Difference between revisions of "Team:Aalto-Helsinki/Modeling propane"
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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> | <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> | ||
+ | <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> | ||
+ | |||
+ | <p>The steady state concentrations can be calculated from the basic differential equations. \[\begin{align*} | ||
+ | \text{Acetoacetyl-CoA}(t) &= \frac{k_{AtoB}\, \text{AcetylCoA}^2}{k_{Hbd}[NADPH]} \\ | ||
+ | \text{3-hydroxybutyryl-CoA}(t) &= \frac{k_{AtoB}\,\text{AcetylCoA}^2}{k_{Crt}} \\ | ||
+ | \text{Crotonyl-CoA}(t) &= \frac{k_{AtoB}\,\text{AcetylCoA}^2}{k_{Ter}[NADH]} \\ | ||
+ | \text{Butyryl-CoA}(t) &= \frac{k_{AtoB}\,\text{AcetylCoA}^2}{k_{YciA}[H_2O]} \\ | ||
+ | \text{Buryric acid}(t) &= \frac{k_{AtoB}\,\text{AcetylCoA}^2}{k_{CAR}[ATP][H_2O][NADPH]}\\ | ||
+ | \text{Butyraldehyde}(t) &= \frac{k_{AtoB}\,\text{AcetylCoA}^2}{k_{ADO}[NADPH]^2[H]^2[O_2]}\\ | ||
+ | \text{Propane}(t) &= \frac{k_{AtoB}\,\text{AcetylCoA}^2}{k_{out}} | ||
+ | \end{align*}\]</p> | ||
+ | |||
+ | <p >Now the relative sensitivities are as follows: | ||
+ | |||
+ | \[ \begin{array} {|l | c|c|c|c|c|c|c|} | ||
+ | \hline | ||
+ | & b(t) & c(t) & d(t) & e(t) & f(t) & g(t) & \text{Propane}(t) \\ | ||
+ | \hline | ||
+ | k_{AtoB} & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ | ||
+ | \hline | ||
+ | k_{Hdb} & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\ | ||
+ | \hline | ||
+ | k_{Crt} & 0 & -1 & 0 & 0 & 0 & 0 & 0 \\ | ||
+ | \hline | ||
+ | k_{Ter} & 0 & 0 & -1 & 0 & 0 & 0 & 0 \\ | ||
+ | \hline | ||
+ | k_{YciA} & 0 & 0 & 0 & -1 & 0 & 0 & 0 \\ | ||
+ | \hline | ||
+ | k_{CAR} & 0 & 0 & 0 & 0 & -1 & 0 & 0 \\ | ||
+ | \hline | ||
+ | k_{ADO} & 0 & 0 & 0 & 0 & 0 & -1 & 0 \\ | ||
+ | \hline | ||
+ | k_{out} & 0 & -1 & 0 & 0 & 0 & 0 & -1 \\ | ||
+ | \hline | ||
+ | \text{AcetylCoA} & 2 & 2 & 2 & 2 & 2 & 2 & 2 \\ | ||
+ | \hline | ||
+ | \text{NADPH} & -1 & 0 & 0 & 0 & -1 & -2 & 0\\ | ||
+ | \hline | ||
+ | \text{NADH} & 0 & 0 & -1 & 0 & 0 & 0 & 0\\ | ||
+ | \hline | ||
+ | H_2O & 0 & 0 & 0 & -1 & -1 & 0 & 0\\ | ||
+ | \hline | ||
+ | \text{ATP} & 0 & 0 & 0 & 0 & -1 & 0 & 0\\ | ||
+ | \hline | ||
+ | \text{H} & 0 & 0 & 0 & 0 & 0 & -2 & 0\\ | ||
+ | \hline | ||
+ | O_2 & 0 & 0 & 0 & 0 & 0 & -1 & 0\\ | ||
+ | \hline | ||
+ | \end{array} \] where $b$ is Acetoacetyl-CoA, $c$ is 3-hydroxybutyryl-CoA and so on, until $g$ is Butyraldehyde.</p> | ||
+ | |||
+ | <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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Revision as of 12:30, 24 June 2015