Team:Edinburgh/modelling(reallifemodelling)

From 2009.igem.org

(Difference between revisions)
Line 333: Line 333:
<div id="abstarct" style="background-color:#e4f5ca;border:1px solid #595151;width:755px;height:160px;margin-top:10px;margin-left:20px;font-size:11px;text-align:justify;padding-left:5px;padding-right:5px;padding-top:5px;padding-bottom:5px;">
<div id="abstarct" style="background-color:#e4f5ca;border:1px solid #595151;width:755px;height:160px;margin-top:10px;margin-left:20px;font-size:11px;text-align:justify;padding-left:5px;padding-right:5px;padding-top:5px;padding-bottom:5px;">
-
if (index==1){
+
if (index==1){ <br />
-
Bact[xbact][ybact]=1;
+
Bact[xbact][ybact]=1;<br />      
-
     
+
}<br /><br />
-
}
+
-
if (index==2){
+
if (index==2){<br />
-
Bact[xbact-1][ybact]=1;
+
Bact[xbact-1][ybact]=1;<br />
-
xbact=xbact-1;
+
xbact=xbact-1;<br />
-
}
+
}<br /><br />
-
if (index==3){
+
if (index==3){<br />
-
Bact[xbact+1][ybact]=1;
+
Bact[xbact+1][ybact]=1;<br />
-
xbact=xbact+1;
+
xbact=xbact+1;<br />
-
}
+
}<br /><br />
-
if (index==4){
+
if (index==4){<br />
-
Bact[xbact][ybact-1]=1;
+
Bact[xbact][ybact-1]=1;<br />
-
ybact=ybact-1;  
+
ybact=ybact-1; <br />
-
}
+
}<br /><br />
       
       
-
if (index==5){
+
if (index==5){<br />
-
Bact[xbact][ybact+1]=1;
+
Bact[xbact][ybact+1]=1;<br />
-
ybact=ybact+1;
+
ybact=ybact+1;<br />
-
}
+
}<br /><br />
-
 
+
</div>
</div>

Revision as of 18:51, 14 October 2009

Modelling - Real Life Modelling
Personal note

Since our system designed to detect landmines it was thought that we should include a visual representation of how the system would operate in real life. It is known that TNT leaks out of the landmine into the soil and we predict that the bacteria will move toward the TNT due to the chemotaxis response of the ribose binding protein which has previously computationally designed TNT receptor1
TNT and Nitrite diffusion has been modelled using a finite difference method which approximates the 2 dimensional time dependent diffusion equation below



where α is the diffusion coefficient, to a numerical solution which can be solved . By splitting the area into a grid M2 by N with a space step of h=1/M (in both the x and y directions) and time step size of k=T/N. This gives a grid of the form



which was set up as a matrix in the program.

An initial concentration of TNT in the field was then set to 107800µg/cm3 and the diffusion of TNT out from this site was calculated from the following equation,


and



The diffusion coefficient for TNT is 1.18 *10-6 cm2 s-1 4 and the diffusion of Nitrite is 1.9*10-5 cm2 s-1 .

This system was coded in both MATLAB and JAVA. MATLAB was used to produce graphs and JAVA was used for the chemotaxis modelling which is described below.

The TNT diffusion graph after a year is shown below



Figure 1 shows the diffusion of TNT over a small area, only 10m by 10m, so that the uniform distribution of the TNT concentration can be shown. However a better representation of what would happen in the field can be shown when the size of the grid is much larger, 100m by 100m as shown below


It is clear from Figure 2 that TNT is only concentrated around the landmines location rather than across the whole field and hence the bacteria could be used to determine the approximate location of the landmine due to the light emit on detection of the TNT. The bacteria also produces enzymes, nitroreducases, which breaks down TNT into various products including Nitrites. Our system is designed to emit light when these Nitrites are detected. For the model it has been assumed that a very low conversion of TNT to Nitrites will be achieved. The diffusion graph for Nitrite is very similar to that for TNT.
As previously stated, it is expected that the bacteria will move toward the landmine due to chemotaxis of the TNT receptor. This was incorporated into the model by assuming the bacteria will move toward the highest concentration of TNT, essentially swimming up the concentration gradient. This was programmed by incorporating a 3rd matrix where the grid matches up with both the TNT and the Nitrite diffusion graphs. The bacteria is then placed in the matrix using a random number generator to get its grid location and this location is set to 1 while the rest of the grid is set to zero.

The model then calculates the concentration of TNT at its grid position and its 4 surrounding grid positions. It then stores the current concentration as the maximum concentration and then compares each of the surrounding locations concentrations to this maximum. If any of the concentrations are greater than the current locations concentration then it set this concentration as the maximum and will then compare subsequent concentrations to this new maximum. It also indexes the location of the maximum concentration which is used to determine where the bacteria should move to. The moving of the bacteria is done by a series of IF statements as shown below

if (index==1){
Bact[xbact][ybact]=1;
}

if (index==2){
Bact[xbact-1][ybact]=1;
xbact=xbact-1;
}

if (index==3){
Bact[xbact+1][ybact]=1;
xbact=xbact+1;
}

if (index==4){
Bact[xbact][ybact-1]=1;
ybact=ybact-1;
}

if (index==5){
Bact[xbact][ybact+1]=1;
ybact=ybact+1;
}

Edinburgh University iGEM Team 2009