Tokyo/Formulation/3.AHL-experssing model

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<br>[[Tokyo/Works|Works top]]　　0.[[Tokyo/Works/Hybrid promoter|Hybrid promoter]]　　'''1.[[Tokyo/Works/Formulation |Formulation]]'''　　2.[[Tokyo/Works/Assay |Assay1]]　　3.[[Tokyo/Works/Simulation |Simulation]]
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<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]]
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<br><br>[[Tokyo/Formulation/1.toggle model |Step1]]　　[[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2]]　　[[Tokyo/Formulation/3.AHL-experssing model|Step3]]　　
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<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]]　　
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== Step.3 Single cell model with hybrid promoter and cell-produced AHL ==
== Step.3 Single cell model with hybrid promoter and cell-produced AHL ==
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<br>The differential equaitons of the system considering AHL produced by E.coli themselves were given as
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<br>The differential equations of the system considering AHL produced by E.coli themselves were given as
<br> [[Image:expression3-4.jpg|400px|left|thumb|Ex 3-1]][[Image:parameter3-1.jpg|200px|none|thumb|Table 3]]
<br> [[Image:expression3-4.jpg|400px|left|thumb|Ex 3-1]][[Image:parameter3-1.jpg|200px|none|thumb|Table 3]]
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<br>[[Image:expression3-3.jpg|300px|none|thumb|Ex 3-4]]
<br>[[Image:expression3-3.jpg|300px|none|thumb|Ex 3-4]]
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<br>Therefore, the phase plane of this system can be plotted as Fig.3.1.A-C and the number of equilibrium points were decided by the value of the parameters:
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<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:step3-3.JPG|300px|left|thumb|Figure 3.1.A]]
<br>[[Image:step3-4.JPG|300px|thumb|none|Figure 3.1.B]]
<br>[[Image:step3-4.JPG|300px|thumb|none|Figure 3.1.B]]
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<br>[[Image:step3-5.JPG|300px|thumb|left|Figure 3.1.C]]
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<br>[[Image:step3-6.JPG|300px|thumb|none|Figure 3.1.D]]
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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.
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<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.
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Fig3.1.A and B indicated that in case of N2=1,N3=1,the phase plane was monostable and in case of N2=2,N3=2,the phase plane was bistable. So, the values of Hill coefficients were needed to be more than a certain value to take bistability. Although, the phase plane depended on the value of parameter λ,this value was controlled by changing the RBS of LuxR or the binding sequence of that.
 
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<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]]
<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]]
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== ==
 
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[[Tokyo/Formulation/3.AHL-experssing model|Step.3]] >> [[Tokyo/Formulation/4.population_model|Step.4]]
 
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== ==
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[[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

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