Difference between revisions of "Team:MIT/ModelingCHutch"

Line 43: Line 43:
 
<div id = "title">
 
<div id = "title">
 
Detailed Description of Modeling Methods
 
Detailed Description of Modeling Methods
−
</div>
 
−
 
−
<div class = "subtitle">
 
−
                      Description of Dynamic Flux Balance Analysis
 
 
</div>
 
</div>
  
Line 62: Line 58:
  
 
<div class = "text" align = "center">
 
<div class = "text" align = "center">
 +
</center>
 +
<br><!--Adds a line break-->
 +
<p>In the absence of chromate, \(C_{V}\)<!--Content surrounded by \(\) represents inline equations and symbols from mathjax, they will be displayed as the latex output symbols and equations.-->, the \(ChrB\) protein forms a dimer, \(D\), which then binds the pChr promoter, forming a closed promoter, \(P_{c}\). This promoter cannot function so no green fluorescent protein, \(GFP\), is produced. In the presence of chromate, the \(ChrB\) dimer instead binds to chromate forming a complex, \([C_{V} \cdot D]\). This allows the open promoter, \(P_{o}\) to function and produce \(GFP\). The reactions can be described as chemical equations, where the parameters \(k\) are the kinetic rates:</p>
 +
<!--Mathjax equations are surrounded by $$ $$ and will be displayed as latex output.-->
 +
<br><font size="4">
 +
    $$
 +
   
 +
\ce{ ->[k_{1}] ChrB ->[k_{2}]}\\
 +
\ce{ ChrB + ChrB <=>[k_{3}][k_{-3}] D ->[k_{5}]}\\
 +
\ce{ D + \text{\(C_{V}\)}  <=>[k_{4}][k_{-4}] [D \cdot C_{V}]}\\
 +
\ce{ D + P_{o} <=>[k_{6}][k_{-6}] P_{c} }\\
 +
\ce{ P_{o} ->[k_{7}] GFP + P_{o} }\\
 +
\ce{GFP ->[k_{8}] }
 +
$$
 +
</font>
 +
<p>This system was written as a system of ODEs and simulations were run with chromate added at specific times to investigate change in concentration over time. The steady state in the presence of chromate was calculated as the \(GFP\) reached a steady level and did not change once there.  Once chromate was removed from the system the \(GFP\) decreased again as expected. The steady state analysis showed that there was a 18927.20% increase of \(GFP\) concentration from the initial concentration.</p>
 +
<p>We wish to compare the modified pathway with the original pathway, where only one plasmid is used:</p>
 +
<a class="anchor" id="cfig2"></a><!--Set anchor so that figure can be referred back to-->
 +
<br><!--Adds a line break-->
 +
<center>
 +
<figure1><!--The figure tag inserts a figure with defined border from the provided source link with a caption (figcaption).-->
 +
<img  src='https://static.igem.org/mediawiki/2015/5/58/TeamDundee_plasmid_wt_tiny.png' height="40%" width="auto"/>
 +
<figcaption>Figure 2: Plasmid map of the original biobrick system, <a href="http://parts.igem.org/Part:BBa_K1058008"><u><b>(BBa_K1058008)</b></u></a>.</figcaption>
 +
</figure1>
 +
</center>
 
</div>
 
</div>
 
</div>
 
</div>

Revision as of 05:29, 18 September 2015


Detailed Description of Modeling Methods
Equations test
\(\require{mhchem}\) \ce{C6H5-CHO} \ce{$A$ ->[\ce{+H2O}] $B$} \ce{SO4^2- + Ba^2+ -> BaSO4 v}

In the absence of chromate, \(C_{V}\), the \(ChrB\) protein forms a dimer, \(D\), which then binds the pChr promoter, forming a closed promoter, \(P_{c}\). This promoter cannot function so no green fluorescent protein, \(GFP\), is produced. In the presence of chromate, the \(ChrB\) dimer instead binds to chromate forming a complex, \([C_{V} \cdot D]\). This allows the open promoter, \(P_{o}\) to function and produce \(GFP\). The reactions can be described as chemical equations, where the parameters \(k\) are the kinetic rates:


$$ \ce{ ->[k_{1}] ChrB ->[k_{2}]}\\ \ce{ ChrB + ChrB <=>[k_{3}][k_{-3}] D ->[k_{5}]}\\ \ce{ D + \text{\(C_{V}\)} <=>[k_{4}][k_{-4}] [D \cdot C_{V}]}\\ \ce{ D + P_{o} <=>[k_{6}][k_{-6}] P_{c} }\\ \ce{ P_{o} ->[k_{7}] GFP + P_{o} }\\ \ce{GFP ->[k_{8}] } $$

This system was written as a system of ODEs and simulations were run with chromate added at specific times to investigate change in concentration over time. The steady state in the presence of chromate was calculated as the \(GFP\) reached a steady level and did not change once there. Once chromate was removed from the system the \(GFP\) decreased again as expected. The steady state analysis showed that there was a 18927.20% increase of \(GFP\) concentration from the initial concentration.

We wish to compare the modified pathway with the original pathway, where only one plasmid is used:


Figure 2: Plasmid map of the original biobrick system, (BBa_K1058008).