Team:HUST-China/Modelling

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          <li class="active"><a href="#Part-1">Overview</a></li>
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<li class="active"><a href="javascript:void;">Overview</a></li>
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          <li><a href="#Part-2"></i>Delay Difference Equations</a></li>
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<li><a href="https://2013.igem.org/Team:HUST-China/Modelling/DDE_Model"></i>Delay Differential Equations</a></li>
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<li><a href="https://2013.igem.org/Team:HUST-China/Modelling/MCOS"></i>Multi Cells Oscillation Simulation</a></li>
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<div id="Part-1">
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<h1 class="page-header"><strong>Overview</strong></h1>
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<h3 class="page-header"><strong>Overview</strong></h3>
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<p>
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The major goal of modeling this year is stimulating the working condition of the oscillation. The genetic oscillation we used is described as below.   
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The genetic pathway we used in modelling work is described as below.   
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<div style="float:right;">
<img src="https://static.igem.org/mediawiki/2013/a/ab/Pathway_HUST.png" width="350px;" />
<img src="https://static.igem.org/mediawiki/2013/a/ab/Pathway_HUST.png" width="350px;" />
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Fig 1.The pathway of genetic oscillator used in this paper
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<p class="small">Fig 1.The pathway of genetic oscillator used in our project.</p
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The enzymes that can induce the expression of propanoic acid is replaced with mRFP. Throughout the whole paper, we choose to study AraC instead of mRFP since they are in the same plasmid and expression rate of both protein is similar. By doing this, we can reduce the number of equations. We put our focus mainly on two aspect:
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></div>
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(1)Oscillator of a single cell (DDEs).
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<h4>Approach and Result</h4>
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(2)Oscillator of a group of cells (MCOS).
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Our modeling work includes 3 parts:
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To be more specifically, we want to find out if this genetic oscillator can oscillate in the first place, if it is stable against environment change, if its period can be adjusted, whether a large group of these oscillators can oscillate as well.
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<strong>
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(1)Feasibility, stability and sensitivity of single genetic oscillator and its parameters;<br>
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(2)Feasibility of multi cells’ oscillator made up by a group of single genetic oscillators and comparison with experiment data;<br>
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(3)Statistically analyzing our wet-lab result.  
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</strong><br>
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</p>
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<p>    To finish part (1), we construct DDEs model, which superb model using <acronym title="Ordinary Differential Equation">ODEs</acronym> because it is capable of describing time interval between expression of regulating protein and their binding to promoters; in other words, our model is much more precise than ODEs model. Moreover, DDEs model is more flexible than ODEs model, as we can degrade it into an ODEs one by setting lag equal to 0.  Result of our model is satisfying, as our oscillator is stable while circumstance(Arabinose and IPTG) varies, and sensitive when itself($\tau$) changes. That is to say, it is easy for manipulate, which is good for further application.</p>
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<p>    To accomplish part (2), we use data from part (1) and simulate using Agent-Based Model. We then compare simulation outcome with our wet-lab data. There comes a promising result, as florescent intensity linearly related to expression of AraC of these two groups of data match each other well, namely our model is supported by our experiment. This model is extendable because it has capability simulating other problem in large population. Also method that used to compar wetlab and drylab data, which is Q-Q plot, provides a quick way for analyzing groups of data correspondent time interval remained unknown.</p>
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<div  id="Part-2">
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<p>    To fulfill part (3), we use Q-Q plot and <acronym title="Kolmogorov-Smirnov">K-S</acronym> test to confirm that single transformed cells and co-transformed cells are different. We then use <acronym title="Shapiro-Wilk">S-W</acronym> test to demonstrate that the oscillatory behavior of our oscillator is not a Brownian motion, which is often neglected regardless of its importance.</p>  
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<h1 class="page-header"><strong>Delay Difference Equations</strong></div>
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<h4>Notes</h4>
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<p>
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    Throughout the whole modelling work, we choose to study AraC instead of mRFP since they are in the same plasmid and we assumed that the expression rate of both protein is similar. By doing this, we can reduce the number of equations.
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$$\tau$$
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<h1 class="page-header"><strong>Overview</strong></h1>
 
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<p>
 
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$\tau$
 
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Latest revision as of 02:50, 29 October 2013

The genetic pathway we used in modelling work is described as below.

Fig 1.The pathway of genetic oscillator used in our project.

Approach and Result

Our modeling work includes 3 parts: (1)Feasibility, stability and sensitivity of single genetic oscillator and its parameters;
(2)Feasibility of multi cells’ oscillator made up by a group of single genetic oscillators and comparison with experiment data;
(3)Statistically analyzing our wet-lab result.

To finish part (1), we construct DDEs model, which superb model using ODEs because it is capable of describing time interval between expression of regulating protein and their binding to promoters; in other words, our model is much more precise than ODEs model. Moreover, DDEs model is more flexible than ODEs model, as we can degrade it into an ODEs one by setting lag equal to 0. Result of our model is satisfying, as our oscillator is stable while circumstance(Arabinose and IPTG) varies, and sensitive when itself($\tau$) changes. That is to say, it is easy for manipulate, which is good for further application.

To accomplish part (2), we use data from part (1) and simulate using Agent-Based Model. We then compare simulation outcome with our wet-lab data. There comes a promising result, as florescent intensity linearly related to expression of AraC of these two groups of data match each other well, namely our model is supported by our experiment. This model is extendable because it has capability simulating other problem in large population. Also method that used to compar wetlab and drylab data, which is Q-Q plot, provides a quick way for analyzing groups of data correspondent time interval remained unknown.

To fulfill part (3), we use Q-Q plot and K-S test to confirm that single transformed cells and co-transformed cells are different. We then use S-W test to demonstrate that the oscillatory behavior of our oscillator is not a Brownian motion, which is often neglected regardless of its importance.

Notes

Throughout the whole modelling work, we choose to study AraC instead of mRFP since they are in the same plasmid and we assumed that the expression rate of both protein is similar. By doing this, we can reduce the number of equations.