Tokyo/Formulation/3.AHL-experssing model
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<br>[[Image:step3-4.JPG|300px|thumb|none|Figure 3.1.D]] | <br>[[Image:step3-4.JPG|300px|thumb|none|Figure 3.1.D]] | ||
| - | 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, | + | 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 bistable. Fig.3.1.C and D represented the phase plane at λ=1. In this case, even if the values of Hill coefficients are changed, the system can’t take bistability. So, although the phase plane depended on the value of parameter λ,this value can be 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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[[Tokyo/Formulation/3.AHL-experssing model|Step.3]] >> [[Tokyo/Works/Formulation|Formulation top]] | [[Tokyo/Formulation/3.AHL-experssing model|Step.3]] >> [[Tokyo/Works/Formulation|Formulation top]] | ||
Revision as of 20:07, 26 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 equaitons of the system considering AHL produced by E.coli themselves were given as
These equations were normalized as follows:
In the steady state,time derivatives are zero.As a result,the nullclines of this system were derived as
By substituting the third equation into the second,the nullclines for Ra and Rb were obtained as
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:
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 bistable. Fig.3.1.C and D represented the phase plane at λ=1. In this case, even if the values of Hill coefficients are changed, the system can’t take bistability. So, although the phase plane depended on the value of parameter λ,this value can be controlled by changing the RBS of LuxR or the binding sequence of that.
Step.3 >> Formulation top
