Difference between revisions of "Team:Aalto-Helsinki/Kinetics"
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+ | background-image: url("https://static.igem.org/mediawiki/2015/1/11/Aalto-Helsinki_modeling_background.png"); | ||
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<li><a href="#" data-scroll="ter"><h4>Ter</h4></a></li> | <li><a href="#" data-scroll="ter"><h4>Ter</h4></a></li> | ||
<li><a href="#" data-scroll="ycia"><h4>YciA</h4></a></li> | <li><a href="#" data-scroll="ycia"><h4>YciA</h4></a></li> | ||
− | <li><a href="#" data-scroll="car"><h4> | + | <li><a href="#" data-scroll="car"><h4>CAR</h4></a></li> |
<li><a href="#" data-scroll="sfp"><h4>Sfp</h4></a></li> | <li><a href="#" data-scroll="sfp"><h4>Sfp</h4></a></li> | ||
− | <li><a href="#" data-scroll="ado"><h4> | + | <li><a href="#" data-scroll="ado"><h4>ADO</h4></a></li> |
<li><a href="#" data-scroll="other"><h4>Other<br/>constants</h4></a></li> | <li><a href="#" data-scroll="other"><h4>Other<br/>constants</h4></a></li> | ||
+ | <li><a href="#" data-scroll="sources"><h4>Sources</h4></a></li> | ||
<li><a href="#"><h4 style="border-top:solid;">To the Top</h4></a></li> | <li><a href="#"><h4 style="border-top:solid;">To the Top</h4></a></li> | ||
+ | <li><a href="https://2015.igem.org/Team:Aalto-Helsinki/Modeling_propane" ><h4>To the Parent Page</h4></a></li> | ||
</ul> | </ul> | ||
− | + | <div class="compscreens"> | |
<div class = "inner-container" > | <div class = "inner-container" > | ||
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<h1 id="kinetics">Kinetics</h1> | <h1 id="kinetics">Kinetics</h1> | ||
− | <p>We modeled our enzyme reactions in propane pathway with Michaelis-Menten enzyme kinetics. It is widely used in | + | <p>We modeled our enzyme reactions in the propane pathway with Michaelis-Menten enzyme kinetics. It is widely used in metabolical modeling of enzymes. Michaelis-Menten kinetics assumes that the reaction an enzyme catalyses is rapid compared to the enzyme and substrate joining together and leaving each other. The archetypical Michaelis-Menten equation for a reaction with one substrate and one product, i.e. \(S \rightarrow P; E \) is \[ \frac{d[P]}{dt} = \frac{V_{max}[S]}{K_{M}+[S]}, \] where \([S]\) is substrate concentration and \( V_{max} \) tells us the maximum speed of the enzyme. \( K_{M} \) is the substrate concentration at which the reaction rate is half of \( V_{max} \), also called the Michaelis constant. Usually we need to calculate \( V_{max} \) by \( K_{cat}\cdot [E] \) where \([E]\) is enzyme concentration. \( K_{cat} \) is the turnover number (unit: \( \tfrac{1}{min} \) ), which describes the speed at which an enzyme processes the substrate to a product. Only few of our reactions follow this very basic equation, and for the most of them we need to use multisubstrate reaction kinetics. For more information, see for example [1].</p> |
+ | |||
+ | <figure id="fig1" style="margin-bottom:3%;"> | ||
+ | <div style="margin-left:auto;margin-right:auto;"><a href="https://static.igem.org/mediawiki/2015/3/37/Aalto-Helsinki_pathway_horizontal_hbd.gif"><img src="https://static.igem.org/mediawiki/2015/3/37/Aalto-Helsinki_pathway_horizontal_hbd.gif" style="max-width:800px;" /></a></div> | ||
+ | <figcaption><b>Figure 1:</b> Propane pathway.</figcaption> | ||
+ | </figure> | ||
+ | |||
+ | <p>We understand and accept the fact that the kinetic data we have used in our model is very rough, due to varying measurement conditions and the fact that the measurements have been done in vitro, whereas our system functions in vivo. However, we believe our model can give us more reliable information about the bottlenecks of the pathway than mere educated guesses.</p> | ||
− | |||
</section> | </section> | ||
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<p>2\(\cdot\)Acetyl-CoA \(\rightarrow\) Acetoacetyl-CoA + CoA</p> | <p>2\(\cdot\)Acetyl-CoA \(\rightarrow\) Acetoacetyl-CoA + CoA</p> | ||
− | <p>AtoB is native to <span style="font-style:italic">Escherichia Coli</span>. The reaction shown above is reversible, but since the ratio of forward and reversible reaction favores strongly the forward one | + | <p>AtoB (acetyl-CoA C-acetyltransferase) is native to <span style="font-style:italic">Escherichia Coli</span>. The reaction shown above is reversible, but since the ratio of forward and reversible reaction favores strongly the forward one (Vf/Vr: 22.3, Source: [2]) we can approximate is as irreversible.</p> |
<p>Based on <a href="http://www.sciencedirect.com/science/article/pii/S0022283605000409">this</a> article, we know that the reaction follows Ping Pong Bi Bi -model and so we get the following rate equation:</p> | <p>Based on <a href="http://www.sciencedirect.com/science/article/pii/S0022283605000409">this</a> article, we know that the reaction follows Ping Pong Bi Bi -model and so we get the following rate equation:</p> | ||
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<td><p>\( K_{cat}^{AtoB} \)</p></td> | <td><p>\( K_{cat}^{AtoB} \)</p></td> | ||
<td><p>10653 1/min</p></td> | <td><p>10653 1/min</p></td> | ||
− | <td><p> | + | <td><p>[3] </p></td> |
− | + | ||
<td><p>Forward reaction</p></td> | <td><p>Forward reaction</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{AtoB:Acetyl\text{-}CoA} \)</p></td> | <td><p>\( K_{M}^{AtoB:Acetyl\text{-}CoA} \)</p></td> | ||
<td><p>0.00047 mol/l</p></td> | <td><p>0.00047 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[2]</p></td> |
− | <td><p> | + | <td><p></p></td> |
</tr> | </tr> | ||
</tbody> | </tbody> | ||
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<p>Acetoacetyl-CoA + NADPH + H\(^+\) \(\rightarrow\) 3-Hydroxybutyryl-CoA + NADP\(^+\)</p> | <p>Acetoacetyl-CoA + NADPH + H\(^+\) \(\rightarrow\) 3-Hydroxybutyryl-CoA + NADP\(^+\)</p> | ||
− | <p>FadB2 is found from<span style="font-style:italic"> Mycobacterium tuberculosis (strain ATCC 25618 / H37Rv)</span>. The reaction it catalyzes is reversible and we have assumed it to follow random bi bi reaction model.</p> | + | <p>FadB2 (3-hydroxybutyryl-CoA dehydrogenase) is found from<span style="font-style:italic"> Mycobacterium tuberculosis (strain ATCC 25618 / H37Rv)</span>. The reaction it catalyzes is reversible and we have assumed it to follow random bi bi reaction model.</p> |
− | <p>The equilibrium constant \(K_{eq}\) in reversible random bi bi model is from Haldane relationship \[ K_{eq} = \frac{V_1\cdot K_{M}^{FadB2:3\text{-}Hydroxybutyryl\text{-}CoA}\cdot K_{M}^{FadB2:NADP^+}}{V_2\cdot K_{M}^{FadB2:Acetoacetyl\text{-}CoA}\cdot K_{M}^{FadB2:NADPH}}.\] See | + | <p>The equilibrium constant \(K_{eq}\) in reversible random bi bi model is from Haldane relationship \[ K_{eq} = \frac{V_1\cdot K_{M}^{FadB2:3\text{-}Hydroxybutyryl\text{-}CoA}\cdot K_{M}^{FadB2:NADP^+}}{V_2\cdot K_{M}^{FadB2:Acetoacetyl\text{-}CoA}\cdot K_{M}^{FadB2:NADPH}}.\] See [1] for reference. We have not taken H\(^+\) concentration into account in this calculation which is justified because it needs to be fairly constant in the cell or otherwise the cell will die off. This yields us the following as our reaction rate equation.</p> |
<p>\[ \frac{[Acetoacetyl\text{-}CoA]\cdot [NADPH]-\frac{[3\text{-}hydroxybutyryl\text{-}CoA]\cdot [NADP^+]}{K_{eq}}} | <p>\[ \frac{[Acetoacetyl\text{-}CoA]\cdot [NADPH]-\frac{[3\text{-}hydroxybutyryl\text{-}CoA]\cdot [NADP^+]}{K_{eq}}} | ||
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<td><p>\( K_{cat1}^{FadB2} \)</p></td> | <td><p>\( K_{cat1}^{FadB2} \)</p></td> | ||
<td><p>0.677 1/min</p></td> | <td><p>0.677 1/min</p></td> | ||
− | <td><p | + | <td><p >[4]</p></td> |
<td><p>Forward reaction</p></td> | <td><p>Forward reaction</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{cat2}^{FadB2} \)</p></td> | <td><p>\( K_{cat2}^{FadB2} \)</p></td> | ||
<td><p>0.723 1/min</p></td> | <td><p>0.723 1/min</p></td> | ||
− | <td><p> | + | <td><p>[4]</p></td> |
− | + | ||
<td><p>Reverse reaction</p></td> | <td><p>Reverse reaction</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{FadB2:Acetoacetyl\text{-}CoA} \)</p></td> | <td><p>\( K_{M}^{FadB2:Acetoacetyl\text{-}CoA} \)</p></td> | ||
<td><p>65.6 mmol/l</p></td> | <td><p>65.6 mmol/l</p></td> | ||
− | <td><p> | + | <td><p>[4]</p></td> |
− | + | ||
<td><p>Forward reaction</p></td> | <td><p>Forward reaction</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{FadB2:NADPH} \)</p></td> | <td><p>\( K_{M}^{FadB2:NADPH} \)</p></td> | ||
<td><p>50 mmol/l</p></td> | <td><p>50 mmol/l</p></td> | ||
− | <td><p> | + | <td><p>[4]</p></td> |
− | + | ||
<td><p>Forward reaction</p></td> | <td><p>Forward reaction</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{FadB2:3\text{-}Hydroxybutyryl\text{-}CoA} \)</p></td> | <td><p>\( K_{M}^{FadB2:3\text{-}Hydroxybutyryl\text{-}CoA} \)</p></td> | ||
<td><p>43.5 mmol/l</p></td> | <td><p>43.5 mmol/l</p></td> | ||
− | <td><p> | + | <td><p>[4]</p></td> |
− | + | ||
<td><p>Reverse reaction</p></td> | <td><p>Reverse reaction</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{FadB2:NADP^+} \)</p></td> | <td><p>\( K_{M}^{FadB2:NADP^+} \)</p></td> | ||
<td><p>29.5 mmol/l</p></td> | <td><p>29.5 mmol/l</p></td> | ||
− | <td><p> | + | <td><p>[4]</p></td> |
− | + | ||
<td><p>Reverse reaction</p></td> | <td><p>Reverse reaction</p></td> | ||
</tr> | </tr> | ||
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<p>Acetoacetyl-CoA + NADPH + H\(^+\) \(\rightarrow\) 3-Hydroxybutyryl-CoA + NADP\(^+\)</p> | <p>Acetoacetyl-CoA + NADPH + H\(^+\) \(\rightarrow\) 3-Hydroxybutyryl-CoA + NADP\(^+\)</p> | ||
− | <p>The enzyme is from <span style="font-style:italic">Clostridium acetobutylicum</span>, but only values to be found were for <span style="font-style:italic">Clostridium Kluyveri</span>. | + | <p>The enzyme used in the propane pathway, Hbd (3-hydroxybutyryl-CoA dehydrogenase), is from <span style="font-style:italic">Clostridium acetobutylicum</span>, but only values to be found were for <span style="font-style:italic">Clostridium Kluyveri</span>. However, since the species are very close relatives, we can assume the values to be close enough for comparison.</p> |
− | <p>The reaction is reversible, but according to | + | <p>The reaction is reversible, but according to [5], the specific activity of 3-hydroxybutyryl-CoA dehydrogenase (forward) as measured in the direction of acetoacetyl-CoA reduction is 478.6 U/mg protein. The rate of the oxidation reaction (reverse) proceeded with 36.6 U / mg protein. Because of the disparity between these rates we approximate the reaction as irreversible.</p> |
− | <p>We don’t consider how \(H^+\) affects the reaction which is justified by knowing that its concentration in the cell should always be quite constant; otherwise the cell will die. | + | <p>We don’t consider how \(H^+\) affects the reaction which is justified by knowing that its concentration in the cell should always be quite constant; otherwise the cell will die. Based on these pieces of information we can assume that the reaction is either random or ordered Bi Bi -reaction so the rate equation is as follows.</p> |
− | + | ||
− | + | ||
<p>\[ \frac{K_{cat}^{Hbd}\cdot [Hbd] \cdot [Acetoacetyl\text{-}CoA]\cdot [NADPH]}{[Acetoacetyl\text{-}CoA]\cdot [NADPH] + K_{M}^{Hbd:NADPH}\cdot [Acetoacetyl\text{-}CoA]+K_{M}^{Hbd:Acetoacetyl\text{-}CoA}\cdot [NADPH]} \]</p> | <p>\[ \frac{K_{cat}^{Hbd}\cdot [Hbd] \cdot [Acetoacetyl\text{-}CoA]\cdot [NADPH]}{[Acetoacetyl\text{-}CoA]\cdot [NADPH] + K_{M}^{Hbd:NADPH}\cdot [Acetoacetyl\text{-}CoA]+K_{M}^{Hbd:Acetoacetyl\text{-}CoA}\cdot [NADPH]} \]</p> | ||
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<td><p>\( K_{cat}^{Hbd} \)</p></td> | <td><p>\( K_{cat}^{Hbd} \)</p></td> | ||
<td><p>336.4 1/min</p></td> | <td><p>336.4 1/min</p></td> | ||
− | <td><p> | + | <td><p>[5]</p></td> |
<td><p>Forward reaction, Clostridium Kluyveri</p></td> | <td><p>Forward reaction, Clostridium Kluyveri</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{Hbd:Acetoacetyl\text{-}CoA} \)</p></td> | <td><p>\( K_{M}^{Hbd:Acetoacetyl\text{-}CoA} \)</p></td> | ||
<td><p>5e-5 mol/l</p></td> | <td><p>5e-5 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[5]</p></td> |
<td><p>Clostridium Kluyveri</p></td> | <td><p>Clostridium Kluyveri</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{Hbd:NADPH} \)</p></td> | <td><p>\( K_{M}^{Hbd:NADPH} \)</p></td> | ||
<td><p>7e-5 mol/l</p></td> | <td><p>7e-5 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[5]</p></td> |
<td><p>Clostridium Kluyveri</p></td> | <td><p>Clostridium Kluyveri</p></td> | ||
</tr> | </tr> | ||
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<p>3-hydroxybutyryl-CoA \(\rightarrow\) Crotonyl-CoA + H\( _2\)O</p> | <p>3-hydroxybutyryl-CoA \(\rightarrow\) Crotonyl-CoA + H\( _2\)O</p> | ||
− | <p>Crt is found from <span style="font-style:italic;">Clostridium acetobutylicum</span>. Since there is only one substrate in the reaction, we can form the rate equation | + | <p>Crt (3-hydroxybutyryl-CoA dehydratase) is found from <span style="font-style:italic;">Clostridium acetobutylicum</span>. Since there is only one substrate in the reaction, we can form the rate equation from basic Michaelis-Menten kinetic model. We assumed the reaction to be irreversible since the enzyme is quite efficient.</p> |
<p>\[ \frac{K_{cat}^{Crt}\cdot [Crt]\cdot [3\text{-}hydroxybutyryl\text{-}CoA]}{K_{M}^{Crt:3\text{-}Hydroxybutyryl\text{-}CoA} +[3\text{-}hydroxybutyryl\text{-}CoA]} \]</p> | <p>\[ \frac{K_{cat}^{Crt}\cdot [Crt]\cdot [3\text{-}hydroxybutyryl\text{-}CoA]}{K_{M}^{Crt:3\text{-}Hydroxybutyryl\text{-}CoA} +[3\text{-}hydroxybutyryl\text{-}CoA]} \]</p> | ||
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<td><p>\( K_{cat}^{Crt} \)</p></td> | <td><p>\( K_{cat}^{Crt} \)</p></td> | ||
<td><p>1279.8 1/min</p></td> | <td><p>1279.8 1/min</p></td> | ||
− | <td><p> | + | <td><p>[6]</p></td> |
<td><p>Forward reaction</p></td> | <td><p>Forward reaction</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{Crt:3\text{-}Hydroxybutyryl\text{-}CoA} \)</p></td> | <td><p>\( K_{M}^{Crt:3\text{-}Hydroxybutyryl\text{-}CoA} \)</p></td> | ||
<td><p>3e-5 mol/l</p></td> | <td><p>3e-5 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[6]</p></td> |
− | <td><p> | + | <td><p></p></td> |
</tr> | </tr> | ||
</tbody> | </tbody> | ||
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<p>Crotonyl-CoA + NADH + H\( ^+\) \(\rightarrow\) Butyryl-CoA + NAD\( ^+\)</p> | <p>Crotonyl-CoA + NADH + H\( ^+\) \(\rightarrow\) Butyryl-CoA + NAD\( ^+\)</p> | ||
− | <p>Ter is from <span style="font-style:italic;">Treponema denticola</span>. Its reaction without H\( ^+\) is an ordered bi-bi reaction mechanism with NADH binding first | + | <p>Ter (trans-2-enoyl-CoA reductase) is from <span style="font-style:italic;">Treponema denticola</span>. Its reaction without H\( ^+\) is an ordered bi-bi reaction mechanism with NADH binding first [7]. Since we found no references for the reaction to be reversible, we modeled it as irreversible.</p> |
<p>\[ \frac{K_{cat}^{Ter}\cdot [Ter] \cdot [Crotonyl\text{-}CoA]\cdot [NADH]}{[Crotonyl\text{-}CoA]\cdot [NADH] + K_{M}^{Ter:NADH}\cdot [Crotonyl\text{-}CoA]+K_{M}^{Ter:Crotonyl\text{-}CoA}\cdot [NADH] + K_{I}^{Ter:Butyryl\text{-}CoA}\cdot K_{M}^{Ter:NADH}} \]</p> | <p>\[ \frac{K_{cat}^{Ter}\cdot [Ter] \cdot [Crotonyl\text{-}CoA]\cdot [NADH]}{[Crotonyl\text{-}CoA]\cdot [NADH] + K_{M}^{Ter:NADH}\cdot [Crotonyl\text{-}CoA]+K_{M}^{Ter:Crotonyl\text{-}CoA}\cdot [NADH] + K_{I}^{Ter:Butyryl\text{-}CoA}\cdot K_{M}^{Ter:NADH}} \]</p> | ||
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<td><p>\( K_{cat}^{Ter} \)</p></td> | <td><p>\( K_{cat}^{Ter} \)</p></td> | ||
<td><p>5460 1/min</p></td> | <td><p>5460 1/min</p></td> | ||
− | <td><p> | + | <td><p>[7]</p></td> |
<td><p>Forward reaction</p></td> | <td><p>Forward reaction</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{Ter:Crotonyl\text{-}CoA} \)</p></td> | <td><p>\( K_{M}^{Ter:Crotonyl\text{-}CoA} \)</p></td> | ||
<td><p>70 µmol/l</p></td> | <td><p>70 µmol/l</p></td> | ||
− | <td><p> | + | <td><p>[7]</p></td> |
− | <td><p> | + | <td><p></p></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><p>\( K_{M}^{Ter:NADH} \)</p></td> | <td><p>\( K_{M}^{Ter:NADH} \)</p></td> | ||
<td><p>5.2e-06 mol/l</p></td> | <td><p>5.2e-06 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[7]</p></td> |
− | <td><p> | + | <td><p></p></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><p>\( K_{I}^{Ter:Butyryl\text{-}CoA} \)</p></td> | <td><p>\( K_{I}^{Ter:Butyryl\text{-}CoA} \)</p></td> | ||
<td><p>1.98e-07 mol/l</p></td> | <td><p>1.98e-07 mol/l</p></td> | ||
− | <td><p | + | <td><p>[7]</p></td> |
− | </p></td> | + | <td><p></p></td> |
− | <td><p> | + | |
</tr> | </tr> | ||
</tbody> | </tbody> | ||
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<p>Butyryl-CoA + H\( _2\)O \(\rightarrow\) Butyrate + CoA</p> | <p>Butyryl-CoA + H\( _2\)O \(\rightarrow\) Butyrate + CoA</p> | ||
− | <p>YciA is found in <span style="font-style:italic">Haemophilus influenzae</span>. | + | <p>YciA (acyl-CoA thioester hydrolase) is found in <span style="font-style:italic">Haemophilus influenzae</span>. When searching for information about this enzyme no references for it being reversible were found. Because of this we modeled it as irreversible. We know that there is abundance of water in the cell, so when considering rate equation we can safely assume that it doesn't have much effect to it. This is why we can again use the basic Michaelis-Menten rate equation.</p> |
<p>\[ \frac{K_{cat}^{YciA}\cdot [YciA]\cdot [Butyryl\text{-}CoA]}{K_{M}^{YciA:Butyryl\text{-}CoA} +[Butyryl\text{-}CoA]} \]</p> | <p>\[ \frac{K_{cat}^{YciA}\cdot [YciA]\cdot [Butyryl\text{-}CoA]}{K_{M}^{YciA:Butyryl\text{-}CoA} +[Butyryl\text{-}CoA]} \]</p> | ||
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<td><p>\( K_{cat}^{YciA} \)</p></td> | <td><p>\( K_{cat}^{YciA} \)</p></td> | ||
<td><p>1320 1/min</p></td> | <td><p>1320 1/min</p></td> | ||
− | <td><p> | + | <td><p>[8]</p></td> |
<td><p>Forward reaction</p></td> | <td><p>Forward reaction</p></td> | ||
</tr> | </tr> | ||
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<td><p>\( K_{M}^{YciA:Butyryl\text{-}CoA} \)</p></td> | <td><p>\( K_{M}^{YciA:Butyryl\text{-}CoA} \)</p></td> | ||
<td><p>3.5e-06 mol/l</p></td> | <td><p>3.5e-06 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[8]</p></td> |
− | <td><p> | + | <td><p></p></td> |
</tr> | </tr> | ||
</tbody> | </tbody> | ||
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− | <!-- | + | <!-- CAR --> |
<section id="car" data-anchor="car"> | <section id="car" data-anchor="car"> | ||
− | <h2> | + | <h2>CAR</h2> |
<p>Butyrate + NADPH + ATP \(\rightarrow\) Butyraldehyde + NADP\(^+\) + AMP + 2P\(_i\)</p> | <p>Butyrate + NADPH + ATP \(\rightarrow\) Butyraldehyde + NADP\(^+\) + AMP + 2P\(_i\)</p> | ||
− | <p> | + | <p>CAR-enzyme (carboxylic acid reductase) is originally from <span style="font-style:italic">Mycobacterium marinum</span>. We assumed that this reaction is irreversible, which is justified because we have ATP in the reactants so we know that the possible reverse reaction can’t be very efficient. |
− | For the same reasons as mentioned before, we didn’t consider \(H^+\) in equations. <a href="http://www.pnas.org/content/110/1/87">We know</a> that the reaction can be modeled using Bi Uni Uni Bi Ping Pong mechanism. | + | For the same reasons as mentioned before, we didn’t consider \(H^+\) in equations. <a href="http://www.pnas.org/content/110/1/87">We know</a> that the reaction can be modeled using Bi Uni Uni Bi Ping Pong mechanism. Thus, the rate equation will be</p> |
− | <p>\[\frac{K_{cat}^{ | + | <p>\[\frac{K_{cat}^{CAR}\cdot [CAR]\cdot [Butyrate]\cdot [NADPH]\cdot [ATP]}{K_{M}^{CAR:Butyrate}\cdot K_{M}^{CAR:NADPH}\cdot [ATP]+K_{M}^{CAR:ATP}\cdot [Butyrate]\cdot [NADPH]+K_{M}^{CAR:NADPH}\cdot [Butyrate]\cdot [ATP]}\]\[\cdots \frac{}{+K_{M}^{CAR:Butyrate}\cdot [NADPH]\cdot [ATP]+ [Butyrate]\cdot [NADPH]\cdot [ATP]}\]</p> |
<table class="table table-bordered"> | <table class="table table-bordered"> | ||
Line 387: | Line 407: | ||
<tbody> | <tbody> | ||
<tr> | <tr> | ||
− | <td><p>\( K_{cat}^{ | + | <td><p>\( K_{cat}^{CAR} \)</p></td> |
<td><p>150 1/min</p></td> | <td><p>150 1/min</p></td> | ||
− | <td><p> | + | <td><p>[9]</p></td> |
<td><p>Forward reaction, calculated from a plot</p></td> | <td><p>Forward reaction, calculated from a plot</p></td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
− | <td><p>\( K_{M}^{ | + | <td><p>\( K_{M}^{CAR:Butyrate} \)</p></td> |
<td><p>0.013 mol/l</p></td> | <td><p>0.013 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[9]</p></td> |
<td><p>Calculated from a plot</p></td> | <td><p>Calculated from a plot</p></td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
− | <td><p>\( K_{M}^{ | + | <td><p>\( K_{M}^{CAR:NADPH} \)</p></td> |
<td><p>4.8e-05 mol/l</p></td> | <td><p>4.8e-05 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[9]</p></td> |
− | <td><p> | + | <td><p></p></td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
− | <td><p>\( K_{M}^{ | + | <td><p>\( K_{M}^{CAR:ATP} \)</p></td> |
<td><p>0.000115 mol/l</p></td> | <td><p>0.000115 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[9]</p></td> |
− | <td><p> | + | <td><p></p></td> |
</tr> | </tr> | ||
</tbody> | </tbody> | ||
Line 414: | Line 434: | ||
</section> | </section> | ||
− | <!-- | + | <!-- CAR ends --> |
Line 420: | Line 440: | ||
<section id="sfp" data-anchor="sfp"> | <section id="sfp" data-anchor="sfp"> | ||
<h2>Sfp</h2> | <h2>Sfp</h2> | ||
− | <p>Sfp does not directly | + | <p>Sfp (4'-phosphopantetheinyl transferase) does not directly affect to the intermediates in our pathway, but instead acts as an activating enzyme for CAR. We have modeled the reactions concerning Sfp <a href="https://2015.igem.org/Team:Aalto-Helsinki/Car-activation">here</a>.</p> |
</section> | </section> | ||
Line 426: | Line 446: | ||
− | <!-- | + | <!-- ADO --> |
<section id="ado" data-anchor="ado"> | <section id="ado" data-anchor="ado"> | ||
− | <h2> | + | <h2>ADO</h2> |
− | <p>\[ \frac{K_{cat}^{ | + | |
+ | <p>Aldehyde deformylating oxygenase is the final enzyme in the propane pathway, turning butyraldehyde into propane. We are using an ADO mutant (A134F) that <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4159587/">has an increased activity</a> towards short-chained aldehydes, such as butyraldehyde. Furthermore, we are enhancing the electron supply to ADO by overexpressing <a href="http://www.biotechnologyforbiofuels.com/content/8/1/61">its presumed</a> natural electron acceptor/donor ferredoxin. To reduce ferredoxin under aerobic conditions, we co-express NADPH/ferredoxin/flavodoxin-oxidoreductase (Fpr).</p> | ||
+ | |||
+ | <p>Using an A134F mutant and a ferredoxin reducing system including Fpr <a href="http://www.nature.com/ncomms/2014/140902/ncomms5731/full/ncomms5731.html">improves propane production</a>. Combining all these improvements is challenging from the modeling point of view, as there are no kinetic parameters available for the reaction where both the ADO A134F mutant and a ferredoxin reducing system are used. As no sufficient data is available, we cannot model the ADO reaction like we have modeled the other reactions in the propane pathway.</p> | ||
+ | |||
+ | <p><a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4159587/">We know</a> that the wild-type ADO together with PMS/NADH reducing system has kcat value 0.0031±0.0001 min−1 and Km value 10.1±0.9 mM for the reaction from butyraldehyde to propane. A134F mutant <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4159587/">has been shown</a> to be more efficient than wild-type ADO and ferredoxin reducing system <a href="http://www.biotechnologyforbiofuels.com/content/6/1/86">more efficient</a> for ADO than a PMS/NADH reducing system. Therefore we can rather safely assume 10.1±0.9 mM to be the maximum Km possible and 0.0031±0.0001 min−1 to be the minimum kcat possible for estimating ADO reaction kinetics in our system.</p> | ||
+ | |||
+ | <p>Since we could not model the reactions that govern ADO's function, we approximated these reactions by simplifying the enzyme kinetics that govern ADO to the simplest case of Miclaelis-Menten kinetics. While this is not ideal, with current data and within these time limitations we can't make better assumptions.</p> | ||
+ | |||
+ | <p>\[ \frac{K_{cat}^{ADO}\cdot [ADO]\cdot [Butyrate]}{K_{M}^{ADO:Butyrate} +[Butyrate]} \]</p> | ||
<table class="table table-bordered"> | <table class="table table-bordered"> | ||
Line 443: | Line 472: | ||
<tbody> | <tbody> | ||
<tr> | <tr> | ||
− | <td><p>\( K_{cat}^{ | + | <td><p>\( K_{cat}^{ADO} \)</p></td> |
<td><p>0.03 1/min</p></td> | <td><p>0.03 1/min</p></td> | ||
− | <td><p | + | <td><p>[10]</p></td> |
<td><p>Forward reaction</p></td> | <td><p>Forward reaction</p></td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
− | <td><p>\( K_{M}^{ | + | <td><p>\( K_{M}^{ADO:Butyraldehyde} \)</p></td> |
<td><p>0.0101 mol/l</p></td> | <td><p>0.0101 mol/l</p></td> | ||
− | <td><p | + | <td><p>[10]</p></td> |
− | <td><p> | + | <td><p></p></td> |
</tr> | </tr> | ||
</tbody> | </tbody> | ||
Line 458: | Line 487: | ||
</section> | </section> | ||
− | <!-- | + | <!-- ADO ends --> |
Line 465: | Line 494: | ||
<h2>Other Constants</h2> | <h2>Other Constants</h2> | ||
− | <p> | + | <p>The following table provides information about typical concentrations in a cell that we use in our model.</p> |
<table class="table table-bordered"> | <table class="table table-bordered"> | ||
Line 480: | Line 509: | ||
<td><p>[Acetyl-CoA]</p></td> | <td><p>[Acetyl-CoA]</p></td> | ||
<td><p>0.00061 mol/l</p></td> | <td><p>0.00061 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[11]</p></td> |
<td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | <td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | ||
</tr> | </tr> | ||
Line 486: | Line 515: | ||
<td><p>[Acetoacetyl-CoA]</p></td> | <td><p>[Acetoacetyl-CoA]</p></td> | ||
<td><p>2.2e-05 mol/l</p></td> | <td><p>2.2e-05 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[11]</p></td> |
<td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | <td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | ||
</tr> | </tr> | ||
Line 492: | Line 521: | ||
<td><p>[CoA]</p></td> | <td><p>[CoA]</p></td> | ||
<td><p>0.00014 mol/l</p></td> | <td><p>0.00014 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[11]</p></td> |
<td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | <td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | ||
</tr> | </tr> | ||
Line 498: | Line 527: | ||
<td><p>[NADPH]</p></td> | <td><p>[NADPH]</p></td> | ||
<td><p>0.00012 mol/l</p></td> | <td><p>0.00012 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[11]</p></td> |
<td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | <td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | ||
</tr> | </tr> | ||
Line 504: | Line 533: | ||
<td><p>[NADP\( ^+\)]</p></td> | <td><p>[NADP\( ^+\)]</p></td> | ||
<td><p>2.1e-06 mol/l</p></td> | <td><p>2.1e-06 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[11]</p></td> |
<td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | <td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | ||
</tr> | </tr> | ||
Line 510: | Line 539: | ||
<td><p>[NADH]</p></td> | <td><p>[NADH]</p></td> | ||
<td><p>8.3e-05 mol/l</p></td> | <td><p>8.3e-05 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[11]</p></td> |
<td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | <td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | ||
</tr> | </tr> | ||
Line 516: | Line 545: | ||
<td><p>[NAD\( ^+\)]</p></td> | <td><p>[NAD\( ^+\)]</p></td> | ||
<td><p>0.0026 mol/l</p></td> | <td><p>0.0026 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[11]</p></td> |
<td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | <td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | ||
</tr> | </tr> | ||
Line 522: | Line 551: | ||
<td><p>[ATP]</p></td> | <td><p>[ATP]</p></td> | ||
<td><p>0.0096 mol/l</p></td> | <td><p>0.0096 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[11]</p></td> |
<td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | <td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | ||
</tr> | </tr> | ||
Line 528: | Line 557: | ||
<td><p>[AMP]</p></td> | <td><p>[AMP]</p></td> | ||
<td><p>0.00028 mol/l</p></td> | <td><p>0.00028 mol/l</p></td> | ||
− | <td><p> | + | <td><p>[11]</p></td> |
<td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | <td><p>glucose-fed, exponentially growing <span style="font-style:italic">E. coli</span></p></td> | ||
</tr> | </tr> | ||
Line 534: | Line 563: | ||
<td><p>[H\( _2\)O]</p></td> | <td><p>[H\( _2\)O]</p></td> | ||
<td><p>38.85 mol/l</p></td> | <td><p>38.85 mol/l</p></td> | ||
− | <td><p>Concentration of water in water is \(\frac{\frac{m}{V}}{M}\). E.coli is about 70% water. Thus, the water concentration in E.coli is \( 70\% \cdot \frac{1000 \frac{g}{l}}{18.01 g/mol} = 38.85 \frac{mol}{l} \)</p></td> | + | <td><p>Concentration of water in water is \(\frac{\frac{m}{V}}{M}\). <i>E.coli</i> is about 70% water. Thus, the water concentration in <i>E.coli</i> is \( 70\% \cdot \frac{1000 \frac{g}{l}}{18.01 g/mol} = 38.85 \frac{mol}{l} \)</p></td> |
<td><p></p></td> | <td><p></p></td> | ||
</tr> | </tr> | ||
</tbody> | </tbody> | ||
</table> | </table> | ||
− | |||
</section> | </section> | ||
<!-- Other constants end --> | <!-- Other constants end --> | ||
− | |||
− | + | <!-- Sources --> | |
+ | <section id="sources" data-anchor="sources"> | ||
+ | <h2>Sources</h2> | ||
+ | <p><b>[1]</b> Enzyme Kinetics: Principals and Methods by Hans Bisswanger (2002)</p> | ||
+ | <p><b>[2]</b> Molecular and catalytic properties of the acetoacetyl-coenzyme A thiolase of <i>Escherichia coli</i>; Archives of Biochemistry and Biophysics Volume 176, Issue 1, September 1976, Pages 159–170 </p> | ||
+ | <p><b>[3]</b> Thiolases of <i>Escherichia coli</i>: purification and chain length specificities | ||
+ | Feigenbaum, J.; Schulz, H.; Journal of Bacteriology, Volume 122, Issue 2, May 1975, Pages 407-411 </p> | ||
+ | <p><b>[4]</b> Characterization of a b-hydroxybutyryl-CoA dehydrogenase from Mycobacterium tuberculosis; Microbiology,Volume 156, July 2010, Pages 1975-1982 </p> | ||
+ | <p><b>[5]</b> Purification and Properties of NADP-Dependent L(+)-3-Hydroxybutyryl -CoA Dehydrogenase from Clostridium kluyveri; Eur. J. Biochem. 32,51-56 (1973) </p> | ||
+ | <p><b>[6]</b> Purification and Characterization of Crotonase from Clostridium acetobutylicum; The journal of Biological Chemistry, Volume 247, Number 16, August 1972, Pages 5266-5271 </p> | ||
+ | <p><b>[7]</b> Biochemical and Structural Characterization of the trans-Enoyl-CoA Reductase from Treponema denticola; Biochemistry 2012, 51, 6827−6837 </p> | ||
+ | <p><b>[8]</b> Divergence of Function in the Hot Dog Fold Enzyme Superfamily: The Bacterial Thioesterase YciA; Biochemistry 2008, 47, 2789–2796 </p> | ||
+ | <p><b>[9]</b> Carboxylic acid reductase is a versatile enzyme for the conversion of fatty acids into fuels and chemical commodities; PNAS | January 2, 2013 | vol. 110 | no. 1 | 87–92 </p> | ||
+ | <p><b>[10]</b> Production of Propane and Other Short-Chain Alkanes by Structure-Based Engineering of Ligand Specificity in Aldehyde-Deformylating Oxygenase, Khara et al (2013) </p> | ||
+ | <p><b>[11]</b> Absolute Metabolite Concentrations and Implied Enzyme Active Site Occupancy in Escherichia coli, Bennett et al, 2009 </p> | ||
+ | </section> | ||
+ | <!-- Sources end --> | ||
− | |||
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+ | <p style="margin-bottom:0;"> | ||
+ | |||
+ | |||
+ | |||
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Latest revision as of 04:25, 29 October 2015