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Team:NCTU Formosa/modeling
From 2011.igem.org
Measurement
A new measurement method can calculate the protein expression rate in the different E. coli population density for the protein expression device
Summary
In previous studies, the transcriptional strengths of promoter and transcriptional strengths of RBSs was defined as a constant values. But in biological concepts, we know the expression rates of most proteins decreased dramatically while the bacteria at the stationary phase. To overcome this problem, our team developed a new measurement method can calculate the protein expression activity of promoter_RBS device changes with cell density in the culture tube directly.
We provide a simple polynomial equation which can describe linear relationship between the protein expression activity p(s) of promoter_RBS device and cell desity s (OD600).
where p0 denotes zero-order coefficient, p1 denotes first-order coefficient. We found that using this linear function to describe the activity of a protein expression device during log phase and stationary phase improved simulation results significantly. That means that the simple model equation can character a protein expression device (a promoter combined with a RBS) during cell grow from log phase to stationary phase. The fitting results indicate this hypothesis is reasonable. Furthermore, this model enable us to rational connect a promote_RBS device with different strength to obtain a target protein expression level in a synthetic genetic circuit.
This equation describes the concentration of GFP in BBa_K098988change with time (Figure. 1). Alpha-Temp is the protein expression rates corresponding to BBa_K098995which is a temperature sensitive expression device. To describe transition during log phase and stationary phase, the alpha-Temp is assumed to zero in stationary phase. Gamma-GFP are decay rates of the GFP proteins. When bacteria divide, the molecular in a bacterium will be dilute. Because bacteria grow faster, the dilution rate d(t) is included in this model and can be calculated from OD ratio of medium (Figure. 2). The values of the kinetic parameters used in the simulation were initially obtained from the literature and experimental data. Data computations were performed with Matlab software. A program was written and used as a subroutine in Matlab for parameter optimization using nonlinear regression (Figure. 3).
Figure 2. The OD ratio is increased faster in log phase than it in stationary phase. The dilution rate d(t) can be calculated from OD ratio and used in out model.
Figure 3. The behavior of high temperature induced device BBa_K098988 at 25°C, 37 °C and 42°C. Experimental data (dot) and simulated results (line) of the model suggest this temperature-dependent device can control the expression level of the target protein by the host cell’s incubation. The fitting results indicate our dynamic model can quantitatively assess the protein expression activity of BBa_K098988during log phase and stationary phase.
Using least squares estimation from experimental data, the relative the protein expression activity of BBa_K098988 at 25°C, 37 °C and 42°C were estimated (Figure. 4).
Figure 4. The relative the protein expression activity of BBa_K098988at 25°C, 37 °C and 42°C estimated using least squares estimation from experimental data. The protein expression activity at 42°C is higher than 25°C, 37 °C
According to the fitting results (Figure. 3), the dynamic model successfully approximated the behavior of our high-temperature induced system. The model equation presents interesting mathematical properties that can be used to explore how qualitative features of the genetic circuit depend on reaction parameters. This method of dynamic modeling can be used to guide the choice of genetic ‘parts’ for implementation in circuit design in the future.
References
Alon, U. (2007) An Introduction to Systems Biology: Design Principles of Biological Circuits. Chapman & Hall/CRC.
