Tokyo/Works/Formulation
From 2007.igem.org
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== [[Tokyo/Formulation/1.toggle model |Step1. toggle model]] == | == [[Tokyo/Formulation/1.toggle model |Step1. toggle model]] == | ||
| + | <!--First,we analysis the simple dimentionless toggle model. | ||
| + | We use the phaseplane analysis to understand the quantitative behavior of the toggle switch. | ||
| + | As a result,the toggle model has three kinds of phaseplanes,from one to three equilibrium points. when one equilibrium point,only one stable equilibrium point | ||
| + | And, we need three equilibrium points for the toggle to be bistable.--> | ||
| + | |||
| + | ＜イントロ＞ | ||
| + | まずは，次元をもっていない単純な式で定性的な振る舞いをみてみる． | ||
| + | その結果，安定点が１つのときと２つのときがある．我々が求めているモデルはA状態とB状態をとる必要があるので， | ||
| + | 安定点が二つのときである．bistalbeになるには，パラメータにおいて，合成rateの強さ比とヒル係数が重要であることが分かった． | ||
| + | '''↑Editをクリックすると英語案が出てきます''' | ||
| + | |||
| + | <!--案１ | ||
| + | <br>Introduction | ||
<br>First, we saw the qualitative nature implied by simple dimentionless equations and found that the number of the stable points is one or two. Since our model must have A and B states, the number of its stable points should be two. | <br>First, we saw the qualitative nature implied by simple dimentionless equations and found that the number of the stable points is one or two. Since our model must have A and B states, the number of its stable points should be two. | ||
<br>For the parameters required for this bistability, we have found that the production rates and Hill coefficients are critical. | <br>For the parameters required for this bistability, we have found that the production rates and Hill coefficients are critical. | ||
| - | + | 上記の英語訳のPhaseplane, Threeは下の日本語訳にないです。 | |
| - | -- | + | --> |
<!--案2 | <!--案2 | ||
<br>Introduction | <br>Introduction | ||
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== [[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2. toggle model with hybrid promoter ]] == | == [[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2. toggle model with hybrid promoter ]] == | ||
| - | Factors of the hybrid promoter should be incorporated into the equations; that is, the | + | |
| + | ＜イントロ＞ | ||
| + | ハイブリットプロモータを式に入れ込む必要がある． | ||
| + | トグルの抑制項に加えてAHLによってactivateされる項が加わる． | ||
| + | これにより，AHL量によって相平面変化するようになる． | ||
| + | AHL量が少ないときはmonoで多いときトグルと同じになりbiになる． | ||
| + | |||
| + | === Introduction === | ||
| + | Factors of the hybrid promoter should be incorporated into the equations; that is, the term of the repression of toggle by LacI and that of the activation by AHL should be added. By these additions, the phase changes dependent on the amount of AHL. Lower concentration of AHL, mono???; while, higher one gives bi | ||
<br>[[Image:expression2-4.jpg|300px|]][[Image:AHLresponse2-2.jpg|300px|]] | <br>[[Image:expression2-4.jpg|300px|]][[Image:AHLresponse2-2.jpg|300px|]] | ||
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== [[Tokyo/Formulation/3.AHL-experssing model|Step3. using cell-produced AHL]] == | == [[Tokyo/Formulation/3.AHL-experssing model|Step3. using cell-produced AHL]] == | ||
| + | |||
| + | ＜イントロ＞ | ||
| + | 今度は，大腸菌の中からAHLを作り出す系に拡張する． | ||
| + | すると，nullclineが非対称になり，従来のトグルとは異なった相平面になる． | ||
| + | この際，新たなパラメータλが入ってくる． | ||
| + | パラメータセットによって，monoになったり，biになったりする． | ||
Now develop this system to the one with cell-produced AHL. | Now develop this system to the one with cell-produced AHL. | ||
| - | This time, the | + | This time, the nullcrine is assymetric and the phaseplane is unconventionally shaped. |
| - | Here the new parameter λ is introduced whether | + | Here the new parameter λ is introduced whether mono or bi of the system depends on the parameter sets |
[[Tokyo/Formulation/3.AHL-experssing model|for more detail]] | [[Tokyo/Formulation/3.AHL-experssing model|for more detail]] | ||
<br>[[Image:expression3-1.jpg|300px|]] | <br>[[Image:expression3-1.jpg|300px|]] | ||
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== [[Tokyo/Formulation/4.population model|Step4. population model]] == | == [[Tokyo/Formulation/4.population model|Step4. population model]] == | ||
| - | |||
| - | However, all the individuals | + | ＜イントロ＞ |
| + | １個体から複数個体に拡張．AHLの式は，AHLの移動がfreelyと論文にあるので大腸菌内と外とを区別していない | ||
| + | ここでも，相平面解析を行った．ｎ個体の振る舞いであっても，その中の１個体に着目することで相平面解析を可能にした． | ||
| + | この際，新たなパラメータとして個体数ｎがはいってくる． | ||
| + | |||
| + | |||
| + | Here the concentration of AHL is assumed the same inside and outside of a cell according to the description that AHL is freely permiable through cell membrane in the referenced articles. In the phaseplane analysis here is mede possible by focusing on an individual in the whole. In this case, the parameter n for the number of the cells is introduced. | ||
| + | |||
| + | ただし，deterministicなため全個体同じ動き．我々のモデルはこれではみれない． | ||
| + | stochasticなシミュレーションが要求される． | ||
| + | |||
| + | However, all the individuals behave in the same way in this deterministic model. To see the bahavior different from each individual, it is necessary to use stocastic simulation. | ||
== [[Tokyo/Formulation/5.poisson stochastic differential equation model |Step5. poisson stochastic differential equation model ]] == | == [[Tokyo/Formulation/5.poisson stochastic differential equation model |Step5. poisson stochastic differential equation model ]] == | ||
Revision as of 01:25, 24 October 2007
Works top 0.Hybrid promoter 1.Formulation 2.Assay1 3.Simulation 4.Assay2 5.Future works
Step1. toggle model
＜イントロ＞ まずは，次元をもっていない単純な式で定性的な振る舞いをみてみる． その結果，安定点が１つのときと２つのときがある．我々が求めているモデルはA状態とB状態をとる必要があるので， 安定点が二つのときである．bistalbeになるには，パラメータにおいて，合成rateの強さ比とヒル係数が重要であることが分かった． ↑Editをクリックすると英語案が出てきます
Step2. toggle model with hybrid promoter
＜イントロ＞ ハイブリットプロモータを式に入れ込む必要がある． トグルの抑制項に加えてAHLによってactivateされる項が加わる． これにより，AHL量によって相平面変化するようになる． AHL量が少ないときはmonoで多いときトグルと同じになりbiになる．
Introduction
Factors of the hybrid promoter should be incorporated into the equations; that is, the term of the repression of toggle by LacI and that of the activation by AHL should be added. By these additions, the phase changes dependent on the amount of AHL. Lower concentration of AHL, mono???; while, higher one gives bi
Step3. using cell-produced AHL
＜イントロ＞
今度は，大腸菌の中からAHLを作り出す系に拡張する．
すると，nullclineが非対称になり，従来のトグルとは異なった相平面になる．
この際，新たなパラメータλが入ってくる．
パラメータセットによって，monoになったり，biになったりする．
Now develop this system to the one with cell-produced AHL.
This time, the nullcrine is assymetric and the phaseplane is unconventionally shaped.
Here the new parameter λ is introduced whether mono or bi of the system depends on the parameter sets
for more detail
Step4. population model
＜イントロ＞ １個体から複数個体に拡張．AHLの式は，AHLの移動がfreelyと論文にあるので大腸菌内と外とを区別していない ここでも，相平面解析を行った．ｎ個体の振る舞いであっても，その中の１個体に着目することで相平面解析を可能にした． この際，新たなパラメータとして個体数ｎがはいってくる．
Here the concentration of AHL is assumed the same inside and outside of a cell according to the description that AHL is freely permiable through cell membrane in the referenced articles. In the phaseplane analysis here is mede possible by focusing on an individual in the whole. In this case, the parameter n for the number of the cells is introduced.
ただし，deterministicなため全個体同じ動き．我々のモデルはこれではみれない． stochasticなシミュレーションが要求される．
However, all the individuals behave in the same way in this deterministic model. To see the bahavior different from each individual, it is necessary to use stocastic simulation.
