Team:Virginia/Modeling

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</head>
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<body>
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/* `Container
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 +
      <div style="clear: both;"></div>
 +
    </ul>
 +
        </header>
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<div id="another">
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<h2><strong>Goals of model</strong></h2>
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The goal of the Nygone project is to grow modified <em>E. coli</em></ins><em> </em>cells on filters that will be put in water treatment plants to remove microplastics. However, due to time constraints, we are unable to engineer the final product. Hence a mathematical model was built in order to:
-
}
+
</p>
 +
<ol>
 +
<li>Give predictions on the amount of bacteria required to produce a sufficient amount of MnP enzyme to degrade micro-particles of nylon in water</li>
 +
<li>Simulate the distribution of MnP enzyme produced by bacteria</li>
 +
<li>Simulate the degradation of nylon micro-particles by MnP particles in water</li>
 +
<li>Analyze the sensitivity of MnP production and nylon degradation to various factors including concentration of bacteria, production rate of MnP by unit bacteria, volume, and flow rate of waste water.</li>
 +
</ol>
 +
<p>
 +
    <strong></strong>
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</p>
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<h2><strong>General model</strong></h2>
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    The model was separated into two parts:
 +
</p>
 +
<ol>
 +
  <li>Kinetics of MnP enzyme in water<br>Rate of change of MnP concentration in water = rate of diffusion + rate of production - rate of elimination</li>
-
.container_12 .grid_1 {
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<center><img src = "https://static.igem.org/mediawiki/2014/a/ae/VGEM_ratechangeMnPConc.JPG"></center>
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    Michaelis-Menten Equation</li>
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+
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/* `Clear Floated Elements
+
-
----------------------------------------------------------------------------------------------------*/
+
-
 
+
-
/* http://sonspring.com/journal/clearing-floats */
+
-
 
+
-
.clear {
+
-
  clear: both;
+
-
  display: block;
+
-
  overflow: hidden;
+
-
  visibility: hidden;
+
-
  width: 0;
+
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  height: 0;
+
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}
+
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+
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/* http://www.yuiblog.com/blog/2010/09/27/clearfix-reloaded-overflowhidden-demystified */
+
-
 
+
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.clearfix:before,
+
-
.clearfix:after,
+
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.container_12:before,
+
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.container_12:after {
+
-
  content: '.';
+
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  display: block;
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  overflow: hidden;
+
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  visibility: hidden;
+
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  font-size: 0;
+
-
  line-height: 0;
+
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  width: 0;
+
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+
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.container_12:after {
+
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  clear: both;
+
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}
+
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+
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/*
+
-
  The following zoom:1 rule is specifically for IE6 + IE7.
+
-
  Move to separate stylesheet if invalid CSS is a problem.
+
-
*/
+
-
 
+
-
.clearfix,
+
-
.container_12 {
+
-
  zoom: 1;
+
-
}
+
-
</style>
+
 +
<p>
 +
    E is the MnP enzyme, S is the nylon substrate. kf and kr are forward and reverse reaction constants of enzyme-substrate complex formation. k<sub>cat</sub>
 +
is the reaction coefficient for oxidation of nylon substrate, and the turnover number, defined as the maximum number of substrate molecules converted to product per enzyme molecule per unit time.
 +
<center><img  id="picsmall" src="https://static.igem.org/mediawiki/2014/b/b7/VGEM_NylonEq.JPG"></center>
 +
<div id="nobullets">
 +
<h2><strong>Simplification:</strong></h2>
 +
After a visit to the local water treatment plant, we obtained a numerical value for the following parameters:
 +
<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Total volume of chamber where filter will be inserted = 0.879 m<sup>3</sup></li>
 +
<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Average flow rate = 0.19 m<sup>3</sup>/min</li>
 +
<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Dimensions of water chamber: 0.46 m (length), 0.91 m (width), 2.1 m (height)</li><br>
 +
<center><img id="picpic" src="https://static.igem.org/mediawiki/2014/3/31/Vgemzipics.JPG"></center><br>
 +
The diffusivity of MnP was estimated as follows: *
 +
  <li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Diffusivity of MnP in water = 0.6e<sup>3</sup> m<sup>2</sup>/s</li>
 +
<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Pe = velocity * linear dimension / mass diffusivity = 74.33>>1</li>
 +
<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Since Pe is much larger than 1, the diffusion term is taken out from the equation.</li>
 +
<li>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The kinetic model is simplified as:</li>
-
<div class="container_12">
 
-
<div class="grid_6">
 
-
<span class="menuHeader">What is the iGEM Competition?</span>
 
-
<p>The International Genetically Engineered Machine competition (iGEM) is the premiere undergraduate Synthetic Biology competition. Student teams are given a kit of biological parts at the beginning of the summer from the Registry of Standard Biological Parts. Working at their own schools over the summer, they use these parts and new parts of their own design to build biological systems and operate them in living cells. <a href="https://igem.org/About">more...</a>
 
-
</div>
 
-
<div class="grid_3">
 
-
<ul>
 
-
<li><a href="https://igem.org/About">What is iGEM?</a></li>
 
-
<li><a href="https://igem.org/Previous_iGEM_Competitions">Previous iGEM Competitions</a></li>
 
-
<li><a href="https://igem.org/Press_Kit">iGEM Press Kit</a></li>
 
-
<li><a href="http://mail.igem.org/mailman/listinfo/interest">Join the iGEM Mailing List</a></li>
 
-
<li><a href="https://igem.org/Sponsors">iGEM 2014 Sponsors</a></li>
 
-
<li><a href="https://igem.org/Sponsorship">Sponsor iGEM</a></li>
 
-
</ul>
 
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</div>
 
-
<div class="grid_3">
 
-
<ul><span class="menuHeader">Quick Links</span>
 
-
<li><a href="https://igem.org">iGEM Foundation</a></li>
 
-
<li><a href="https://2014hs.igem.org">iGEM 2014 High School</a></li>
 
-
<li><a href="https://2013.igem.org">iGEM 2013 Competition</a></li>
 
-
<li><a href="http://parts.igem.org">Registry of Standard Biological Parts</a></li>
 
-
</ul>
 
-
</div>
 
</div>
</div>
 +
<center><img src="https://static.igem.org/mediawiki/2014/f/f7/VGEM_perkEq.JPG"></center>
 +
<center><span id="smallText"> *The diffusivity of MnP was not found, this estimation was based on the diffusivity table of salt)
 +
Using the above values, the Peclet number was calculated<span id="smallText"></center>
 +
<h2><strong>Assumptions: </strong></h2>
 +
<ol>
 +
    <li>Monolayer of bacteria growth on the surface of the filter inserts (i.e. MnP produced will not be trapped inside the biofilms of <em>E.coli</em> ).</li>
-
</div>
+
<li>In this model, the total number of bacteria is assumed to be constant.</li>
-
</li>
+
-
<li>
+
-
<a href="#" class="dropToggle">COMPETITION</a>
+
-
<div class="navDropMenu">
+
-
+
-
<style type="text/css">
+
-
/*
+
-
  960 Grid System ~ Core CSS.
+
-
  Learn more ~ http://960.gs/
+
-
  Licensed under GPL and MIT.
+
<li>Rate of production of MnP enzyme is assumed to be linearly related to the total amount of bacteria. However, this relationship can be easily modified in the model.</li>
-
*/
+
<li>MnP and nylon micro-particles are distributed evenly in the water (i.e. minimal time is taken for MnP and nylon particles to diffuse out evenly inside the chamber).</li>
 +
<li>The size (width and height only) of the chamber is small.</li>
 +
</ol>
 +
<p>
 +
    <strong></strong>
 +
</p>
-
/*
+
<h2><strong>Limits and constraints:</strong></h2>
-
  Forces backgrounds to span full width,
+
<ol>
-
  even if there is horizontal scrolling.
+
<li>The model is only applicable to a small container where diffusion across space takes little time to occur.</li>
-
  Increase this if your layout is wider.
+
-
  Note: IE6 works fine without this fix.
+
<li>When the number of bacteria is large, multiple layers of bacteria will be built up. This may hinder the diffusion of MnP particles as they would be trapped within the biofilm. As a result, the linear relationship between bacteria number and MnP production rate would no longer be valid.</li>
-
*/
+
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+
-
 
+
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/* http://sonspring.com/journal/clearing-floats */
+
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+
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.clear {
+
-
  clear: both;
+
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  display: block;
+
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  overflow: hidden;
+
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  visibility: hidden;
+
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  width: 0;
+
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  height: 0;
+
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}
+
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/* http://www.yuiblog.com/blog/2010/09/27/clearfix-reloaded-overflowhidden-demystified */
+
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+
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+
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+
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.container_12:before,
+
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.container_12:after {
+
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  content: '.';
+
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  display: block;
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  visibility: hidden;
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+
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  clear: both;
+
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/*
+
-
  The following zoom:1 rule is specifically for IE6 + IE7.
+
-
  Move to separate stylesheet if invalid CSS is a problem.
+
-
*/
+
-
 
+
-
.clearfix,
+
-
.container_12 {
+
-
  zoom: 1;
+
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}
+
-
</style>
+
 +
<h2><strong>Result and Interpretation:</strong></h2>
 +
<p>
 +
    Since some of our parameters are not yet finalized, this main purpose of this section is a demonstration of the capability of the model and the ability to predict an expected outcome. The shape of the graphs may change if a different set of parameters is used.
 +
</p>
-
<div class="container_12">
+
<div>
-
<div class="grid_3">
+
<center><h6><b>Figure 1.1</b></h6></center>
-
<ul><span class="menuHeader">Getting Started</span>
+
<center><img id="picsmall" src="https://static.igem.org/mediawiki/2014/c/cc/VGEM_resultsAndInterp.JPG"><center>
-
<li><a href="https://2014.igem.org/Start_A_Team">Start a Team</a></li>
+
-
<li><a href="https://2014.igem.org/Funding">Funding How-To</a></li>
+
-
<li><a href="https://2014.igem.org/Gender">Gender Balance</a></li> 
+
-
<li><a href="https://2014.igem.org/Requirements">Requirements</a></li>
+
-
</ul>
+
-
</div>
+
-
<div class="grid_3">
+
-
<ul><span class="menuHeader">Participation</span>
+
-
<li><a href="https://2014.igem.org/Calendar_of_Events">Calendar of Events</a></li>
+
-
<li><a href="https://igem.org/IGEM_2014_Registration">2014 Registration</a></li>
+
-
<li><a href="https://2014.igem.org/Fees">2014 Fees</a></li>
+
-
<li><a href="https://2014.igem.org/Sections">Sections: Undergrad &amp; Overgrad</a></li>
+
-
<li><a href="https://2014.igem.org/Tracks">Tracks</a></li>
+
-
<li><a href="https://2014.igem.org/Meetups">Team Meetups</a></li>
+
-
</ul>
+
-
</div>
+
-
<div class="grid_3">
+
-
<ul><span class="menuHeader">&nbsp;</span>
+
-
<li><a href="https://2014.igem.org/Workshops">Teacher's Workshops</a></li>
+
-
<li><a href="https://2014.igem.org/Community">Community</a></li>
+
-
<li><a href="https://2014.igem.org/Safety">Safety</a></li>
+
-
<li><a href="https://igem.org/Security">Security</a></li>
+
-
<li><a href="https://2014.igem.org/Judging">Judging</a></li>
+
-
<li><a href="https://2014.igem.org/Giant_Jamboree">Giant Jamboree</a></li>
+
-
</ul>
+
-
</div>
+
-
<div class="grid_3">
+
-
<ul><span class="menuHeader">Media</span>
+
-
<li><a href="https://2014.igem.org/Photo_Gallery">iGEM Photo Gallery</a></li>
+
-
<li><a href="https://2014.igem.org/IGEM_Publicity">iGEM Publicity</a></li>
+
-
<li><a href="https://2014.igem.org/IGEM_Publications">Publications</a></li>
+
-
</ul>
+
-
</div>
+
</div>
</div>
 +
<p>Figure 1.1 shows the production of MnP and degradation of nylon over time. MnP reaches a constant level of 3000 units after 30 hours while nylonconcentration decreases to zero within 10 hours. MnP is in excess and therefore a smaller amount of starting bacteria can be used.</p>
 +
<center><table border="0">
 +
<tr><td><center><h6>Figure 2.1</h6></center><img id="picpic" src="https://static.igem.org/mediawiki/2014/8/8e/VGEM_model_2.1.JPG"></td>
 +
<td><center><h6>Figure 2.2</h6></center><img id="picpic" src="https://static.igem.org/mediawiki/2014/7/74/VGEM_model_2.2.JPG"></td></tr>
 +
</table></center>
 +
<p>
 +
    The concentration of MnP and nylon after 60 hours with respect to different starting concentrations of bacteria. Figure 2.1: MnP increase exponentially
 +
    with exponential increase in starting concentration of bacteria. Figure 2.2: Given the current set of parameters, all nylon will be degraded after 60 hours
 +
    for a small number of starting bacteria.
 +
</p>
 +
<center><table border="0">
 +
<tr><td><center><h6>Figure 2.1</h6></center><img id="picpic" src="https://static.igem.org/mediawiki/2014/3/36/VGEM_mnpGraph1.JPG"></td>
 +
<td><center><h6>Figure 2.2</h6></center><img id="picpic" src="https://static.igem.org/mediawiki/2014/5/5f/VGEM_mnpGraph2.JPG"></td></tr>
 +
</table></center>
 +
<p>
 +
    Response of MnP concentration to a range of parameters: Figure 2.1 shows the concentration of MnP over time for different values of p, which is the rate of
 +
    production of MnP per unit of bacteria. Figure 2.2 is the concentration of MnP after 60 hours with respect to different values of p.
 +
</p>
 +
<center><table border="0">
 +
<tr><td><center><h6>Figure 3.1</h6></center><img id="picpic" src="https://static.igem.org/mediawiki/2014/c/c5/Vgem_modelsensative1.JPG"></td>
 +
<td><center><h6>Figure 3.2</h6></center><img id="picpic" src="https://static.igem.org/mediawiki/2014/e/e5/Vgem_modelsensative2.JPG"></td></tr>
 +
</table></center>
 +
<p>
 +
    Sensitivity analysis: Figure 3.1 gives the sensitivity of MnP concentration when there is a 1 percent increase in a given set of parameters. The parameters
 +
    from left to right are: rate of production of MnP, starting amount of bacteria, volume of chamber, flow rate, forward reaction constant of MnP-nylon
 +
    complex formation, reverse reaction constant of MnP-nylon complex formation, forward reaction constant of oxidation of nylon particles (degradation). The
 +
    sensitivity will change if a different percentage increase is used. Figure 3.2 shows the perturbation on the level of MnP concentration, bacterial level,
 +
    Nylon concentration and Nylon-MnP complex concentration with respect to one percent change in the set of parameters.
 +
</p>
-
</div>
+
<h2><b>Downloads</b></h2>
-
</li>
+
<div id="theLinks">
-
<li>
+
<div id="nobullets">
-
<a href="#">RESOURCES</a>
+
-
<div class="navDropMenu">
+
-
+
-
<style type="text/css">
+
-
/*
+
-
  960 Grid System ~ Core CSS.
+
-
  Learn more ~ http://960.gs/
+
-
 
+
-
  Licensed under GPL and MIT.
+
-
*/
+
-
 
+
-
/*
+
-
  Forces backgrounds to span full width,
+
-
  even if there is horizontal scrolling.
+
-
  Increase this if your layout is wider.
+
-
 
+
-
  Note: IE6 works fine without this fix.
+
-
*/
+
-
 
+
-
body {
+
-
min-width: 960px;
+
-
color: #000;
+
-
}
+
-
 
+
-
/* `Container
+
-
----------------------------------------------------------------------------------------------------*/
+
-
 
+
-
.container_12 {
+
-
  margin-left: auto;
+
-
  margin-right: auto;
+
-
  width: 960px;
+
-
}
+
-
 
+
-
/* `Grid >> Global
+
-
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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/* `Grid >> Children (Alpha ~ First, Omega ~ Last)
+
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+
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+
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.alpha {
+
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+
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}
+
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+
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.omega {
+
-
  margin-right: 0;
+
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+
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+
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/* `Grid >> 12 Columns
+
-
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+
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+
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+
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+
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+
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+
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</style>
+
-
 
+
-
 
+
-
<div class="container_12">
+
-
<div class="grid_3">
+
-
<ul><span class="menuHeader">Team Links</span>
+
-
<li><a href="https://igem.org/Team_List?year=2014">2014 Team List</a></li>
+
-
<li><a href="https://igem.org/Team_Wikis?year=2014">2014 Team Wikis</a></li>
+
-
<li><a href="https://igem.org/Team_Parts?year=2014">2014 Team Parts</a></li>
+
-
<li><a href="https://igem.org/Team_Tracks?year=2014">2014 Team Tracks</a></li>
+
-
<li><a href="https://igem.org/Team_Judging?year=2014">2014 Team Judging Forms</a></li>
+
-
</ul>
+
-
</div>
+
-
<div class="grid_3">
+
-
<ul><span class="menuHeader">General</span>
+
-
<li><a href="https://igem.org/Previous_iGEM_Competitions">Previous iGEM Competitions</a></li>
+
-
<li><a href="https://2014.igem.org/Wiki_How-To">Wiki How-To</a></li>
+
-
<li><a href="https://igem.org/Videos">Videos</a></li>
+
-
<li><a href="https://igem.org/Forum">Forums</a></li>
+
-
<li><a href="https://igem.org/FAQ">FAQ</a></li>
+
-
</ul>
+
-
</div>
+
-
<div class="grid_3">
+
-
<ul><span class="menuHeader">Lab Resources</span>
+
-
<li><a href="http://parts.igem.org">Registry of Standard Biological Parts</a></li>
+
-
<li><a href="http://parts.igem.org">Protocols</a></li>
+
-
</ul>
+
-
</div>
+
-
<div class="grid_3">
+
-
<ul><span class="menuHeader">Affiliated</span>
+
-
<li><a href="https://2014.igem.org/Partner_Offers">Partner Offers</a></li>
+
-
<li><a href="https://2014.igem.org/Funding">Funding Opportunities</a></li>
+
-
</ul>
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+
-
<p style="color:red;"> <b> Please note that all information on this page is in a draft version. Please check back often for details. </b> </p>
+
-
 
+
-
<p> In this page you will find information about:</p>
+
-
 
+
<ul>
<ul>
-
<li>Wiki Requirements</li>
+
<table id="downloadstab">
-
<li>Wiki Restrictions</li>
+
<tr>
-
<li>Team Wiki examples</li>
+
<td><a target="_blank" href="https://static.igem.org/mediawiki/2014/9/9b/MnPDesensitization.m">MnP Desensitization</a></td>
-
<li>Design Tips and suggestions</li>
+
<td><a target="_blank" href="https://static.igem.org/mediawiki/2014/1/1a/MnPfunc.m">MnP Function</a></td>
-
<li> <a href= "#wikitemplates"> Wiki templates </a></li>
+
<td><a target="_blank" href="https://static.igem.org/mediawiki/2014/9/98/ResponseToP.m">Response To P</a></td>
-
<li>FAQS</li>
+
</tr>
-
</ul>
+
</table>
-
 
+
-
 
+
-
 
+
-
 
+
-
<p>Your team's project must be documented on the iGEM 2014 wiki, the parts used in your project must be documented on the <a href="http://parts.igem.org">Registry of Standard Biological Parts</a>. You have the freedom to be creative, but a few specific rules apply:</p>
+
-
 
+
-
<h3>2014.igem.org/Team:Team_Name</h3>
+
-
<p>All iGEM 2014 teams will be given a namespace on the iGEM 2014 wiki with their team name. Teams are allowed to create and edit pages within their respective team namespace.</p>
+
-
 
+
-
<h3>Upload to 2014.igem.org server</h3>
+
-
<p>All team pages, images, documents and code must be hosted on the 2014.igem.org server. We preserve all iGEM content on our own servers so future teams can learn from what you have done. When you store content on your own sites or servers, after time, links might become broken, sites might go down, and information will be lost.
+
-
<ul>Use the <a href="https://2014.igem.org/Special:Upload">wiki upload tool</a> to upload your files.
+
-
<li>Please make sure to name your files clearly and uniquely: <i>File:</i><b>Team_Name_Flow_Cytometry_01.png</b>, instead of <i>File:</i><b>1.png</b></li>
+
-
</ul>
+
-
</p>
+
-
 
+
-
<h3>No Adobe Flash</h3>
+
-
<p>Flash is not permitted on the iGEM 2014 wiki. Adobe flash is 100% proprietary and you cannot view the source like you can with our wiki. We chose wikis for teams to build their projects so the source code would be available for future teams, to build on the concept of open source. Flash can also be hosted on external sites and we want 100% of the content of our wikis to be on our wikis. </p>  
+
-
 
+
-
<h3>Deadlines and the Wiki Freeze</h3>
+
-
<p>The team's project description must be documented on their iGEM Team Wiki by the deadline. The project description should be 1-3 paragraphs and only needs to include an up-to-date explanation of the project.</p>
+
-
<p>The team's wiki must include a link to the completed Safety form and an attributions section.</p>
+
-
 
+
-
<h3>iGEM Logo</h3>
+
-
<p>All iGEM Team Wikis must include the iGEM logo at the top of the page and a visible link back to the iGEM 2014 Wiki Main Page in the header (or at the top of the page). All wiki pages must preserve the user editing menu (notifications, username, messages, history, edit). In the case where the user heading is not visible, an automatic heading will be overlaid on top of the wiki page(s) where the heading is missing. </p>
+
-
 
+
-
<h3>The iGEM Login Bar</h3>
+
-
<p>The iGEM Login Bar is a 20 pixel high, full-width menu bar that exists on all 2014.igem.org pages. It contains:
+
-
<ul>
+
-
<li>wiki tools (edit, history, watch, etc.)</li>
+
-
<li>login</li>
+
-
</ul>
+
-
All iGEM 2014 Team Wikis are required to have the Login Bar. Please keep this in mind as you design your wiki.</p>
+
-
 
+
-
 
+
-
 
+
-
<h3 id="wikitemplates"> Wiki Templates </h3>
+
-
<p> This year we have created a set of template pages that you may for your wiki! Feel free to edit them as much as you want </p>
+
-
<a href="https://2014.igem.org/WikitemplateA_home ">Wiki Template A </a></br>
+
-
<a href="https://2014.igem.org/WikitemplateB_home ">Wiki Template B </a>
+
-
 
+
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<li><a href="https://igem.org/Sponsors">Sponsors</a></li>
 
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<li><a href="https://igem.org/Main_Page">  igem.org</a></li>
 
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<li><a href="http://parts.igem.org/Main_Page"> Registry</a> </li>
 
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.newfooter, .pushfooter {height: 130px; clear:both; margin-top: 15px;}
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#footerheaderdesc img {display: block; position: relative; padding-right: 20px; float:left;}
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                <li id="t-upload"><a href="/Special:Upload"
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                  title="Upload files [u]" accesskey="u">Upload file</a>
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Latest revision as of 23:01, 21 November 2014


Modeling

Goals of model

The goal of the Nygone project is to grow modified E. coli cells on filters that will be put in water treatment plants to remove microplastics. However, due to time constraints, we are unable to engineer the final product. Hence a mathematical model was built in order to:

  1. Give predictions on the amount of bacteria required to produce a sufficient amount of MnP enzyme to degrade micro-particles of nylon in water
  2. Simulate the distribution of MnP enzyme produced by bacteria
  3. Simulate the degradation of nylon micro-particles by MnP particles in water
  4. Analyze the sensitivity of MnP production and nylon degradation to various factors including concentration of bacteria, production rate of MnP by unit bacteria, volume, and flow rate of waste water.

General model

The model was separated into two parts:

  1. Kinetics of MnP enzyme in water
    Rate of change of MnP concentration in water = rate of diffusion + rate of production - rate of elimination
    2. c is the current concentration of MnP, dp/dt is the rate of production of MnP, and J is the flow rate.
  2. Reaction of MnP particles with nylon
    Michaelis-Menten Equation

E is the MnP enzyme, S is the nylon substrate. kf and kr are forward and reverse reaction constants of enzyme-substrate complex formation. kcat is the reaction coefficient for oxidation of nylon substrate, and the turnover number, defined as the maximum number of substrate molecules converted to product per enzyme molecule per unit time.

Simplification:

After a visit to the local water treatment plant, we obtained a numerical value for the following parameters:
  •           Total volume of chamber where filter will be inserted = 0.879 m3
  •           Average flow rate = 0.19 m3/min
  •           Dimensions of water chamber: 0.46 m (length), 0.91 m (width), 2.1 m (height)


    • The diffusivity of MnP was estimated as follows: *
  •           Diffusivity of MnP in water = 0.6e3 m2/s
  •           Pe = velocity * linear dimension / mass diffusivity = 74.33>>1
  •           Since Pe is much larger than 1, the diffusion term is taken out from the equation.
  •           The kinetic model is simplified as:
    • *The diffusivity of MnP was not found, this estimation was based on the diffusivity table of salt) Using the above values, the Peclet number was calculated

    Assumptions:

    1. Monolayer of bacteria growth on the surface of the filter inserts (i.e. MnP produced will not be trapped inside the biofilms of E.coli ).
    2. In this model, the total number of bacteria is assumed to be constant.
    3. Rate of production of MnP enzyme is assumed to be linearly related to the total amount of bacteria. However, this relationship can be easily modified in the model.
    4. MnP and nylon micro-particles are distributed evenly in the water (i.e. minimal time is taken for MnP and nylon particles to diffuse out evenly inside the chamber).
    5. The size (width and height only) of the chamber is small.

    Limits and constraints:

    1. The model is only applicable to a small container where diffusion across space takes little time to occur.
    2. When the number of bacteria is large, multiple layers of bacteria will be built up. This may hinder the diffusion of MnP particles as they would be trapped within the biofilm. As a result, the linear relationship between bacteria number and MnP production rate would no longer be valid.

    Result and Interpretation:

    Since some of our parameters are not yet finalized, this main purpose of this section is a demonstration of the capability of the model and the ability to predict an expected outcome. The shape of the graphs may change if a different set of parameters is used.

    Figure 1.1

    Figure 1.1 shows the production of MnP and degradation of nylon over time. MnP reaches a constant level of 3000 units after 30 hours while nylonconcentration decreases to zero within 10 hours. MnP is in excess and therefore a smaller amount of starting bacteria can be used.

    Figure 2.1
    Figure 2.2

    The concentration of MnP and nylon after 60 hours with respect to different starting concentrations of bacteria. Figure 2.1: MnP increase exponentially with exponential increase in starting concentration of bacteria. Figure 2.2: Given the current set of parameters, all nylon will be degraded after 60 hours for a small number of starting bacteria.

    Figure 2.1
    Figure 2.2

    Response of MnP concentration to a range of parameters: Figure 2.1 shows the concentration of MnP over time for different values of p, which is the rate of production of MnP per unit of bacteria. Figure 2.2 is the concentration of MnP after 60 hours with respect to different values of p.

    Figure 3.1
    Figure 3.2

    Sensitivity analysis: Figure 3.1 gives the sensitivity of MnP concentration when there is a 1 percent increase in a given set of parameters. The parameters from left to right are: rate of production of MnP, starting amount of bacteria, volume of chamber, flow rate, forward reaction constant of MnP-nylon complex formation, reverse reaction constant of MnP-nylon complex formation, forward reaction constant of oxidation of nylon particles (degradation). The sensitivity will change if a different percentage increase is used. Figure 3.2 shows the perturbation on the level of MnP concentration, bacterial level, Nylon concentration and Nylon-MnP complex concentration with respect to one percent change in the set of parameters.

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