From 2011.igem.org

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.
  

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.

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.

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.

3.Exponential state model

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

3-3.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
  

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.

From these answers, we can get this graph.

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.

4.Discussion

complex model

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

We can apply stable state model to the results of SOC medium and M9 medium. Moreover, we can apply exponential model to the result of Plus grow medium.