Team:UT-Tokyo/Data/Modeling/Model01

From 2011.igem.org

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=Method=
=Method=
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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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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>.
{{:Team:UT-Tokyo/Templates/Image|file=utt_m1_fig1.png|caption=Figure 1. Molecular Weight v.s. Diffusion Constant}}
{{: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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We used 0.25% agar gel in our experiment and according to a paper<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 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_fig3.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 using 1st order finite difference method.
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We simulated the diffusion equation using 1st order finite difference method.
[[File:utt_m1_eqn1.png]]
[[File:utt_m1_eqn1.png]]
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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)}}
{{: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)}}
The time change of logarithmic values of L-Asp concentration at 2, 6, 8 mm from the center is shown in figure 3.
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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=Discussion=
 
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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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<div id="references">
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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>
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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>
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{{:Team:UT-Tokyo/Templates/EndContent}}

Revision as of 16:49, 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 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
Figure 1. Molecular Weight v.s. Diffusion Constant

The estimated value was D = 0.001 [mm2/sec]. We used 0.25% agar gel in our experiment and according to a paper[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

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.

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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