Team:Aberdeen Scotland/Modeling/Assay

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<p>Hi, there. We are a team of Aberdeen Uni undergrads trying to do our part in the fight against Sleeping Sickness. There's six of us - 5 biologists and 1 physicist.
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<p>A crucial part of the assay is the antibody-to-antigen binding. In this section we try to analyse its behaviour and try to determine if the system is going to have the appropriate amount of sensitivity.</p>
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We are very excited to be able to take part in iGEM and we would like to take you on a tour around our project.</p>
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<p>We have worked all summer towards what we hope would turn out to be some peace of mind for a lot of people. The goal is to develop a novel method for diagnosing
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<p>Consider and antibody 'A' and its complimentary antigen 'a'. We have looked at a simple model, which can be illustrated by the following equations<sup>[1]</sup>:</p>
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Trypanosomiasis. A simpler, cheaper alternative to current methods that would be more versatile in developing countries and their remote regions. We wish to create a
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$$\frac{d[A-a]}{dt}=k_a[A][a] \\
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test that would be portable, endure harsh environmental conditions and most importantly be sensitive to the early stages of the disease.</p>
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  \frac{d[A]}{dt}=-k_a[A][a]  \\
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<p>This would give a lot of unsuspecting sufferers the chance to get diagnosed early. This way they can get cured quickly, before the disease reaches its later
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  \frac{d[a]}{dt}=-k_a[A][a]$$
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stages, when it is virtually incurable.</p>
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<ul>
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<li>where
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<table style="width:70%">
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<tbody>
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<tr>
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<td>[A]</td>
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<td>- concentration of antibody 'A'</td>
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</tr>
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<tr>
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<td>[a]</td>
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<td>- concentration of antigen 'a'</td>
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</tr>
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<tr>
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<td>k<sub>a</sub></td>
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<td>- affinity of antibody and antigen</td>
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</tr>
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<tr>
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<td>[A-a]</td>
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<td>- concentration of antibody 'A'</td>
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</tr>
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</tbody>
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</table>
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</li>
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</ul>
 +
 
 +
<p>In our case, as the antibody and antigen concentrations do not change in time individually, we can simplify this system to the following:</p>
 +
 
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$$ \frac{[A-a]}{dt}=k_{a}(A_{0}-[A-a])(a_{0}-[A-a])$$
 +
 
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<p>where A<sub>0</sub> and a<sub>0</sub> are the initial concentrations of the antibody and antigen.</p>
 +
 
 +
<p>We can clearly see that this system is not linear, but we can simulate it and analyse it.</p>
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<img src="https://static.igem.org/mediawiki/2014/5/5a/Affinit.png">
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<p>Fig.1 Antibody-to-Antigen binding time evolution curves, according to different affinity values</p>
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<p>From this model we deduced several important points.</p>
 +
<p>Firstly, the abundance of the antigen is a limiting factor. In fact, the less the antigen concentration is the slower the binding process is going to be. This can
 +
be partially counteracted by increasing the amount of antibodies available. However, this is generally a good sign, as that means the system is less prone to false
 +
positives.</p>
 +
<p>Moreover, as initial antigen concentration increases the efficiency of the binding increases exponentially, thus making it much easier to detect the antigen.</p>
 +
<p>Furthermore, on Fig.1 we can see how the binding lag is influenced by different affinities. From the highest to the lowest curve, the affinity differs by 1 order
 +
of magnitude, but we still get at least 30% binding after just an hour. This further confirms that our system is stable enough to handle different types of
 +
antibodies.</p>
 +
<p>This is an important point as we are detecting for two different antigens with two different antibodies and are demanding similar behaviour from both.</p>
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<h3>References</h3>
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<p>[1] McFadden, R., Kwok, C. S., "Mathematical Model of Simultaneous Diffusion and Binding of Antitumor Antibodies in Multicellular Human Tumor Spheroids, CancerRes 1988; 48:4032-4037</p>
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Latest revision as of 21:34, 17 October 2014

Team:Aberdeen Scotland/Modelling - 2014.ogem.org



Assay Model


A crucial part of the assay is the antibody-to-antigen binding. In this section we try to analyse its behaviour and try to determine if the system is going to have the appropriate amount of sensitivity.

Consider and antibody 'A' and its complimentary antigen 'a'. We have looked at a simple model, which can be illustrated by the following equations[1]:

$$\frac{d[A-a]}{dt}=k_a[A][a] \\ \frac{d[A]}{dt}=-k_a[A][a] \\ \frac{d[a]}{dt}=-k_a[A][a]$$
  • where
    [A] - concentration of antibody 'A'
    [a] - concentration of antigen 'a'
    ka - affinity of antibody and antigen
    [A-a] - concentration of antibody 'A'

In our case, as the antibody and antigen concentrations do not change in time individually, we can simplify this system to the following:

$$ \frac{[A-a]}{dt}=k_{a}(A_{0}-[A-a])(a_{0}-[A-a])$$

where A0 and a0 are the initial concentrations of the antibody and antigen.

We can clearly see that this system is not linear, but we can simulate it and analyse it.

Fig.1 Antibody-to-Antigen binding time evolution curves, according to different affinity values

From this model we deduced several important points.

Firstly, the abundance of the antigen is a limiting factor. In fact, the less the antigen concentration is the slower the binding process is going to be. This can be partially counteracted by increasing the amount of antibodies available. However, this is generally a good sign, as that means the system is less prone to false positives.

Moreover, as initial antigen concentration increases the efficiency of the binding increases exponentially, thus making it much easier to detect the antigen.

Furthermore, on Fig.1 we can see how the binding lag is influenced by different affinities. From the highest to the lowest curve, the affinity differs by 1 order of magnitude, but we still get at least 30% binding after just an hour. This further confirms that our system is stable enough to handle different types of antibodies.

This is an important point as we are detecting for two different antigens with two different antibodies and are demanding similar behaviour from both.

References

[1] McFadden, R., Kwok, C. S., "Mathematical Model of Simultaneous Diffusion and Binding of Antitumor Antibodies in Multicellular Human Tumor Spheroids, CancerRes 1988; 48:4032-4037



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