimental data.<br></p>
+					<p class="normal_text" style="text-align: center;">Fluorescence intensity = 31.8 [GFP]<br></p>
+					<p class="normal_text">From this parameter, we determined the parameters of the promoters.<br>
+					<br>
+					We defined the following set of differential equations.<br>
+					$$ \frac{d[GFP]}{dt} = leak_{Prhl} + \frac{\kappa_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} $$<br>
+					The same holds true for Lux system.<br>
+					$$ \frac{d[GFP]}{dt} = leak_{Plux} + \frac{\kappa_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} $$
+					We used MATLAB to fit the parameters to the experimental data and we fit them to the experimental concentrations.
 					</p>
-                                        <div align="center"><p class="normal_text">Second toxin&#8208;antitoxin: YafO / YafN</p></div>
+					<div align="center"><img src="https://static.igem.org/mediawiki/2016/6/6a/T--Tokyo_Tech---FittingPromoter1.png" height ="500"><br></div>
-                                        <p class="normal_text">YafO is a toxin protein, and YafN is its cognate antitoxin protein.  YafO is a ribosome-associated mRNA interferase that cleaves mRNAs’ downstream 11&#8208;13 bases of the translation initiation sites. When 70S ribosome is dissociated, YafO associates with 50S ribosome subunit and gets endoribonuclease activity. YafO and YafN forms a complex Via binding with YafN, YafO is neutralized. YafN is labile, subjected to degradation by Lon protease, whereas YafO is more stable.<br><br>
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-3-3-1. Fitted to the experimental data of Rhl system</span>
+					</div>
+					<p class="normal_text">We obtained these parameters as follows:<br></p>
+					<p class="normal_text" style="text-align: center;">Leak<sub>Prhl</sub> = 0.86  <br>
+					                                                                             κ<sub>Rhl</sub> &=& 1.326<br>
+					                                                                             n<sub>Rhl</sub> &=& 5 <br>
+					                                                                             K<sub>mRhl</sub> &=& 1000 <br>
+				   </p>
-					</p>
+				   <div align="center"><img src="https://static.igem.org/mediawiki/2016/3/35/T-Tokyo_Tech--FittingPromoter2.png" height ="500"><br></div>
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-3-3-2. Fitted to the experimental data of Lux system</span>
-				</div>
+				   </div>
-				</div>
+					<p class="normal_text" style="text-align: center;">Leak<sub>Plux</sub> = 0.86  <br>
+					                                                                             κ<sub>Lux</sub> = 1.326 <br>
-				<div id="sys2_header">
+					                                                                             n<sub>Lux</sub> = 5 <br>
-					<h3><span>3.2 The art of MazF / MazE </span></h3>
+					                                                                             K<sub>mLux</sub> = 1000 <br>
+				    </p>
+			    </div> <!--promoters_contents-->
+		    </div><!--promoters-->
+</div>
+			<div id="more">
+				<div id="more_header">
+					<h3><span>3-4. More realistic model with mRNA</span></h3>
 				</div><!-- /_header -->
-				<div id="sys2">
+				<div id="more_contents">
-				<div id="sys2_contents">
-					<p class="normal_text">In our project, mazF and mazE are incorporated as a toxin and an antitoxin, respectively. Functions of these two proteins makes it possible to evaluate the beauty of Snow White with GFP and RFP. <br>
+<div onclick="obj=document.getElementById('open5').style; obj.display=(obj.display=='none')?'block':'none';">
-<p class="normal_text">We will give you an example for a better understanding. Imagine that RFP is expressed little by little in <span style="font-style : italic;">E. coli</span>. <a href="https://static.igem.org/mediawiki/2016/5/5d/T--Tokyo_Tech--Project_RFP.png"><img src="https://static.igem.org/mediawiki/2016/5/5d/T--Tokyo_Tech--Project_RFP.png" width="200px" /></a></p>
+<a style="cursor:pointer;">▼Read more</a>
-<p class="normal_text">When MazF expression is induced, the mRNA of GFP is cut, so GFP cannot be translated. Additionally, when MazE is induced, MazE and MazF forms a complex. MazF loses its function, which restarts GFP translation. <a href="https://static.igem.org/mediawiki/2016/d/d8/T--Tokyo_Tech--Project_MazFE.png"><img src="https://static.igem.org/mediawiki/2016/d/d8/T--Tokyo_Tech--Project_MazFE.png" width="200px" /></a></p>
+</div>
-<p class="normal_text">In this way, we can control protein translation. That's why we decided to represent Snow White story. <a href="https://static.igem.org/mediawiki/2016/a/aa/T--Tokyo_Tech--Project_MazF_GFP.png"><img src="https://static.igem.org/mediawiki/2016/a/aa/T--Tokyo_Tech--Project_MazF_GFP.png" width="200px" /></a>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open5" style="display:none;clear:both;">
+					<p class="normal_text">We defined the differential equations and estimated the parameters in the AHL - GFP system as described in 3-3. However, the translation from mRNA to protein was not considered in the model. To simulate the story of ‘Snow White,’ the translation is essential because the whole system includes the toxin-antitoxin system involving the cleavage of mRNA. We also had to take in account in our fitting that the AHL inputted at the beginning decreases with time.<br>
+					Then, we redefined the following set of differential equations.<br>
+					$$ \frac{d[mRNA_{GFP}]}{dt} = leak_{Prhl} + \frac{κ_{Rhl}[C4]^{n_{Rhl}}}{K_{mRhl}^{n_{Rhl}} + [C4]^{n_{Rhl}}} - d[mRNA_{GFP}]$$<br>
+					$$ \frac{d[GFP]}{dt} = α[mRNA_{GFP}] - d_{GFP}[GFP] $$<br>
+					$$ \frac{d[C4]}{dt} = - d_{C4}[C4] $$<br>
+					The same holds true for Lux system.<br>
+					$$ \frac{d[mRNA_{GFP}]}{dt} = leak_{Plux} + \frac{κ_{Lux}[C12]^{n_{Lux}}}{K_{mLux}^{n_{Lux}} + [C12]^{n_{Lux}}} - d[mRNA_{GFP}]$$<br>
+					$$ \frac{d[GFP]}{dt} = α[mRNA_{GFP}] - d_{GFP}[GFP] $$<br>
+					$$ \frac{d[C12]}{dt} = - d_{C12}[C12] $$<br>
+					As a result, we obtained these parameters as follows:</p>
+					<p class="normal_text" style="text-align: center;">Leak<sub>Prhl</sub> = 4.65  <br>
+					                                                                             κ<sub>Rhl</sub> = 14.95<br>
+					                                                                             n<sub>Rhl</sub> = 5 <br>
+					                                                                             K<sub>mRhl</sub> = 1000 <br>
+					                                                                             and<br>
+					                                                                             Leak<sub>Plux</sub> = 2.26  <br>
+					                                                                             κ<sub>Lux</sub> = 6.98 <br>
+					                                                                             n<sub>Lux</sub> = 0.76 <br>
+					                                                                             K<sub>mLux</sub> = 116.24 <br>
 					</p>
-				</div>
+					<p class="normal_text">Using these parameters we simulated the reproduction of the story of Snow White.</p>
-				</div>
+			    </div> <!--more_contents-->
+		    </div><!--more-->
+</div>
+			</div><!-- /fitting_contents -->
+		</div><!-- /fitting -->
-			</div><!-- /system_contents -->
-		</div><!-- /system -->
-		<div id="circuit" class="container">
+		<div id="analysis" class="container">
-			<div id="circuit_header" class="container_header">
+			<div id="analysis_header" class="container_header">
-				<h2><span>4. Our genetic circuit design</span></h2>
+				<h2><span>4. Analysis</span></h2>
-			</div><!-- /_header -->
+			</div><!-- /analysis_header -->
-			<div id="circuit_contents" class="container_contents">
+			<div id="analysis_contents" class="container_contents">
-				<p class="normal_text">Next, we will introduce the genetic circuits that we have designed.
-<p class="normal_text">Our project begins from the scene where the Magic Mirror answers the Queen's question.</p>
-<p class="normal_text">We will split the story into 4 scenes and introduce how our genetic circuits work in each scene. </p><br><br>
-				</p>
+			<div id="prince_coli">
+				<div id="prince_coli_header">
-				<div id="sce1_header">
+					<h3><span>4-1. The Prince <span style ="font-style : italic">coli</span> should be put in during the process</span></h3>
-					<h3><span>4.1 Scene1 : The magic mirror’s answer</span></h3>
 				</div><!-- /_header -->
-				<div id="sce1">
+				<div id="prince_coli_contents">
-				<div id="sce1_contents">
+					<p class="normal_text">We run simulations in order to determine whether we would get a better behavior let we introduce the Prince <span style ="font-style : italic">coli</span> at the beginning or halfway of the story.</p>
-					<div style="float: left;"><a href="https://static.igem.org/mediawiki/2016/f/f5/T--Tokyo_Tech--koma1.png"><img src="https://static.igem.org/mediawiki/2016/f/f5/T--Tokyo_Tech--koma1.png" height ="200"></a><br></div>
-					<div style="float:left; width: 400px; "><p class="normal_text" style="float: left; margin-left: 15px;">
- <span style="color:#4169e1;">"Magic mirror on the wall, who is the fairest one of all?"<br>
-The mirror answered,<br>
-"Snow White is the fairest one."<br></span>
-					</p></div>
+				    <div class="floating"><img src="https://static.igem.org/mediawiki/2016/1/1f/T--Tokyo_Tech--Population-miss.png" height ="300" class="align_left">
-					<p class="clear"></p>
+				    <p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-1-1. Number of individuals when the Prince <span style ="font-style : italic">coli</span> is introduced from the beginning</span></p></div>
+				    <div class="floating"><img src="https://static.igem.org/mediawiki/2016/f/f1/T--Tokyo_Tech--AHL-miss.png" height ="300" class="align_right">
+				    <p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-1-2. AHL concentrations when the Prince <span style ="font-style : italic">coli</span> is introduced from the beginning</span></p></div>
-					<div style="text-align: center;  margin-top: 10px;"><a href="https://static.igem.org/mediawiki/2016/a/a0/T--Tokyo_Tech--Project_Queen_Mirror.png"><img src="https://static.igem.org/mediawiki/2016/a/a0/T--Tokyo_Tech--Project_Queen_Mirror.png" width="400px" /></a>< br />
-					<p class="caption"></p></div>
-					<p class="normal_text">The story starts with the scene where it snows and gets cold. The Magic Mirror <span style="font-style: italic;">coli</span> can produce RhlI protein under low temperature condition. RhlI protein leads to the production of a signaling molecule C4HSL, which is received by the Queen <span style="font-style: italic;">coli</span> telling that Snow White is the fairest of the all.</p><br>
+                   <p class="normal_text">As a result, if we introduce the Prince <span style ="font-style : italic">coli</span> from the beginning, the number of Prince <span style ="font-style : italic">coli</span> increases too much (Fig.5-4-1-1) so the AmiE the Prince <span style ="font-style : italic">coli</span> produces augments and the decomposition of C12 also occurs overly. So C12 is almost inexistent in the medium (Fig.5-4-1-2).</p>
-				</div>
+                   <div class="floating"><img src="https://static.igem.org/mediawiki/2016/e/e7/T--Tokyo_Tech--Population.png" height ="300" class="align_left"><br>
-				</div>
+				    <p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-1-3. Number of individuals when the Prince <span style ="font-style : italic">coli</span> is introduced at t = 700</span></div>
+				    <div class="floating"><img src="https://static.igem.org/mediawiki/2016/4/4f/T--Tokyo_Tech--AHL.png" height ="300" class="align_right"><br>
+				    <p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-1-4. AHL concentrations when the Prince <span style ="font-style : italic">coli</span> is introduced at t = 700</span></div>
-				<div id="sce2_header">
+                   <p class="normal_text">On the other hand, if we introduce the Prince <span style ="font-style : italic">coli</span> at t = 600, the number of Prince <span style ="font-style : italic">coli</span> does not increment much (Fig.5-4-1-3), so C12 can exist until t = 700 and then decreases thanks to the augment of AmiE (Fig.5-4-1-4).<br>In conclusion, if we introduce the Prince <span style ="font-style : italic">coli</span> at t = 700, the circuit will behave accordingly.</p>
-					<h3><span>4.2 Scene2 : The Queen’s trap</span></h3>
+</p>
+</div></div> <!-- header -->
+<br>
+			<div id="prhl">
+				<div id="prhl_header">
+					<h3><span>4-2. Prhl should be changed</span></h3>
 				</div><!-- /_header -->
-				<div id="sce2">
+				<div id="prhl_contents">
-				<div id="sce2_contents">
+					<p class="normal_text">In order to confirm the feasibility of the story with our gene circuit by the combination of the existing promoters, we performed some simulations based on the results of our assays.</p>
-					<div style="float: left;"><a href="https://static.igem.org/mediawiki/2016/8/8e/T--Tokyo_Tech--koma2.png"><img src="https://static.igem.org/mediawiki/2016/8/8e/T--Tokyo_Tech--koma2.png" height ="200"></a><br></div>
+					<div align="center"><img src="https://static.igem.org/mediawiki/2016/6/68/T--Tokyo_Tech--projct_model1.png" height ="450"><br></div>
-					<div style="float: left;width: 400px;"><p class="normal_text" style="float: left; margin-left: 15px;">------<br>
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-2. The intensity of Plux and Prhl promoters</span>
-					<font color="#4169e1">The Queen prepared a poisoned apple.<br />
+                   <p class="normal_text">The diagram above shows that the intensity of the two promoters should be in the red region of the figure.The combination of promoters which we were originally going to use is shown in the graph by the green point. To move this point into the red region, we had to improve Prhl to raise its expression level.</p>
-					She decided to transform into a Witch and give the apple to Snow White.</font></p></div>
+</p>
+</div>
-					<p class="clear"></p>
+</div></div>
-					<div style="text-align: center;  margin-top: 10px;"><a href="https://static.igem.org/mediawiki/2016/0/0a/T--Tokyo_Tech--Project_Queen_And_Mirror.png"><img src="https://static.igem.org/mediawiki/2016/0/0a/T--Tokyo_Tech--Project_Queen_And_Mirror.png" width="400px" /></a></div>
 <br>
-<p class="normal_text">The Queen, which has received C4HSL, produces LasI and MazF.</p>
+			<div id="requirements">
-<p class="normal_text">LasI produces a signaling molecule, 3OC12HSL which is the Poisoned Apple.</p>
+				<div id="requirements_header">
-<p class="normal_text">Additionally, produced MazF inhibits the translation in the Queen. If the translation is inhibited the moment MazF is expressed, sufficient amount of LasI will not be produced, and neither will 3OC12HSL. Then the Queen will fail the assassination of Snow White.</p>
+					<h3><span>4-3. Requirements</span></h3>
+				</div><!-- /_header -->
+				<div id="requirements_contents">
+<div onclick="obj=document.getElementById('open6').style; obj.display=(obj.display=='none')?'block':'none';">
+<a style="cursor:pointer;">▼Read more</a>
+</div>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open6" style="display:none;clear:both;">
+					<p class="normal_text">We performed the sensitivity analysis descried in this section in order to examine which parameter dominates the story. We defined these requirements as the “successful Snow White story.”<br>
+)	At t = 150<br>
+					    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;concentration of RFP > concentration of GFP<br>
+)	At t = 700<br>
+					    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;concentration  of RFP< concentration of GFP<br>
+)	At t = 1500<br>
+					    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;concentration  of RFP > concentration of GFP<br></p>
+					<p class="normal_text">We the began to analyze the graph that satisfies these requirements that we could say that recreates the story correctly. In the table bellow we show the range in which we modified each parameter. They were modified one step size at a time.<br></p>
+					    <table border="1" style="margin: auto;">
+								<tbody>
+									<tr><td>Parameter </td><td> Range </td><td> Step size </td></tr>
+									<tr><td>D </td><td> $$ 0.0001 < D < 0.001 $$ </td><td>0.0001</td></tr>
+									<tr><td>p<sub>C4</sub></td><td> $$ 0.0001 < p_{C4} < 1 $$</td><td> 0.001 </td></tr>
+									<tr><td>p<sub>C12</sub></td><td> $$ 0.0001 < p_{C12} < 1 $$</td><td> 0.001 </td></tr>
+									<tr><td>α</td><td> $$ 0.01 < α < 0.2 $$</td><td> 0.01 </td></tr>
+									<tr><td>d<sub>AmiE</sub> $$</td><td> $$ 0.001 < d_{AmiE} < 1 $$ </td><td> 0.001 </td></tr>
+							    </tbody>
+					    </table>
-				<div id="sce3_header">
+                   <p class="normal_text">As a result, we obtained the following parameter ranges.</p>
-					<h3><span>4.3 Scene3 : Snow White's sleep</span></h3>
+					    <table border="1" style="margin: auto;">
-				</div><!-- /_header -->
+								<tbody>
-				<div id="sce3">
+									<tr><td>Parameter </td><td> Value </td></tr>
-				<div id="sce3_contents">
+									<tr><td> D </td><td> $$ 0.0056 < D < 0.001 $$ </td></tr>
-					<div style="float: left;"><img src="https://static.igem.org/mediawiki/2016/6/6f/T--Tokyo_Tech--koma3.png" height ="200"><br></div>
+									<tr><td> p<sub>C4</sub> </td><td> $$ 0.0029 < p_{C4} < 0.778 $$ </td></tr>
-					<div style="float: left; width: 400px;"><p class="normal_text">-----<br>
+									<tr><td> p<sub>C12</sub> </td><td> $$ 0.001 < p_{C12} < 0.217 $$ </td></tr>
-<p class="normal_text"><font color="#4169e1">Snow White, who always takes people at their word, bit the apple, then sank into unconsciousness soon.</font></p></div>
+									<tr><td> α </td><td> $$ 0.01 < α < 0.16 $$ </td></tr>
+									<tr><td> d<sub>AmiE</sub> </td><td> $$ 0.001 < d_{AmiE} < 1 $$ </td></tr>
+							    </tbody>
+					    </table>
+</p>
+</div>
+</div> </div> <!-- requirements-->
 <br>
+			<div id="production_ahl">
+				<div id="production_ahl_header">
+					<h3><span>4-4. Production rate of C4HSL and 3OC12HSL by RhlI and LasI</span></h3>
+				</div><!-- /_header -->
+				<div id="production_ahl_contents">
+<div onclick="obj=document.getElementById('open7').style; obj.display=(obj.display=='none')?'block':'none';">
+<a style="cursor:pointer;">▼Read more</a>
+</div>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open7" style="display:none;clear:both;">
+					<p class="normal_text">The signaling molecule production rates by RhlI and LasI can be changed by modifying RhlI and LasI to make more or less signaling molecule in silico.</p>
-					<p class="clear"></p>
+					<div align="center"><img src="https://static.igem.org/mediawiki/2016/9/9f/T--Tokyo_Tech--Production-AHL.png" height ="450"><br></div>
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-4-1. Concentrations of GFP and RFP dependencies of production rate of C4 by RhlI</span>
-					<div style="text-align:center; margin-top: 10px;"><a href="https://static.igem.org/mediawiki/2016/a/a5/T--Tokyo_Tech--Project_Queen_And_Snow_White.png"><img src="https://static.igem.org/mediawiki/2016/a/a5/T--Tokyo_Tech--Project_Queen_And_Snow_White.png" width="400px" /></a></div>
+                   <p class="normal_text">Each line corresponds to the transition of the concentration of RFP and GFP with a certain production rate of C12. Red and green lines correspond to RFP and GFP, respectively. Blighter one indicates higher production rate of C12.<br>
-<p class="normal_text">The basic design of Snow White <span style="font-style: italic;">coli</span>'s genetic circuit is almost the same as the Queen <span style="font-style: italic;">coli</span>'.
+                   If the production rate of C4 is between 0.029 and 0.778, our system can recreate the story. If this parameter is too small, the production of LasI by the Queen <span style ="font-style : italic">coli</span> is insufficiently inhibited by MazF so C12 increases greatly. As a result, The concentration of GFP overcomes the concentration of RFP and the story does not develop correctly. And if this parameter is too big, the production of LasI by the Queen <span style ="font-style : italic">coli</span>  is overly inhibited by MazF so C12 does not increase.<br>
-Snow White coli receives 3OC12HSL, the Poisoned Apple, and expresses RhlI and MazF. RhlI synthesizes signaling molecule C4HSL. As described  in the previous section, the Queen <span style="font-style: italic;">coli</span> receives C4HSL and monitor Snow White coli through it. MazF, on the other hand, inhibits the translation in Snow White <span style="font-style: italic;">coli</span>.
+                   As a result, the concentration of RFP is always greater than the GFP concentration and the story does not develop either.</p>
-<br>
+		   </div>
+                   <div align="center"><img src="https://static.igem.org/mediawiki/2016/0/05/T--Tokyo_Tech--Production-AHL2.png" height ="450"><br></div>
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-4-2. Concentrations of GFP and RFP dependencies of production rate of C12 by LasI</span>
-					</p><br>
+                   <p class="normal_text">Each line corresponds to the transition of the concentration of RFP/GFP with a certain production rate of C4. Red and green lines correspond to RFP and GFP, respectively. Blighter one indicates higher production rate of C4.<br>
-				</div>
+                    If production rate of C12 is between 0.001 and 0.217, our system can recreate the story.</p>
-				</div>
+</p>
+</div>
-				<div id="sce4_header">
+</div></div> <!--4-4-->
-					<h3><span>4.4. Scene4 : The Prince’s rescue</span></h3>
+</div>
+<br>
+			<div id="translation">
+				<div id="translation_header">
+					<h3><span>4-5. Translation rate of protein</span></h3>
 				</div><!-- /_header -->
-				<div id="sce4">
+				<div id="translation_contents">
-				<div id="sce4_contents">
-					<div style="float: left;"><a href="https://static.igem.org/mediawiki/2016/4/40/T--Tokyo_Tech--koma4.png"><img src="https://static.igem.org/mediawiki/2016/4/40/T--Tokyo_Tech--koma4.png" height ="200"></a><br></div>
+<div onclick="obj=document.getElementById('open8').style; obj.display=(obj.display=='none')?'block':'none';">
-					<div style="float: left; width: 400px;"><p class="normal_text">-----<br>
+<a style="cursor:pointer;">▼Read more</a>
-<font color="#4169e1">Although he knew her death, he couldn’t help lifting her up because of her beauty.<br>
+</div>
-Then, she opened her eyes!<br></font></div>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open8" style="display:none;clear:both;">
+					<p class="normal_text">Translation rate affects the production of protein.</p>
+					<div align="center"><img src="https://static.igem.org/mediawiki/2016/0/03/T-Tokyo_Tech--Translation.png" height ="450"><br></div>
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-5. Concentrations of GFP and RFP dependencies of translation rate of proteins</span>
+                   <p class="normal_text">Each line corresponds to the transition of the concentration of RFP and GFP with a certain translation rate. Red and green lines correspond to RFP and GFP, respectively. Blighter one indicates higher translation rate.<br>
+                   If translation rate of protein is between 0.01 and 0.16, our system can recreate the story.
+</p>
+</div>
+</div></div> <!-- 4-5-->
+</div>
 <br>
-<br>
+			<div id="decomposition">
-				<p class="clear"></p>
+				<div id="decomposition_header">
+					<h3><span>4-6. Decomposition rate of C12 by AmiE</span></h3>
-				<div style="text-align: center; margin-top: 10px;"><a href="https://static.igem.org/mediawiki/2016/7/70/T--Tokyo_Tech--Project_Snow_White_Prince.png"><img src="https://static.igem.org/mediawiki/2016/7/70/T--Tokyo_Tech--Project_Snow_White_Prince.png" width="400px" /></a></div>
+				</div><!-- /_header -->
-				<p class="normal_text">The Prince coli which receives 3OC12HSL expresses AmiE. AmiE is said to degrade HSL with more than 6 carbons, which means that AmiE degrades the Poisoned Apple, 3OC12HSL.By the degradation of the Poisoned Apple, MazF expression is inhibited in Snow White and its function is counteracted by MazE. Then, translation restarts in Snow White <span style="font-style: italic;">coli</span>.</p>
+				<div id="decomposition_contents">
-				</div>
-				</div>
+<div onclick="obj=document.getElementById('open9').style; obj.display=(obj.display=='none')?'block':'none';">
-			</div><!-- /circuit_contents -->
+<a style="cursor:pointer;">▼Read more</a>
-		</div><!-- /circuit -->
+</div>
-</div></div>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open9" style="display:none;clear:both;">
+					<p class="normal_text">AmiE decomposes C12. The concentration of C12 after input of the Prince <span style ="font-style : italic">coli</span> is changed by AmiE. If the decomposition rate of C12 is too small, C12 does not decrease enough so the MazF inside Snow White <span style ="font-style : italic">coli</span> continues being expressed and the concentration of RFP decreases.</p>
-		<div id="Q.E.D." class="container">
+					<div align="center"><img src="https://static.igem.org/mediawiki/2016/0/08/T--Tokyo_Tech--Decomposition.png" height ="450"><br></div>
-<div id="Q.E.D._header" class="container_header">
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-6. Concentrations of GFP and RFP dependencies of decomposition rate of C12 by AmiE</span>
-				<h2><span>5. Replication of “Snow White” by our genetic circuit</span></h2>
+                   <p class="normal_text">Each line corresponds to the transition of the concentration of RFP and GFP with a certain decomposition rate of C12. Red and green lines correspond to RFP and GFP, respectively. Blighter one indicates higher value of decomposition rate of C12.<br>
-			</div><!-- /_header -->
+                   If degradation rate of C12 is higher than 0.00056, our system can recreate the story.</p>
-			<div id="Q.E.D._header" class="container_contents">
+</p>
-				<h2><span></span></h2>
+</div>
-                        <p class="normal_text">We conducted an experiment and simulated to confirm that the above four scenes can be represented. Based on them, we simulated the representation of Snow White story.</p><br>
+</div></div> <!--4-6-->
-			<div id="sys1_header">
+</div>
-					<h3><span>5.1 Cold inducible promoter functions at 18°C in Scene 1</span></h3>
+<br>
+			<div id="degradation_amie">
+				<div id="degradation_amie_header">
+					<h3><span>4-7. Degradation rate of AmiE</span></h3>
 				</div><!-- /_header -->
-				<div id="sys1">
+				<div id="degradation_amie_contents">
-				<div id="sys1_contents">
-<div align="center"><img src="https://static.igem.org/mediawiki/2016/f/f5/T--Tokyo_Tech--koma1.png" height ="200"></div>
-                                <p class="normal_text">The experiment was conducted by BBa_1949001. We cultivated each sample at 18°C or 37°C and measured the [GFP / Turbidity] with a plate reader. The experimental result showed that samples cultured at 18°C had higher fluorescence intensity of GFP than those cultured at 37°C.</p>
-                                <p class="normal_text">Thus, we found that the story begins with lowering the culture temperature .</p>
-<a href="https://2016.igem.org/Team:Tokyo_Tech/Promoter_Assay/Pcold ">Read Pcold Assay page </a>.
-<br><br></p>
+<div onclick="obj=document.getElementById('open10').style; obj.display=(obj.display=='none')?'block':'none';">
+<a style="cursor:pointer;">▼Read more</a>
+</div>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open10" style="display:none;clear:both;">
-  				<p class="normal_text">5.2 The screening of Prhl with optimal strength for Scene 2<br>
+				<div align="center"><img src="https://static.igem.org/mediawiki/2016/d/d4/T--Tokyo_Tech--DegradationAmiE.png" height ="450"><br></div>
-					<div style="float: left;"><a href="https://static.igem.org/mediawiki/2016/8/8e/T--Tokyo_Tech--koma2.png"><img src="https://static.igem.org/mediawiki/2016/8/8e/T--Tokyo_Tech--koma2.png" height ="200"></a><br></div>
+				<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-7. Concentration of GFP and RFP dependencies of degradation rate of AmiE</span>
-  				<p class="normal_text">Eating the Poisoned Apple given by the Queen <span style="font-style : italic">coli</span>, Snow White <span style="font-style : italic">coli</span> falls asleep. We use cell-cell communication to represent this scene, so we need the reporter with optimal strength to make the genetic circuit designed by us work properly.</p>
-<p class="normal_text">Therefore, we introduce rhl system assay as a concept in this Scene. We improved the function of Prhl through the process listed below and succeeded in newly obtaining of optimal Prhl mutants for our project. </p>
-<p class="normal_text">  5.2.1　Reporter assay<br>
+                 <p class="normal_text">Each line corresponds to the transition of the concentration of RFP and GFP with a certain degradation rate of AmiE. Red and green lines correspond to RFP and GFP, respectively. Blighter one indicates higher degradation rate of AmiE.<br>
-<p class="normal_text">First, we evaluated the activities the existing promoters: Prhl(BBa_I14017), Plux(BBa_R0062), Plas(BBa_R0079) by adding 3 types of AHLs.
+                   Even if we modify the values of the parameters inside the defined range, the concentration of RFP overcomes the concentration of GFP. And even if the degradation rate of AmiE is small, the decomposition rate of C12 by AmiE is high enough so C12 decreases sufficiently.</p>
-					</p>
+</p>
-					<div align="center"><img src="https://static.igem.org/mediawiki/2016/0/00/T--Tokyo_Tech--assay_ahl_reporter.png" height ="200"></div>
+</div>
-					<p class="normal_text">Even adding 3OC12HSL to Plux promoter, the promoter activity was still observed. The graph also shows that Prhl has a large leak, and the Prhl activity can be hardly seen compared to the others when C4HSL is added.</p>
+</div></div> <!--4-7-->
+</div>
-<a href="https://2016.igem.org/Team:Tokyo_Tech/AHL_Assay/AHL_Reporter_Assay
+<br>
- ">Read AHL Reporter Assay</a>.
+			<div id="degradation_protein">
+				<div id="degradation_protein">
+					<h3><span>4-8. Degradation rate of RFP and GFP</span></h3>
-				<br>
-					</p><br>
-				<p class="normal_text">  5.2.2 Simulation regarding Prhl strength　<br>
-<p class="normal_text">Using the experimental results of preceding paragraph, we simulated to confirm that the genetic circuit which we designed works properly when using the existing Prhl.<br>
-<p class="normal_text">The above diagram shows the intensity of the two promoters should be in the red region in the figure. The green point shows the relationships of the promoters which we intended to use primarily. In order to move to the red region, we found that it is needed to improve Prhl and increase its expression level.</p>
-<p class="normal_text">The graph below shows the result of recreating “Snow White” when using existing rhl promoter. Only the fluorescence intensity of the Queen coli got lowered. It means that the Queen coli failed to poison Snow White coli and she killed herself.</p>
-<div align="center"><img src="https://static.igem.org/mediawiki/2016/6/68/T--Tokyo_Tech--projct_model1.png" height ="300"><br></div>
-					<div align="center">
-<a href="https://2016.igem.org/Team:Tokyo_Tech/Model#prhl ">Read Model page</a>.
-			</p><br>
-					</p><br>
-				<p class="normal_text">  5.2.3　Improvement of Prhl<br>
-We made mutants of Prhl by inserting a point mutation into the wild type (WT) Prhl.
-In the experiment, we added reagent AHLs into the reporters and examined their fluorescence intensities.
-As a result, we succeeded in newly obtaining stronger mutants than the WT Prhl (NM).<br>
-iGEM Tokyo_Tech has improved Prhl in the past. However, comparing the Prhl (NM) to Prhl (LR), the SN ratio of Prhl (NM) was higher than that of Prhl (LR). Futuremore, the result shows that Prhl (LR)has crosstalk with C12-AHL at a constant rate. When representing Snow White story, and the crosstalk to C12 happens, the Queen <span style="font-style : italic">coli</span> will suicide by eating the Poisoned Apple made by herself. Therefore, we made the mutants using WT as a template.<a href="https://2016.igem.org/Team:Tokyo_Tech/AHL_Assay/Rhl_System_Assay ">Read Rhl System Assay </a>.<br>
-								</p><br>
-			<div id="sce2_header">
-					<h3><span>5.3 MazF-MazE system as Toxin-Antitoxin system can be controlled in Scene 3</span></h3>
 				</div><!-- /_header -->
-					<div align="center"><img src="https://static.igem.org/mediawiki/2016/6/6f/T--Tokyo_Tech--koma3.png" height ="200"></div>
+				<div id="degradation_protein_contents">
-<p class="normal_text">In this Scene, we introduce TA system as a concept.</p>
-<p class="normal_text">If we do not show that translation is inhibited by MazF, and translation is restarted by MazE, we cannot represent the key part of the story that "Snow White falls down by the Poisoned Apple and wake up again by the Prince.”</p>
+<div onclick="obj=document.getElementById('open11').style; obj.display=(obj.display=='none')?'block':'none';">
-<div align="center"><img src="https://2016.igem.org/File:T--Tokyo_Tech--maz1.png" height ="200"></div>
+<a style="cursor:pointer;">▼Read more</a>
-<p class="normal_text">In this experiment, we used the BBa_K1949100 and Bba_1949102.</p>
+</div>
-<p class="normal_text">First, MazF was expressed by arabinose, and 2 h later, the MazE was expressed by IPTG/p.
+<!--// 折り畳み展開ポインタ -->
-<p class="normal_text">From the experimental results, we found that the turbidity of samples without MazE did not rise. However, we also found that <span style="font-style : italic">E. coli</span> restarts its cell growth when MazE is expressed by adding IPTG.
+<!-- 折り畳まれ部分 -->
-Moreover, when only MazF worksed, the RFU of GFP hardly rose, but when MazE was induced, the RFU of GFP rose. (link: toxin assay)<br>
+<div id="open11" style="display:none;clear:both;">
-</p><p class="normal_text">From the above, we found that MazF stops cell growth and translation of <span style="font-style : italic">E. coli</span>, but MazE restarts cell growth that have stopped and furthermore restarts translation.</p>
-According to the experiments, we showed that TA system works properly.</p> <a href="https://2016.igem.org/Team:Tokyo_Tech/Toxin_Assay/mazEF_System_Assay
- ">Read mazEF System Assay</a>.
-                                                                    </p><br>
-                                                              <p class="normal_text">5.4 AmiE degrades 3OC12HSl selectively and does not degrade C4HSL in Scene 4<br>
-<div align="center"><img src="https://static.igem.org/mediawiki/2016/4/40/T--Tokyo_Tech--koma4.png" height ="200"></div>
-In the final Scene, we introduce the selective degradation of AHLs by AmiE as a concept.
-As shown in the TA system, we found that Snow White can wake up again because MazE counteracts the function of MazF. However, we have not showed the trigger, that is, the degradation of only 3OC12HSL by the Prince <span style="font-style : italic">coli</span>. Therefore, we examined whether AmiE selectively degrades AHLs.<br>
-From the experimental results, when C12 was added to the culture skution of <span style="font-style : italic">E. coli</span> where AmiE was expressed, C12 was degraded, whereas C4 was hardly degraded.
-For these reasons, we showed that AmiE selectively degrades AHLs, only C12 in this project.<br><a href="https://2016.igem.org/Team:Tokyo_Tech/AmiE_Assay
- ">Read AmiE Assay</a>.
-                                                                    </p><br>
-                                                              <p class="normal_text">5.5　the simulation related to the story<br>
-From the results of wet lab, it was showed that the designed circuit works properly at each point. We simulated the representation of the story in a combination of these Points.<br>
-                                                                    </p><br>
-                                                              <p class="normal_text">5.5.1. When the Prince comes?<br>
-We simulated to confirm which is better, the Prince <span style="font-style : italic">coli</span> exist from the beginning, that is, the Prince has known Snow White and watches her grow or he comes across her, in order to make our genetic circuit work.
-As a result, we found that when the Prince <span style="font-style : italic">coli</span> is added from the beginning, AmiE produced by the Prince <span style="font-style : italic">coli</span> increases and C12 is overdegraded. Then, C12 cannot exist in the medium (Fig. 2), and the circuit does not work correctly.<br>
-On the other hand, when the Prince <span style="font-style : italic">coli</span> is added at t = 700, the number of the Prince <span style="font-style : italic">coli</span> does not increase greatly (Fig3). Therefore, C12 can exist until t = 70, and after that C12 decreases with an increase in AmiE (Fig4).<br>
-From this result, it was found that the genetic circuit works well by adding the Prince <span style="font-style : italic">coli</span> at t=700. In other words, as with the original story, the Prince <span style="font-style : italic">coli</span> comes across Snow White <span style="font-style : italic">coli</span> at t=700 and rescues her.<br><a href="https://2016.igem.org/Team:Tokyo_Tech/Model#prince_coli ">Read Model page</a>.
-                                                                    </p><br>
-                                                              <p class="normal_text">5.5.2　representation of the story<br>
-As a result of simulation, 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.<br>
-Based on the simulation, we will show you which one is a real beauty, Snow White <span style="font-style : italic">coli</span> or the Queen <span style="font-style : italic">coli</span>.<br>
-In the blue area of Fig, the fluorescence intensity of Snow White <span style="font-style : italic">coli</span> exceeds the Queen <span style="font-style : italic">coli</span>’s.
-That is because one day, Snow White <span style="font-style : italic">coli</span>’s beauty exceeded the Queen <span style="font-style : italic">coli</span>’s beauty. Snow White got fairer and fairer.<br>
-In the pink area of Fig, added C4 leads to production of C12. Because of this, MazF, a toxin, increases in the Queen <span style="font-style : italic">coli</span>, and suppresses increase of fluorescence protein. It looks as if after the Magic Mirror’s answer, the Queen transformed herself into a Witch and gave the Poisoned Apple to Snow White. This is the scene where the Queen is mad with jealousy and drifts into crime<br>
-In the green area of Fig, incereased C12 induces MazF in Snow White <span style="font-style : italic">coli</span>, which causes GFP excess over RFP. It looks as if Snow White bit the apple, then sank into unconsciousness soon<br>
-In the yellow area of Fig, since AmiE produced by the added Prince <span style="font-style : italic">coli</span> degrades C12, MazF in Snow White <span style="font-style : italic">coli</span> decreases and increases C4. It looks as if the Prince lifted Snow White and she opened her eyes.<br>
-From the above, we were able to represent the story by the genetic circuit we designed, and furthermore, it was found that Snow White <span style="font-style : italic">coli</span> is a real beauty. <br><a href="https://2016.igem.org/Team:Tokyo_Tech/Model#results">Read Model page</a>.
+					<p class="normal_text">The degradation rate of RFP and GFP is key to the success the story of ‘"Snow White".<br>
-                                                                    </p>
+					These parameters are closely related to the concentrations of GFP and RFP, so we conjectured that if they do not take appropriate values the story can not be correctly recreated.</p>
-			</div><!-- /Q.E.D._contents -->
+					<div align="center"><img src="https://static.igem.org/mediawiki/2016/a/a0/T--Tokyo_Tech--DegradationGFP.png" height ="450"><br></div>
-		</div><!-- /Q.E.D. -->
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4-8 Relation of degradation rate of GFP and RFP</span>
-</div></div>
-	 <div id="hp" class="container">
-			<div id="hp_header" class="container_header">
-				<h2><span>6．Integrated Human Practice</span></h2>
-			</div><!-- /_header -->
-			<div id="hp_contents" class="container_contents">
-				<p class="normal_text"> In promoting our project, we had dialogues with the public and experts. Based on the opinions from them, we developed our project. This led to success in creation of a well-rounded project with the connection between the public and experts, keeping from our narrow view.
+                   <p class="normal_text">The story is recreated only if the degradation rate of RFP and GFP are the same.</p>
+</div>
+</div>
+</div></div> <!--4-8-->
+		</div><!-- /analysis_contents -->
+		</div><!-- /analysis -->
+		<div id="software" class="container">
+			<div id="software_header" class="container_header">
+				<h2><span>5. Software</span></h2>
+			</div><!-- /software_header -->
+			<div id="software_contents" class="container_contents">
 <br>
+			<div id="abstract">
-                        	</p><br><br>
+				<div id="abstract_header">
-				<div id="cha1_header">
+					<h3><span>5-1. Abstract</span></h3>
-					<h3><span>6.1 “Snow White”</span></h3>
 				</div><!-- /_header -->
-				<div id="cha1">
+				<div id="abstract_contents">
-				<div id="cha1_contents">
+				<img src="https://static.igem.org/mediawiki/2016/8/8b/T--Tokyo_Tech--ACA_Dwarfs.jpg" height ="300"><br></div>
-					<p class="normal_text">Why we are going to participate in the iGEM with the theme of Snow White? It is resulted from drawing on the opinion obtained through various dialogues with the public. This time, we decided to deal with Snow White, which was easy-to-follow, familiar, and attracted the public.<br>
+					<p class="normal_text">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. <br>Then we improve the practicality of the characteristic of the <span style ="font-style : italic"> mazEF </span> system. For example you can let protein A express constantly by eliminating ACA sequences of the sequence, while letting protein B stop being expressed, at the desirable timing, by expression of MazF.<br>This software also evades the use of rare codons, so you don’t have to worry about them.</p>
-					<h3><span>6.2 Addition of other characters</span></h3>
+<br>
+			<div id="key_achievements">
+				<div id="key_achievements_header">
+					<h3><span>5-2. Key achievements</span></h3>
 				</div><!-- /_header -->
-				<div id="cha21">
+					<p class="normal_text">・Provided the tool regulating the number of ACA sequences<br></p>
-				<div id="cha2_contents">
+					<p class="normal_text">・Released under open-source license so everyone can use it<br></p>
-					<p class="normal_text">Initially, only 3 characters, Snow White, the Queen, and the Prince, appeared in our story. However, we got the simple question from junior high school and high school students that why other characters did not appear in our story. Then we decided to add other characters. We designed the Magic Mirror’s genetic circuit and conducted an experiment. Additionally, as dwarfs, we prepared the <span style="font-style : italic">E. coli</span> (strain name). As you can see in the photograph, they have round shapes and are very charming compared to the general <span style="font-style : italic">E. coli</span>. <br><br></div></div><!-- /cha21 -->
+					<p class="normal_text">・Able to correspond to any base arrangements<br></p>
+					<p class="normal_text">・Rare codons are evaded<br></p>
+					<p class="normal_text">・Extend the application field of <span style ="font-style : italic">mazEF</span> system<br></p>
+</p>
-                                      				<div id="sof_header">
-					<h3><span>6.3. The software development for future work</span></h3>
-				</div><!-- /_header -->
-				<div id="sof">
-				<div id="sof_contents">
-					<p class="normal_text">One students asked the question, "Can you apply this project to contribute society?" After we thought what we could do, we decided to have a dialogue with an expert.<br><br>
-					</p>
-                                <div id="dia_header">
-					<h4><span>6.3.1 The dialogue with an expert</span></h4>
-				</div><!-- /_header -->
-				<div id="dia">
-				<div id="dia_contents">
-					<p class="normal_text">We developed a new software named ACA Dwarfs. This software helps to control the sensitivity of the protein to MazF by regulating the number of ACA sequences in the mRNA sequence. ACA Dwarfs can increase or decrease the number of ACA sequences on mRNA without changing amino acid sequences that the mRNA specifies or frameshift resulted from insertion of bases without considering.</p>
-<br><br>
-					</p></div>
-                                <div id="dwa_header">
-					<h4><span>6.3.2 ACA Dwarfs</span></h4>
-				</div><!-- /_header -->
-				<div id="dwa">
-				<div id="dwa_contents">
-					<p class="normal_text">After having dialogue with experts, we obtained a comment that TA system has a potential to be linked to development of effective technology.
-However, at present, there exits problems when using a TA system to control the protein production.<br>
-<p class="normal_text">We cannot selectively produce only desired protein because other proteins would be also produced at the same time.
-Then, our dry lab used Java to develop software named “ACA Dwarfs” adjusting number of ACA base sequence as a solution to the problem.</p>
 <br>
-  This graph shows that the simulation result when changing the base sequences of GFP and RFP with ACA Dwarfs. In case of GFP and RFP, their concentrations decreases earlier than original ones.<br>
+			<div id="work_flow">
-Using ACADwarfs enabled us to make GFP and RFP more reactive to MazF.<br>
+				<div id="work_flow_header">
+					<h3><span>5-3. Work flow</span></h3>
+				</div><!-- /_header -->
+<div onclick="obj=document.getElementById('open12').style; obj.display=(obj.display=='none')?'block':'none';">
+<a style="cursor:pointer;">▼Read more</a>
+</div>
+<!--// 折り畳み展開ポインタ -->
+<!-- 折り畳まれ部分 -->
+<div id="open12" style="display:none;clear:both;">
-					</p></div>
+				<style type="text/css">
-				</div>
+				<!--
-				</div>
+/*
+				#main_contents .list_parentheses li{
+						list-style: none;
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+					display: marker;
+					content: counter(cnt) ") ";
+				}*/
+				-->
+				</style>
+					<ol type="1" class="list_parentheses">
+					 <li><p class="normal_text"> Start ACADwarfs<br></p>
+					       <p class="normal_text"> Download the zip file and open it.<br></p>
+					        <img src="https://static.igem.org/mediawiki/2016/e/e7/T--Tokyo_Tech--open.png" height ="400"></li>
-			</div><!-- /sof_contents -->
+					 <li><p class="normal_text"> Put in the part sequence<br></p>
-		</div><!-- /sof -->
+					        <p class="normal_text">Put the part sequence you want to regulate the effect of the <span style ="font-style : italic">mazEF</span> system on in the upper window.<br></p>
-	</div><!-- additional -->
+					        <img src="https://static.igem.org/mediawiki/2016/6/6b/T--Tokyo_Tech--putin.png" height ="400"></li>
-	</div><!-- additional -->
-        </div><!-- additional -->
+					 <li><p class="normal_text"> Choose operation<br></p>
+					        <p class="normal_text">If you want to magnify the effect of <span style ="font-style : italic">mazEF</span> system, choose “increase ACA”.<br></p>
+					        <p class="normal_text">If you want to lessen the effect of <span style ="font-style : italic">mazEF</span> system, choose “decrease ACA”.<br></p>
+					        <img src="https://static.igem.org/mediawiki/2016/7/73/T--Tokyo_Tech--choose.png" height ="400"></li>
-		<div id="reference" class="container">
+				     <li><p class="normal_text">Get sequences<br></p>
-			<div id="reference_header" class="container_header">
+				            <p class="normal_text">You can get the modified part sequences in the lower window. Modified codons will be written in capital letters and while the rest will be in small letters so you can easily locate the modified parts.<br>And under this window you can see the number of ACA sequences on the sequence before the modification of the following "previous number" and the number of ACA sequences on the sequence after the modification of the following "new number".<br></p>
-				<h2><span>7. Reference</span></h2>
+				            <img src="https://static.igem.org/mediawiki/2016/6/6a/T--Tokyo_Tech--get.png" height ="400"></li>
-			</div><!-- /_header -->
+</ol>
-                      <div id="reference_contents" class="container_contents">
+</p>
-				<p class="normal_text">[1] Unterholzner SJ, Poppenberger B, Rozhon W. Toxin-antitoxin systems: Biology, identification, and ampicillin. Mob Genet Elements. 2013 Sep; 3(5): e26219.</p>
-<p class="normal_text">[2]Zielenkiewicz U., Ceglowski P. The toxin-antitoxin system of the streptococcal plasmid pSM19035.J. Bacteriol. 2005;187:6094–6105.</p>
-<p class="normal_text">[3] Fozo EM, Makarova KS, Shabalina SA, Yutin N, Koonin EV, Storz G. Abundance of type I toxin–antitoxin systems in bacteria: searches for new candidates and discovery of novel families. Nucleic Acids Res. 2010 Jun; 38(11): 3743–59.</p>
-<p class="normal_text">[4] Gerdes K, Wagner EG. RNA antitoxins. Curr. Opin. Microbiol. 2007 Apr; 10 (2): 117–24. </p>
-<p class="normal_text">[5] Zhang J., Y Zhang, L Zhu, Suzuki M, Inouye M. Interference of mRNA function by sequence-specific endoribonuclease PemK. J. Biol. Chem. 2004 Mar; 279:20678-20684.</p>
-<p class="normal_text">[6] Park J.-H., Yamaguchi Y., Inouye M. Intramolecular regulation of the sequence-specific mRNA interferase activity of MazF fused to a MazE fragment with a linker cleavable by specific proteases. Appl. Environ. Microbiol. 2012 Jun; 78(11): 3794–3799.</p>
-<p class="normal_text">[7] Aizenman E., H Engelberg-Kulka, G Glaser. An Escherichia coli chromosomal “addiction module” regulated by guanosine 3′,5′-bispyrophosphate: a model for programmed bacterial cell death. Proc Natl Acad Sci U S A. 1996 Jun; 93(12): 6059–6063. </p>
-<p class="normal_text">[8] Brown J. M., and Shaw K. J. A Novel Family of Escherichia coli Toxin-Antitoxin Gene Pairs. J Bacteriol. 2003 Nov; 185(22): 6600–6608.</p>
-<p class="normal_text">[9] Zhang Y, Yamaguchi Y, Inouye M. Characterization of YafO, an Escherichia coli toxin. J Biol Chem. 2009 Sep; 284(38): 25522–25531.</p>
-<p class="normal_text">[10]Christensen-Dalsgaard M., Jorgensen M.G., Gerdes K. Three new RelE-homologous mRNA interferases of Escherichia coli differentially induced by environmental stresses. Mol. Microbiol. 2010 Jan; 75:333–348. </p>
-<p class="normal_text">[11]Ochiai S, Yasumoto S, Morohoshi T, Ikeda T. AmiE, a Novel N-Acylhomoserine Lactone Acylase Belonging to the Amidase Family, from the Activated-Sludge Isolate Acinetobacter sp. Strain Ooi24. Appl Environ Microbiol.2014 Nov;80(22):6919-25.</p>
-<p class="normal_text">
-[12] Gerardo Medina et al. Mechanism of Pseudomonas aeruginosa RhlR Transcriptional Regulation of the rhlAB Promoter. J Bacteriol. 2003 Oct; 185(20): 5976–5983.</p>
-			</div><!-- /reference_contents -->
-		</div><!-- /reference -->
-                       </div>
-		</div>
 </div>
+<br>
+			<div id="demo">
+				<div id="demo_header">
+					<h3><span>5-4. Demonstration</span></h3>
+				</div><!-- /_header -->
+					<p class="normal_text">We created a demo to present the features of this software. Using this, we regulated the number of ACA sequences and control the sensitivity of the protein to MazF.</p>
+					 <table border="1" style="margin: auto;">
+								<tbody>
+									<tr><td> Gene </td><td> Pre number of ACA sequences </td><td>Post number of ACA sequences </td></tr>
+									<tr><td> RFP</td><td> 10 </td><td> 30 </td></tr>
+									<tr><td> GFP </td><td> 23 </td><td> 39 </td></tr>
+									<tr><td> MazF </td><td> 2 </td><td> 1 </td></tr>
+									<tr><td> MazE </td><td> 2 </td><td> 1 </td></tr>
+							    </tbody>
+					    </table>
-	<script>
+					<p class="normal_text">We increased the numbers of ACA sequences of RFP and GFP decreased the numbers of ACA sequences of MazF and MazE .<br>
+                    <div align="center"><img src="https://static.igem.org/mediawiki/2016/c/c9/T--Tokyo_Tech--ACAmodel1.jpg" height ="450"><br></div>
+					<div align="center"><p class="caption" style="font-size: 16px; text-align: center;"><span style="font-weight: bold;">Fig.5-4. Comparison between the results of simulations using original sequences and modified sequences</span></p></div>
+					<p class="normal_text">We can see that the concentration of expressed MazF reacts more keenly after adjusting the ACA sequences than before doing so.</p>
+</p>
+<br>
+			<div id="download">
+				<div id="download_header">
+					<h3><span>5-5. Download</span></h3>
+				</div><!-- /_header -->
+				<p class="normal_text">To download click <a href="https://static.igem.org/mediawiki/2016/3/32/T--Tokyo_Tech--ACA_Dwarfs.zip">here</a>.</p>
+				<p class="normal_text">The code is available on <a href="https://github.com/Ryuta339/ACADwarfs">github</a>.</p>
+			</div><!-- /software_contents -->
+		</div><!-- /software -->
+	</div><!-- /main_contents -->
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Difference between revisions of "Team:Tokyo Tech/Project"

Revision as of 21:32, 19 October 2016

Model

Contents

1. Overview

2. Story simulation

2-1. Mathematical model

Snow White

Queen

Prince

2-2. Results

3. Fitting

3-1. Population growth

3-2. Toxin-Antitoxin system

3-3. Promoters

3-4. More realistic model with mRNA

4. Analysis

4-1. The Prince coli should be put in during the process

4-2. Prhl should be changed

4-3. Requirements

4-4. Production rate of C4HSL and 3OC12HSL by RhlI and LasI

4-5. Translation rate of protein

4-6. Decomposition rate of C12 by AmiE

4-7. Degradation rate of AmiE

4-8. Degradation rate of RFP and GFP

5. Software

5-1. Abstract

5-2. Key achievements

5-3. Work flow

5-4. Demonstration

5-5. Download