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| − | <h1>Modeling</h1>
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| − | <h2>Metabolic Modeling</h2>
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| − | <h3>Starting model</h3>
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| − | <p>In the following we modeled the Nootkatone biosynthesis pathway, to get an insight into its behaviour and dynamics. We started with an oversimplified model to get a sense for the behaviour of the enzymes in the pathway. The basic reactions without cofactors are the following:
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| − | $$\text{FPP} \ce{->[ValS]} \text{Valencene} \ce{->[HPO + CPR]} \text{Nootkatol} \ce{<->[ADH]} \text{Nootkatone}$$
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| − | With ValS = Valencene Synthase (4.2.3.73), HPO = Hyoscyamus muticus premnaspirodiene oxygenase (1.14.13.121), CPR = Cytochrome P450 reductase (1.6.2.4) and ADH = alcohol dehydrogenase (1.1.1.1).<br>
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| − | For the model we assumed non-reversible Michaelis-Menten kinetics for all reactions except the dehydrogenation of Nootkatol for which we used reversible Michaelis-Menten kinetics. For the FPP concentration we assumed a constant production proportional to the deviation from an assumed standard concentration. This gave us the following system of differential equations:
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| − | $$\frac{dFPP}{dt} = \mu_{FPP} \cdot (Max_{FPP} - c_{FPP}) - \frac{V_{Max,ValS} \cdot c_{FPP}}{K_{M, ValS} + c_{FPP}} $$
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| − | $$\frac{dValencene}{dt} =
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| − | \frac{V_{Max,ValS} \cdot c_{FPP}}{K_{M, ValS} + c_{FPP}} -
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| − | \frac{V_{Max,HPO + CPR} \cdot c_{Valencene}}{K_{M, HPO + CPR} + c_{Valencene}}$$
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| − | $$\frac{dNootkatol}{dt} = \frac{V_{Max,HPO + CPR} \cdot c_{Valencene}}{K_{M, HPO + CPR} + c_{Valencene}} - \frac{\frac{V_{M,ADH+} \cdot c_{Nootkatol}}{K_{M,ADH+}} - \frac{V_{M,ADH-} \cdot c_{Nootkatone}}{K_{M,ADH-}}}{1 + \frac{c_{Nootkatol}}{K_{M,ADH+}} + \frac{c_{Nootkatone}}{K_{M,ADH-}}}
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| − | $$
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| − | $$\frac{dNootkatone}{dt} = \frac{\frac{V_{M,ADH+} \cdot c_{Nootkatol}}{K_{M,ADH+}} - \frac{V_{M,ADH-} \cdot c_{Nootkatone}}{K_{M,ADH-}}}{1 + \frac{c_{Nootkatol}}{K_{M,ADH+}} + \frac{c_{Nootkatone}}{K_{M,ADH-}}}$$
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| − | A simulation in python using scipy's integrate.ode function yielded the following results:</p>
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| − | <img src="Nootkatone-Production-Model-1-g.svg" style="max-width:100%">
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| − | <p>With these kinetic parameters</p>
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| − | <table>
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| − | <tr>
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| − | <th>Enzyme</th>
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| − | <th>Km [µM]</th>
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| − | <th>kcat [1/s]</th>
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| − | <th>Source</th>
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| − | <td>ValS</td>
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| − | <td>1.04</td>
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| − | <td>0.0032</td>
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| − | <td><a href="http://www.brenda-enzymes.org/enzyme.php?ecno=4.2.3.73">Brenda</a></td>
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| − | </tr>
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| − | <td>HPO</td>
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| − | <td>11.5</td>
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| − | <td>0.1</td>
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| − | <td><a href="http://www.jbc.org/content/282/43/31744.short">Takashi 2007</a></td>
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| − | </tr>
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| − | <td>CPR</td>
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| − | <td>32.4 (NADPH)</td>
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| − | <td>5.435</td>
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| − | <td><a href="http://www.brenda-enzymes.org/enzyme.php?ecno=1.6.2.4">Brenda</a></td>
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| − | </tr>
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| − | <td>ADH-21</td>
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| − | <td>161 </td>
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| − | <td>2.619</td>
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| − | <td><a href="http://onlinelibrary.wiley.com/doi/10.1002/cctc.201402952/full">Schulz 2015</a></td>
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| − | </tr>
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| − | </table>
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| − | <p>We could not find information about the physiological FPP concentration in yeast cells, so we deduced from <a href="http://www.sciencedirect.com/science/article/pii/S0003269704007602">Tong 2004</a> (Typical fibroblast FPP concentration = $0.125 \frac{pmol}{10^6 cells}$) and <a href="http://book.bionumbers.org/how-big-is-a-human-cell/">Bionumbers</a> (Volume of a typical fibroblast = $2*10^{-12} L$) that the FPP concentration in a fibroblast is around $\frac{c_{FPP}}{V_{Fibroblast}} = \frac{0.125 \frac{pmol}{L}}{2 pL} = 0.0625 \frac{mol}{L}$, which we used as a starting point for our simulation in yeast as well. Another assumption we made is the a five-fold reduction in the speed of the reversible reaction of the ADH-21, based on the knowledge, that the forward reaction is favored.
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| − | </p>
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| − | <h3>Bioreactor model</h3>
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| − | <p>In order to check the validity of our model we took the results <a href="http://www.sciencedirect.com/science/article/pii/S1096717614000421">Wriessnegger 2014</a>, 208 mg/L Nootkatone production after 108 h, as a point of reference. For that we assumed half of the maximal yeast density in a bioreactor (<a href="https://microbialcellfactories.biomedcentral.com/articles/10.1186/s12934-015-0295-4">Source</a>) and simulated the yield.</p>
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| − | <img src="Nootkatone-Production-Model-2-g-per-liter.svg" style="max-width:100%">
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| − | <p>The maximal yield of Wriessnegger 2014 was 208 mg/L with a $\frac{Nootkatone}{Nootkatol}$ ratio of $\frac{208}{44} \approx 4.7$
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| − | Our maximal yield was 335 mg/L Nootkatol and 1484 mg/L Nootkatone with a $\frac{Nootkatone}{Nootkatol}$ ratio of $= \frac{1484}{335} \approx 4.4$. While our yield was way higher the $\frac{Nootkatone}{Nootkatol}$ ratio was quite similar and we therefore deduced that the reaction mechanism we assumed seems to be quite accurate and that the overly high yield was probably based on an overly high FPP supply or bioreactor cell density.</p>
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