Team:XMU-China/Model
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Revision as of 15:06, 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 model 1 XXX
XXX model 2 XXXare the rate constants(/h).
XXX model 3 XXXis the carrying capacity in the Limited medium without the cell-death circuit.
At steady state, we can get the following equations:
XXX model 4XXX
Where subscript ‘s’ represents steady state. There are two steady-state solutions:
XXX model 5XXX
We can get the following equation (9) from equation (8) .
XXX model 6XXX
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 model 7 XXX
Computed from our experimental data, we can get the data listed in Table 1.
XXX model 8 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 model 9 XXX
C is -4.96322E-09 in our experiment.