Team:UT-Tokyo/Data/Modeling/Model01

From 2011.igem.org

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{{:Team:UT-Tokyo/Templates/BeginContent|fullpagename=Team:UT-Tokyo/Data/Modeling/Model01|subpagename=Model1: L-Asp diffusion}}
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{{:Team:UT-Tokyo/Templates/BeginContent|fullpagename=Team:UT-Tokyo/Data/Modeling/Model01|subpagename=Model1}}
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=[[Team:UT-Tokyo/Data/Modeling|Modeling]]/Model1: L-Asp diffusion=
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=[[Team:UT-Tokyo/Data/Modeling/Model01/applet|Interactive demo]]=
=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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It was required 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 experimentally checked 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 estimated the value of diffusion coefficient by interpolating molecular mass of L-Asp (133) from the relationship between molecular weight and diffusion constant as shown in figure 1<html><sup class="ref">[1]</sup></html>.
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¥[fig. 1]
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{{:Team:UT-Tokyo/Templates/Image|file=utt_m1_fig1.png|caption=Figure 1. Molecular Weight v.s. Diffusion Constant (1% agar. gel)}}
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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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We used 0.25% agar gel in our experiment and according to the previous study<html><sup class="ref">[2]</sup></html>, there is no practical difference of diffusion coefficient between 1% and 0.25% agar gel.
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Then we verify the value by comparing the result of numerical simulations and experiments.
 
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 simulated the diffusion equation using 1st order finite difference method.
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¥[eqn. 1]
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using 1st order finite difference method.
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[[File:utt_m1_eqn1.png]]
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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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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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{{:Team:UT-Tokyo/Templates/Image|file=utt_m1_fig2.png|caption=Figure 3. Change in L-Asp Concentration Over Time (2, 6, 8 mm from the center)}}
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=Discussion=
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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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<div id="references">
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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, 377</li>
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  <li id="ref_2">[2] W. Derbyshire, I. D. Duff "N.m.r of Agarose Gels" Chem. Soc., 1974, 57, 243-254</li>
</ul>
</ul>
</div>
</div>
</html>
</html>
{{:Team:UT-Tokyo/Templates/EndContent}}
{{:Team:UT-Tokyo/Templates/EndContent}}

Latest revision as of 20:51, 5 October 2011

Modeling/Model1: L-Asp diffusion

Interactive demo

Aim

It was required to know the behavior of L-Asp diffusion to perform our entire simulation (model3). We experimentally checked 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 estimated the value of diffusion coefficient by interpolating molecular mass of L-Asp (133) from the relationship between molecular weight and diffusion constant as shown in figure 1[1].

Figure 1. Molecular Weight v.s. Diffusion Constant (1% agar. gel)
Figure 1. Molecular Weight v.s. Diffusion Constant (1% agar. gel)

The estimated value was D = 0.001 [mm2/sec]. We used 0.25% agar gel in our experiment and according to the previous study[2], there is no practical difference of diffusion coefficient between 1% and 0.25% agar gel.

We simulated the time development of the L-Asp concentration distribution. We simulated 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

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

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)

References

  • [1] Toshiko M, Masayuki N "measurement of diffusion coefficient using agar. gel" Chemical Society of Japan, 1978, 26, 5, 377
  • [2] W. Derbyshire, I. D. Duff "N.m.r of Agarose Gels" Chem. Soc., 1974, 57, 243-254

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