Tokyo/Formulation/1.toggle model

From 2007.igem.org

(Difference between revisions)
(1.toggle model)
Line 1: Line 1:
== 1.toggle model ==
== 1.toggle model ==
-
First,we obtain the ordinary differential equations(ODEs) of the toggle switch.
+
First,the ordinary differential equations(ODEs) of the toggle switch were derived as
<br>[[Image:expression1-1.jpg|200px|]]  [[Image:parameter1-1.jpg|200px|]]  
<br>[[Image:expression1-1.jpg|200px|]]  [[Image:parameter1-1.jpg|200px|]]  
-
<br>And,we normalize these expressions to analyze easily.So,ODEs become dementionless.
+
<br>These equations were normalized as follows:
-
なるってbecomeであってる??
+
<br>[[Image:expression1-2.jpg|200px|]]
<br>[[Image:expression1-2.jpg|200px|]]
-
<br>if the system goes to the steady state,time variation equal to zero.So we solve righe-hand side=0.
+
<br>In the steady state,time derivations are zero:
 +
 
 +
<br>[[Image:expression3-5.jpg|100px|]]
 +
 
 +
<br>As a result,the nullclines of this system were derived as
<br>[[Image:Siki2.jpg|200px|]]
<br>[[Image:Siki2.jpg|200px|]]
-
<br>These graph are below.The lines of graph are nullcline,and the intersection of nullclines is the equillibrium point.
+
<br>Therefore,the phase plane of this system can be plotted as Fig●
<br>About parameters,we use three sets of parameters.
<br>About parameters,we use three sets of parameters.

Revision as of 12:36, 23 October 2007

1.toggle model

First,the ordinary differential equations(ODEs) of the toggle switch were derived as


Expression1-1.jpg Parameter1-1.jpg


These equations were normalized as follows:


Expression1-2.jpg


In the steady state,time derivations are zero:


Expression3-5.jpg


As a result,the nullclines of this system were derived as


Siki2.jpg


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.
Parameter1-2.jpgParameter1-3.JPGParameter1-4.JPG
Toggle1.jpgToggle2.jpgToggle1-4.jpg


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)


Toggle3.jpg Toggle4.JPG Toggle5.JPGToggle1-1.jpg


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.


Toggle6.JPG Toggle7.JPG Toggle8.JPGToggle1-2.jpg


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.