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 Varying the Value of Parameter K3 effect on lacZ
Fig.5 Varying the Value of Parameter K7 effect on lacZ
Fig.5 Varying the Value of Parameter K13 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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