Team:Sheffield/Chimeric protein system

Model of the chimeric protein system

Explanation of the system

The diagram below explains the process of our cholera detection biosensor with the chimeric protein system.

Signalling molecule CAI-1 binds to CqsS protein and this causes a change in the fusion receptor. This change triggers autophosphorylation of the histadine kinase BarA and it starts the phosphorylation pathway which ends in the response regulator UvrY. Phosphorylated UvrY acts as a transcription factor activating the promoter which causes the expression of the reporter gene.

Model for signal transduction

The phosphorylation pathway in e-coli is modelled as a two component systems starting with a histadine kinase and ending in a response regulator. Research into the literature [1,2] has shown that these two component systems contain intermediate layers of proteins which accept and transfer the phosphates during phosphorylation

The BarA/UvrY two component system can be modelled as having 4 layers [1,2] which are Histadine Kinase(HK - BarA ) , proteins with receiver domains (REC), His-containing phosphotransfer proteins (Hpt) and Response Regulator (RR - UvrY) in the given order as shown in Figure 2. When BarA starts phosphorylation a phosphate is passed through all these layers resulting in a phosphorylated response regulator UvrY. It has been shown through previous literature[2] that the phosphorylated response regulator can undergo dephosphorylation due to several reasons such as hydrolysis activity intrinsic to RRs or due to a specific phosphatise or a bifunctional HK.

This process can be represented by the following chemical equations. ( the equations were obtained from reference [2] )

where:

Li represents ith layer

ki represent reaction rate constants

Equation (1) describes the autophosphorylation of the first layer that occurs when CAi – 1 is detected.

Equations (2), (3) and (4) represent the phosphate passing from the upper layer to the layer below.

Equation (5) shows the dephosphorylation of the last layer.

Using these equations we create the following mathematical model for the system with the assumptions that

1. The input CAI-1 will control the rate of autophosphorylation of BarA and therefore is included in the rate constant for the reaction.

2. ATP is in abundance in e-coli and therefore will not be a parameter in the system signalling process.

3. The total concentration of all the proteins will remain constant throughout the signalling process.

4. The reverse reactions occurring in system (if any) are negligible.

According to these assumptions the mathematical model is developed as shown below.

Model for the gene expression

Our chimeric system works on the principle that; phosphorylated UvrY which is the transcription factor produced at the end of the phosphorylation kinase binds to our chosen reporter DNA gene which causes transcription of the reporter DNA gene to mRNA to begin. Interactions between the phosphorylated UvrYs and the RNA polymerase transcriptional machinery however plays an important role in determining the order of transcriptional activation which as a result affect the frequency at which mRNA transcripts are produced. Also, the effects of phosphorylated UvrYs at different promoters could vary due to changes in the sequence of the DNA binding site and its distance from the orientation with respect to the promoter. These discrepancies therefore tend to influence the order in which the promoter respond to increasing concentration of the phosphorylated UvrY and seemingly could have important functional consequences. Taking into consideration the above factors stated we constructed a mathematical model for transcription; the first procedure in gene expression, using these following assumptions:

1. The RNA polymerase in the E. Coli is in abundant, hence all the phosphorylated UvrYs produced, bind to the reporter DNA gene resulting to high level of transcription activation.

2. That the PgaAB promoter used is always active and tight; meaning there is high expression of gene, hence all the DNAs are transcribed to mRNA.

3. The degradation rate of mRNA is very negligible, so most of the mRNAs are translated to proteins.

With these assumptions we create following differential equation for the transcription.

where:

t1 = the rate of transcription

UvrYp = phosphorylated UvrY

d1 = transcription degradation