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From 2011.igem.org

Contents 1 results 1.1 2 odes and equations 3 parameters and references

results

We have been working hard to model our system.

Fisrt, we will present some basic character of our system

    In a single cell, the system acts like a fast switch upon AHL concentration, on the other hand, cheZ ouput is a slow switch of theophylline concentration.

    We can see that cheZ concentration rises rapidly when AHL concentration rises from 3nM to 4nM. For the switch is so fast that we can use quorum system in our design. CheZ output rises relatively rapid when theophylline concentration is around 210nM.

    For the system without quorum part, If AHL concentration is low, regulate ci protein accumulates, the toggle switch is in the ci state, cheZ production is very low, so the cell can rarely move. And when AHL concentration is high, not enough regulate ci protein is produced, the toggle switch is in the ci434 state, cheZ production is high, so the cell can spend less time tumbling, and will move to the direction where cheZ concentration rises.

Following pictures show how steady-state cheZ concentrations change under conditions of different AHL and theophylline concentrations.

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Following pictures show how cheZ concentrations change on time under conditions of different AHL and theophylline concentrations.

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Following pictures show how a single cell moves on time under conditions of different AHL and theophylline concentrations in one single round of simulation.

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Following pictures show how a single cell moves and how cheZ concentration changes on time under conditions of different AHL and gradient of theophylline concentration (30,600) in one single round of simulation.

    AHL = 10 nM

    AHL = 3 nM

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    Following pictures show 100 cells move under 10nM AHL and gradient of theophylline concentration (25,500).

图片+flash

    For the whole system with quorum part, in the beginning, we assume that the concentrations of all related macromolecules are zero. Cells begin to divide, cell number is growing, and AHL is accumulating, when AHL concentration is high enough, toggle switch in some of the cells turns to the ci434 state, and these cells is moving out. After some time, AHL concentration in these cells will drop, and the toggle switch will most likely turn to the ci state, cells stop moving.

    For this part we assume that numbers of the cells grow under the rate of k=0.97*exp(-t/5), the unit of time is hour.

For no gradient of theophylline
图片
For theophylline gradient (25,500)
图片
results odes parameters and references

odes and equations

Odes and equations

     C1, regulate ci mRNA concentration

     C2, regulate ci protein concentration

     C3, bistable ci mRNA concentration

     C4, total ci protein concentration

     C5, bistable ci434 mRNA concentration

     C6, bistable ci434 protein concentration

     C7, cheZ mRNA concentration

     C8, cheZ protein concentration

     C9, I mRNA concentration

     C10, I protein concentration

     C11, AHL produced

     A, AHL concentration

     For regulatory ci mRNA and protein

    

     For Bistable Part

    

     For cheZ mRNA and protein

    

     For Quorum Sensing Part

    

     The real AHL concentration is no the AHL produced. Considering about fast diffusivity of AHL, we assume that external AHL concentration is zero, although it is not quite exact, but it can describe the character of AHL well. That is, for cell i, the compact of cell j is,

    

     Tumbling frequency of a cell is determined by its cheYp concentration

    

     CheYp concentration is related to cheZ concentration, and for the reaction is so fast, we assume that current cheZ concentration determines current cheYp concentration

    

     We assume that cells move at the speed of 0.025um/s on our semisolid plate. For the movement of a single cell, if the cell tumbles, it will stay of the current second, and change its direction later, if not, the cell keeps on moving in one direction.

    

     For the gradient of theophylline,

    

     For cell number growth

    

    
results odes parameters and references

parameters and references

Parameters