Team:XMU-China/Model
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+ | Different RBS sequences lead 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. | ||
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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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+ | are the rate constants(/h). | ||
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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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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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We can get the following equation (9) from equation (8) . | We can get the following equation (9) from equation (8) . | ||
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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. | ||
- | And we define that: | + | 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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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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C is -4.96322E-09 in our experiment. | C is -4.96322E-09 in our experiment. | ||
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+ | ==reference== | ||
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+ | [1]You L, Cox RS, Weiss R, Arnold FH. Programmed population control by cell-cell communication and regulated killing[J]. Nature, 2004, 428(6985): 868-871. |
Latest revision as of 12:07, 28 October 2011