Team:Paris/Analysis/Math+Sim
From 2008.igem.org
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[[Image:Subsystem1.jpg|400px|left]][[Image:essai_with_fliAbis.jpg|500px|center]] | [[Image:Subsystem1.jpg|400px|left]][[Image:essai_with_fliAbis.jpg|500px|center]] | ||
- | (note that you can have an explanation on the way they have been built on the [[Team:Paris/Network_analysis_and_design/Core_system/Model_construction|Model Construction]] page): | + | Here is the set of equations used for the numerical simulations, with the parameters found in bibliographical studies (note that you can have an explanation on the way they have been built on the [[Team:Paris/Network_analysis_and_design/Core_system/Model_construction|Model Construction]] page): |
[[Image:FliA_dynamics.jpg|center]] | [[Image:FliA_dynamics.jpg|center]] | ||
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where CFP, YFP, and RFP will be denoted below as respectively Z1,Z2 and Z3. | where CFP, YFP, and RFP will be denoted below as respectively Z1,Z2 and Z3. | ||
We have implemented this system using Matlab (see the [[Team:Paris/Modeling/BOB/Simulations/Codes#FIFO|corresponding codes]]) | We have implemented this system using Matlab (see the [[Team:Paris/Modeling/BOB/Simulations/Codes#FIFO|corresponding codes]]) | ||
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* Then, in order to obtain simulations of the expected FIFO behaviour, we set ideal conditions, by imposing flhDC as a step function, equal to one then to zero. | * Then, in order to obtain simulations of the expected FIFO behaviour, we set ideal conditions, by imposing flhDC as a step function, equal to one then to zero. | ||
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* Then, we simulated the entire system (that means '''with FliA'''), to check if we had | * Then, we simulated the entire system (that means '''with FliA'''), to check if we had | ||
** the lasting burst due to FliA (more important for Z3 than for Z2, and more important for Z2 than Z1) in the increasing phase. | ** the lasting burst due to FliA (more important for Z3 than for Z2, and more important for Z2 than Z1) in the increasing phase. | ||
- | ** the effect of fliA which maintained the concentrations to their maximum (more important for Z3 than for Z2, and more important for Z2 than Z1) in the decreasing phase. We have obtained the following curves, which are in perfect agreement with the theoretical definition of a 'FIFO' process | + | ** the effect of fliA which maintained the concentrations to their maximum (more important for Z3 than for Z2, and more important for Z2 than Z1) in the decreasing phase. We have obtained the following curves, which are in perfect agreement with the theoretical definition of a 'FIFO' process as previously shown. |
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* FliA enables the curves to cross, and adds a delay on the genes that are most affected, with gives a better observability of the FIFO behavior. | * FliA enables the curves to cross, and adds a delay on the genes that are most affected, with gives a better observability of the FIFO behavior. | ||
Revision as of 08:39, 28 October 2008
Mathematical analysis and simulations
FIFO
Here is the set of equations used for the numerical simulations, with the parameters found in bibliographical studies (note that you can have an explanation on the way they have been built on the Model Construction page): where CFP, YFP, and RFP will be denoted below as respectively Z1,Z2 and Z3. We have implemented this system using Matlab (see the corresponding codes)
Indeed, we may see that there is a LIFO behavior rather than the FIFO we expect...
Oscillations
If you want more details about the way we have built them, you can go to the model construction page. If one tries to draw simulations of this system, he will obtain this kind of results : In a nutshell : It does not work !
↓ mathematical analysis ↑
↓ Impact of integration methods ↑
System analysisSimulations of the core system displayed above reveal that it does not exhibit an oscillatory behavior. In this section we use the model of the core system to try to figure out the contribution of some key characteristics of the network topology on the dynamics of the system. This analysis is done by successively simulating altered forms of the system. The following table lists the different forms of the system considered and their respective outcome :
In the next section, we examine significant topology improvements of the core system that are potentially better for oscillations and that preserve FIFO required interactions. |