From 2011.igem.org

Digestion Modeling

We preformed modeling to improve usability of the results of Team Digestion.
The aim of these modelings 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.

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 sugnificant difference of cell population.
  
• Second, nutrients in medium don't sufficenetly exist for E.coli to grow.
  

We thought about each reasons and .

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 don't digest N-acetylgulcosamin
• chitin as substrate of chitinase is sufficient for reaction with chitinase
• E.coli don'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 equation by followig procedures.

From these answers, we can get this graph.

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.

Exponetial state model

At first, we defined these things. In these premises

• 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 grow exponentialy
  

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 equation by followig procedures.

From these answers, we can get this graph.

Second, we creat anothre graph. In this graph, E.coli digest N-acetylgulcosamin. In this model, following equatio was used.

Discussion

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.