Difference between revisions of "Team:UC San Diego/Modeling/Kinetics"

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<p>Parameter Table</p>
 
<p>Parameter Table</p>
 +
<table class="table-fill">
 +
<thead>
 +
                                <tr>
 +
                                <th class="text-left">Rate Constant</th>
 +
                                <th class="text-left">Value</th>
 +
                                <th class="text-left">Reference</th>
 +
</tr>
 +
</thead>
  
 +
<tbody class="table-hover">
 +
<tr>
 +
<td class="text-left">k<sup>1</sup></td>
 +
<td class="text-left">unknown</td>
 +
<td class="text-left"></td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>2</sup></td>
 +
<td class="text-left">unknown</td>
 +
<td class="text-left"></td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>3</sup></td>
 +
<td class="text-left">unknown</td>
 +
<td class="text-left"></td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>4</sup></td>
 +
<td class="text-left">unknown</td>
 +
<td class="text-left"></td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>5</sup></td>
 +
<td class="text-left">unknown</td>
 +
<td class="text-left"></td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>6</sup></td>
 +
<td class="text-left">unknown</td>
 +
<td class="text-left"></td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>7</sup></td>
 +
<td class="text-left">21.2 s<sup>-1</sup></td>
 +
<td class="text-left">(14)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>8</sup></td>
 +
<td class="text-left">10 s<sup>-1</sup></td>
 +
<td class="text-left">(9)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>9</sup></td>
 +
<td class="text-left"> 6.0*10<sub>5</sub>  M<sup>-1</sup>s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>10</sup></td>
 +
<td class="text-left">4.6 s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>11</sup></td>
 +
<td class="text-left">2.4*10<sub>6</sub>  M<sup>-1</sup>s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>12</sup></td>
 +
<td class="text-left">0.1 s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>13</sup></td>
 +
<td class="text-left">1.2*10<sub>5</sub> M<sup>-1</sup>s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>14</sup></td>
 +
<td class="text-left">0.1 s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>15</sup></td>
 +
<td class="text-left">9.5 s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>16</sup></td>
 +
<td class="text-left">0.5 s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>17</sup></td>
 +
<td class="text-left"> 3*10<sub>3</sub> M<sup>-1</sup>s<sup>-1</sup></td>
 +
<td class="text-left">(2)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>18</sup></td>
 +
<td class="text-left">0.06 s<sup>-1</sup></td>
 +
<td class="text-left">(2)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>19</sup></td>
 +
<td class="text-left">1.9*10<sub>-3</sub> s<sup>-1</sup></td>
 +
<td class="text-left">(3)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>20</sup></td>
 +
<td class="text-left">1*10<sub>5</sub> M<sup>-1</sup>s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>21</sup></td>
 +
<td class="text-left">40 s<sup>-1</sup></td>
 +
<td class="text-left">(12)</td>
 +
</tr>
 +
</tbody>
 +
</table>
 
<p>Enzyme Table</p>
 
<p>Enzyme Table</p>
 +
<table class="table-fill">
 +
<thead>
 +
                                <tr>
 +
                                <th class="text-left">Enzyme</th>
 +
                                <th class="text-left">Parameter</th>
 +
<th class="text-left">Value</th>
 +
</tr>
 +
</thead>
  
 +
<tbody class="table-hover">
 +
<tr>
 +
<td class="text-left"  rowspan="5">lux AB</td>
 +
<td class="text-left">Vmax<sup>luxAB</sup></td>
 +
<td class="text-left">71.58</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">r<sup>22</sup></td>
 +
<td class="text-left">0.62</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>41</sup></td>
 +
<td class="text-left">0.22</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>42</sup></td>
 +
<td class="text-left">81.5</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>43</sup></td>
 +
<td class="text-left">72.2</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left"  rowspan="5">lux EC</td>
 +
<td class="text-left">Vmax<sup>luxEC</sup></td>
 +
<td class="text-left">198.93</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">r<sup>44</sup></td>
 +
<td class="text-left">0.04</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>61</sup></td>
 +
<td class="text-left">90.9</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>62</sup></td>
 +
<td class="text-left">95.3</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>63</sup></td>
 +
<td class="text-left">24.35</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>64</sup></td>
 +
<td class="text-left">76.5</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left"  rowspan="5">frp</td>
 +
<td class="text-left">Vmax<sup>frp</sup></td>
 +
<td class="text-left">51.8</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">r<sup>12</sup></td>
 +
<td class="text-left">1</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>31</sup></td>
 +
<td class="text-left">0.72</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>32</sup></td>
 +
<td class="text-left">49.5</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left"  rowspan="5">lux D</td>
 +
<td class="text-left">Vmax<sup>luxD</sup></td>
 +
<td class="text-left">45.8</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">r<sup>33</sup></td>
 +
<td class="text-left">unknown</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>51</sup></td>
 +
<td class="text-left">0.37</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">k<sup>52</sup></td>
 +
<td class="text-left">unknown</td>
 +
</tr>
 +
</tbody>
 +
</table>
 
<p>Cofactor Table</p>
 
<p>Cofactor Table</p>
 +
<table class="table-fill">
 +
<thead>
 +
<tr>
 +
<th class="text-left">Chemical Species</th>
 +
<th class="text-left">Concentration (uM)</th>
 +
<th class="text-left">Reference</th>
 +
</tr>
 +
</thead>
 +
 +
<tbody class="table-hover">
 +
<tr>
 +
<td class="text-left">NADPH</td>
 +
<td class="text-left">560</td>
 +
<td class="text-left">(6)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">ATP</td>
 +
<td class="text-left">1310</td>
 +
<td class="text-left">(6)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">O<sup>2</sup></td>
 +
<td class="text-left">550</td>
 +
<td class="text-left">(27)</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">H<sup>2</sup>O</td>
 +
<td class="text-left">500</td>
 +
<td class="text-left">unknown</td>
 +
</tr>
 +
<tr>
 +
<td class="text-left">H+</td>
 +
<td class="text-left">300</td>
 +
<td class="text-left">unknown</td>
 +
</tr>
 +
</tbody>
 +
</table>
  
 
<h3>Scripts</h3>
 
<h3>Scripts</h3>

Revision as of 23:49, 18 September 2015

post image

Introduction

We developed a mathematical model to understand the relationship between the enzymes in our genetic constructs and their immediate microenvironment a priori. Using the MATLAB numerical solver ode23 and kinetic information from in vitro experiments found in literature (Table 1 and 2), we modeled the bioluminescence reaction network as an isolated system under steady state conditions and acquired preliminary light emission results for our different genetic constructs.

Chemical Reaction Network

The microbial Lux system can be interpreted as a two-component module, the aldehyde synthesis pathway and the light production pathway, coupled by an aldehyde and fatty acid.

Figure 1. The reactions in the aldehyde synthesis pathway are tightly coupled by the LuxCDE genes given the 1:1 ratio amongst substrate and product15.

In the aldehyde synthesis pathway (Fig. 1), the transferase (LuxD) first cleaves acyl-ACP and forms a fatty acid (RCOOH), via hydrolysis, which is subsequently activated by the synthetase subunit (LuxE) and reversibly transferred to the reductase subunit (LuxC) before being reduced with NADPH to an aldehyde (RCHO)5,8,18,19,20. The fatty acid activation process in the synthetase subunit occurs at very low levels in the absence of reductase15. However, when the synthetase and reductase subunits are co-expressed with luciferase, the system proceeds to emit light in the absence of transferase16; albeit at lower levels.

LIGHT PRODUCTION PATHWAY

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Modeling

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LIST OF ASSUMPTIONS

SYSTEM OF EQUATIONS

Induction Curves and Parameter Sensitivity




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FIGURES

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Model Reduction

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SYSTEM OF EQUATIONS

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Velocity Equations

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EQUATIONS

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EQUATIONS

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Results


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Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

Future Directions

Parameter Table

Rate Constant Value Reference
k1 unknown
k2 unknown
k3 unknown
k4 unknown
k5 unknown
k6 unknown
k7 21.2 s-1 (14)
k8 10 s-1 (9)
k9 6.0*105 M-1s-1 (12)
k10 4.6 s-1 (12)
k11 2.4*106 M-1s-1 (12)
k12 0.1 s-1 (12)
k13 1.2*105 M-1s-1 (12)
k14 0.1 s-1 (12)
k15 9.5 s-1 (12)
k16 0.5 s-1 (12)
k17 3*103 M-1s-1 (2)
k18 0.06 s-1 (2)
k19 1.9*10-3 s-1 (3)
k20 1*105 M-1s-1 (12)
k21 40 s-1 (12)

Enzyme Table

Enzyme Parameter Value
lux AB VmaxluxAB 71.58
r22 0.62
k41 0.22
k42 81.5
k43 72.2
lux EC VmaxluxEC 198.93
r44 0.04
k61 90.9
k62 95.3
k63 24.35
k64 76.5
frp Vmaxfrp 51.8
r12 1
k31 0.72
k32 49.5
lux D VmaxluxD 45.8
r33 unknown
k51 0.37
k52 unknown

Cofactor Table

Chemical Species Concentration (uM) Reference
NADPH 560 (6)
ATP 1310 (6)
O2 550 (27)
H2O 500 unknown
H+ 300 unknown

Scripts

Link to Enzyme Kinetics Scripts

References

REFERENCES