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	<br>[[Image:AHLresponse2-1.jpg|300px|]]		<br>[[Image:AHLresponse2-1.jpg|300px|]]
-	<br>AHLを産生しない系を仮定し，外から入れたAHL量に対してどのような振る舞いを示すか見てみる．	+	<br>Assuming the system where ''E. coli'' does not produce AHL by themselves, we have observed the system's reaction to ''ab extra'' AHL. The ODEs were obtained as
-	<br>定式化において，プロモータｂはAHLによってactivateされる項を加える必要がある．すると，以下のようになる．	+
-	<br>Assuming the system where ''E. coli'' does not produce AHL by themselves, we have observed the system's reaction to ''ab extra'' AHL.
-	<br>In formulation, it is necessary to add the term of promoter b activation by AHL as follows;
	<br>[[Image:expression2-1.jpg|200px|]]		<br>[[Image:expression2-1.jpg|200px|]]
-	<br>我々のモデルの理想的な振る舞いは図のようである．	+	<br>where the factor surrounded in the orange box represents the activation of promoter B.
-	<br>AHLが少ないとき，B状態の大腸菌は不安定化してA状態に遷移する．一方，AHLが多いときは，A状態の大腸菌，B状態の大腸菌はそれぞれ安定化している．	+
	<br>The ideal behavior shown in the figure below is:		<br>The ideal behavior shown in the figure below is:
-	<br>- with little AHL, the B state becomes unstable and shifts to A.	+	<br>- with low concentration of AHL, the B state becomes unstable. so that the cells at the B state move to the A state which is stable.
-	<br>- with lots of AHL, both A and B states are stable.	+	<br>- with hign concentration of AHL, both A and B states are stable.The cells at the A state keep the A state,that at the B state keep the B state.
	<br>[[Image:AHLresponse2-2.jpg|300px|]]		<br>[[Image:AHLresponse2-2.jpg|300px|]]

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Revision as of 12:52, 23 October 2007

Assuming the system where E. coli does not produce AHL by themselves, we have observed the system's reaction to ab extra AHL. The ODEs were obtained as

where the factor surrounded in the orange box represents the activation of promoter B.

The ideal behavior shown in the figure below is:
- with low concentration of AHL, the B state becomes unstable. so that the cells at the B state move to the A state which is stable.
- with hign concentration of AHL, both A and B states are stable.The cells at the A state keep the A state,that at the B state keep the B state.　

実際に，式を解いて相平面を書いてみると図のようになる．
The phaseplane drawn by solving the equations is the following: