"
Team:UC Davis/Signal Processing
From 2014.igem.org
| Line 29: | Line 29: | ||
To model our system, we first focused our attention on the linear range of our enzyme's Michaelis Menten plot. The linear range of this plot is governed by the above relationship. This was useful for describing single aldehydes, but Olive Oil contains many aldehydes and the enzymatic response is different for each one.</p><br> | To model our system, we first focused our attention on the linear range of our enzyme's Michaelis Menten plot. The linear range of this plot is governed by the above relationship. This was useful for describing single aldehydes, but Olive Oil contains many aldehydes and the enzymatic response is different for each one.</p><br> | ||
<div style="margin:auto;display:block;float:center"> | <div style="margin:auto;display:block;float:center"> | ||
| - | <img src="https://static.igem.org/mediawiki/2014/b/b5/RelativeVelocity.png" style="margin-left:auto;margin-right:auto;float:center;"/></div><br> | + | <p align="center"><img src="https://static.igem.org/mediawiki/2014/b/b5/RelativeVelocity.png" style="margin-left:auto;margin-right:auto;float:center;"/></p> |
| + | </div><br> | ||
<p>To describe this mathematically we started with the assumption that none of the substrates would induce competitive inhibition. If this was the case, the modeling would be simple. We would consider the observed velocity to be a linear combination of the three singular responses to aldehyde.</p><br> | <p>To describe this mathematically we started with the assumption that none of the substrates would induce competitive inhibition. If this was the case, the modeling would be simple. We would consider the observed velocity to be a linear combination of the three singular responses to aldehyde.</p><br> | ||
<div style="margin-left:auto;margin-right:auto;"> | <div style="margin-left:auto;margin-right:auto;"> | ||
| - | <img src="https://static.igem.org/mediawiki/2014/5/56/ThreeSubstrates.png" style="border:1.5px solid #212f20;"/></div><br> | + | <p align="center"><img src="https://static.igem.org/mediawiki/2014/5/56/ThreeSubstrates.png" style="border:1.5px solid #212f20;"/></p> |
| + | </div><br> | ||
<p> | <p> | ||
Now our model has three unknown concentrations, but only one equation: <b>this is why we need three enzymes</b>. Now we consider the entire model:<br> | Now our model has three unknown concentrations, but only one equation: <b>this is why we need three enzymes</b>. Now we consider the entire model:<br> | ||
<div style="margin:auto;display:block;float:center"> | <div style="margin:auto;display:block;float:center"> | ||
| - | <img src="https://static.igem.org/mediawiki/2014/5/54/CatalyticMatrix.png" width="400px" style="margin-left:auto;margin-right:auto;border:1.5px solid #212f20;"/><br></div> | + | <p align="center"><img src="https://static.igem.org/mediawiki/2014/5/54/CatalyticMatrix.png" width="400px" style="margin-left:auto;margin-right:auto;border:1.5px solid #212f20;"/></p> |
| + | <br></div> | ||
<br><p> | <br><p> | ||
To test our model we built a combinatorial set of aldehydes. We chose three representative aldehydes from each bin, saturated medium, saturated long, and unsaturated. The three aldehydes were chosen such that the enzymes response to each would best represent their respective groups. We created a total of 64 different combinations by mixing Pentanal, Decanal, and <i>E</i>-2-Decenal in four different values, 0 µM, 10 µM, 100 µM, & 1000 µM. Three combinatorial well plates were made and mixed with each enzyme separately. The observed velocity is recorded in each well.</p><br> | To test our model we built a combinatorial set of aldehydes. We chose three representative aldehydes from each bin, saturated medium, saturated long, and unsaturated. The three aldehydes were chosen such that the enzymes response to each would best represent their respective groups. We created a total of 64 different combinations by mixing Pentanal, Decanal, and <i>E</i>-2-Decenal in four different values, 0 µM, 10 µM, 100 µM, & 1000 µM. Three combinatorial well plates were made and mixed with each enzyme separately. The observed velocity is recorded in each well.</p><br> | ||
<div style="margin:auto;display:block;float:center"> | <div style="margin:auto;display:block;float:center"> | ||
| - | <img src="https://static.igem.org/mediawiki/2014/1/1d/64Combinations.png" width="800px" style="margin-left:auto;margin-right:auto;"/><br></div> | + | <p align="center"><img src="https://static.igem.org/mediawiki/2014/1/1d/64Combinations.png" width="800px" style="margin-left:auto;margin-right:auto;"/></p> |
| + | <br></div> | ||
<p><br> | <p><br> | ||
The catalytic matrix is inverted and multiplied by the observed velocity in each well.<br> | The catalytic matrix is inverted and multiplied by the observed velocity in each well.<br> | ||
</p> | </p> | ||
<div style="margin:auto;display:block;float:center"> | <div style="margin:auto;display:block;float:center"> | ||
| - | <img src="https://static.igem.org/mediawiki/2014/1/1f/Inverse.png" width="400px" style="margin-left:auto;margin-right:auto;border:1.5px solid #212f20;"/></div> | + | <p align="center"><img src="https://static.igem.org/mediawiki/2014/1/1f/Inverse.png" width="400px" style="margin-left:auto;margin-right:auto;border:1.5px solid #212f20;"/></p> |
| + | </div> | ||
</p> | </p> | ||
<p><div style="margin:auto;display:block;float:center"> | <p><div style="margin:auto;display:block;float:center"> | ||
| - | <img src="https://static.igem.org/mediawiki/2014/1/19/OliVEoil_Set.jpg" style="margin-left:auto;margin-right:auto;border:1.5px solid #212f20;"/></div> | + | <p align="center"><img src="https://static.igem.org/mediawiki/2014/1/19/OliVEoil_Set.jpg" style="margin-left:auto;margin-right:auto;border:1.5px solid #212f20;"/></p> |
| + | </div> | ||
</p> | </p> | ||
Revision as of 01:14, 18 October 2014
Our signal processing data set can be downloaded here.
Mathematical Approach
To model our system, we first focused our attention on the linear range of our enzyme's Michaelis Menten plot. The linear range of this plot is governed by the above relationship. This was useful for describing single aldehydes, but Olive Oil contains many aldehydes and the enzymatic response is different for each one.
To describe this mathematically we started with the assumption that none of the substrates would induce competitive inhibition. If this was the case, the modeling would be simple. We would consider the observed velocity to be a linear combination of the three singular responses to aldehyde.
Now our model has three unknown concentrations, but only one equation: this is why we need three enzymes. Now we consider the entire model:
To test our model we built a combinatorial set of aldehydes. We chose three representative aldehydes from each bin, saturated medium, saturated long, and unsaturated. The three aldehydes were chosen such that the enzymes response to each would best represent their respective groups. We created a total of 64 different combinations by mixing Pentanal, Decanal, and E-2-Decenal in four different values, 0 µM, 10 µM, 100 µM, & 1000 µM. Three combinatorial well plates were made and mixed with each enzyme separately. The observed velocity is recorded in each well.
The catalytic matrix is inverted and multiplied by the observed velocity in each well.
