Difference between revisions of "Team:Hong Kong HKUST/Modelling Prediction Model"

 
(21 intermediate revisions by 3 users not shown)
Line 1: Line 1:
 
{{Hong_Kong_HKUST}}
 
{{Hong_Kong_HKUST}}
 
<html>
 
<html>
 +
<head>
 +
<link rel="stylesheet" type="text/css" href="https://2016.igem.org/Template:Hong_Kong_HKUST/css_style_sheet?action=raw&ctype=text/css">
 +
<script type="text/javascript" src="https://2016.igem.org/Template:Hong_Kong_HKUST/JSAbout?action=raw&ctype=text/javascript"></script>
  
−
<div class="column full_size" >
+
</head>
−
<h1><b>Modelling - Prediction Model</b></h1>
+
<body>
−
<h4>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean nec magna quis lacus malesuada pellentesque sit amet et quam. Nam lectus nunc, congue sed bibendum vitae, tincidunt vitae odio. Nullam porta posuere risus consequat hendrerit. Proin ante arcu, elementum in ullamcorper sed, tempor eget purus. Nullam convallis dui vitae quam condimentum, quis rutrum diam blandit. Nam consectetur, leo eu sollicitudin venenatis, ex metus luctus arcu, et commodo mauris elit ut mi. Donec luctus diam eu tortor fringilla pharetra.<br><br><br>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean nec magna quis lacus malesuada pellentesque sit amet et quam. Nam lectus nunc, congue sed bibendum vitae, tincidunt vitae odio. Nullam porta posuere risus consequat hendrerit. Proin ante arcu, elementum in ullamcorper sed, tempor eget purus. Nullam convallis dui vitae quam condimentum, quis rutrum diam blandit. Nam consectetur, leo eu sollicitudin venenatis, ex metus luctus arcu, et commodo mauris elit ut mi. Donec luctus diam eu tortor fringilla pharetra.</h4>
+
<section class="section jumbotron">
−
</div>
+
<div class="content_wrapper_neo">
  
−
<!--<div class="column full_size" >
+
<h1 class="title text-center">
−
<h2> Welcome to iGEM 2016! </h2>
+
<b>Prediction Model</b>
−
<p>Your team has been approved and you are ready to start the iGEM season! </p>
+
</h1>
 +
  <blockquote><p>The last step is to predict the behaviour of the system. For a global prediction, all species and processes that are related to the system should be covered. Therefore, we also consider the dynamic of mRNA and fluorescent proteins in the prediction model. Nevertheless, another problem is brought about because this setting is contradictory to our model as the dynamic of mRNA is ignored before. In fact, the equilibrium of mRNA is a fast process when compared to proteins so we argue that the inclusion of mRNA dynamic will not give a picture differs a lot from the case in which mRNA dynamic is neglected. In addition, the dynamic of inducers is introduced, the cooperativity and the binding affinity of inducer to repressor proteins are also considered.
 +
</p></blockquote>
 +
                </div>
 +
        </section>
 +
<section class="section">
 +
<div class="content_wrapper_neo">
 +
<br><br>
 +
<p style="font-size: 1.2em;">By applying the findings from the stability analysis to the modeling equations, we obtain the following prediction graphs:</p>
 +
<center>
 +
<img class="img-responsive" src="https://static.igem.org/mediawiki/2016/5/55/T--Hong_Kong_HKUST--Modelling_pic6.png">
 +
<Figp style="font-size:14px; padding: 0 0.9em;"><b>Fig. 5. Prediction model of Tristable Switch.</b> Graphs in the 1st row represent the inducer concentration change over time, in this case, a pulse of inducer molecule 2 is introduced to the system from t=100 mins to t=200 mins. The graphs in the 2nd row represent the dynamic of mRNAs corresponding to each of the three operons in the tristable system. The plots in the 3rd row represent the dynamic of the three repressors (i.e. LacI, TetR and Phl). While the graphs in the 4th row describe the reporter proteins’ (i.e. fluorescent proteins) dynamic over time.</Figp>
 +
</center>
 +
<br><br>
 +
<p style="font-size: 1.2em;">From the graph, when a pulse of inducer 2 is introduced to the system, mRNA 2 and reporter protein 2 respond afterwards with concentrations increase from 0 to a high level, and the outputs (mRNA 2 and reporter protein 2) maintain at ‘on-state’ (i.e. high level of output) without decreasing back to ‘off-state’ (i.e. zero output level).
 +
In conclusion, from the prediction model, by applying suitable parameter values obtained from the stability analysis, it is simulated that upon addition of inducers, the corresponding state is switched on, which is indicated by the high and steady output level of the reporter protein. This behavior fits the design of Tristable Switch.</p>
 +
<br><br>
 +
<div class="table-responsive">
 +
<table id="safety_table" class="table-responsive" border="2px" align="center">
 +
<thead>
 +
<tr>
 +
<th><b>Parameters</b></th>
 +
<th><b>Notation</b></th>
 +
<th><b>Value</b></th>
 +
</tr>
 +
</thead>
 +
 +
<tbody>
 +
<tr>
 +
<td>Maximum transcription rate 1</td>
 +
<td>$k_{tx,\;1}$</td>
 +
<td>1</td>
 +
</tr>
 +
 +
<tr>
 +
<td>Maximum transcription rate 2</td>
 +
<td>$k_{tx,\;2}$</td>
 +
<td>1</td>
 +
</tr>
  
−
</div>  
+
<tr>
 +
<td>Maximum transcription rate 3</td>
 +
<td>$k_{tx,\;3}$</td>
 +
<td>1</td>
 +
</tr>
  
−
<div class="column half_size" >
+
<tr>
−
<h5>Before you start: </h5>
+
<td>mRNA degradation rate 1</td>
−
<p> Please read the following pages:</p>
+
<td>$d_1$</td>
−
<ul>
+
<td>0.12</td>
−
<li> <a href="https://2016.igem.org/Requirements">Requirements page </a> </li>
+
</tr>
−
<li> <a href="https://2016.igem.org/Wiki_How-To">Wiki Requirements page</a></li>
+
<tr>
−
<li> <a href="https://2016.igem.org/Resources/Template_Documentation"> Template Documentation </a></li>
+
<td>mRNA degradation rate 2</td>
−
</ul>
+
<td>$d_2$</td>
 +
<td>0.12</td>
 +
</tr>
 +
<tr>
 +
<td>mRNA degradation rate 3</td>
 +
<td>$d_3$</td>
 +
<td>0.12</td>
 +
</tr>
 +
<tr>
 +
<td>Maximum translation rate 1</td>
 +
<td>$k_{tl,\;1}$</td>
 +
<td>1</td>
 +
</tr>
 +
<tr>
 +
<td>Maximum translation rate 2</td>
 +
<td>$k_{tl,\;2}$</td>
 +
<td>1</td>
 +
</tr>
 +
<tr>
 +
<td>Maximum translation rate 3</td>
 +
<td>$k_{tl,\;3}$</td>
 +
<td>1</td>
 +
</tr>
 +
<tr>
 +
<td>Degradation of repressor protein 1</td>
 +
<td>$k_{deg3}$</td>
 +
<td>0.12</td>
 +
</tr>
 +
<tr>
 +
<td>Degradation of repressor protein 2</td>
 +
<td>$k_{deg2}$</td>
 +
<td>0.12</td>
 +
</tr>
 +
<tr>
 +
<td>Degradation of repressor protein 3</td>
 +
<td>$k_{deg1}$</td>
 +
<td>0.12</td>
 +
</tr>
 +
<tr>
 +
<td>Degradation of reporter protein 1</td>
 +
<td>-</td>
 +
<td>0.12</td>
 +
</tr>
 +
<tr>
 +
<td>Degradation of reporter protein 2</td>
 +
<td>-</td>
 +
<td>0.12</td>
 +
</tr>
 +
<tr>
 +
<td>Degradation of reporter protein 3</td>
 +
<td>-</td>
 +
<td>0.12</td>
 +
</tr>
 +
<tr>
 +
<td>Dissociation Constant for DNA-Repressor Protein 1 interaction</td>
 +
<td>$K_1$</td>
 +
<td>1e-8</td>
 +
</tr>
 +
<tr>
 +
<td>Dissociation Constant for DNA-Repressor Protein 2 interaction</td>
 +
<td>$K_2$</td>
 +
<td>1e-8</td>
 +
</tr>
 +
<tr>
 +
<td>Dissociation Constant for DNA-Repressor Protein 3 interaction</td>
 +
<td>$ø_1$</td>
 +
<td>1.5e-8</td>
 +
</tr>
 +
<tr>
 +
<td>Dissociation Constant for DNA-Repressor Protein 1 interaction</td>
 +
<td>$ø_1$</td>
 +
<td>1.5e-8</td>
 +
</tr>
 +
<tr>
 +
<td>Dissociation Constant for DNA-Repressor Protein 2 interaction</td>
 +
<td>$ø_2$</td>
 +
<td>1.5e-8</td>
 +
</tr>
 +
<tr>
 +
<td>Dissociation Constant for DNA-Repressor Protein 3 interaction</td>
 +
<td>$ø_3$</td>
 +
<td>1e-8</td>
 +
</tr>
 +
<tr>
 +
<td>Hill Coefficient of Repressor 1 (DNA-Repressor)</td>
 +
<td>$n_1$</td>
 +
<td>3</td>
 +
</tr>
 +
<tr>
 +
<td>Hill Coefficient of Repressor 2 (DNA-Repressor)</td>
 +
<td>$n_2$</td>
 +
<td>3</td>
 +
</tr>
 +
<tr>
 +
<td>Hill Coefficient of Repressor 3 (DNA-Repressor)</td>
 +
<td>$n_3$</td>
 +
<td>3</td>
 +
</tr>
 +
<tr>
 +
<td>Hill Coefficient of Inducer 1</td>
 +
<td>$m_1$</td>
 +
<td>2</td>
 +
</tr>
 +
<tr>
 +
<td>Hill Coefficient of Inducer 2</td>
 +
<td>$m_2$</td>
 +
<td>2</td>
 +
</tr>
 +
<tr>
 +
<td>Hill Coefficient of Inducer 3</td>
 +
<td>$m_3$</td>
 +
<td>2</td>
 +
</tr>
 +
</tbody>
 +
</table>
 
</div>
 
</div>
 +
<br>
  
−
<div class="column half_size" >
+
<div class="table-responsive">
−
<div class="highlight">
+
<table id="safety_table" class="table-responsive" border="2px" align="center">
−
<h5> Styling your wiki </h5>
+
<thead>
−
<p>You may style this page as you like or you can simply leave the style as it is. You can easily keep the styling and edit the content of these default wiki pages with your project information and completely fulfill the requirement to document your project.</p>
+
<tr>
−
<p>While you may not win Best Wiki with this styling, your team is still eligible for all other awards. This default wiki meets the requirements, it improves navigability and ease of use for visitors, and you should not feel it is necessary to style beyond what has been provided.</p>  
+
<th><b>Variables</b></th>
−
</div>
+
<th><b>Notation</b></th>
−
</div>
+
</tr>
 +
</thead>
 +
 +
<tbody>
 +
<tr>
 +
<td>mRNA 1 concentration</td>
 +
<td>$r_x$</td>
 +
</tr>
 +
 +
<tr>
 +
<td>mRNA 2 concentration</td>
 +
<td>$r_y$</td>
 +
</tr>
  
−
<div class="column full_size" >
+
<tr>
−
<h5> Wiki template information </h5>
+
<td>mRNA 3 concentration</td>
−
<p>We have created these wiki template pages to help you get started and to help you think about how your team will be evaluated. You can find a list of all the pages tied to awards here at the <a href="https://2016.igem.org/Judging/Pages_for_Awards/Instructions">Pages for awards</a> link. You must edit these pages to be evaluated for medals and awards, but ultimately the design, layout, style and all other elements of your team wiki is up to you!</p>
+
<td>$r_z$</td>
−
 
+
</tr>
−
</div>
+
−
 
+
−
 
+
−
 
+
−
 
+
−
<div class="column half_size" >
+
−
<h5> Editing your wiki </h5>
+
−
<p>On this page you can document your project, introduce your team members, document your progress and share your iGEM experience with the rest of the world! </p>
+
−
<p> <a href="https://2016.igem.org/wiki/index.php?title=Team:Example&action=edit"> </a>Use WikiTools - Edit in the black menu bar to edit this page</p>
+
  
 +
<tr>
 +
<td>Repressor 1 concentration</td>
 +
<td>x</td>
 +
</tr>
 +
<tr>
 +
<td>Repressor 2 concentration</td>
 +
<td>y</td>
 +
</tr>
 +
<tr>
 +
<td>Repressor 3 concentration</td>
 +
<td>z</td>
 +
</tr>
 +
<tr>
 +
<td>Inducer 1 concentration</td>
 +
<td>$u_1$</td>
 +
</tr>
 +
<tr>
 +
<td>Inducer 2 concentration</td>
 +
<td>$u_2$</td>
 +
</tr>
 +
<tr>
 +
<td>Inducer 3 concentration</td>
 +
<td>$u_3$</td>
 +
</tr>
 +
</tbody>
 +
</table>
 
</div>
 
</div>
 +
<br>
 +
<p style="font-size: 1.2em;">To view the codes we employed in our model programming, please click <a href="https://static.igem.org/mediawiki/2016/5/58/T--Hong_Kong_HKUST--ModellingCodes.pdf">here</a>.</p>
 +
                </div>
 +
        </section>
 +
<section class="section jumbotron">
 +
<div class="content_wrapper_neo">
  
 +
<h2 class="text-muted">
 +
<b><em>REFERENCE</em></b>
 +
</h2> 
 +
<p style="font-size:1.0em;">
 +
Gardner, T. S., Cantor, C. R., & Collins, J. J. (2000). Construction of a genetic toggle switch in escherichia coli. Nature, 403(6767), 339.
 +
<br><br>
 +
Jutta,Gebert & Nicole,Radde & Gerhard-Wilhelm,Weber. (2007). Modeling gene regulatory networks with piecewise linear differential equations. European Journal of Operational Research, Volume 181(Issue 3)
 +
<br><br>
 +
P, H. (2009). Analysis of ODE models.
 +
<br><br>
 +
Phillips, R., 1960-. (2013). Physical biology of the cell (2nd ed, / Rob Phillips, Jane Kondev, Julie Theriot, Hernan G. Garcia. ed.). New York, NY: Garland Science.
 +
<br><br>
 +
Polynikis, A., Hogan, S. J., & Di Bernardo, M. (2009). Comparing different ODE modelling approaches for gene regulatory networks. Journal of Theoretical Biology, 261(4), 511-530.
 +
<br> <br>
 +
Principle of synthetic biology -- stability analysis.
 +
<br><br>
 +
Sneppen, K., Krishna, S., & Semsey, S. (2010). Simplified Models of Biological Networks. Annu. Rev. Biophys. Annual Review of Biophysics, 39(1), 43-59. doi:10.1146/annurev.biophys.093008.131241
 +
<br><br>
 +
Szallasi, Z., Stelling, J., & Periwal, V. (2010). System modeling in cellular biology: From concepts to nuts and bolts. Cambridge, MA: MIT Press.
 +
</p>
  
−
<div class="column half_size" >
+
                </div>
−
<h5>Tips</h5>
+
        </section>
−
<p>This wiki will be your team’s first interaction with the rest of the world, so here are a few tips to help you get started: </p>
+
−
<ul>
+
−
<li>State your accomplishments! Tell people what you have achieved from the start. </li>
+
−
<li>Be clear about what you are doing and how you plan to do this.</li>
+
−
<li>You have a global audience! Consider the different backgrounds that your users come from.</li>
+
−
<li>Make sure information is easy to find; nothing should be more than 3 clicks away.  </li>
+
−
<li>Avoid using very small fonts and low contrast colors; information should be easy to read.  </li>
+
−
<li>Start documenting your project as early as possible; don’t leave anything to the last minute before the Wiki Freeze. For a complete list of deadlines visit the <a href="https://2016.igem.org/Calendar">iGEM 2016 calendar</a> </li>
+
−
<li>Have lots of fun! </li>
+
−
</ul>
+
−
</div>
+
−
 
+
−
 
+
−
<div class="column half_size" >
+
−
<h5>Inspiration</h5>
+
−
<p> You can also view other team wikis for inspiration! Here are some examples:</p>
+
−
<ul>
+
−
<li> <a href="https://2014.igem.org/Team:SDU-Denmark/"> 2014 SDU Denmark </a> </li>
+
−
<li> <a href="https://2014.igem.org/Team:Aalto-Helsinki">2014 Aalto-Helsinki</a> </li>
+
−
<li> <a href="https://2014.igem.org/Team:LMU-Munich">2014 LMU-Munich</a> </li>
+
−
<li> <a href="https://2014.igem.org/Team:Michigan"> 2014 Michigan</a></li>
+
−
<li> <a href="https://2014.igem.org/Team:ITESM-Guadalajara">2014 ITESM-Guadalajara </a></li>
+
−
<li> <a href="https://2014.igem.org/Team:SCU-China"> 2014 SCU-China </a></li>
+
−
</ul>
+
−
</div>
+
−
 
+
−
<div class="column half_size" >
+
−
<h5> Uploading pictures and files </h5>
+
−
<p> You can upload your pictures and files to the iGEM 2016 server. Remember to keep all your pictures and files within your team's namespace or at least include your team's name in the file name. <br />
+
−
When you upload, set the "Destination Filename" to <br><code>T--YourOfficialTeamName--NameOfFile.jpg</code>. (If you don't do this, someone else might upload a different file with the same "Destination Filename", and your file would be erased!)</p>
+
−
 
+
−
 
+
−
<div class="button_click"  onClick=" parent.location= 'https://2016.igem.org/Special:Upload '"> 
+
−
UPLOAD FILES
+
−
</div>-->
+
−
 
+
−
</div>
+
−
 
+
−
 
+
−
 
+
−
 
+
−
 
+
  
  
 +
      <script type="text/x-mathjax-config">
 +
                  MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
 +
</script>
 +
<script type="text/javascript" async
 +
  src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
 +
</script>
 +
<script>
 +
    $(document).ready(function(){
 +
        $("div#ustMenuWrapper li#ustModellingTab").addClass("ustActiveTab");
 +
    });
 +
</script>
 +
</body>
 
</html>
 
</html>
−
{{Hong_Kong_HKUST_Sitemap}}
 
−
 
−
 
−
<!--<div class="column full_size" >
 
−
 
−
<p>Here you can describe the results of your project and your future plans. </p>
 
−
 
−
<h5>What should this page contain?</h5>
 
−
<ul>
 
−
<li> Clearly and objectively describe the results of your work.</li>
 
−
<li> Future plans for the project </li>
 
−
<li> Considerations for replicating the experiments </li>
 
−
</ul>
 
−
 
−
</div>
 
−
 
−
<div class="column half_size" >
 
−
 
−
 
−
<h5> Project Achievements </h5>
 
−
 
−
<p>You can also include a list of bullet points (and links) of the successes and failures you have had over your summer. It is a quick reference page for the judges to see what you achieved during your summer.</p>
 
−
 
−
<ul>
 
−
<li>A list of linked bullet points of the successful results during your project</li>
 
−
<li>A list of linked bullet points of the unsuccessful results during your project. This is about being scientifically honest. If you worked on an area for a long time with no success, tell us so we know where you put your effort.</li>
 
−
</ul>
 
−
 
−
</div>
 
−
 
−
 
−
<div class="column half_size" >
 
−
 
−
<h5>Inspiration</h5>
 
−
<p>See how other teams presented their results.</p>
 
−
<ul>
 
−
<li><a href="https://2014.igem.org/Team:TU_Darmstadt/Results/Pathway">2014 TU Darmstadt </a></li>
 
−
<li><a href="https://2014.igem.org/Team:Imperial/Results">2014 Imperial </a></li>
 
−
<li><a href="https://2014.igem.org/Team:Paris_Bettencourt/Results">2014 Paris Bettencourt </a></li>
 
−
</ul>-->
 

Latest revision as of 03:30, 20 October 2016

Home

Prediction Model

The last step is to predict the behaviour of the system. For a global prediction, all species and processes that are related to the system should be covered. Therefore, we also consider the dynamic of mRNA and fluorescent proteins in the prediction model. Nevertheless, another problem is brought about because this setting is contradictory to our model as the dynamic of mRNA is ignored before. In fact, the equilibrium of mRNA is a fast process when compared to proteins so we argue that the inclusion of mRNA dynamic will not give a picture differs a lot from the case in which mRNA dynamic is neglected. In addition, the dynamic of inducers is introduced, the cooperativity and the binding affinity of inducer to repressor proteins are also considered.



By applying the findings from the stability analysis to the modeling equations, we obtain the following prediction graphs:

Fig. 5. Prediction model of Tristable Switch. Graphs in the 1st row represent the inducer concentration change over time, in this case, a pulse of inducer molecule 2 is introduced to the system from t=100 mins to t=200 mins. The graphs in the 2nd row represent the dynamic of mRNAs corresponding to each of the three operons in the tristable system. The plots in the 3rd row represent the dynamic of the three repressors (i.e. LacI, TetR and Phl). While the graphs in the 4th row describe the reporter proteins’ (i.e. fluorescent proteins) dynamic over time.


From the graph, when a pulse of inducer 2 is introduced to the system, mRNA 2 and reporter protein 2 respond afterwards with concentrations increase from 0 to a high level, and the outputs (mRNA 2 and reporter protein 2) maintain at ‘on-state’ (i.e. high level of output) without decreasing back to ‘off-state’ (i.e. zero output level). In conclusion, from the prediction model, by applying suitable parameter values obtained from the stability analysis, it is simulated that upon addition of inducers, the corresponding state is switched on, which is indicated by the high and steady output level of the reporter protein. This behavior fits the design of Tristable Switch.



Parameters Notation Value
Maximum transcription rate 1 $k_{tx,\;1}$ 1
Maximum transcription rate 2 $k_{tx,\;2}$ 1
Maximum transcription rate 3 $k_{tx,\;3}$ 1
mRNA degradation rate 1 $d_1$ 0.12
mRNA degradation rate 2 $d_2$ 0.12
mRNA degradation rate 3 $d_3$ 0.12
Maximum translation rate 1 $k_{tl,\;1}$ 1
Maximum translation rate 2 $k_{tl,\;2}$ 1
Maximum translation rate 3 $k_{tl,\;3}$ 1
Degradation of repressor protein 1 $k_{deg3}$ 0.12
Degradation of repressor protein 2 $k_{deg2}$ 0.12
Degradation of repressor protein 3 $k_{deg1}$ 0.12
Degradation of reporter protein 1 - 0.12
Degradation of reporter protein 2 - 0.12
Degradation of reporter protein 3 - 0.12
Dissociation Constant for DNA-Repressor Protein 1 interaction $K_1$ 1e-8
Dissociation Constant for DNA-Repressor Protein 2 interaction $K_2$ 1e-8
Dissociation Constant for DNA-Repressor Protein 3 interaction $ø_1$ 1.5e-8
Dissociation Constant for DNA-Repressor Protein 1 interaction $ø_1$ 1.5e-8
Dissociation Constant for DNA-Repressor Protein 2 interaction $ø_2$ 1.5e-8
Dissociation Constant for DNA-Repressor Protein 3 interaction $ø_3$ 1e-8
Hill Coefficient of Repressor 1 (DNA-Repressor) $n_1$ 3
Hill Coefficient of Repressor 2 (DNA-Repressor) $n_2$ 3
Hill Coefficient of Repressor 3 (DNA-Repressor) $n_3$ 3
Hill Coefficient of Inducer 1 $m_1$ 2
Hill Coefficient of Inducer 2 $m_2$ 2
Hill Coefficient of Inducer 3 $m_3$ 2

Variables Notation
mRNA 1 concentration $r_x$
mRNA 2 concentration $r_y$
mRNA 3 concentration $r_z$
Repressor 1 concentration x
Repressor 2 concentration y
Repressor 3 concentration z
Inducer 1 concentration $u_1$
Inducer 2 concentration $u_2$
Inducer 3 concentration $u_3$

To view the codes we employed in our model programming, please click here.

REFERENCE

Gardner, T. S., Cantor, C. R., & Collins, J. J. (2000). Construction of a genetic toggle switch in escherichia coli. Nature, 403(6767), 339.

Jutta,Gebert & Nicole,Radde & Gerhard-Wilhelm,Weber. (2007). Modeling gene regulatory networks with piecewise linear differential equations. European Journal of Operational Research, Volume 181(Issue 3)

P, H. (2009). Analysis of ODE models.

Phillips, R., 1960-. (2013). Physical biology of the cell (2nd ed, / Rob Phillips, Jane Kondev, Julie Theriot, Hernan G. Garcia. ed.). New York, NY: Garland Science.

Polynikis, A., Hogan, S. J., & Di Bernardo, M. (2009). Comparing different ODE modelling approaches for gene regulatory networks. Journal of Theoretical Biology, 261(4), 511-530.

Principle of synthetic biology -- stability analysis.

Sneppen, K., Krishna, S., & Semsey, S. (2010). Simplified Models of Biological Networks. Annu. Rev. Biophys. Annual Review of Biophysics, 39(1), 43-59. doi:10.1146/annurev.biophys.093008.131241

Szallasi, Z., Stelling, J., & Periwal, V. (2010). System modeling in cellular biology: From concepts to nuts and bolts. Cambridge, MA: MIT Press.