Team:Paris/Analysis/Model2 Analysis

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[[Image:Core0.png|400px|left|thumb|Simulaiton of the core system]]
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[[Image:Core0.png|400px|left|thumb|Simulation of the core system]]
[[Image:System4.png|400px|right|thumb|Simulation of the bimodular system]]
[[Image:System4.png|400px|right|thumb|Simulation of the bimodular system]]
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Coupling these two modules has a positive effect on the overall behavior but it still does not provide sustained oscillations.
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Coupling these two modules has a positive effect on the overall behavior but it still does not provide sustained oscillations.  The core system interfere with the behavior of the HSL module and the HSL module is not strong enough to retain its oscillatory behavior.
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It seems that obtaining oscillations by coupling two modules is possible only if each module taken separately is functional.  
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==== Oscillations ====
==== Oscillations ====
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Effect of auto activation loop. Effect of EnvZ threshold. It can provide oscillations as long as auto loop and threshold.
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We consider now the unimodular system. Its kinetic parameter values are obtained from the literature for all interactions already in the core system and from the parameter search carried above for the three unknown parameters in common with the HSL module. Here is the simulation obtained.
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[[Image:System2.png|400px|center|thumb|Simulation of the unimodular system]]
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This system shows sustained oscillations. It is worth noticing that this is obtained without removing the auto-activation loop on Flia and the activation of lasI by FlhDC even though these two interactions hamper the oscillatory behavior as shown in the analysis of the core system.
==== FIFO ====
==== FIFO ====
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FIFO behavior ok even without auto loop.  
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All FIFO related interactions of the core system remain in the unimodular system. The behavior is therefore the same as observed in the core system. But whereas one had to impose FlhDC as a step function in the core system to be able to observe the FIFO behavior, FlhDC oscillatons are here inherent to the dynamics of the system. Below is a close-up view of
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FIFO reporters concentrations for one period of the unimodular system :
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[[Image:S2fifo.png|400px|center|thumb|FIFO behavior in the unimodular system]]
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==== Synchronization ====
==== Synchronization ====
synchro ok (fct dilution eta)
synchro ok (fct dilution eta)
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== Conclusion ==

Revision as of 15:30, 28 October 2008

Model Analysis


Contents

Model Analysis

Bimodular system

Parameter search

In this system we rely on kinetic parameter values taken from the literature. However, three kinetic parameters remain unknown : HSL production rate, the threshold value of HSL above which EnvZ is expressed and the threshold value of EnvZ above which lasI is inhibited. We assume, as Ojalvo did, that this loop is functional and thus look for values of these three parameters such that concentration values of species in this loop oscillate.

For the HSL production rate we find that HSL time scale has to be similar to lasI time scale, that is the following is required : betaHSL/gammaHSLext =(betalasI/gamma)*(c) (TODO :latex) Besides we observe that the threshold value of EnvZ needs to be low and that the loop is functional for any threshold value of HSL. For three parameter values validating these requirements, the HSL loop alone has the following behavior :

Simulation of the HSL loop

We will use for all forthcoming use of the interactions appearing in this loop the parameter values deducted from this parameter search.

Coupling results

The two modules of the bimodular system are the the negative loop involving HSL, and the core system. These two modules are coupled by EnvZ. The HSL module is functional whereas the core system is not. We compare below the behavior of the core system alone to the behavior of the system coupling these two modules.


Simulation of the core system
Simulation of the bimodular system



















Coupling these two modules has a positive effect on the overall behavior but it still does not provide sustained oscillations. The core system interfere with the behavior of the HSL module and the HSL module is not strong enough to retain its oscillatory behavior. It seems that obtaining oscillations by coupling two modules is possible only if each module taken separately is functional.


Unimodular system

Oscillations

We consider now the unimodular system. Its kinetic parameter values are obtained from the literature for all interactions already in the core system and from the parameter search carried above for the three unknown parameters in common with the HSL module. Here is the simulation obtained.

Simulation of the unimodular system

This system shows sustained oscillations. It is worth noticing that this is obtained without removing the auto-activation loop on Flia and the activation of lasI by FlhDC even though these two interactions hamper the oscillatory behavior as shown in the analysis of the core system.

FIFO

All FIFO related interactions of the core system remain in the unimodular system. The behavior is therefore the same as observed in the core system. But whereas one had to impose FlhDC as a step function in the core system to be able to observe the FIFO behavior, FlhDC oscillatons are here inherent to the dynamics of the system. Below is a close-up view of FIFO reporters concentrations for one period of the unimodular system :

FIFO behavior in the unimodular system

Synchronization

synchro ok (fct dilution eta)

Conclusion

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