Intestine gene expression model
Before we started the project, we wanted to verify its feasibility by conducting pre-experimental predictions to understand the effect of engineering bacteria. Limited by the competition rules, we cannot directly conduct experiments and observations in the intestines of animals, so we established a mathematical model for the pre-experimental prediction in order to predict the effect of engineering bacteria and provide a strong basis for carrying out the project.
System specification:
We used E. coli Nissle 1917, and plasmid pET28a, for our project with a minimum copy number of 10 (each bacterium will replicate 10 plasmids). The process we hope to simulate is: Cultivate the engineering bacteria in a laboratory environment, then find when the system reaches a steady state, the efficiency of the engineered bacteria in producing LacZ enzyme. (Where the specific cell concentration of LacZ enzyme is the judgment indicator).
It is noted that our calculated specific cell concentration of LacZ enzyme is still within a normal range even with relatively small constants used, which strongly support the development of our project.
Reasonable assumptions:
1. The resources need for bacteria to survive are sufficient.
2. The number of plasmids in each engineered bacteria are the same as the plasmid copy number
3. We only consider the transcription and translation of the gene of interest
4. We do not take into account the heterogeneity between bacteria
Modelling:
The resource needed for the bacteria to survive is efficient, which can be considered as an ideal condition and suitable for the classical logistic growth model. As shown in formula (1.1), K is the environmental capacity, and r is the internal growth rate. Assuming that the transcription rate of bacteria is “a” and the translation rate is “b”, the production rate of mRNA is affected by plasmid concentration, self-degradation, transcription rate, and its own negative feedback regulation (not infinite transcription). As shown in formula (1.2), is the negative feedback regulator of mRNA, and n represents the strength of negative feedback regulation. The rate of protein production is similar, as shown in Equation (1.3), “” is the rate at which the transporter transports the protein product out of the cell.
| Symbols | Definition | Note |
|---|---|---|
| 𝐶 | Cell concentration | Units：/ml |
| 𝑀 | mRNA Concentration | Units：/ml |
| 𝑃 | Intracellular protein concentration | Units：/ml |
| 𝑟 | Internal factor growth rate | Approximate value：0.9/ml*h |
| 𝐾 | Maximum environment capacity | Approximate value：10^9/ml |
| 𝑎 | Transcription rate | Approximate value：31/h |
| 𝑐 | Number of Plasmid replication | Minimum Value：10 |
| 𝑏 | Translation rate | Approximate value：34/h |
| 𝑑1 | mRNA degradation rate | Approximate value：0.33/h |
| 𝑑2 | Protein degradation rate | Approximate value：0.3/h |
| 𝛽 | Rate of transport for transporters | Approximate value: 0.3/ml*h |
| 𝑛 | Negative feedback intensity | Approximate value：0.1 |
| 𝑡 | time | Units：h |
Figure 1: Table for parameters in the model
Through research, calculations and experimentations, we decided on a reasonable value for our constants needed in the model as listed in Figure 1.
Figure 2 is obtained through MATLAB. It can be determined from the figure that the concentration of the protein product is 4.6.*10^11/ml in steady state, which can be converted to 89ug/L. According to the data, the transport efficiency of the transporter is 30%, and the total protein specific cell concentration released in the extracellular and intracellular is 1.27.*10^-7ug, meaning that each engineering bacteria can produce 1.27.*10^-7ug of protein.
In the case where the relevant parameters such as transcription rate, plasmid copy number, and translation rate take on small values, this value of protein released is reasonable, and our final result will likely be greater than this value, thus indicating that the success rate of our project is quite high. Our model provided us with support that our experiment has a huge chance of success because it has more optimal conditions than that of the model, so we began our actual project in creating E-coli with LacZ inside the intestine.