Team:RDFZ-China/Model
Model
The production of protein is primarily influenced by the expression level of operon, which is lac operon in our case. In order to increase the yield of protein of interest, we use IPTG as inducer in our experiment. LacI (lac repressor) is constitutively expressed in bacteria cells, and it represses the production of our protein of interest in the absence of IPTG. When IPTG is added, the pathway is “de-repressed”, as LacI binds to IPTG to form LacI-IPTG complex and is removed from the system. Therefore, by controlling IPTG induction, we can control the production of the protein. Here, we examine the production of GFP, the reporter of CDS (coding sequence) expression, as it is easier to be quantified by examining the light intensity. This model could give a better description on how to use our parts in order to achieve maximum yield.
Assumptions
1. There is no lactose present in the culture and the LacI gene product is the only repressing entity in the system.
2. The range of IPTG concentration used in the experiments has no toxicity to bacterial cells.
3. Production of GFP is inversely proportional to mRNA concentration of the repressor LacI.
Simulation: Gene expression
We modified the lac operon model from Santill´an et al., 2007, making IPTG concentration the only influencing factor in gene repression since our culture does not contain lactose. Thus, we get the following equation about the relationship between inducer IPTG and the repressor LacI:
As LacI is being removed from the system, the production of our protein of interest, GFP, increases.
According to the model, the more IPTG added, the higher the output of protein of interest. However, as the concentration of IPTG reaches a certain value, the LacI present in the cell would be used up. Therefore, any concentration above that value add no influence to protein production.
Modelling terms table
To confirm the validity of our model, we also introduced an exponential regression for comparison using the lab data we collected. We can get the equation: f(x) = a*exp(b*x) + c*exp(d*x), where
a = 5432
b = -0.007733
c = -54.11
d = -6.15
Our model agrees with our experimental data in the overall trend, confirming the proportional relationship between IPTG concentration and production of protein of interest.
Reference
1. Avinash M. Baktula and Genise A. Nolan. Effect of Variable Isopropyl Beta-Thiogalactoside Concentrations on beta-Galactosidase Activity
2. Brian I. (2018). Mathematical Modelling in Systems Biology: An Introduction
3. Yildirim, N., & Mackey, M. C. (2003). Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data. Biophysical Journal, 84(5), 2841–2851. doi:10.1016/s0006-3495(03)70013-7
