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− | <p>In order to estimate the propane production, we needed the speed constants for every reaction and estimates of certain concentrations in the cell. We found values for some of them from literature (sources), and some we had to estimate. </p>
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− | \[ \begin{array} {|c | c|}
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− | \hline
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− | \textbf{constant} & \textbf{value} \\
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− | \hline
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− | k_{AtoB} & 0.47 \\
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− | \hline
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− | k_{Hdb} & 0.05 \\
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− | \hline
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− | k_{Crt} & 0.03 \\
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− | \hline
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− | k_{Ter} & 0.0052 \\
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− | \hline
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− | k_{YciA} & 0.013 \\
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− | \hline
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− | k_{CAR} & 0.048 \\
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− | \hline
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− | k_{ADO} & 1\text{ (estimate)} \\
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− | \hline
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− | k_{out} & - \\
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− | \hline
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− | \text{AcetylCoA} & - \\
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− | \hline
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− | \text{NADPH} & - \\
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− | \hline
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− | \text{NADH} & - \\
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− | \hline
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− | H_2O & 38.85\text{ (estimate)}\\
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− | \hline
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− | \text{ATP} & 0.00000223\\
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− | \hline
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− | \text{H} & 2.511e-8 \\
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− | \hline
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− | O_2 & 0.2360\\
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− | \hline
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− | \end{array} \]
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− |
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− | <p>With these values, we modeled the pathway. Picture below.</p>
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| <!-- Sensitivity analysis --> | | <!-- Sensitivity analysis --> |
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| <h2>Results</h2> | | <h2>Results</h2> |
− | <!--<p>The steady state concentrations can be calculated from the basic differential equations. \[\begin{align*}
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− | [\text{Acetoacetyl-CoA}](t) &= \frac{k_{AtoB}\, [\text{AcetylCoA}]^2}{k_{Hbd}[NADPH]} \\
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− | [\text{3-hydroxybutyryl-CoA}](t) &= \frac{k_{AtoB}\, [\text{AcetylCoA}]^2}{k_{Crt}} \\
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− | [\text{Crotonyl-CoA}](t) &= \frac{k_{AtoB}\, [\text{AcetylCoA}]^2}{k_{Ter}[NADH]} \\
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− | [\text{Butyryl-CoA}](t) &= \frac{k_{AtoB}\, [\text{AcetylCoA}]^2}{k_{YciA}[H_2O]} \\
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− | [\text{Buryric acid}](t) &= \frac{k_{AtoB}\, [\text{AcetylCoA}]^2}{k_{CAR}[ATP][H_2O][NADPH]}\\
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− | [\text{Butyraldehyde}](t) &= \frac{k_{AtoB}\, [\text{AcetylCoA}]^2}{k_{ADO}[NADPH]^2[H]^2[O_2]}\\
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− | [\text{Propane}](t) &= \frac{k_{AtoB}\, [\text{AcetylCoA}]^2}{k_{out}}
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− | \end{align*}\]</p>
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− |
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− | <p >Now the relative sensitivities are as follows:
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− |
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− | \[ \begin{array} {|l | c|c|c|c|c|c|c|}
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− | \hline
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− | & b(t) & c(t) & d(t) & e(t) & f(t) & g(t) & \text{Propane}(t) \\
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− | \hline
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− | k_{AtoB} & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
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− | \hline
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− | k_{Hdb} & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
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− | \hline
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− | k_{Crt} & 0 & -1 & 0 & 0 & 0 & 0 & 0 \\
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− | \hline
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− | k_{Ter} & 0 & 0 & -1 & 0 & 0 & 0 & 0 \\
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− | \hline
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− | k_{YciA} & 0 & 0 & 0 & -1 & 0 & 0 & 0 \\
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− | \hline
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− | k_{CAR} & 0 & 0 & 0 & 0 & -1 & 0 & 0 \\
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− | \hline
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− | k_{ADO} & 0 & 0 & 0 & 0 & 0 & -1 & 0 \\
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− | \hline
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− | k_{out} & 0 & -1 & 0 & 0 & 0 & 0 & -1 \\
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− | \hline
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− | \text{AcetylCoA} & 2 & 2 & 2 & 2 & 2 & 2 & 2 \\
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− | \hline
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− | \text{NADPH} & -1 & 0 & 0 & 0 & -1 & -2 & 0\\
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− | \hline
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− | \text{NADH} & 0 & 0 & -1 & 0 & 0 & 0 & 0\\
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− | \hline
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− | H_2O & 0 & 0 & 0 & -1 & -1 & 0 & 0\\
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− | \hline
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− | \text{ATP} & 0 & 0 & 0 & 0 & -1 & 0 & 0\\
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− | \hline
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− | \text{H} & 0 & 0 & 0 & 0 & 0 & -2 & 0\\
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− | \hline
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− | O_2 & 0 & 0 & 0 & 0 & 0 & -1 & 0\\
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− | \hline
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− | \end{array} \] where $b$ is Acetoacetyl-CoA, $c$ is 3-hydroxybutyryl-CoA and so on, until $g$ is Butyraldehyde.</p>
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− | <p>The table tells us which concentrations or speed constants affect the most to the reaction. It seems that the system is robust with respect to many perturbations of the parameters, and that the propane production could be controlled mainly trough Acetyl-CoA (and the speed of the first reaction). Also -2 values in NADPH and H must be noted.</p>-->
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| <!-- Stability analysis --> | | <!-- Stability analysis --> |