Team:Tsinghua-A/Modeling/P3A

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<P><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling"><FONT FACE="Arial, sans-serif"><SPAN LANG="en-US"><FONT SIZE=5 STYLE="font-size: 20pt">Modeling</A>::</FONT><FONT COLOR="#0099ff"><FONT SIZE=5 STYLE="font-size: 20pt">Dimensionless
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<P><A HREF="https://2011.igem.org/Team:Tsinghua-A/Modeling"><FONT FACE="Arial, sans-serif"><SPAN LANG="en-US"><FONT SIZE=5 STYLE="font-size: 20pt">Modeling</A>::</FONT><FONT COLOR="#0099ff"><FONT SIZE=5 STYLE="font-size: 20pt">Dimensionless Model</FONT></FONT></SPAN></FONT></P>
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Model</FONT></FONT></SPAN></FONT></P>
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<P ALIGN=LEFT STYLE="text-decoration: none"><FONT COLOR="#99284c"><FONT FACE="Arial, sans-serif"><FONT SIZE=4 STYLE="font-size: 16pt"><SPAN LANG="en-US"><SPAN STYLE="background: #ffffff">NOTICE:
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please enable the pdf_application PlugIns to load this page</SPAN></SPAN></FONT></FONT></FONT></P>
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<div id="toctitle">
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<P ALIGN=CENTER><embed id="e" width="900" height="1200" type="application/pdf" src="https://static.igem.org/mediawiki/2011/c/ce/Modeling_Wiki-Part3.pdf"></embed></P>
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<h2>Contents</h2>
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</div>
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<ul>
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<li class="toclevel-1 tocsection-1"><a href="#Dimensionless process"><span class="tocnumber">1</span> <span class="toctext">Dimensionless process</span></a></li>
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<li class="toclevel-1 tocsection-2"><a href="#Parameters"><span class="tocnumber">2</span> <span class="toctext">Parameters</span></a></li>
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<li class="toclevel-1 tocsection-3"><a href="#Results"><span class="tocnumber">3</span> <span class="toctext">Results</span></a>
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<ul>
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<li class="toclevel-2 tocsection-1"><a href="#Sensitivity analysis"><span class="tocnumber">3.1</span> <span class="toctext">Sensitivity analysis</span></a></li>
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<li class="toclevel-2 tocsection-2"><a href="#Stability analysis"><span class="tocnumber">3.2</span> <span class="toctext">Stability analysis</span></a></li>
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<li class="toclevel-2 tocsection-3"><a href="#Feedback analysis"><span class="tocnumber">3.3</span> <span class="toctext">Feedback analysis</span></a></li>
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<h1 id="Dimensionless process">Dimensionless process</h1><hr width="100%" size=2 color=gray>
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<p>In order to make a further analysis on stability of the system, sensitivity of parameters,
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feedback factors-we manipulate all the arguments and parameters to make them dimensionless.
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Analysis of this part is crucial since parameters in vivo experiment may be different and
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even at odds with modeling ones but a proper dimensionless can reveal the mathematical essence
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of our model.</p>
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<p> Considering the Hill equation in the simplification DDEs, A1<sub>c1</sub> and K<sub>M1</sub>/ρ<sub>1</sub>  should be the same order of magnitude, thus K<sub>M1</sub>/ρ<sub>1</sub>  is a well measurement of quantities of A1<sub>c1</sub>. We have:</p>
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<p><img src="https://static.igem.org/mediawiki/2011/b/be/Part3-1.png" width="705px" height="1237px"></p>
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<h1 id="Parameters">Parameters</h1><hr width="100%" size=2 color=gray>
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<h1 id="Results">Results</h1><hr width="100%" size=2 color=gray>
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<h2 id="Sensitivity analysis">Sensitivity analysis</h2>
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<h2 id="Stability analysis">Stability analysis</h2>
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<h2 id="Feedback analysis">Feedback analysis</h2>
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Modeling::Dimensionless Model

Contents

Dimensionless process

In order to make a further analysis on stability of the system, sensitivity of parameters, feedback factors-we manipulate all the arguments and parameters to make them dimensionless. Analysis of this part is crucial since parameters in vivo experiment may be different and even at odds with modeling ones but a proper dimensionless can reveal the mathematical essence of our model.

Considering the Hill equation in the simplification DDEs, A1c1 and KM1/ρ1 should be the same order of magnitude, thus KM1/ρ1 is a well measurement of quantities of A1c1. We have:

Parameters

Results

Sensitivity analysis

Stability analysis

Feedback analysis

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