Tokyo/Formulation/5.stochastic differential equation model with poisson random variables
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+ | __NOTOC__ | ||
+ | <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]]''' 4.[[Tokyo/Works/Assay2 |Assay2]] 5.[[Tokyo/Works/Future works |Future works]] | ||
+ | <br><br>[[Tokyo/Formulation/1.toggle model |Step1]] [[Tokyo/Formulation/2.toggle model with hybrid promoter |Step2]] [[Tokyo/Formulation/3.AHL-experssing model|Step3]] [[Tokyo/Formulation/4.population model|Step4]] [[Tokyo/Formulation/5.stochastic differential equation model with poisson random variables|Step5]] | ||
+ | <br> | ||
+ | == == | ||
we introduced the terms of [[Tokyo/Formulation/4.population model|Ex 4-1]] into a stochastic process to simulate the sthochastic behavior.we used Poisson random variables as a sthochastic process. Threfore,a stochastic differential equations were given as | we introduced the terms of [[Tokyo/Formulation/4.population model|Ex 4-1]] into a stochastic process to simulate the sthochastic behavior.we used Poisson random variables as a sthochastic process. Threfore,a stochastic differential equations were given as | ||
- | <br>[[Image:expression5-1.jpg|500px| | + | <br>[[Image:expression5-1.jpg|500px|none|thumb|Ex 5-1]] |
+ | <!--[[Image:parameter4-1.jpg|150px|none|thumb|Table 5]]--> | ||
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+ | ''' ここより下は独立したページにすべき? ''' | ||
+ | <!-- | ||
<br>The values of parameters in the right table were used and the results of simulation were shown in Fig 5.1-3. | <br>The values of parameters in the right table were used and the results of simulation were shown in Fig 5.1-3. | ||
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<br>where α2 = 1(μM) in Fig 5.1,α2 = 2.7(μM) in Fig 5.2,α2 = 4(μM) in Fig 5.3. and it has been estimated that 1(μM) = 1000 molecules (count). | <br>where α2 = 1(μM) in Fig 5.1,α2 = 2.7(μM) in Fig 5.2,α2 = 4(μM) in Fig 5.3. and it has been estimated that 1(μM) = 1000 molecules (count). | ||
- | [[Image:3d-1-0.2.JPG| | + | <br>Fig.5.1 indicates that all cells shift to A state in the steady state and Fig 5.3 indicates that all cells shift to B state in the steady state.These results doesn't represent coexistence stable. |
- | [[Image:3d-1-0.8.JPG| | + | <br>Fig.5.2 indicates that a portion of cells shift to A state and the others shift to B state in steady state;that is,individual cells are stable under stable coexistence. |
- | [[Image:3d-1-30.JPG| | + | |
+ | [[Image:3d-1-0.2.JPG|200px|left|thumb|Figure 5.1.A t=0.2(min)]] | ||
+ | [[Image:arrow2.JPG|50px|left|thumb]] | ||
+ | [[Image:3d-1-0.8.JPG|200px|left|thumb|Figure 5.1.B t=0.8(min)]] | ||
+ | [[Image:arrow2.JPG|50px|left|thumb]] | ||
+ | [[Image:3d-1-30.JPG|200px|none|thumb|Figure 5.1.C t=30(min) only A]] | ||
+ | ===[[Tokyo/Formulation/5.stochastic differential equation model with poisson random variables/only A movie/|movie here!!]]=== | ||
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<br> | <br> | ||
- | [[Image:3d-2.7-0.2.JPG| | + | [[Image:3d-2.7-0.2.JPG|200px|left|thumb|Figure 5.2.A t=0.2(min)]] |
- | [[Image:3d-2.7-0.8.JPG| | + | [[Image:arrow2.JPG|50px|left|thumb]] |
- | [[Image:3d-2.7-30.JPG| | + | [[Image:3d-2.7-0.8.JPG|200px|left|thumb|Figure 5.2.B t=0.8(min)]] |
+ | [[Image:arrow2.JPG|50px|left|thumb]] | ||
+ | [[Image:3d-2.7-30.JPG|200px|none|thumb|Figure 5.2.C t=30(min)''' success!! coexistence''']] | ||
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+ | ===[[Tokyo/Formulation/5.stochastic differential equation model with poisson random variables/ A and B coexistence movie/ |movie here!!]]=== | ||
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<br> | <br> | ||
- | [[Image:3d-4-0.2.JPG| | + | [[Image:3d-4-0.2.JPG|200px|left|thumb|Figure 5.3.A t=0.2(min)]] |
- | [[Image:3d-4-0.8.JPG| | + | [[Image:arrow2.JPG|50px|left|thumb]] |
- | [[Image:3d-4-30.JPG| | + | [[Image:3d-4-0.8.JPG|200px|left|thumb|Figure 5.3.B t=0.8(min)]] |
+ | [[Image:arrow2.JPG|50px|left|thumb]] | ||
+ | [[Image:3d-4-30.JPG|200px|none|thumb|Figure 5.3.C t=30(min) ''' only B''']] | ||
+ | |||
+ | ===[[Tokyo/Formulation/5.stochastic differential equation model with poisson random variables/only B movie/|movie here!!]]=== | ||
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+ | <br>Next,the relation between the results of simulation and phase plane are shown in Fig.5.4.1-3,where the nullclines of this system were [[Tokyo/Formulation/4.population model|Ex 4-3]] | ||
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+ | [[Image:phase plane and simulation-1.JPG|270px|left|thumb|Figure 5.4.1]] | ||
+ | [[Image:phase plane and simulation-2.7.JPG|270px|left|thumb|Figure 5.4.2]] | ||
+ | [[Image:phase plane and simulation-4.JPG|270px|none|thumb|Figure 5.4.3]] | ||
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+ | <br>Fig.5.4.1-3 indicate that the distribution of the cells corresponds with the stable equilibrium points. | ||
+ | --> | ||
- | + | == == | |
- | + | [[Tokyo/Formulation/5.stochastic differential equation model with poisson random variables|Step.5]] >> [[Tokyo/Works/Formulation|Formulation TOP]] |
Latest revision as of 13:03, 25 October 2007
Works top 0.Hybrid promoter 1.Formulation 2.Assay1 3.Simulation 4.Assay2 5.Future works
Step1 Step2 Step3 Step4 Step5
we introduced the terms of Ex 4-1 into a stochastic process to simulate the sthochastic behavior.we used Poisson random variables as a sthochastic process. Threfore,a stochastic differential equations were given as
ここより下は独立したページにすべき?
Step.5 >> Formulation TOP