Difference between revisions of "Team:Manchester/Model/MechanismUncertainty"

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<p id ="TopTitle" style="border-bottom: 1px black solid ;font-size:25px;text-weight:bold;display:inline-block">Network Mechanism Analysis</p>
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</br>
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<p> Contents </p>
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<a href="#OverviewTitle">Overview and Motivation</a> </br>
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<a href="#MethodologyTitle">Methodology</a> </br>
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<a href="#ResultsTitle">Results</a> </br>
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<a href="#ConclusionsTitle">Conclusions</a> </br>
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</br>
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<p id = "OverviewTitle" style="border-bottom: 1px black solid ;font-size:25px;text-weight:bold;display:inline-block">Overview and Motivation</p>
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<p> During discussions with the experimental team it became clear to us that the exact reaction mechanism in place was not clearly understood. By modelling a range of different potential mechanisms and comparing the outputs to experimental data we could draw conclusions about the accuracy of the mechanisms and hence refine the model in an effort to produce more accurate predictions and improve our understanding of the system. </p>
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<p> There were a few different mechanisms tested in this analysis </p>
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<table>
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  <tr>
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    <th>Step One</th>
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    <th>Step Two</th>
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  </tr>
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  <tr>
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    <td>Irreversible Michaelis-Menten Kinetics</td>
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    <td>Irreversible Michaelis-Menten Kinetics</td>
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  </tr>
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  <tr>
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    <td>Reversible Michaelis-Menten Kinetics</td>
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    <td>Reversible Michaelis-Menten Kinetics</td>
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  </tr>
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  <tr>
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    <td>Uni-Bi Kinetics</td>
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    <td>Bi-Uni Kinetics</td>
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  </tr>
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</table>
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<p> While this analysis is regarding Glucose not Alcohol it is included as a proof of concept of the system rather than to provide informative results. Since the majority of the project focused on Alcohol however these constraints were still used as all analyses should be informed and guided by the human practices. </p>
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</br>
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<a href="#TopTitle">Return to top of page</a>
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</br>
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<p id = "MethodologyTitle" style="border-bottom: 1px black solid ;font-size:25px;text-weight:bold;display:inline-block">Methodology</p>
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<p> Time independant analysis </p>
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<p>The model was run for a range of different enzyme ratios, maintaining a constant total amount of enzyme</p>
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 +
$$ [E_{total}] = [GOx] + [HRP]$$
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<p> All simulations that didn't violate the constraints were recorded</p>
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 +
$$[ABTS_{Oxidised}]_{t_{max}} > [ABTS_{Oxidised}]_{min}$$
 +
<p>The cost of the simulation was estimated assuming the cost of everything but the enzyme costs are negligible</p>
 +
 
 +
$$Cost_{total} = Cost_{GOx}  [GOx] + Cost_{HRP} [HRP]$$
 +
<p>Total Cost vs Fraction of GOx was then plotted</p>
 +
 
 +
</br>
 +
<p> Time dependant analysis </p>
 +
<p>The model was run for a range of different enzyme ratios, maintaining a constant total amount of enzyme</p>
 +
 
 +
$$ [E_{total}] = [GOx] + [HRP]$$
 +
 
 +
<p> All simulations that didn't violate the constraints were recorded</p>
 +
 
 +
$$[ABTS_{Oxidised}]_{t} > [ABTS_{Oxidised}]_{min}$$
 +
$$t < t_{max}$$
 +
 
 +
 
 +
<p>The cost of the simulation was estimated assuming the cost of everything but the enzyme costs are negligible</p>
 +
 
 +
$$Cost_{total} = Cost_{GOx}  [GOx] + Cost_{HRP} [HRP]$$
 +
 
 +
<p>The resulting surface was then filtered to return only the curve associated with the lower bound of the surface, for any given time or enzyme ratio there is only a single cost associated which is the lowest of all generated</p>
 +
<p>Total Cost vs Fraction of GOx vs Time to minimum expression was then plotted</p>
 +
 
 +
</br>
 +
<a href="#TopTitle">Return to top of page</a>
 +
</br>
 +
<p id = "ResultsTitle" style="border-bottom: 1px black solid ;font-size:25px;text-weight:bold;display:inline-block">Results</p>
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<p>
 +
PLACEHOLDER FOR GRAPHS, 2D and 3D
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</p>
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</br>
 +
<a href="#TopTitle">Return to top of page</a>
 +
</br>
 +
<p id = "ConclusionsTitle" style="border-bottom: 1px black solid ;font-size:25px;text-weight:bold;display:inline-block">Conclusions</p>
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<p>
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From the graphs you can clearly see that the minimum cost can be achieved with the range GOx fraction = XXX-YYY, however it is also shown that at additional cost expense, the time to expression can be reduced if required. The ranges identified as of interest should be tested experimentally to further validate these results.
 +
 
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In some situations the constraints are not met for example at a GOx fraction of 0 or 1 in all situations, but also some ranges between these dependant on the constraint set. The points of constraint failure could also be experimentally validated.
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</p>
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</br>
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</br>
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<a href="#TopTitle">Return to top of page</a>
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</br>
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<a href="https://2016.igem.org/Team:Manchester/Model">Return to overview</a>
 +
 
 +
</div>
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 +
</html>
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{{Manchester/CSS/footer}}

Revision as of 23:12, 17 October 2016

Manchester iGEM 2016

Network Mechanism Analysis


Contents

Overview and Motivation
Methodology
Results
Conclusions

Overview and Motivation

During discussions with the experimental team it became clear to us that the exact reaction mechanism in place was not clearly understood. By modelling a range of different potential mechanisms and comparing the outputs to experimental data we could draw conclusions about the accuracy of the mechanisms and hence refine the model in an effort to produce more accurate predictions and improve our understanding of the system.

There were a few different mechanisms tested in this analysis

Step One Step Two
Irreversible Michaelis-Menten Kinetics Irreversible Michaelis-Menten Kinetics
Reversible Michaelis-Menten Kinetics Reversible Michaelis-Menten Kinetics
Uni-Bi Kinetics Bi-Uni Kinetics

While this analysis is regarding Glucose not Alcohol it is included as a proof of concept of the system rather than to provide informative results. Since the majority of the project focused on Alcohol however these constraints were still used as all analyses should be informed and guided by the human practices.


Return to top of page

Methodology

Time independant analysis

The model was run for a range of different enzyme ratios, maintaining a constant total amount of enzyme

$$ [E_{total}] = [GOx] + [HRP]$$

All simulations that didn't violate the constraints were recorded

$$[ABTS_{Oxidised}]_{t_{max}} > [ABTS_{Oxidised}]_{min}$$

The cost of the simulation was estimated assuming the cost of everything but the enzyme costs are negligible

$$Cost_{total} = Cost_{GOx} [GOx] + Cost_{HRP} [HRP]$$

Total Cost vs Fraction of GOx was then plotted


Time dependant analysis

The model was run for a range of different enzyme ratios, maintaining a constant total amount of enzyme

$$ [E_{total}] = [GOx] + [HRP]$$

All simulations that didn't violate the constraints were recorded

$$[ABTS_{Oxidised}]_{t} > [ABTS_{Oxidised}]_{min}$$ $$t < t_{max}$$

The cost of the simulation was estimated assuming the cost of everything but the enzyme costs are negligible

$$Cost_{total} = Cost_{GOx} [GOx] + Cost_{HRP} [HRP]$$

The resulting surface was then filtered to return only the curve associated with the lower bound of the surface, for any given time or enzyme ratio there is only a single cost associated which is the lowest of all generated

Total Cost vs Fraction of GOx vs Time to minimum expression was then plotted


Return to top of page

Results

PLACEHOLDER FOR GRAPHS, 2D and 3D


Return to top of page

Conclusions

From the graphs you can clearly see that the minimum cost can be achieved with the range GOx fraction = XXX-YYY, however it is also shown that at additional cost expense, the time to expression can be reduced if required. The ranges identified as of interest should be tested experimentally to further validate these results. In some situations the constraints are not met for example at a GOx fraction of 0 or 1 in all situations, but also some ranges between these dependant on the constraint set. The points of constraint failure could also be experimentally validated.



Return to top of page
Return to overview

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