Team:XMU-China/Model Description
Firstly, we built a model in order to analyse the gene expression dynamics of our whole circuit.In our model, we simply the actual biology process into a model that only remains the promoter, the transcription gene, mRNA and goal polymerase or molecule. In our circuit, the metal sensitive promoters we used is ars promoter with arsR repressor gene that is sensitive to metal ion. Metal ion binds to the repressor protein ArsR, resulting in inability to repress the promoter and activating transcription of T7 RNA polymerase. And T7 RNA polymerase will then bind to T7 promoter and largely activate the expression of reporter gene like lacZ or GFP. In the next process, the substrate PAPG will be catalyzed by LacZ to form PAP. Also, both mRNA and T7RNA polymerase has a leaky expression.
In order to describle our model, we make some assumption. Firstly, mRNA and proteins will decay following Poisson distribution. Secondly, combinations of two proteins are considered as quick reactions. Based on these, we wrote chemical kinetic equations in represent of each process.
The symbol declaration is:
X1: metal ion
D1: metal ion sensing promoter
X1D1: the metal ion- ArsR complex
X2: the mRNA of T7 RNA polymerase
X3: T7 RNA polymerase
D2:T7 promoter
X4: the mRNA of lacZ or GFP
X5: lacZ or GFP
K1/K-1: the rate of turning of the state of metal ion sensing promoter
K2: the rate of formation of he mRNA of T7 RNA polymerase
K3: the rate of formation of T7 RNA polymerase
K4: degradation rate of the mRNA of T7 RNA polymerase
K5/K-5: the rate of turning of the state of T7 promoter
K6: the rate of formation of the mRNA of lacZ or GFP
K7: degradation rate of T7 RNA polymerase
K8: the rate of formation of lacZ or GFP
K9: degradation rate of the mRNA of lacZ or GFP
K10: the rate of the following reaction
According to the analysis, in our circuit ,metal ion binds to the repressor protein ArsR, resulting in inability to repress the promoter and activating transcription of T7 RNA polymerase, which meets the situation that the transcription factor (either activator or repressor) binds to the site in promoter and regulates the gene expression which eventually determines the transcription rate of mRNA. Here we use Hill equation to describe the activity of the metal ion sensing promoter.
Here [DTot] is the total concerntration of the DNA site. Then we solve the equations.
Based on Hill Equation , we can determine the rate of transcription from a free binding site to be called as maximal transcription rate, β. The rate of mRNA production or the promoter activity is β times the probability that the binding site is free (value of β ranges from approximately 10-4 to 1 mRNA/s).
According to the analysis, we wrote down the ODEs:
Next we will do some algebra to simplify the equations and solve the differential equations. To simplify the model, we consider the rate of T7 promoter activity as certained.
Xiamen University, Fujian, China
No. 422, Siming South Road, Xiamen, Fujian, P. R. China 361005
