Team:Kyoto/Digestion/Modeling

From 2011.igem.org

(Difference between revisions)
(Digestion Modeling)
(3.Exponential state model)
 
(12 intermediate revisions not shown)
Line 4: Line 4:
='''Digestion Modeling'''=
='''Digestion Modeling'''=
 +
=='''1.Introduction'''==
We preformed modeling to improve usability of the results of Team Digestion.<br>
We preformed modeling to improve usability of the results of Team Digestion.<br>
The aim of these modeling is the creation of the relationship of time and the cell population of E.coli and the concentration of chitinase and N-acetylglucosamin.<br>
The aim of these modeling is the creation of the relationship of time and the cell population of E.coli and the concentration of chitinase and N-acetylglucosamin.<br>
We created two models; Stable state model and exponential state model.
We created two models; Stable state model and exponential state model.
-
=='''Stable state model'''==
+
=='''2.Stable state model'''==
We can apply this model when cell population of E.coli don't change. In this case, we can think about two reasons why cell population don't change.<br>  
We can apply this model when cell population of E.coli don't change. In this case, we can think about two reasons why cell population don't change.<br>  
*First, cell population is too small for us to see the significant difference of cell population.<br>   
*First, cell population is too small for us to see the significant difference of cell population.<br>   
Line 15: Line 16:
We thought about each reasons and .
We thought about each reasons and .
-
==='''no feedback model'''===
+
==='''2-1.no feedback model'''===
We defined these following equations. In defining these equations, we premised the following four things, that is,
We defined these following equations. In defining these equations, we premised the following four things, that is,
*Chitinase in medium isn't decomposed.
*Chitinase in medium isn't decomposed.
Line 39: Line 40:
[[File:Modeling_Modeling1.jpg]]<br>
[[File:Modeling_Modeling1.jpg]]<br>
-
==='''negative feedback'''===
+
==='''2-2.negative feedback'''===
-
We creat anothre graph. In this graph, E.coli digests N-acetylgulcosamin. Therefore, the speed of increase of the concentration of N-acetylglucosamin is lower than no feedback model. In this model, we used the following equation.
+
We creat anothre graph. In this graph, E.coli digests N-acetylgulcosamin. Therefore, negative feedback occurs on N-acetylglucosmine and the speed of increase of the concentration is lower than no feedback model. In this model, we used the following equation.
Line 50: Line 51:
[[File:Modeling_Modeling3.jpg]]<br>
[[File:Modeling_Modeling3.jpg]]<br>
-
=='''Exponential state model'''==
+
=='''3.Exponential state model'''==
-
At first, we defined these things. In these premises
+
We can apply this model when cell population of E.coli exponentially increase.
 +
 
 +
 
 +
 
 +
==='''3-1.no feed back model'''===
 +
We defined these following equations. In defining these equations, we premised the following four things, that is,
*chitinase in medium isn't decomposed
*chitinase in medium isn't decomposed
*E.coli don't digest N-acetylgulcosamin
*E.coli don't digest N-acetylgulcosamin
*chitin as substrate of chitinase is sufficient for reaction with chitinase
*chitin as substrate of chitinase is sufficient for reaction with chitinase
-
*E.coli grow exponentially <br>
+
*E.coli exponentially grow<br>
Line 62: Line 68:
-
Two under equations of this figure show the production of citinase by E.coli and the decomposition reaction of chitin. In this decompositon reaction, the concentration of chitin isn't related because chitin is solid and don't dissolve in water.<br>   
+
Two under equations of this figure show the production of chitinase by E.coli and the decomposition reaction of chitin. In this decompositon reaction, the concentration of chitin isn't related because chitin is solid and don't dissolve in water.<br>   
We sought the answers of these equation by followig procedures.
We sought the answers of these equation by followig procedures.
Line 74: Line 80:
[[File:Modeling_Modeling2.jpg]]<br>
[[File:Modeling_Modeling2.jpg]]<br>
-
 
+
==='''3-2.negative feedback model'''===
-
Second, we creat anothre graph. In this graph, E.coli digest N-acetylgulcosamin. In this model, following equatio was used.
+
We creat anothre graph. In this graph, E.coli digests N-acetylgulcosamin. Therefore, negative feedback occurs on N-acetylglucosmine and the speed of increase of the concentration is lower than no feedback model. In this model, we used the following equation.  
Line 83: Line 89:
[[File:Modeling_Modeling4.jpg]]<br>
[[File:Modeling_Modeling4.jpg]]<br>
-
=='''Discussion'''==
+
=='''4.Discussion'''==
 +
==='''4-1.complex model'''===
 +
In fact, the function of cell population of E.coli seems to be more complex. However, the function can be expressed by the following equation, complex model, because every function will be expressed by the combination of stable state model and exponential state model.
 +
 
 +
[[File:Digestion_Modeling10.png]]
-
We can apply stable state model to the results of SOC medium and M9 medium.
+
[[File:Digestion_equation4.png]]
-
Moreover, we can apply exponential model to the result of Plus grow medium.
+

Latest revision as of 04:05, 6 October 2011

Contents

Digestion Modeling

1.Introduction

We preformed modeling to improve usability of the results of Team Digestion.
The aim of these modeling is the creation of the relationship of time and the cell population of E.coli and the concentration of chitinase and N-acetylglucosamin.
We created two models; Stable state model and exponential state model.

2.Stable state model

We can apply this model when cell population of E.coli don't change. In this case, we can think about two reasons why cell population don't change.

  • First, cell population is too small for us to see the significant difference of cell population.
  • Second, nutrients in medium don't sufficiently exist for E.coli to grow.

We thought about each reasons and .

2-1.no feedback model

We defined these following equations. In defining these equations, we premised the following four things, that is,

  • Chitinase in medium isn't decomposed.
  • E.coli doesn't digest N-acetylgulcosamin.
  • Chitin as substrate of chitinase is sufficient for reaction with chitinase.
  • E.coli doesn't grow.


Modeling Equation1.png


Two under equations of this figure show the production of citinase by E.coli and the decomposition reaction of chitin. In this decompositon reaction, the concentration of chitin isn't related because chitin is solid and don't dissolve in water.
We sought the answers of these equations by followig procedures.


Modeling Equation2.png


From these answers, we can get this graph.
This graph is the most simply model. In this graph, the each concentration continuously increses by time goes on, and we can easily seek the concrete constants.


Modeling Modeling1.jpg

2-2.negative feedback

We creat anothre graph. In this graph, E.coli digests N-acetylgulcosamin. Therefore, negative feedback occurs on N-acetylglucosmine and the speed of increase of the concentration is lower than no feedback model. In this model, we used the following equation.


Modeling Equation3.png


Modeling Modeling3.jpg

3.Exponential state model

We can apply this model when cell population of E.coli exponentially increase.


3-1.no feed back model

We defined these following equations. In defining these equations, we premised the following four things, that is,

  • chitinase in medium isn't decomposed
  • E.coli don't digest N-acetylgulcosamin
  • chitin as substrate of chitinase is sufficient for reaction with chitinase
  • E.coli exponentially grow


Modeling Equation4.png


Two under equations of this figure show the production of chitinase by E.coli and the decomposition reaction of chitin. In this decompositon reaction, the concentration of chitin isn't related because chitin is solid and don't dissolve in water.
We sought the answers of these equation by followig procedures.


Modeling Equation5.png


From these answers, we can get this graph.


Modeling Modeling2.jpg

3-2.negative feedback model

We creat anothre graph. In this graph, E.coli digests N-acetylgulcosamin. Therefore, negative feedback occurs on N-acetylglucosmine and the speed of increase of the concentration is lower than no feedback model. In this model, we used the following equation.


Modeling Equation6.png


Modeling Modeling4.jpg

4.Discussion

4-1.complex model

In fact, the function of cell population of E.coli seems to be more complex. However, the function can be expressed by the following equation, complex model, because every function will be expressed by the combination of stable state model and exponential state model.

Digestion Modeling10.png

Digestion equation4.png