Tokyo/Formulation/3.AHL-experssing model
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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]] | ||
| - | <br>Therefore, the phase plane of this system can be plotted as Fig.3.1.A- | + | <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]] | ||
| + | <br>[[Image:step3-4.JPG|300px|thumb|left|Figure 3.1.C]] | ||
| + | <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, to take bistability the values of Hill coefficients were needed to be more than a certain value. 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. | 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, to take bistability the values of Hill coefficients were needed to be more than a certain value. 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. | ||
Revision as of 19:48, 26 October 2007
Works top 0.Hybrid promoter 1.Formulation 2.Assay1 3.Simulation
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, to take bistability the values of Hill coefficients were needed to be more than a certain value. 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.
