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Latest revision as of 21:14, 21 October 2021
The model of production
Background
Integrate the models we build, the final model of production can be established.
Here, the population of E. coli can influence the production rate in the model of synthesis of tryptophan, while the concentration of pyruvate can influence the growth rate of E. coli. Meanwhile, the production of catalyzers in synthesis of tryptophan is controlled by the genetic circuits.
With these models, we can study the final output (relative concentration) of tryptophan, and determine the optimal production strategy.
Theory
According to the model of population dynamics,
According to the model of genetic circuits, for promoters, we have
and for protein, we have
According to the model of synthesis of tryptophan,
Parameter
The parameters are shown in the table below.
Meanwhile, the correction is performed according to the CDS length.
NAME | LENGTH | CORRECTION RATE |
---|---|---|
RFP (Benchmark) |
|
|
lacI |
|
|
aroG |
|
|
trpB |
|
|
trpA |
|
|
cl857 |
|
|
pykA |
|
|
Result and conclusion
Let the initial value of
From the figure, we can see that:
- When
, the output of tryptophan increases slowly as increases; - When
, the maximun output of tryptophan is ( of ); - When
, the output of tryptophan drops sharply as increases; - Finally, when
, the output of tryptophan is around ( of ).
Next, let the time of raising temperature be
From the figure, we can see that:
- When
, the population density grows exponentially; - When
, the environmental resources have a restrictive effect on E. coli; - Finally the population density approaches
; - The population density reach balance at about
.
The figure below shows the concentration change of gene product.
From the figure, we can see that:
- There are two stable states during the period of time;
- After raising temperature at
, the concentrations of cl857 and pykA go down, while the concentrations of lacI, aroG, trpA and trpB go up.
The figure below shows the concentration change during the synthesis of tryptophan.
From the figure, we can see that:
- When reaction starts, Glc begin to convert to PEP, and PEP immediately turns into Pyr and DAHP;
- The concentration of DAHP reaches maximum at about
, and after that it goes down; - The product of DAHP is 3IGP, and 3IGP immediately converts to Trp;
- The final products of reactions are Pyr and Trp, whose concentrations are stable at
.
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