# Team:NCTU Formosa/Model-TC

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- | + | The first equation describes the temperature control in strand A (Fig. 1). Alpha-Temp is the production rates corresponding to transcriptional rate of constitutive promoter and the translation rate of the RBS<a href="http://partsregistry.org/wiki/index.php?title=Part:BBa_K115002"> BBa_K115002</a> which is a temperature sensitive post-transcriptional regulator. The second equation describes the concentration of GFP change with time. Alpha-B is production rates of the GFP, which are assumed to be given constants. To describe transition during log phase and stationary phase, the alpha-Temp and alpha-B and is assumed to zero when the Terminator in stationary phase. Gamma-TetR, and gamma-GFP are decay rates of the corresponding 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 (Fig. 2). For an inhibition of TetR protein, Hill function is an S-shaped curve which can be described in the form 1 / (1 +x^n) (Alon, 2007). 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 (Fig. 3) <br><br> | |

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<p><span style="font-weight:normal;font-size:150%;line-height:150%"><img class= "center"src="http://2009.igem.org/wiki/images/0/04/TC_mod3.jpg" alt="Image description" width="604" title="Part" /></span></p> | <p><span style="font-weight:normal;font-size:150%;line-height:150%"><img class= "center"src="http://2009.igem.org/wiki/images/0/04/TC_mod3.jpg" alt="Image description" width="604" title="Part" /></span></p> |

## Revision as of 00:39, 28 October 2010

# Modeling >**Low-temperature Release** System Contral modeling

**The dynamics model constructed for 'Low-temperature Release System'**

# Motivation

A low-temperature release system was designed and constructed in the Mosquito Intelligent Terminator (MIT or Terminator) to control target protein expression. A specific ribosome binding site (RBS) BBa_K115002 with high translation activity at high temperature(> 37°C) and low translation activity at room temperature was used to design the temperature-dependent genetic circuit in E. coli, with a green fluorescent protein (GFP) used as the reporter protein (Fig. 1). We analyzed fluorescence intensity during E. coli growth at log phase and stationary phase at temperatures 25°C, 30°C, 30°C and 40°C. Our experimental results indicates that high temperature decreased the translation rate of the target protein, and this temperature-dependent genetic circuit can control the expression level of the target protein by the host cell's incubation temperature. However, the translational activity of the RBSBBa_K115002 at different temperatures can not be quantified directly from experimental data. To overcome this problem, we provided a dynamic model which can quantitatively assess the translation strength of the RBS BBa_K115002 at temperatures 25°C, 30°C, 37°C and 40°C.

# Modeling and simulations

Low-temperature release system consists of two genes: TetR and GFP. The expression level of tetR protein is the input to the system, and the concentration of GFP is the output.

This system can be modeled by differential equations as follows.

The first equation describes the temperature control in strand A (Fig. 1). Alpha-Temp is the production rates corresponding to transcriptional rate of constitutive promoter and the translation rate of the RBS BBa_K115002 which is a temperature sensitive post-transcriptional regulator. The second equation describes the concentration of GFP change with time. Alpha-B is production rates of the GFP, which are assumed to be given constants. To describe transition during log phase and stationary phase, the alpha-Temp and alpha-B and is assumed to zero when the Terminator in stationary phase. Gamma-TetR, and gamma-GFP are decay rates of the corresponding 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 (Fig. 2). For an inhibition of TetR protein, Hill function is an S-shaped curve which can be described in the form 1 / (1 +x^n) (Alon, 2007). 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 (Fig. 3)

Fig. 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.

Fig. 3: The behavior of low temperature release circuit at 25°C, 30°C, 37 °C and 40°C. Experimental data (dot) and simulated results (line) of the model suggest this temperature-dependent genetic circuit 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 relative translational activity of RBS during log phase and stationary phase.

Using least squares estimation from experimental data, the relative translational activity of this RBS BBa_K115002 at 25°C, 30°C, 37 °C and 40°C were estimated (Fig. 4).

Fig. 4: The relative translation activity of this RBS (BBa_K115002) at 25C, 30C, 37 C and 40C estimated using least squares estimation from experimental data. This means our dynamic model can accurately quantify the translational activity of the RBS from experimental data.

According to the fitting results (Fig. 3), the dynamic model successfully approximated the behavior of our low-temperature release system. The model equations present 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.