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| | <p> In our mathematical model our goal is to grasp the important concepts underlying the experiments made in the lab, and to see how those concepts could help us produce more propane. By having a better understanding of the ideas that govern our project, we could see the influence of each compound in the reaction pathway and have a basis to make decisions that would have a long term impact in our results.</p> | | <p> In our mathematical model our goal is to grasp the important concepts underlying the experiments made in the lab, and to see how those concepts could help us produce more propane. By having a better understanding of the ideas that govern our project, we could see the influence of each compound in the reaction pathway and have a basis to make decisions that would have a long term impact in our results.</p> |
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| − | <p>We separated our modeling in four modules:</p>
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| − | <!-- Deterministic model -->
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| − | <h1>Derministic modeling of the reaction pathway</h1>
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| − | <h2> Background</h2>
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| − | <p>Finding bottlenecks in our reactions, identifying which substrates could be overproduced, and comprehending better the role each component, as the substrates concentrations, plays in our pathway are a few of the reasons we decided to do a deterministic model. With the help of differential equations applied to each reaction, we could have simultaneously a specific and a broad view of our pathway.</p>
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| − | <h2>Results</h2>
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| − | <p>We made differential equations of our pathway.
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| − | <!-- Sensitivity analysis -->
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| − | <h1>Sensitivity analysis</h1>
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| − | <h2>Background</h2>
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| − | <p>We wanted to go further in our understanding of the main reaction pathway. By completing our deterministic model, it became easier for us to interpret how each substrate affects another one in our system. This is crucial for us to then invest more resources in those substrates that affect the most our propane production, the main goal of this project.</p>
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| − | <p>Relative sensitivity of concentration in steady state, $s^{ss}$, with respect to variable $p$, is defined as \[\frac{p}{s^{ss}}\frac{ds^{ss}}{dp}.\] It relates the size of a relative perturbation in $p$ to a relative change in $s^{ss}$. If a system shows a small sensitivity coefficient with respect to a parameter, then behaviour is robust with respect to perturbations of that parameter. Large values suggest 'control points' at which interventions will have significant effects.</p>
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| − | <h2>Results</h2>
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| − | <!-- Stability analysis -->
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| − | <h1>Stability analysis</h1>
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| − | <p>We wanted to know whether our pathway could produce propane steadily. In order to understand if this would be plausible, we performed a stability analysis of our reaction. To conclude these calculations, we used again the ideas behind our deterministic modeling.</p>
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| − | <!-- Cobra model(s) -->
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| − | <h1>Modeling the whole cell</h1>
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| − | <p>Although our models tell a lot about the reaction pathway, they are still lacking since not everything can be taken into account. This is why we did modeling with Cobra toolbox, for which there is a ready model of e. coli that could be modified to take into account our pathway.</p>
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