Team:SCUT/Biosensor
Bio-sensor
This device has two parts, including a new promoter PcadA, which can be induced by cadmium ion; and the Tetracycline induced promoter Ptet, which we are familiar with. We devoted ourselves to establishing an accurate mathematical model to predict the result that Bio-sensor Device could achieve.
To the whole Bio-sensor Device, whether it shows red or blue is controlled by the concentration of cadmium ion and the length of time. In other words, this two influencing factors are the two independent variables in the model which simulates how this device works and the dependent variables are the expression level of RFP or cjBlue. In order to establish an accurate model, we need to analyze two parts respectively.
Part 1: PcadA Strength
I.Goal
We design a quantitative experiment to measure the concentration of extracellular cadmium ion, biomass of E.coli (OD600) and fluorescence quantity of RFP protein in different time point. Then we establish a suitable mathematical model and work out the relationship between the concentration of intracellular cadmium ion and the PcadA strength. After this model is built, we can easily figure out the expression level of csgA-EC and tetR as long as we know the concentration of intracellular cadmium ion.
II.Principle
1)Master Model
PcadA strength is repressed by merR mutant, but cadmium ion can combine with merR and disable it, eventually leads to derepression of PcadA. Therefore, PcadA can be regarded as a cadmium ion induced promoter. [1]
Hill equation can be used to simulate the effect of inducible promoter. In PcadA Strength model, the independent variable is the concentration of intracellular cadmium ion, and the dependent variable is the strength of PcadA.
2)Sub Model for the relationship between concentration of extracellular and intracellular cadmium ion
Before measuring the data of mater model, we have measured a series of quantitative data about the concentration of extracellular and intracellular cadmium ion. We attempt to build a sub model. [2]
But we felt pity that because of extremely low concentration of intracellular cadmium ion, we have no idea how to measure that data accurately. Therefore, we are forced to give up our work of building this sub model. We have to replace the concentration of intracellular cadmium ion with its extracellular concentration directly as an independent variable.
After that, we have measured the quantitative data of mater model primarily. By analyzing the tendency of these data, we draw a conclusion that the abandonment of this sub model almost have no influence when building master model.
However, if time permits, we still hope to improve our measuring method, making it possible for us to build the sub model. We think this will make the master model to be more accurate.
3)Sub Model for measuring RFP fluorescence
The common light bulb gives out constant, stable light whose intensity doesn’t change a lot. However, the situation of RFP fluorescence is not like that. Because the expression of polypeptides and the maturation of RFP protein need certain time, so there is a lag phase between the activation of PcadA and the present of fluorescence. In addition, the constant expression of RFP protein, the degradation of RFP protein and dilution of RRP protein due to cell division make fluorescence quantity of RFP changes. [3]
In order to measure the quantitative data of the strength of PcadA more accurately, we must build a sub model for measuring RFP fluorescence.
III.Parameter Measuring and Data Processing
1) Parameter Measuring
We have designed a quantitative experiment and measured a series of data primarily.
2)Data Processing [3]
Sp1.work out the fluorescence value per OD based on the total fluorescence value and total OD number.
Sp2.draw the curve of the fluorescence value per OD vs the incubating time.
Sp3.choose the data in stable phase from aforementioned curve.
Sp4.draw the curve of the fluorescence value per OD vs the incubating time during the stable phase. And calculate its slope, that is
.
Sp5.draw the curve of ln[OD] vs incubating time and calculate its slope, namely,
.
Sp6.work out the strength of the promotor: 
Sp7.use the Logarithmic mapping method to work out m and Xm, then we let PMAX equal with the strength of promotor when the concentration of Cd2+ is 10-4 mol/L.
Appendix:
1.Monod equation: 
2.RFP maturity constant: λ=1.45h-1.
IV. Result
These figures show the data we have measured primarily.
We have also consulted some relative literatures. Some useful parameters have selected to draw graphs of the tendency of our model. [1]
Figure 1 Figure 2
Figure 1 and Figure 2 show the general tendency of expression level of csgA-EC & tetR when the concentration of extracellular cadmium ion is 10^(-8), 10^(-7), 10^(-6), 10^(-5), 10^(-4) mol/L, respectively. Here we assume an ideal situation that csgA-ECs and tetR won’t degrade or be secreted.
Figure 1 and Figure 2 show the general tendency of expression level of csgA-EC & tetR when the concentration of extracellular cadmium ion is 10^(-8), 10^(-7), 10^(-6), 10^(-5), 10^(-4) mol/L, respectively. Here we assume an ideal situation that csgA-ECs and tetR won’t degrade or be secreted.
According to these two figures and the value of Hill constant ( 3.7*10^(-6) ), the expression level of csgA-ECs and tetR shows great difference in order of magnitude when the concentration of extracellular cadmium ion is 10^(-6), 10^(-5), 10^(-4) mol/L respectively with one when the concentration of extracellular cadmium ion is 10^(-8), 10^(-7) respectively.
Then we assume that after E.coli is incubated for 40min, the expression of csgA-ECs and tetR enters the stationary phase. In this situation, a graph can indicate this great difference more accurately as follow.
Figure 3 shows the tendency of PcadA Strength Kinetic Model. Here the value of incubating time is constant value.
Finally, two 3D graphs are presented.
Figure 4
Figure 5
Figure 4 and Figure 5 shows the tendency of PcadA Strength Kinetic Model. Here the incubating time is independent variable.
Under the guidance of this model, we used a series of concentration of cadmium to induce the expression of RFP and have obtained a visible effect of color change.Figure 6 shows the color change.
Figure 6 shows the color change which reflect PcadA strength.
Then we narrowed the concentration range of cadmium ion and devoted to finding out the lower limit of detection. Figure 7 shows the lower limit of detection.
Figure 7 shows the lower limit of detection.
Part 2: Ptet Indicator
I. Goal
We are going to establish a suitable mathematical model by finding out the relative useful parameters and find out the relationship between the concentration of intracellular cadmium ion and the Ptet strength. After this model is built, we can easily figure out the lower limit of detection, which is the specific concentration of extracellular cadmium ion when the system presents obvious color change (from blue to red).
II. Principle
Ptet which we are using comes from iGEM committee. We are very familiar with its mechanism. Similar to PcadA, Ptet strength is limited by tetR, but tetracycline can combine with tetR and disable it, eventually , it leads to derepression of Ptet.
However, tetracycline wasn’t used in our project. Besides, expression level of tetR is controlled by PcadA strength, so there is a negative correlation between PcadA strength and Ptet strength.
Hill equation can be used to simulate the effect of Ptet too. In Ptet indicator model, the independent variable is the concentration of intracellular cadmium ion, and the dependent variable is the strength of Ptet.
III.Parameter Measuring and Data Processing
We are familiar with the mechanism of Ptet. Besides, we only use this model for semiquantitative analysis in our project. Therefore, we don’t need to design a quantitative experiment for this model to measure data.
2008 EPF-Lausanne Team and 2013 UC_Davis Team have used Ptet in their projects. In modeling part, they have provided the relative useful parameter data for us. [4][5] However, the mechanism of Ptet activation is different which they figure out respectively. 2013 UC_Davis Team’s is more concrete, involving the parallel function of the two operons. 2008 EPF-lausanne Team’s was analysed as a whole.
In order to establish a more accurate mathematical model and figure out the lower limit of detection, we analysed these two models by ourselves and used Chebyshev approximation and Parameter sweeping method to compare them.
2008 EPF-lausanne Team’s
2013 UC_Davis Team’s [6]
IV．Result
Figure 8 and Figure 9 shows the process of comparison of two models mentioned above.
In Figure 8, the tendency of the two curves is very similar. However, in Figure 9, when two models are linear treated, the slopes are quite different. We will improve the method of parameter sweeping, hoping that two models will be more similar.After comparison, we finally determined the value of parameters.
Figure 10
Figure 10 shows the tendency of Ptet Strength Kinetic Model. Here the value of incubating time is constant value.Figure 10 shows that when the expression level of tetR reach 1.5, expression level of cjBlue will have a great change. Then its expression will be repressed. Here we assume an ideal situation that tetR won’t degrade or be secreted. The expression level of tetR is regarded as independent variable.
However, the expression level of tetR is regarded as intermediate dependent variable. After superposition of the models, a graph shows different colors in different concentration of intracellular cadmium ion which reflects the effect of our system as follow.
Figure 11
Figure 11 shows the tendency of PcadA Strength and Ptet Strength Kinetic Model. Here the value of incubating time is constant value.Figure 11 shows that when the concentration of intracellular cadmium ion approximately equal to 0.75 μmol/L, the system will reach the color transition point (from blue to red). Its color change interval approximately equals to 10^(-0.4)~10^1.4 μmol/L.
For the whole system, two 3D graphs shows the situation of the color change more vividly and scientifically.
Figure 12
Figure 12 shows the tendency of Ptet Strength Kinetic Model. Here the incubating time is independent variable.
Figure 13
Figure 13 shows the tendency of PcadA Strength Kinetic Model. Here the incubating time is independent variable.Figure 13 shows that if cadmium ion with low concentration is put into the system, the expression level of cjBlue will have a transient rise, then fall rapidly. If cadmium ion with high concentration is put into the system, the expression level of cjBlue almost keep repressed. However, according to Figure 13, although the expression level of cjBlue reaches the maximum, the expression level of RFP is much more higher than cjBlue’s. Therefore, it is very difficult to see the color change from blue to red when cadmium ion is put into the system at the beginning of incubation.
Under the guidance of this model, the time when the cadmium ion is put into the system should be delayed. Figure 14 shows the cadmium ion is put into the system after the E.coli is incubated for 48h. The color change from blue red is so obvious.
Figure 14 shows the cadmium ion is put into the system after the E.coli is incubated for 48h. The color change from blue red is so obvious.
Part 3：References
[1] Kaisa M. Hakkila et al. Cd-Specific Mutants of Mercury-Sensing Regulatory Protein MerR,
Generated by Directed Evolution. APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Vol. 77, No. 17, Sept. 2011, p. 6215–6224.
[2] NICK ZAGORSKI AND DAVID B. WILSON. Characterization and Comparison of Metal Accumulation in Two Escherichia coli Strains Expressing Either CopA or MntA, Heavy Metal Transporting Bacterial P-Type Adenosine Triphosphatases. Applied Biochemistry and Biotechnology Vol. 117, 2004, p.33-48.
[3] JOHAN H. J. LEVEAU AND STEVEN E. LINDOW. Predictive and Interpretive Simulation of Green Fluorescent Protein Expression in Reporter Bacteria. JOURNAL OF BACTERIOLOGY, Vol. 183, No. 23,Dec. 2001, p. 6752–6762.
[4] 2008 EPF-Lausanne Team iGEM wiki. https://2008.igem.org/Team:EPF-Lausanne/Modeling
[5]2013 UC_Davis Team iGEM wiki. https://2013.igem.org/Team:UC_Davis/Modeling
[6] Tamsir et al. Robust multicellular computing using genetically encoded NOR gates and chemical ‘wires’: Supplementary Information. Nature 469, 13 January 2011, p.212–215.