Team:UT-Tokyo/Data/Modeling/Model03

From 2011.igem.org

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=[[Team:UT-Tokyo/Data/Modeling/Model03/applet|Interactive demo]]=
=[[Team:UT-Tokyo/Data/Modeling/Model03/applet|Interactive demo]]=
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== Simulation 3-1 Chemotaxis==
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= Simulation 3-1 Chemotaxis=
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=Abstract=
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==Abstract==
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We simulated the chemotactic behavier of one colony composed of 10<html><sup>8</sup></html> E.coli cells using Asp diffusion model in model1 and the approximation of chemotaxis we derived in model2.
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We simulated the chemotactic behavier of one colony composed of 10<html><sup>8</sup></html> ''E.coli'' cells using Asp diffusion model in model1 and the approximation of chemotaxis we derived in model2.
The result was consistent with the experimental result.  
The result was consistent with the experimental result.  
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=Methods=
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==Methods==
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We considered the dynamics of E.coli colony as following simultaneous partial differential equations.
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We considered the dynamics of ''E.coli'' colony as following simultaneous partial differential equations.
[[File:utt_m3_eqn1.png]]
[[File:utt_m3_eqn1.png]]
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We already knew the values of parameters V, D<html><sub>E</sub></html>, D<html><sub>A</sub></html> using model1 and model2.
We already knew the values of parameters V, D<html><sub>E</sub></html>, D<html><sub>A</sub></html> using model1 and model2.
In this section we use the hypothesis that the cells digest Asp.  However, the digestion rate was not clear so we ran the simulation with some different digestion rates: k= 3.3&times;10<html><sup>-21</sup></html>,  3.3&times;10<html><sup>-20</sup></html>, and  3.3&times;10<html><sup>-19</sup></html>  [mol].
In this section we use the hypothesis that the cells digest Asp.  However, the digestion rate was not clear so we ran the simulation with some different digestion rates: k= 3.3&times;10<html><sup>-21</sup></html>,  3.3&times;10<html><sup>-20</sup></html>, and  3.3&times;10<html><sup>-19</sup></html>  [mol].
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To be exact, we had to consider the growth of E.coli, but the colony growth is so complex a process that we could not find out an appropriate colony growth model (i.e. A growth rate as a function of E.coli density).  For this reason we did not consider the growth in our simulation.  
+
To be exact, we had to consider the growth of ''E.coli'', but the colony growth is so complex a process that we could not find out an appropriate colony growth model (i.e. A growth rate as a function of ''E.coli'' density).  For this reason we did not consider the growth in our simulation.  
We simulated the time development of above equations using 1st order finite difference method.
We simulated the time development of above equations using 1st order finite difference method.
The initial state was shown in fig.1.
The initial state was shown in fig.1.
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{{:Team:UT-Tokyo/Templates/Image|file=utt_m3_fig1.png|caption=Figure 1. Initial state}}
{{:Team:UT-Tokyo/Templates/Image|file=utt_m3_fig1.png|caption=Figure 1. Initial state}}
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Following movies are the result of the simulation.  Color strength indicates the concentration of E.coli.
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==Results==
 +
 
 +
Following movies are the result of the simulation.  Color strength indicates the concentration of ''E.coli''.
<html>
<html>
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</html>
</html>
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Movie 1.  k= 3.3&times;10<html><sup>-21</sup></html>
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Movie 1.  k= 3.3&times;10<html><sup>-21</sup></html>.
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Left side indicates Asp diffusion and right side indicates E.coli distribution.
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Left side indicates Asp diffusion and right side indicates ''E.coli'' distribution.
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If you cannot load the file, click [http://igem-ut.net/2011/model/model3/utt_m3_mov1.mov|here].
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If you cannot load the file, click [[http://igem-ut.net/2011/model/model3/utt_m3_mov1.mov here]].
<html>
<html>
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Movie 2.  k= 3.3&times;10<html><sup>-20</sup></html>
Movie 2.  k= 3.3&times;10<html><sup>-20</sup></html>
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 +
If you cannot load the file, click [[http://igem-ut.net/2011/model/model3/utt_m3_mov2.mov here]].
<html>
<html>
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Movie 3.  k= 3.3&times;10<html><sup>-19</sup></html>
Movie 3.  k= 3.3&times;10<html><sup>-19</sup></html>
 +
 +
If you cannot load the file, click [[http://igem-ut.net/2011/model/model3/utt_m3_mov3.mov here]].
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{{:Team:UT-Tokyo/Templates/Image|file=utt_m3_fig2.png|caption=Figure 2. The result of the chemotaxis experiment}}
{{:Team:UT-Tokyo/Templates/Image|file=utt_m3_fig2.png|caption=Figure 2. The result of the chemotaxis experiment}}
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Judging from comparison between the movies and the result of experiment, the simulation whose digestion rate was k= 3.3&times;10<html><sup>-20</sup></html> reproduces the experimental result well. It can be said that we succeeded in simulating the Asp chemotaxis of E.coli.
+
Judging from comparison between the movies and the result of experiment, the simulation whose digestion rate was k= 3.3&times;10<html><sup>-20</sup></html> reproduces the experimental result well. It can be said that we succeeded in simulating the Asp chemotaxis of ''E.coli''.
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==Simulation 3-2  Inducing to substrate==
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=Simulation 3-2  Inducing to substrate=
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=Aim=
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==Aim==
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In our experiment we ended up not showing the entire system i.e. “Some E.coli detect substrates and they secret Asp and then make other E.coli assemble”.
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In our experiment we ended up not showing the entire system i.e. “Some ''E.coli'' detect substrates and they secret Asp and then make other ''E.coli'' assemble”.
So we aimed to show it numerically and to present the advantage of this system by comparing with the old way.
So we aimed to show it numerically and to present the advantage of this system by comparing with the old way.
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=Methods=
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==Methods==
We modified the program used in simulation 3-1 to replicate the Asp secretion in Substrate area.
We modified the program used in simulation 3-1 to replicate the Asp secretion in Substrate area.
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According to the paper <html><sup class="ref">[1]</sup></html>, we can make 50mg (dry weight) E.coli produce Asp at 0.1mmol/min. Given a single cell weighs 3.0&times;10<html><sup>-13</sup></html>g (dry weight)<html><sup class="ref">[2]</sup></html>, the maximum Asp production rate is 10<html><sup>-17</sup></html> mol/(sec*cell).  We used this value in the simulation.
+
According to the paper <html><sup class="ref">[1]</sup></html>, we can make 50mg (dry weight) ''E.coli'' produce Asp at 0.1mmol/min. Given a single cell weighs 3.0&times;10<html><sup>-13</sup></html>g (dry weight)<html><sup class="ref">[2]</sup></html>, the maximum Asp production rate is 10<html><sup>-17</sup></html> mol/(sec*cell).  We used this value in the simulation.
We used k= 3.3&times;10<html><sup>-20</sup></html> as the Asp digestion rate.
We used k= 3.3&times;10<html><sup>-20</sup></html> as the Asp digestion rate.
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We located E.coli colony at the center of agar gel and substrate area which diameter was 10mm at 25mm distant from the center. We ran the simulation and measured the cell density over time.
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We located ''E.coli'' colony at the center of agar gel and substrate area which diameter was 10mm at 25mm distant from the center. We ran the simulation and measured the cell density over time.
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We also simulated E.coli with no Asp secretion as the control.  This case was intended to replicate the old way that lets E.coli to diffuse and no induction happens.
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We also simulated ''E.coli'' with no Asp secretion as the control.  This case was intended to replicate the old way that lets ''E.coli'' to diffuse and no induction happens.
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=Results=
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==Results==
Following movies are the result of the simulation.  
Following movies are the result of the simulation.  
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Movie 4.  Asp induction
Movie 4.  Asp induction
 +
 +
If you cannot load the file, click [[http://igem-ut.net/2011/model/model3/utt_m3_mov4.mov here]].
<html>
<html>
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Movie 5. mere diffusion
Movie 5. mere diffusion
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=Discussion=
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If you cannot load the file, click [[http://igem-ut.net/2011/model/model3/utt_m3_mov5.mov here]].
 +
 
 +
==Discussion==
The results clearly showed that Asp secretion significantly raised the cell density around substrate area.  
The results clearly showed that Asp secretion significantly raised the cell density around substrate area.  
-
This simulation has the limitation that it did not consider the factors that lead cell density to decrease (effect of E.coli density limit, Asp saturation etc) and therefore E.coli gathered at a single point with very high density.
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This simulation has the limitation that it did not consider the factors that lead cell density to decrease (effect of ''E.coli'' density limit, Asp saturation etc) and therefore ''E.coli'' gathered at a single point with very high density.
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==Simulation 3-3　Bioremediation and the effect of “Arrest”==
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=Simulation 3-3　Bioremediation and the effect of “Arrest”=
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=Aim=
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==Aim==
We aimed to show the validity of our system in bioremediation which is our ultimate objective.
We aimed to show the validity of our system in bioremediation which is our ultimate objective.
We also evaluated the effect of “Arrest”.
We also evaluated the effect of “Arrest”.
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=Methods=
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==Methods==
We evaluated the effectiveness of bioremediation by comparing the degradation rate of substrate.
We evaluated the effectiveness of bioremediation by comparing the degradation rate of substrate.
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In this simulation E.coli degrades substrates and its degradation rate increases as the square of E.coli density.  The reason for this was the Arrest system was suitable for the target which requires high E.coli density.
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In this simulation ''E.coli'' degrades substrates and its degradation rate increases as the square of ''E.coli'' density.  The reason for this was the Arrest system was suitable for the target which requires high ''E.coli'' density.
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“Arrest” system was intended to slow down E.coli movement.  When Arrest switch turns ON, the probability of “tumbling” increase and they become less mobile.  In this simulation if E.coli detect substrate, the switch turns ON.
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“Arrest” system was intended to slow down ''E.coli'' movement.  When Arrest switch turns ON, the probability of “tumbling” increase and they become less mobile.  In this simulation if ''E.coli'' detect substrate, the switch turns ON.
We had to know the moving velocity and the diffusion coefficient when the cell was arrested.
We had to know the moving velocity and the diffusion coefficient when the cell was arrested.
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{{:Team:UT-Tokyo/Templates/Image|file=utt_m3_fig5.png|caption=Figure 4. Arrest-OFF colony after 20 hours of the beginning}}
{{:Team:UT-Tokyo/Templates/Image|file=utt_m3_fig5.png|caption=Figure 4. Arrest-OFF colony after 20 hours of the beginning}}
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At the beginning, E.coli colony was located at the center of the gel and both of them were same size.
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At the beginning, ''E.coli'' colony was located at the center of the gel and both of them were same size.
Figure 3 indicates the Arrest-ON colony after 20 hours of the beginning.
Figure 3 indicates the Arrest-ON colony after 20 hours of the beginning.
Figure 4 indicates the Arrest-OFF.
Figure 4 indicates the Arrest-OFF.
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2. Asp induction only
2. Asp induction only
3. Asp induction and Arrest
3. Asp induction and Arrest
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The initial states of E.coli and substrate are shown in fig. 5.
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The initial states of ''E.coli'' and substrate are shown in fig. 5.
{{:Team:UT-Tokyo/Templates/Image|file=utt_m3_fig3.png|caption=Figure 5. Initial state}}
{{:Team:UT-Tokyo/Templates/Image|file=utt_m3_fig3.png|caption=Figure 5. Initial state}}
We recorded the time development of total degradation amount in each case.
We recorded the time development of total degradation amount in each case.
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=Results=
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==Results==
<html>
<html>
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Movie 6.  mere diffusion
Movie 6.  mere diffusion
 +
 +
If you cannot load the file, click [[http://igem-ut.net/2011/model/model3/utt_m3_mov6.mov here]].
<html>
<html>
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Movie 7.  Asp induction
Movie 7.  Asp induction
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 +
If you cannot load the file, click [[http://igem-ut.net/2011/model/model3/utt_m3_mov7.mov here]].
<html>
<html>
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Movie 8.  Asp induction + Arrest
Movie 8.  Asp induction + Arrest
 +
 +
If you cannot load the file, click [[http://igem-ut.net/2011/model/model3/utt_m3_mov8.mov here]].
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{{:Team:UT-Tokyo/Templates/Image|file=utt_m3_fig6.png|caption=Figure 6. The time development of the amount of work}}
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{{:Team:UT-Tokyo/Templates/Image|file=utt_m2_finalfigure.png|caption=Figure 6. The time development of the amount of remediation}}
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=Discussion=
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==Discussion==
The effectiveness was greatly improved when using Asp-induction system and the arrest system brought some improvements.
The effectiveness was greatly improved when using Asp-induction system and the arrest system brought some improvements.
-
The result clearly showed our SMART E.coli system works well in bioremediation.
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The result clearly showed our SMART ''E.coli'' system works well in bioremediation.

Latest revision as of 02:17, 6 October 2011

Modeling/Model3: Entire System Simulation

Interactive demo

Simulation 3-1 Chemotaxis

Abstract

We simulated the chemotactic behavier of one colony composed of 108 E.coli cells using Asp diffusion model in model1 and the approximation of chemotaxis we derived in model2. The result was consistent with the experimental result.

Methods

We considered the dynamics of E.coli colony as following simultaneous partial differential equations.

Utt m3 eqn1.png

We already knew the values of parameters V, DE, DA using model1 and model2. In this section we use the hypothesis that the cells digest Asp. However, the digestion rate was not clear so we ran the simulation with some different digestion rates: k= 3.3×10-21, 3.3×10-20, and 3.3×10-19 [mol]. To be exact, we had to consider the growth of E.coli, but the colony growth is so complex a process that we could not find out an appropriate colony growth model (i.e. A growth rate as a function of E.coli density). For this reason we did not consider the growth in our simulation. We simulated the time development of above equations using 1st order finite difference method. The initial state was shown in fig.1.

Figure 1. Initial state
Figure 1. Initial state

Results

Following movies are the result of the simulation. Color strength indicates the concentration of E.coli.

Movie 1. k= 3.3×10-21. Left side indicates Asp diffusion and right side indicates E.coli distribution.

If you cannot load the file, click http://igem-ut.net/2011/model/model3/utt_m3_mov1.mov here.

Movie 2. k= 3.3×10-20

If you cannot load the file, click http://igem-ut.net/2011/model/model3/utt_m3_mov2.mov here.

Movie 3. k= 3.3×10-19

If you cannot load the file, click http://igem-ut.net/2011/model/model3/utt_m3_mov3.mov here.


Figure 2 is the result of the experiment.

Figure 2. The result of the chemotaxis experiment
Figure 2. The result of the chemotaxis experiment

Judging from comparison between the movies and the result of experiment, the simulation whose digestion rate was k= 3.3×10-20 reproduces the experimental result well. It can be said that we succeeded in simulating the Asp chemotaxis of E.coli.


Simulation 3-2 Inducing to substrate

Aim

In our experiment we ended up not showing the entire system i.e. “Some E.coli detect substrates and they secret Asp and then make other E.coli assemble”. So we aimed to show it numerically and to present the advantage of this system by comparing with the old way.

Methods

We modified the program used in simulation 3-1 to replicate the Asp secretion in Substrate area.

According to the paper [1], we can make 50mg (dry weight) E.coli produce Asp at 0.1mmol/min. Given a single cell weighs 3.0×10-13g (dry weight)[2], the maximum Asp production rate is 10-17 mol/(sec*cell). We used this value in the simulation.

We used k= 3.3×10-20 as the Asp digestion rate.

We located E.coli colony at the center of agar gel and substrate area which diameter was 10mm at 25mm distant from the center. We ran the simulation and measured the cell density over time.

We also simulated E.coli with no Asp secretion as the control. This case was intended to replicate the old way that lets E.coli to diffuse and no induction happens.

Results

Following movies are the result of the simulation.

Movie 4. Asp induction

If you cannot load the file, click http://igem-ut.net/2011/model/model3/utt_m3_mov4.mov here.

Movie 5. mere diffusion

If you cannot load the file, click http://igem-ut.net/2011/model/model3/utt_m3_mov5.mov here.

Discussion

The results clearly showed that Asp secretion significantly raised the cell density around substrate area.

This simulation has the limitation that it did not consider the factors that lead cell density to decrease (effect of E.coli density limit, Asp saturation etc) and therefore E.coli gathered at a single point with very high density.


Simulation 3-3　Bioremediation and the effect of “Arrest”

Aim

We aimed to show the validity of our system in bioremediation which is our ultimate objective. We also evaluated the effect of “Arrest”.

Methods

We evaluated the effectiveness of bioremediation by comparing the degradation rate of substrate. In this simulation E.coli degrades substrates and its degradation rate increases as the square of E.coli density. The reason for this was the Arrest system was suitable for the target which requires high E.coli density.

“Arrest” system was intended to slow down E.coli movement. When Arrest switch turns ON, the probability of “tumbling” increase and they become less mobile. In this simulation if E.coli detect substrate, the switch turns ON.

We had to know the moving velocity and the diffusion coefficient when the cell was arrested. The DNA parts for “Arrest” was made and the effect was verified experimentally. Figure 3 and Figure 4 are the result of the experiment.

Figure 3. Arrest-ON colony after 20 hours of the beginning
Figure 3. Arrest-ON colony after 20 hours of the beginning

Figure 4. Arrest-OFF colony after 20 hours of the beginning
Figure 4. Arrest-OFF colony after 20 hours of the beginning

At the beginning, E.coli colony was located at the center of the gel and both of them were same size. Figure 3 indicates the Arrest-ON colony after 20 hours of the beginning. Figure 4 indicates the Arrest-OFF.

The area of the colony in figure 3 was about ten times smaller than that in figure 4. According to the theory of physics, the area of diffusing material increases in proportional to its diffusion coefficient. So in our program, the diffusion coefficient was timed 1/10 when they are in substrate area.

Next we simulated the effectiveness of bioremediation for following three cases. 1. mere diffusion (old way) 2. Asp induction only 3. Asp induction and Arrest The initial states of E.coli and substrate are shown in fig. 5.

Figure 5. Initial state
Figure 5. Initial state

We recorded the time development of total degradation amount in each case.

Results

Movie 6. mere diffusion

If you cannot load the file, click http://igem-ut.net/2011/model/model3/utt_m3_mov6.mov here.

Movie 7. Asp induction

If you cannot load the file, click http://igem-ut.net/2011/model/model3/utt_m3_mov7.mov here.

Movie 8. Asp induction + Arrest

If you cannot load the file, click http://igem-ut.net/2011/model/model3/utt_m3_mov8.mov here.


Figure 6. The time development of the amount of remediation
Figure 6. The time development of the amount of remediation

Discussion

The effectiveness was greatly improved when using Asp-induction system and the arrest system brought some improvements. The result clearly showed our SMART E.coli system works well in bioremediation.


References

  • [1] Yun-Peng Chao, Tsuey-Er Lo Neng-Shing Luo (2000) Selective production of L-aspertic acid and L-phenylalanine by coupling reactions of aspartase and aminotransferase in Escherichia coli. Enzyme and Microbial Technology, 27, 19-25
  • [2] E.coli statistics http://www.ccdb.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi

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