Tokyo/Formulation/1.toggle model
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Revision as of 13:39, 23 October 2007
1.toggle model
First,the ordinary differential equations(ODEs) of the toggle switch were derived as
These equations were normalized as follows:
In the steady state,time derivatives are zero:
As a result,the nullclines of this system were derived as
Therefore,the phase plane of this system can be plotted as Fig●
About parameters,we use three sets of parameters.
1)the maximum expression rate of repressor A and repressor B is balanced,and hill coefficient of both A and B is three.
2)the maximum expression rate of repressor A and repressor B is equal,and hill coefficient of A is one.
3)the maximum expression rate of repressor A and repressor B is not balanced,and hill coefficient of both A and B is three.
we correlate phaseplane analysis and simulation results.
First,we simulate about the phaseplane of two stable equilibrium points(the upper left figure) and use three kinds of initial values.
1. (Ra:low , Rb:high) 2. (Ra:high , Rb:low) 3. (Ra:middle , Rb:middle)
安定点B付近から始めるとB状態で安定し，安定点A付近から始めるとA状態で安定しているのが分かる．
不安定点付近から始めるとどちらかで安定化する．
Next,
次に，安定点が一つしかない場合のシミュレーション結果は下のようになる．
安定点が一つしかない場合は，安定点B付近から始めてもA状態で安定化してしまうのが分かる．
As a result,taking two stable status need the phaseplane of two stable equilibrium points and we have to set proper parameters.
