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 Fig.124 XXX
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[[Image:XMU_China_124.jpg|left]]
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XXX Fig.125 XXXare the rate constants(/h).
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[[Image:XMU_China_125.jpg|left]]
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XXX Fig.126 XXXis the carrying capacity in the Limited medium without the cell-death circuit.
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<img src="http://partsregistry.org/wiki/images/4/41/XMU_China_block.jpg">
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are the rate constants(/h).
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[[Image:XMU_China_126.jpg|left]]
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<img src="http://partsregistry.org/wiki/images/4/41/XMU_China_block.jpg">
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is 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 Fig.127 XXX
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[[Image:XMU_China_127.jpg|left]]
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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 Fig.128 XXX
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[[Image:XMU_China_128.jpg|left]]
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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 Fig.129 XXX
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[[Image:XMU_China_129.jpg|left]]
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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 Fig.130 XXX
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And we define that:[[Image:XMU_China_130.jpg|left]]
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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 Fig.131 XXX
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[[Image:XMU_China_131.jpg|left]]
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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 Fig.132 XXX
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C is -4.96322E-09 in our experiment.
C is -4.96322E-09 in our experiment.

Revision as of 01:59, 6 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.

XMU China 124.jpg
XMU China 125.jpg



are the rate constants(/h).

XMU China 126.jpg



is the carrying capacity in the Limited medium without the cell-death circuit.

At steady state, we can get the following equations:

XMU China 127.jpg



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

XMU China 128.jpg


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

XMU China 129.jpg



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:
XMU China 130.jpg



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

XMU China 131.jpg



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).

XMU China 132.jpg



C is -4.96322E-09 in our experiment.

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