Team:Manchester/Model/MechanismUncertainty
Network Mechanism Analysis
Contents
Overview and Motivation Methodology Results ConclusionsOverview 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 pageMethodology
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 pageResults
PLACEHOLDER FOR GRAPHS, 2D and 3D
Return to top of pageConclusions
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.
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