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Team:WHU-China/Project/Modeling
From 2011.igem.org
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This is our gene circuit designed to equip our E.coli with the ability to change color with time.</br> | This is our gene circuit designed to equip our E.coli with the ability to change color with time.</br> | ||
Revision as of 15:48, 28 October 2011
This is our gene circuit designed to equip our E.coli with the ability to change color with time. The key players are LsrR and LsrK. The alternation of their expression results in the oscillating concentration of the reporter—GFP, and thus yield the periodically changing color. Theoretically, at the very beginning, LsrR is expressed and inhibits LsrK. After some time, LsrR inhibits itself and its concentration drops. Therefore LsrK has a chance to express and climbs due to its self-enlarging. However, LsrK induces the re-expression of LsrR at the same time. In this way, their concentrations wave alternatively. C1’s function is to delay the oscillation and stabilize the system. In the mathematic modeling section , we make stimulation about the oscillator and consider two possible circumstance.
Where
means the volume of
,
means the volume of
,
means the delay time of the reaction.
This is the classic DDE , using the matlab software, we got the solution image ;
We mainly consider the system including three protein: We also use ODE to describe the system:
where:
means the volume of 
though dimensionless:
The balance point of the equation is
and 
Using the MATLAB software to plot we got the solution image:
is the Hopf bifurcation point, when
,it is able to generate a stable periodic solution.
is the Hopf bifurcation point, when
,it is able to generate a stable periodic solution.
is the Hopf bifurcation point, when
,it is able to generate a stable periodic solution.
is the Hopf bifurcation point, when
,it is able to generate a stable periodic solution.
Cycle with the curve of each parameter:
As the changes of cycle time with the change of the parameters in the image , we can get the conclusion that:
1.
have little influence on the range.
2.
do not have much influence on the cycle time.
3.
have inversely proportional relationship with the cycle time , it have a huge influence on the cycle time , but little impact on the range (Can be used to adjust the cycle to maintain constant amplitude)
4.When
,
have little influence on the range.
This conclusion we get before can be used to guide the design of biological systems, in order to achieve the adjustment period, amplitude can adjust the size of some parameters.
days
hours
minutes
seconds
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