Team:XMU-China/Model

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We assume that：(1) without the circuit，changes in viable cell density（N,/ml）follow logistic kinetics;(2)for population-circuit growth, the cell death rate is proportional to the intracellular concentration of the kill protein(E, nM) ;(3)the production rate of E is proportional to AHL concentration(A, nM) ; (4)AHL production rate is proportional to N;(5)degradation of the kill protein and AHL follows first-order kinetics.
We assume that：(1) without the circuit，changes in viable cell density（N,/ml）follow logistic kinetics;(2)for population-circuit growth, the cell death rate is proportional to the intracellular concentration of the kill protein(E, nM) ;(3)the production rate of E is proportional to AHL concentration(A, nM) ; (4)AHL production rate is proportional to N;(5)degradation of the kill protein and AHL follows first-order kinetics.
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XXX model 1 XXX  
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XXX Fig.124 XXX
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XXX model 2 XXXare the rate constants(/h).
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XXX Fig.125 XXXare the rate constants(/h).
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XXX model 3 XXXis the carrying capacity in the Limited medium without the cell-death circuit.
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XXX Fig.126 XXXis the carrying capacity in the Limited medium without the cell-death circuit.
At steady state, we can get the following equations:
At steady state, we can get the following equations:
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XXX model 4XXX
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XXX Fig.127 XXX
Where subscript ‘s’ represents steady state.
Where subscript ‘s’ represents steady state.
There are two steady-state solutions:  
There are two steady-state solutions:  
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XXX model 5XXX
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XXX Fig.128 XXX
We can get the following equation (9) from equation (8) .
We can get the following equation (9) from equation (8) .
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XXX model 6XXX
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XXX Fig.129 XXX
With time limited, we only conducted the experiment on the viable cell density at steady-state with the population-control device with RBS0.07 ,RBS0.3, RBS0.6 and RBS1.0.  
With time limited, we only conducted the experiment on the viable cell density at steady-state with the population-control device with RBS0.07 ,RBS0.3, RBS0.6 and RBS1.0.  
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And we define that:XXX model 7 XXX
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And we define that:XXX Fig.130 XXX
Computed from our experimental data, we can get the data listed in Table 1.
Computed from our experimental data, we can get the data listed in Table 1.
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XXX model 8 XXX
+
XXX Fig.131 XXX
From the model and Table 1, we can conclude that: the efficiency of RBS (a) may have close relationship with kE . Based on the device of RBS1.0, the viable cell density at steady-state (NS ) of other devices with different efficiency of RBS can be shown as equation(10).
From the model and Table 1, we can conclude that: the efficiency of RBS (a) may have close relationship with kE . Based on the device of RBS1.0, the viable cell density at steady-state (NS ) of other devices with different efficiency of RBS can be shown as equation(10).
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XXX model 9 XXX
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XXX Fig.132 XXX
C is -4.96322E-09 in our experiment.
C is -4.96322E-09 in our experiment.

Revision as of 23:38, 5 October 2011

Different RBS sequences leads to different levels of expression of the killer protein CcdB which is directly linked to the effects of our programmed cell-death circuit. So we constructed a series of circuits with different RBS sequences so as to detect how RBS of different efficiency can affect the viable cell density at steady state. We build a model to search for a theory to predict growth rule of bacteria with the programmed cell-death circuit. We assume that：(1) without the circuit，changes in viable cell density（N,/ml）follow logistic kinetics;(2)for population-circuit growth, the cell death rate is proportional to the intracellular concentration of the kill protein(E, nM) ;(3)the production rate of E is proportional to AHL concentration(A, nM) ; (4)AHL production rate is proportional to N;(5)degradation of the kill protein and AHL follows first-order kinetics.

XXX Fig.124 XXX

XXX Fig.125 XXXare the rate constants(/h).

XXX Fig.126 XXXis the carrying capacity in the Limited medium without the cell-death circuit.

At steady state, we can get the following equations:

XXX Fig.127 XXX

Where subscript ‘s’ represents steady state. There are two steady-state solutions:

XXX Fig.128 XXX

We can get the following equation (9) from equation (8) .

XXX Fig.129 XXX

With time limited, we only conducted the experiment on the viable cell density at steady-state with the population-control device with RBS0.07 ,RBS0.3, RBS0.6 and RBS1.0.

And we define that:XXX Fig.130 XXX

Computed from our experimental data, we can get the data listed in Table 1.

XXX Fig.131 XXX

From the model and Table 1, we can conclude that: the efficiency of RBS (a) may have close relationship with kE . Based on the device of RBS1.0, the viable cell density at steady-state (NS ) of other devices with different efficiency of RBS can be shown as equation(10).

XXX Fig.132 XXX

C is -4.96322E-09 in our experiment.

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