Team:Osaka/Modeling

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iGEM Osaka Theory Group have made mathematical models to understand how colony patterns look like.

Syuichi Iwakiri built differential equations to describe the movement of E.coli and nutrition.

And Hiroki Nishiyama did simulations of the equations.

In the equation on the picture , A means the number of type A-Ecoli , B means the number of type B-Ecoli ,

and N means the concentration of nutrition.






The first partial differential equation of A has 3 factors.

The first one is the diffusion of A , the second one is the growth of A ,

and the third one is the transition from A to B. The transition happens only when N is smaller than No.

The second partial differential equation of B has 2 factors.

The first one is the diffusion of B , and the second one is the transition from A to B.

The third partial differential equation of N has 3 factors.

The first one is the diffusion of N , and the second one is the consume by A ,

the third one is the virtual consume by B (b is the consume rate and c is the produce rate).

The Theory Group have discovered a unique patterns ,

for example , a fractal pattern and cross-like pattern.



We show several patterns that we got from the simulations below.

The gif files show how the number of A type bacterias(Z-axis) develop in 2D area(X-Y plate).