Tokyo/Formulation/3.AHL-experssing model

From 2007.igem.org

< Tokyo/Formulation(Difference between revisions)
(Step.3 Single cell model with hybrid promoter and cell-produced AHL)
 
(35 intermediate revisions not shown)
Line 1: Line 1:
-
<中身>
+
__NOTOC__
-
(相平面)
+
<br>[[Tokyo/Works|Works top]]&nbsp;&nbsp;&nbsp;0.[[Tokyo/Works/Hybrid promoter|Hybrid promoter]]&nbsp;&nbsp;&nbsp;'''1.[[Tokyo/Works/Formulation |Formulation]]'''&nbsp;&nbsp;&nbsp;2.[[Tokyo/Works/Assay |Assay1]]&nbsp;&nbsp;&nbsp;3.[[Tokyo/Works/Simulation |Simulation]]&nbsp;&nbsp;&nbsp;4.[[Tokyo/Works/Assay2 |Assay2]]&nbsp;&nbsp;&nbsp;5.[[Tokyo/Works/Future works |Future works]]
-
3本目の微分方程式が入ることにより,新たなパラメターλが出てくる.
+
<br><br>[[Tokyo/Formulation/1.toggle model |Step1]]&nbsp;&nbsp;&nbsp;[[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2]]&nbsp;&nbsp;&nbsp;[[Tokyo/Formulation/3.AHL-experssing model|Step3]]  
-
このλの値によって相平面が変化する.
+
<br>
 +
== Step.3 Single cell model with hybrid promoter and cell-produced AHL ==
-
<br>大腸菌の中からAHLを産生している系を考えてみる.すると,微分方程式がもう一本増え3連立の微分方程式になる.
+
<br>The differential equations of the system considering AHL produced by E.coli themselves were given as
-
<br>[[Image:expression3-1.jpg|300px|]]
+
<br> [[Image:expression3-4.jpg|400px|left|thumb|Ex 3-1]][[Image:parameter3-1.jpg|200px|none|thumb|Table 3]]
-
<br>定常状態では,
+
<br>These equations were normalized as follows:
 +
<br>[[Image:expression3-1.jpg|300px|none|thumb|Ex 3-2]]
-
<br>[[Image:expression3-2.jpg|300px|]]
+
<br>In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as
-
<br>となる.すると,3本目の式を2本目の式に代入することができ,結局RaとRbの2変数になる.これより,今までと同様RaとRbの相平面が描ける.
+
<br>[[Image:expression3-2.jpg|300px|none|thumb|Ex 3-3]]
-
<br>[[Image:expression3-3.jpg|300px|]]
+
<br>By substituting the third equation into the second,the nullclines for Ra and Rb were obtained as
 +
 
 +
<br>[[Image:expression3-3.jpg|300px|none|thumb|Ex 3-4]]
 +
 
 +
<br>Therefore, the phase plane of this system can be plotted as Fig.3.1.A-D and the number of equilibrium points were decided by the value of the parameters:
 +
 
 +
<br>[[Image:step3-3.JPG|300px|left|thumb|Figure 3.1.A]]
 +
<br>[[Image:step3-4.JPG|300px|thumb|none|Figure 3.1.B]]
 +
<br>[[Image:step3-5.JPG|300px|thumb|left|Figure 3.1.C]]
 +
<br>[[Image:step3-6.JPG|300px|thumb|none|Figure 3.1.D]]
 +
 
 +
Comparison between Fig3.1.A and B indicated that Hill coefficients are critical parameters even in the cell-produced AHL model. In the case of N2=1, N3=1, and λ=3, the phase plane was monostable. In contrast, in the case of N2=2, N3=2, and λ=3, the phase plane was bistable.
 +
<br>  In the cases of λ=1 (Fig.3.1.C and D), the system can not take bistability even if the values of Hill coefficients are changed. For the implementation of the circuit in a cell, the parameter λ should be controlled by changing the RBSs and/or promoter sequences of LuxR.
 +
 
 +
 
 +
<!--
 +
<br>[[Image:Phaseplane3-1.jpg|300px|left|thumb|Figure 3.1.A]] [[Image:Phaseplane3-2.jpg|290px|left|thumb|Figure 3.1.B]] [[Image:Phaseplane3-3.jpg|270px|none|thumb|Figure 3.1.C]]
 +
-->
 +
 
 +
== ==
 +
[[Tokyo/Formulation/3.AHL-experssing model|Step.3]] >> [[Tokyo/Works/Formulation|Formulation top]]

Latest revision as of 05:00, 27 October 2007


Works top   0.Hybrid promoter   1.Formulation   2.Assay1   3.Simulation   4.Assay2   5.Future works

Step1   Step2   Step3  

Step.3 Single cell model with hybrid promoter and cell-produced AHL


The differential equations of the system considering AHL produced by E.coli themselves were given as


Ex 3-1
Table 3


These equations were normalized as follows:


Ex 3-2


In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as


Ex 3-3


By substituting the third equation into the second,the nullclines for Ra and Rb were obtained as


Ex 3-4


Therefore, the phase plane of this system can be plotted as Fig.3.1.A-D and the number of equilibrium points were decided by the value of the parameters:


Figure 3.1.A

Figure 3.1.B

Figure 3.1.C

Figure 3.1.D

Comparison between Fig3.1.A and B indicated that Hill coefficients are critical parameters even in the cell-produced AHL model. In the case of N2=1, N3=1, and λ=3, the phase plane was monostable. In contrast, in the case of N2=2, N3=2, and λ=3, the phase plane was bistable.
In the cases of λ=1 (Fig.3.1.C and D), the system can not take bistability even if the values of Hill coefficients are changed. For the implementation of the circuit in a cell, the parameter λ should be controlled by changing the RBSs and/or promoter sequences of LuxR.


Step.3 >> Formulation top