EdinburghModeling

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Contents

System Diagram of Arsenic Biosensor

Model Diagram2.JPG

Reaction set

No. Name Equation Rate Law Parameters
1 ArsD binding to Arsenic (III) ArsD+2As(III)=ArsD-2As(III)Mass Action K1=1000 K-1=0.65
2 ArsD binding to promoter1 2 ArsD+promoter1=2ArsD-promoter1 Mass ActionK2=10000, K-2=0.65
3 ArsD degradation ArsD->null Mass ActionK3=0.05
4 ArsD production promoter1->promoter1+ArsDMichaelis-Menten V4m=0.5, K4m=75
5 ArsR binding to Arsenic (III) ArsR+2As(III)=ArsR-2As(III) Mass Action K5=1000, K-5=0.65
6 ArsR binding to promoter2 2ArsR+promoter2=2ArsR-promoter2 Mass Action K6=10000, K-6=0.65
7 ArsR degradation ArsR->null Mass Action K7=0.05
8 ArsR production promoter2->promoter2+ArsR Michaelis-Menten V8m=10, K8m=25
9 LacI binding to allolactose LacI+allolactose=LacI-allolactose Mass Action K9=10000, K-9=0.1
10 LacI binding to promoter4 LacI+promoter4 = LacI-promoter4 Mass Action K10=1000, K-10=0.5
11 LacI degradation LacI->null Mass Action K11=0.1
12 LacI production promoter3->promoter3+LacI Michaelis-Menten V12m=0.5, K12m=40
13 lacZ degradation lacZ->null Mass Action K13=0.1
14 lacZ production promoter1->promoter1+lacZ Michaelis-Menten V14m=25, K14m=10
15 LCI binding to promoter 4 LCI+promoter4=LCI-promoter4 Mass Action K15=10000, K-15=0.5
16 LCI degradation LCI->null Mass Action K16=0.1
17 LCI production promoter2->promoter2+LCI Michaelis-Menten V17m=10, K17m=25
18 Urease degradation Urease->null Mass Action K18=0.1
19 Urease production promoter4->promoter4+Urease Michaelis-Menten V19m=10, K19m=40

Note: The units for first, second and third order rate constants are expressed in units of second^-1, nMol^-1*second^-1 and nMol^-2*second^-1 respectively.

Reaction Map.JPG

This reaction map is generated from the reaction set above using Simbiology Toolbox.

Initial concentration

No. Species Intial Concentration (nMol)
1 ArsD 25
2 As(III) 40
3 2ArsD-promoter1 25
4 promoter1 5
5 ArsR 25
6 2ArsR-promoter2 25
7 promoter2 5
8 LCI 4
9 LacI 0.1
10 LacI-allolactose 0.1
11 allolactose 1000
12 LacI-promoter4 0.1
13 promoter4 25
14 LCI-promoter4 0.1
15 Urease 0.1
16 promoter3 5
17 Other species 0

Methodology

Results

System response

Fig.1 System response with 5ppb arsenic input
Fig.2 System response with 20ppb arsenic input

Parameter sensitivity analysis

Fig.3 Sensitivity of lacZ with Respect to Model Parameters 1-16
Fig.4 Sensitivity of lacZ with Respect to Model Parameters 17-32

The most sensitive parameters affecting lacZ

Nanme Description Peak value of sensitivity Normal value
K-1 ArsD-2AS(III) dissociate rate -20.65/s
K-2 2ArsD-promoter1 dissociate rate 4 0.65/s
K3 ArsD degradation rate 90 0.05/s
K7 ArsR degradation rate 12 0.05/s
K13 LacZ degradation rate -35 0.1/s


Fig.5 Varying the Value of Parameter K-1 effect on lacZ


Fig.5 Varying the Value of Parameter K-2 effect on lacZ
Fig.5 Sensitivity of Urease with Respect to Model Parameters 1-16
Fig.6 Sensitivity of Urease with Respect to Model Parameters 17-32

The most sensitive parameters affecting Urease

Nanme Description Peak value of sensitivity Normal value
k3 ArsD degradation rate -300.05/s
k-6 2ArsR-promoter2 dissociate rate -5 0.65/s
k7 ArsR degradation rate -120 0.05/s
K18 Urease degradation rate -350 0.1/s
V19m Urease production maxium rate 3.5 10 nMol/s

Species sensitivity analysis

Fig.7 Sensitivity of lacZ with Respect to Model Species

The most sensitive species affecting lacZ

NameInitial concentration (nMol)
promoter1 5.0
promoter2 5.0
ArsD-2As(III) 0
ArsD 25
ArsR 25
Fig.8 Sensitivity of Urease with Respect to Model Species

The most sensitive species affecting Urease

NameInitial concentration (nMol)
LCI 4
LacI-promoter4 0.1
promoter4 25
promoter2 5
promoter1 5

Conclusion

Future work

Reference

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