When exploring experimental parameters, a good mathematical model can greatly simplify the experimental process. At the beginning of the project design, we wanted to obtain the maximum target protein yield, so we constructed a molecular dynamics model of different RBS for protein yield. According to the results, we finally selected B0034 as the RBS of the final gene circuit.
As the project progressed, we found that blindly pursuing output was not the most efficient design idea. The large amount of exogenous proteins expressed in cell will greatly increase the metabolic pressure, resulting in the slow growth of cell, and then reduce the yield of proteins. Therefore, we constructed a model of lac operon to simulate the effect of different concentrations of IPTG on protein expression. From the results, the IPTG concentration of 1mM was the best concentration in the experiment. At this concentration, cell could both stop LacI inhibition of transcription and reduce metabolic stress
In this project, protein expression was only affected by RBS transcription rate, so we constructed this model on the basis of the same mRNA content. B0034 was selected as the RBS in the gene circuit according to the numerical modulus results.
Reaction formula:
Ordinary Differential Equations:
Figure：
Lactose operon is an operon responsible for lactose transport and metabolism in Escherichia coli and other intestinal flora. lac operon promotes transcription in the absence of LacI protein. Transcription is inhibited in the presence of LacI and CAP proteins. The addition of IPTG(Isopropyl-beta-D-thiogalactopyranoside) could combine to LacI protein and induce transcription. lac operon is widely used for prokaryotic expression because of its universality of regulatory conditions, and the expression effect can be further optimized by controlling the concentration of IPTG. After consulting the literature [1], we constructed the mathematical model of lac operon.
Reaction formula:
Ordinary Differential Equations:
To test whether the model was correct, we first mapped the relationship between the LacI2 protein, which binds to lacO and suppresses transcription, and lacO. The results showed that the amount of lacO decreased with increasing LacI2.
Next, we investigated the relationship between IPTG and LacI2-IPTG2, and found that IPTG increased briefly when LacI2 protein was low, and then decreased to a very low concentration. This is because the binding activity of IPTG and LacI2 is very high, so once IPTG is present, LacI2 will quickly bind to IPTG and unlock the inhibition of transcription. These results indicate that the model reflects the correct molecular mechanism.
After proving that the model is correct, we need to explore at which concentration IPTG is most suitable for cell growth and product expression. According to the results in Figure4, 5,6, it can be seen that when IPTG concentration is 0.1mM, IPTG cannot completely unlock the transcription inhibition of LacI2 protein. When the IPTG concentration was 10mM, all the inhibition was relieved, which was likely to bring great metabolic pressure. Therefore, we finally decided to use 1mM concentration of IPTG to induce protein expression in the experiment.
