Team:UT-Tokyo/Data/Modeling/Model01

From 2011.igem.org

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=Aim=
=Aim=
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We determined the diffusion coefficient of L-Asp by comparing the result of numerical simulations and experiments
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We needed to know the behavior of L-Asp diffusion to perform our entire simulation (model3).
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to support the main simulation (model03).
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We experimentaly researched Asp diffusion using TLC method but the results were insufficient for the entire simulation.
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So we decided to investigate the Asp diffusion by numerical simulation.
=Method=
=Method=
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We first estimated the value of diffusion coefficient by interpolating molecular mass of L-Asp (133)<html><sup class="ref">[1]</sup></html> in figure 1.
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We first estimated the value of diffusion coefficient by interpolating molecular mass of L-Asp (133) from the relationship between molecular weight and diffusion constant<html><sup class="ref">[1]</sup></html> as shown in figure 1.
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{{:Team:UT-Tokyo/Templates/Image|file=UT-Tokyo_Model01_Fig1.png|caption=Figure 1. Molecular Weight v.s. Diffusion Constant}}
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{{:Team:UT-Tokyo/Templates/Image|file=utt_m1_fig1.png|caption=Figure 1. Molecular Weight v.s. Diffusion Constant}}
The estimated value was D = 0.001 [<html>mm<sup>2</sup>/sec</html>].
The estimated value was D = 0.001 [<html>mm<sup>2</sup>/sec</html>].
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Then we verify the value by comparing the result of numerical simulations and experiments.
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Then we tried to verify the value was correct by showing we could predict the experimental result theoretically using this value as a diffusion constant.
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Experimental data of L-Asp diffusion are shown in figure 2.
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This is the result of TLC experiment.  We dropped 2&times;10<html><sup>-7</sup></html> mol L-Asp on the center of agar gel at the beginning.
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Horizontal rows indicates elapssed time and vertical columns indicates the distance from the center.
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{{:Team:UT-Tokyo/Templates/Image|file=utt_m1_fig2.png|caption=Figure 2.The Result of TLC Experiment}}
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We simulated the time development of the L-Asp concentration distribution.
We simulated the time development of the L-Asp concentration distribution.
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We solved the diffusion equation
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We solved the diffusion equation using 1st order finite difference method.
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[[File:UT-Tokyo Model01 Eqn1.png]]
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[[File:utt_m1_eqn1.png]]
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using 1st order finite difference method.
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A indicates the L-Asp concentration and D means the diffusion coefficient.
The shape of system was a circle with radius 5cm.
The shape of system was a circle with radius 5cm.
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We dropped <html>10<sup>-2</sup>M</html> Asp at the center of the circle as the initial state.
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We dropped 2&times;10<html><sup>-7</sup></html> mol Asp at the center of the circle as the initial state.
=Result=
=Result=
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{{:Team:UT-Tokyo/Templates/Image|file=UT-Tokyo_Model01_Fig2.png|caption=Figure 2. Change in L-Asp Concentration Over Time (2, 6, 8 mm from the center)}}
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{{:Team:UT-Tokyo/Templates/Image|file=utt_m1_fig3.png|caption=Figure 3. Change in L-Asp Concentration Over Time (2, 6, 8 mm from the center)}}
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The time change of logarithmic values of L-Asp concentration is shown in figure 2.
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The time change of logarithmic values of L-Asp concentration at 2, 6, 8 mm from the center is shown in figure 3.
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The vertical axis indicates relative values of L-Asp concentration under condition that let its concentration where and when it is dropped to be 10,000.
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=Discussion=
=Discussion=
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{{:Team:UT-Tokyo/Templates/Image|file=UT-Tokyo_Model01_Fig3.png|caption=Figure 3.The Result of TLC Experiment}}
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The result of the simulation shown in fig. 3 were similar to the result of experiment shown in fig. 2.
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So we judged that the diffusion coefficient D=0.001 was adequate value.
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The result shows that L-Asp was detected at 8mm from the center (where the L-Asp is dropped) 3~6 hours after the samples were applied.
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According to our simulation, its concentration at 8mm changes earlier. However, because there are some uncertain factors such as temperature, gel condition (which change diffusion coefficient) or experimental error, we judged that the diffusion coefficient D=0.001 was correct in its order and adopted this value in model 03.
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<html>
<html>
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<div id="references">
<div id="references">
<ul>
<ul>
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   <li id="ref_1">[1] Toshiko M, Masayuki N. "寒天ゲルを用いる拡散係数の測定" Chemical Society of Japan (1978) 26 5 p.377.</li>
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   <li id="ref_1">[1] Toshiko M, Masayuki N "measurement of diffusion coefficient using agar. gel" Chemical Society of Japan (1978) 26 5 p.377</li>
</ul>
</ul>
</div>
</div>
</html>
</html>
{{:Team:UT-Tokyo/Templates/EndContent}}
{{:Team:UT-Tokyo/Templates/EndContent}}

Revision as of 13:30, 5 October 2011

Aim

We needed to know the behavior of L-Asp diffusion to perform our entire simulation (model3). We experimentaly researched Asp diffusion using TLC method but the results were insufficient for the entire simulation. So we decided to investigate the Asp diffusion by numerical simulation.

Method

We first estimated the value of diffusion coefficient by interpolating molecular mass of L-Asp (133) from the relationship between molecular weight and diffusion constant[1] as shown in figure 1.

Figure 1. Molecular Weight v.s. Diffusion Constant
Figure 1. Molecular Weight v.s. Diffusion Constant

The estimated value was D = 0.001 [mm2/sec].

Then we tried to verify the value was correct by showing we could predict the experimental result theoretically using this value as a diffusion constant.

Experimental data of L-Asp diffusion are shown in figure 2. This is the result of TLC experiment. We dropped 2×10-7 mol L-Asp on the center of agar gel at the beginning. Horizontal rows indicates elapssed time and vertical columns indicates the distance from the center.

Figure 2.The Result of TLC Experiment
Figure 2.The Result of TLC Experiment

We simulated the time development of the L-Asp concentration distribution. We solved the diffusion equation using 1st order finite difference method.

Utt m1 eqn1.png

A indicates the L-Asp concentration and D means the diffusion coefficient. The shape of system was a circle with radius 5cm. We dropped 2×10-7 mol Asp at the center of the circle as the initial state.

Result

Figure 3. Change in L-Asp Concentration Over Time (2, 6, 8 mm from the center)
Figure 3. Change in L-Asp Concentration Over Time (2, 6, 8 mm from the center)

The time change of logarithmic values of L-Asp concentration at 2, 6, 8 mm from the center is shown in figure 3.

Discussion

The result of the simulation shown in fig. 3 were similar to the result of experiment shown in fig. 2. So we judged that the diffusion coefficient D=0.001 was adequate value.

References

  • [1] Toshiko M, Masayuki N "measurement of diffusion coefficient using agar. gel" Chemical Society of Japan (1978) 26 5 p.377

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