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Team:USTC-China/modeling
From 2012.igem.org
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<p>where</p> | <p>where</p> | ||
| - | <h2><a name="2">Toggle Switch with designed genetic route</h2> | + | <h2><a name="2">Toggle Switch with designed genetic route</a></h2> |
<p>There is a di�erence if we add our designed genetic route:</p> | <p>There is a di�erence if we add our designed genetic route:</p> | ||
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<p>Once obtained [mcro], substitute it into the following to get the �nal equation</p> | <p>Once obtained [mcro], substitute it into the following to get the �nal equation</p> | ||
| - | <h2><a name="3">Result</h2> | + | <h2><a name="3">Result</a></h2> |
<p>We found that for the parameters in the value table, there is no real solution for both the two part in the following | <p>We found that for the parameters in the value table, there is no real solution for both the two part in the following | ||
equation <img>The reason of this problem probably stems from the[img] | equation <img>The reason of this problem probably stems from the[img] | ||
Revision as of 15:49, 25 September 2012
MODELING
We study the steady state property of two system, without and with our designed genetic route separately.
Toggle Switch without designed genetic route
The chemical reactions are:
According to the Law of mass action, we can easily write down the equation approximations to reduce these equations.
First of all, we do quasi-steady state approximation for dimerization reactions
where [cIT] and [croT] are the total concentration of cI and cro.
Besides, we decide to take the degradation into account in the very end step. So, considering the conservation of binding site
Where R is the total binding site number, we get
The above equations give us the expression of [cro2 �OR3 ];[cI2 �OR1 ];[cI2 �OR1 �cI2 �OR2 ]. The �nal step is to write down the evolution equations for [cI] and [cro].
where
Toggle Switch with designed genetic route
There is a di�erence if we add our designed genetic route:
where �mcro refers to
�mcro.
Three additional equation should be taken into account
The above gives us the expression for [img], which is a function of [img]. It is then straightforward to derive [mcro] from the following
Once obtained [mcro], substitute it into the following to get the �nal equation
Result
We found that for the parameters in the value table, there is no real solution for both the two part in the following
equation The reason of this problem probably stems from the[img]
arameters|�1 ;�2 di�ers too much wich �3 ;�4 ;�5 , thus it is impossible for the equation to have real solution. We
lot the stream diagram for [cIT] and [croT]:
After adding our designed route, the stream flow diagram is
We can see that after adding our designed part, the system goes through double steady state to single steady state.
