Team:Dundee/Project/DetectionComparison

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          <h2><b>Insight to the Mathematical World</b> </h2>
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<h2><b>Detection Time</b></h2>
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          <h2>Aims:</h2>
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          <p>Using mathematical tools to allow us to predict the limiting factors in the production of PP1 and its mopping applications. Working alongside the biologists to produce models which are relevant and can predict what is expected to happen during the synthetic engineering of the mop and detection bacteria.</p>
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<p>The  direct  method for detecting microcystin in water samples is high performance liquid chromatography (HPLC). This  process takes approximately 24 hours and is expensive due to the equipment required.  For this reason, the current method for regulating toxic microcystin levels in Scotland uses the indirect approach of cyanobacterial cell counts. However, this  process takes even longer. Using our biological detector we hope to reduce the time and cost of microcystin detection.<br><Br>
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First, we considered  the effect that a 24 hr detection time could  have on the numbers of cyanobacteria and microcystin level  found in a water body.  This then allowed us to determine whether faster detection methods are necessary.
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<h2>Theory</h2>
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Making the following assumptions:
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<li> t = 0 is the time water samples are taken
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<li> b<sub>0</sub> is the initial number of cyanobacteria at t=0
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<li> t is the time in hours after the water samples are taken
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<li> cyanobacteria undergo binary fission every hour
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<li> cyanobacteria growth is uninhibited
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<li> each cyanobacteria releases N microcystin molecules
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<p>We arrive at these equations:</p>
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<img src="https://static.igem.org/mediawiki/2013/0/0b/Equations_Image_1.jpg"><br>
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<p>where b(t) is the number of cyanobacteria at time t and MC(t) the number of microcystin molecules.</p>
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<p> Since earliest result could  be obtained via  HPLC  in 24 hours after the water samples are taken i.e. t=24, we compared this against our aim of a 1 hour detection time t=1 by evaluating equation (2).  </p>
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<p>Dividing MC(24) by MC(1) we recover an expression for MC(24) in terms of MC(1). <br></p>
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  <h2>Results</h2>
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At the detection times, t = 24 hours and t = 1 hour, the ratio for the number of microcystin molecules is 8.4 million : 1.<br><Br>
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Than is,  after 24 hours there can be up to 8.4 million times more microcystin molecules present than there is after 1 hour. Putting this ratio into perspective, this is the same as the height of the Empire State Building being compared to  the combined height of 7 <i>E. coli</i>.<Br><Br>
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Therefore, in the time period between collection of samples and obtaining results there could potentially  be  a vast increase in the concentration of microcystin present in the water body. This emphasises that HPLC, or even slower alternatives,  are  less than optimal  for toxin detection and that  early detection would provide a huge advantage. <br><br>
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  <h2>Conclusion</h2>
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We  conclude that faster detection methods are useful and our biological detector is worthwhile pursuing if we can reduce this detection time.  <br><br>
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         <p class="muted credit"> Created for <a href="https://igem.org/Main_Page">iGEM 2013</a> Dundee. Based upon <a href ="http://twitter.github.io/bootstrap/">Bootstrap</a> and <a href="http://jquery.com/">JQuery</a>. Design by <a href="www.kyleharrison.co.uk"> Kyle Harrison </a>. </p>
         <p class="muted credit"> Created for <a href="https://igem.org/Main_Page">iGEM 2013</a> Dundee. Based upon <a href ="http://twitter.github.io/bootstrap/">Bootstrap</a> and <a href="http://jquery.com/">JQuery</a>. Design by <a href="www.kyleharrison.co.uk"> Kyle Harrison </a>. </p>

Latest revision as of 20:03, 23 October 2013

iGEM Dundee 2013 · ToxiMop

Dundee 2013

Detection Time


The direct method for detecting microcystin in water samples is high performance liquid chromatography (HPLC). This process takes approximately 24 hours and is expensive due to the equipment required. For this reason, the current method for regulating toxic microcystin levels in Scotland uses the indirect approach of cyanobacterial cell counts. However, this process takes even longer. Using our biological detector we hope to reduce the time and cost of microcystin detection.

First, we considered the effect that a 24 hr detection time could have on the numbers of cyanobacteria and microcystin level found in a water body. This then allowed us to determine whether faster detection methods are necessary.

Theory

Making the following assumptions:

  • t = 0 is the time water samples are taken
  • b0 is the initial number of cyanobacteria at t=0
  • t is the time in hours after the water samples are taken
  • cyanobacteria undergo binary fission every hour
  • cyanobacteria growth is uninhibited
  • each cyanobacteria releases N microcystin molecules


We arrive at these equations:


where b(t) is the number of cyanobacteria at time t and MC(t) the number of microcystin molecules.


Since earliest result could be obtained via HPLC in 24 hours after the water samples are taken i.e. t=24, we compared this against our aim of a 1 hour detection time t=1 by evaluating equation (2).


Dividing MC(24) by MC(1) we recover an expression for MC(24) in terms of MC(1).

Results

At the detection times, t = 24 hours and t = 1 hour, the ratio for the number of microcystin molecules is 8.4 million : 1.

Than is, after 24 hours there can be up to 8.4 million times more microcystin molecules present than there is after 1 hour. Putting this ratio into perspective, this is the same as the height of the Empire State Building being compared to the combined height of 7 E. coli.

Therefore, in the time period between collection of samples and obtaining results there could potentially be a vast increase in the concentration of microcystin present in the water body. This emphasises that HPLC, or even slower alternatives, are less than optimal for toxin detection and that early detection would provide a huge advantage.



Conclusion

We conclude that faster detection methods are useful and our biological detector is worthwhile pursuing if we can reduce this detection time.

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