To get the best yield of amilCP, we designed a system to control the bacteria death by cracking the cells, but the best harvest time is still unknown. So we set up a model of gene expression to explore the best time to harvest. Gene expression can be divided into two steps: transcription and translation. The products of transcription and translation are mRNA and protein. After a specific time, those products will degrade by specific enzymes. The approximate mechanism is shown in the figure below.
Fig.1 Expression Model: Gene Expression in E. coli
To explore when these proteins reach the maximum value, we established an ODE model to describe the biochemical process in the figure above. 1.Let us assume the protein and mRNA levels were 0 before induction. 2.We assumed that the transcription speed of E. coli RNA polymerase is 50 nt/s. The process in Figure 1. is symbolized as follows:
Tabel 1. Biochemical reaction in the Expression model
Through the above biochemical reactions, we can obtain our related variables and ODE models:
Tabel 2. Variables, Biochemical species and Units in the Expression model
Among them, the average number of copies of the pUC57 plasmid in E. coli cells was 40. The size of the amilCP gene was 669bp. So the amilCP protein size was 222aa. The parameter values can be obtained from the above data[1]:
Tabel 3.Parameter and values in the Expression model
We solved the ODE model as followed, where theαand β were integral constants.
Then we used MATLAB to obtain the following image through simulation:
Fig.2Simulated result
In this result, we can find the time for the amilCP to reach its peak is about 80 min. [1]R. Milo and R. Phillips. Cell Biology by the Numbers. First edition, 2015. ISBN9780815345374.
