Team:Kyoto/GSDD/Modelling

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==Modeling==
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=Modeling=
Recently, many biologists try to grasp biological systems behavior with computational and mathematical approach. But, when we make a model, in its process, we are apt to lose our sight about what kind things we want to grasp with those approach. So this time firstly we set our position to be clear.
Recently, many biologists try to grasp biological systems behavior with computational and mathematical approach. But, when we make a model, in its process, we are apt to lose our sight about what kind things we want to grasp with those approach. So this time firstly we set our position to be clear.
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In our simulation, we want to make our intuitive anticipation in our project to be more likely. By making some simple equations and numerically calculating it, we can confirm whether it is theoretically certain or not.
 
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This time we check timer vector’s behavior after we transform yeast with it, for the simplization, we assume each number of base pairs cut off by the end replication problem to be 100 bps. Actually in each replication, by the fluctuation of the length of RNA primers, which are used in the DNA replication at the part of 5’ directing side from replication origin, and by the randomness of the length cut off by the end replication problem, the number of base pairs lost in the process distributes from 0 to about 200 bps.  
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==Problem==
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We considered the accuracy of Timer vector. It is supposed that when the length of repetitive sequence is short, the length of DNA cut off in each replication varies from cell to cell, and as a result, the fluctuation affects on the dynamics of the population, and the accuracy of our timer is reduced.
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We wondered if we make repetitive sequence of lacI binding site longer, the fluctuation among population is reduced and the accuracy increase. To confirm this, we simulated the time development of cell population.
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And we assume the number of cell changes only by the effect of the behavior of timer vector and each cell has no interaction with other cells. In addition, we assume the life duration does not exist and cells die only because of the behavior of timer vector.
 
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Lastly we set the length of LacI binding site repeated sequence to be 10,000 bps. Then we express following equations about cell population and numerically analyze its time development.
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==Assumption==
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We assume following conditions.
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# The length decreased in each DNA replication varies from 15 to 185 bps with uniform randomness.
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# Each cell division is synchronized with all other cell’s division.
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# There is no cell to cell interaction and the life duration only depends on the behavior of Timer vector.
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# Each cell’s division is synchronized with other cell’s division.
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==Numerical calculation==
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We run below program in mathematica for four cases, and plot each result.
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==Result==
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グラフ
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軸の説明
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==Discussion==
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As the result shows, by making repetitive sequences longer, the fluctuation becomes smaller and the time-developing behavior of cell population is averaged. Then we concluded our assumption is certain.
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Revision as of 21:05, 21 October 2009

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  3. Modelling

Modeling

Recently, many biologists try to grasp biological systems behavior with computational and mathematical approach. But, when we make a model, in its process, we are apt to lose our sight about what kind things we want to grasp with those approach. So this time firstly we set our position to be clear.


Problem

We considered the accuracy of Timer vector. It is supposed that when the length of repetitive sequence is short, the length of DNA cut off in each replication varies from cell to cell, and as a result, the fluctuation affects on the dynamics of the population, and the accuracy of our timer is reduced. We wondered if we make repetitive sequence of lacI binding site longer, the fluctuation among population is reduced and the accuracy increase. To confirm this, we simulated the time development of cell population.


Assumption

We assume following conditions.

  1. The length decreased in each DNA replication varies from 15 to 185 bps with uniform randomness.
  2. Each cell division is synchronized with all other cell’s division.
  3. There is no cell to cell interaction and the life duration only depends on the behavior of Timer vector.
  4. Each cell’s division is synchronized with other cell’s division.


Numerical calculation

We run below program in mathematica for four cases, and plot each result.

Result

グラフ 軸の説明

Discussion

As the result shows, by making repetitive sequences longer, the fluctuation becomes smaller and the time-developing behavior of cell population is averaged. Then we concluded our assumption is certain.

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