Revision as of 21:56, 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	$$ 0.001 < d_{AmiE} < 1 $$

@@ Line 212: / Line 212: @@
 							\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}
+							\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]
+							\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}
@@ Line 230: / Line 232: @@
 							\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]
+							\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}
@@ Line 242: / Line 245: @@
 							\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]
+							\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}
@@ Line 251: / Line 255: @@
 							\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]
+							\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}
@@ Line 257: / Line 262: @@
 							\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]
+							\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}

Difference between revisions of "Team:Tokyo Tech/Model"

Revision as of 21:56, 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