Team:Kyoto/ProjectTuring

From 2013.igem.org

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= Motivation =
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=Turing Model -the problems between wet and dry-=
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 自然界には多くのパターンが見られる。流れ動く雲、揺れ崩れる水面、繰り返し続ける砂の丘、流れる水に削り取られた川岸。動物の体表面も例外ではない。捕食者から隠れるため、外的刺激を防ぐため、さまざまな模様が自然淘汰の結果生み出されてきた。<br>
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==Motivation==
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 その中でも有名なのがチューリングパターンである。数学者であるアラン・チューリングが示した、とても単純なパターンから生み出される豊穣なパターンは動物の体表面の模様のいくつかを内包している。<br>
+
Turing pattern is a theme which some teams of iGEM have already been working on. However, all of them have stopped at the dry step, and no team has actually succeeded in creating a pattern so far. What is the reason? This year, iGEM Kyoto considered the formation of Turing pattern, and attempted to span dry and wet approaches with a bridge.
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 複雑怪奇な動物の模様がこれほど単純なモデルで再現、説明できるということは、実際の動物の体内で起きていることがこの理論に基づいていることを強く示唆している。その強い証拠を手に入れるためには、生物の持つ様々な物質を用いて同様の模様が形成できることを確認するとよい。<br>
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==Introduction==
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 チューリングパターンを生物を用いて再現しようという試みが長く行われてきた。
+
Turing Pattern is one of the achievements by a mathematician A. Turing. From a mathematical viewpoint, he tried to solve the enigma of how the animal skin pattern is formed. Inspired by this trial Turing model was proposed. According to Turing, the animals’ skin pattern can be explained by a simple model. S. Kondo suggests that Turing pattern is existent in the natural world, though it has not yet been completely proved.<
 +
 
 +
Turing pattern is a kind of a mathematic model. Let’s imagine two diffusible substances which interact with each other. Among these two diffusible factors, one activates itself and the other, and the other represses itself.
 +
 
 +
The two diffusible substances increase and decrease through interaction and create a difference in the density. This shading in the density causes the Turing pattern.
 +
 
 +
Turing model is an abstract mathematic model. In order to understand intuitively, let me set a field divided into many cell units. In each cell there are the diffusible substances. Let’s consider how a pattern is formed here. Firstly, you focus on only one cell unit.
 +
 
 +
Each of the two diffusible substances have two characters as we mentioned: interaction affects to the amount of substances themselves and diffusibility.
 +
 
 +
Affecting the density by in-flow and out-flow to the cell unit by a diffusion velocity peculiar to the substance (fig)
 +
 
 +
Turing arranged these two factors and established the Reaction-diffusion equation below.
 +
 
 +
(便宜上2つの仮想因子をそれぞれA,Bと呼ぶ事とする)よう(図)。
 +
 
 +
How is the difference between the two diffusion substances formed?
 +
 
 +
 
 +
The nature of the diffusion substances are “diffusion”, and “increase and decrease by interaction”.
 +
Therefore, the density of the diffusion substances change little by little by the “increase and decrease by the interaction” and the “in-flow and out-flow by the diffusion”
 +
 
 +
“The increase and decrease by the interaction” is a diffusion velocity peculiar to each factor, and affects the density by flowing into and out of the cell units.
 +
Another characteristic of the Turing pattern is that the width of the pattern changes depending on the difference between the diffusion velocities.
 +
 
 +
どのようなpatternかが決まるのである。
 +
So, the difference in the density created from the interaction of the two diffusion substances form the pattern, and the “difference of the diffusion velocity” defines the width.
 +
As I’ve said before, A. Turing is a mathematician.
 +
However, I hadn’t listed any formulas because I wanted you to understand at least the image of the Turing pattern first.
 +
Of course, Turing presented the pattern formation by using some formula.
 +
Now, let’s check out the “Reaction- diffusion equations”
 +
(2つの仮想因子をそれぞれA,Bと名づける)
 +
 
 +
I believe it’s difficult to understand the content of these formulae, so I’ll explain briefly.
 +
 
 +
The Reaction-diffusion equation shows the increase and decrease of the two diffusion substances in the fixed domain (i) of the space where the pattern is formed.
 +
 
 +
Kiα, Kiβ, Kiγは領域iにおいてそれぞれ仮想因子が相互作用する際の増減変化の定数であり、これらは全て任意の領域iにおいて常に一定である。
 +
DiA and DiB stands for the constant peculiar to each of the diffusion substances, and shows the diffusionのしやすさ。
 +
 
 +
すなわち、ある時間の微小領域における2つの仮想因子A, Bの存在量に応じて、その両方が微小時間後にどう増減するかを表しているのだ。
 +
In other words,
 +
 
 +
 
 +
 
 +
We focused on three constants, Kiα,Kiβ, and Kiγ in this formula.
 +
これらはTuring pattern形成の為に「任意の領域iにおいて常に一定である」という前提がある。
 +
 
 +
しかし大腸菌でTuring patternを形成する際には、これらは本当に任意のiにおいて常に一定だろうか。
 +
However, when we form a Turing pattern by E.coli,, can these constants really stay at a fixed number at any domain (i)?
 +
 
 +
We considered that this pattern formation may not function in wet.
 +
This is because when we realize the Turing pattern by using E.coli, the increase of both A and B is caused by the synthesis of E.coli. Therefore, the variation velocity of both A and B might be dependent on the density of the E.coli in 一定領域内
 +
 
 +
「一定領域内の大腸菌密度」に「A,Bの増減速度」が依存してしまうからである。
 +
 
 +
大腸菌が定常状態に至るまではまばらに生育している限り、どうしても大腸菌密度に差が生じてしまう。この密度差によって、「Kiα, Kiβ, Kiγ」がiによって異なると考えられるのだ。
 +
それではこの「Kiα, Kiβ, Kiγ」の差は無視出来るものだろうか。これを確認するための実験系を考えた。dryとwetとの差を埋めるために、私たちはこの実験をdryと本実験との間に行うことを提案する。
 +
 
 +
==idea==
 +
==Discussion==
 +
==conclusion==
= Introduction =
= Introduction =

Revision as of 23:03, 26 September 2013

count down

Contents

Turing Model -the problems between wet and dry-

Motivation

Turing pattern is a theme which some teams of iGEM have already been working on. However, all of them have stopped at the dry step, and no team has actually succeeded in creating a pattern so far. What is the reason? This year, iGEM Kyoto considered the formation of Turing pattern, and attempted to span dry and wet approaches with a bridge.

Introduction

Turing Pattern is one of the achievements by a mathematician A. Turing. From a mathematical viewpoint, he tried to solve the enigma of how the animal skin pattern is formed. Inspired by this trial Turing model was proposed. According to Turing, the animals’ skin pattern can be explained by a simple model. S. Kondo suggests that Turing pattern is existent in the natural world, though it has not yet been completely proved.<

Turing pattern is a kind of a mathematic model. Let’s imagine two diffusible substances which interact with each other. Among these two diffusible factors, one activates itself and the other, and the other represses itself.

The two diffusible substances increase and decrease through interaction and create a difference in the density. This shading in the density causes the Turing pattern.

Turing model is an abstract mathematic model. In order to understand intuitively, let me set a field divided into many cell units. In each cell there are the diffusible substances. Let’s consider how a pattern is formed here. Firstly, you focus on only one cell unit.

Each of the two diffusible substances have two characters as we mentioned: interaction affects to the amount of substances themselves and diffusibility.

Affecting the density by in-flow and out-flow to the cell unit by a diffusion velocity peculiar to the substance (fig)

Turing arranged these two factors and established the Reaction-diffusion equation below.

(便宜上2つの仮想因子をそれぞれA,Bと呼ぶ事とする)よう(図)。

How is the difference between the two diffusion substances formed?


The nature of the diffusion substances are “diffusion”, and “increase and decrease by interaction”. Therefore, the density of the diffusion substances change little by little by the “increase and decrease by the interaction” and the “in-flow and out-flow by the diffusion”

“The increase and decrease by the interaction” is a diffusion velocity peculiar to each factor, and affects the density by flowing into and out of the cell units. Another characteristic of the Turing pattern is that the width of the pattern changes depending on the difference between the diffusion velocities.

どのようなpatternかが決まるのである。 So, the difference in the density created from the interaction of the two diffusion substances form the pattern, and the “difference of the diffusion velocity” defines the width. As I’ve said before, A. Turing is a mathematician. However, I hadn’t listed any formulas because I wanted you to understand at least the image of the Turing pattern first. Of course, Turing presented the pattern formation by using some formula. Now, let’s check out the “Reaction- diffusion equations” (2つの仮想因子をそれぞれA,Bと名づける)

I believe it’s difficult to understand the content of these formulae, so I’ll explain briefly.

The Reaction-diffusion equation shows the increase and decrease of the two diffusion substances in the fixed domain (i) of the space where the pattern is formed.

Kiα, Kiβ, Kiγは領域iにおいてそれぞれ仮想因子が相互作用する際の増減変化の定数であり、これらは全て任意の領域iにおいて常に一定である。 DiA and DiB stands for the constant peculiar to each of the diffusion substances, and shows the diffusionのしやすさ。

すなわち、ある時間の微小領域における2つの仮想因子A, Bの存在量に応じて、その両方が微小時間後にどう増減するかを表しているのだ。 In other words,


We focused on three constants, Kiα,Kiβ, and Kiγ in this formula. これらはTuring pattern形成の為に「任意の領域iにおいて常に一定である」という前提がある。

しかし大腸菌でTuring patternを形成する際には、これらは本当に任意のiにおいて常に一定だろうか。 However, when we form a Turing pattern by E.coli,, can these constants really stay at a fixed number at any domain (i)?

We considered that this pattern formation may not function in wet. This is because when we realize the Turing pattern by using E.coli, the increase of both A and B is caused by the synthesis of E.coli. Therefore, the variation velocity of both A and B might be dependent on the density of the E.coli in 一定領域内

「一定領域内の大腸菌密度」に「A,Bの増減速度」が依存してしまうからである。

大腸菌が定常状態に至るまではまばらに生育している限り、どうしても大腸菌密度に差が生じてしまう。この密度差によって、「Kiα, Kiβ, Kiγ」がiによって異なると考えられるのだ。 それではこの「Kiα, Kiβ, Kiγ」の差は無視出来るものだろうか。これを確認するための実験系を考えた。dryとwetとの差を埋めるために、私たちはこの実験をdryと本実験との間に行うことを提案する。

idea

Discussion

conclusion

Introduction

・大腸菌の増減をファクターの一つとして扱うと、チューリングが提唱したものと違ってしまう上に、計算式がとても解きづらいものとなってしまう
・このモデルでも縞ができるという可能性は否定できないものの、チューリングが提唱し、主だったシミュレータが計算しているモデルとは根本的に異なる
・そのため、「真のチューリングパターン」を再現しようと考えた場合、チューリングパターンを成立させる条件に加えて、以下のような条件が考えられる

  • 大腸菌はシャーレ上に一様に分布している
  • 単一の種類の大腸菌が、因子の量の多少によって二つのStateを取りうる
  • 単一の大腸菌が、相互作用する二つの因子を分泌してシャーレ上に拡散できる

ここで、片方の因子がもう片方の因子の生産分泌速度に影響を与える(大腸菌の菌体数に影響を与えない)というモデルは、タンパク質の生産量やそれにかかる時間がシャーレ上のどの場所でも、また二つのタンパク質のどちらもで同一であるという近似の上では、プロモータと転写調節因子を挟んで生産させることで表現できる。 ・この実験系が成り立つかどうかについて、この条件を満たすタンパク質はとても少ないものの、細胞側の条件は別のタンパク質によって確認することが可能だろう

Assay

細胞の増殖状況によってタンパク質の発現レベルがシャーレ上で一定かどうか確認するために、GFPの蛍光強度を測定する

Result

Reference

The chemical basis of morphogenesis --A.M. Turing