Team:NTU-Singapore/Modeling

From 2008.igem.org

(Difference between revisions)
 
(36 intermediate revisions not shown)
Line 1: Line 1:
 +
<html><link rel="stylesheet" href="http://greenbear88.googlepages.com/ntu_igem.css" type="text/css"></html>
 +
 +
<div id="header">{{User:Greenbear/sandbox/header}}</div>
 +
 +
<div id="maincontent" style="margin-top:100px;">
 +
 +
[[Image:Blackboard.jpg|center|400px]]
=Introduction=
=Introduction=
 +
 +
The primary objective of this section is to assist us in developing an understanding of the dynamic behaviour of the systems that we would create in our iGEM project. A requirement for assessing the dynamic behaviour is a time-dependent mathematical model of the bio-chemical processes that take place.
 +
 +
 +
 +
-----------------------------------------------------------------------------------------------------------------
 +
Dictionary Definitions : Model
 +
 +
Model is derived from the Latin word ''modus'', which stands for ''measure''. As a noun it means, " a small representation of a planned or exiting object" (Webster's New World Dictionary)
 +
 +
"A mathematical or physical system, obeying certain specified conditions, whose behaviour is used to understand a physical, biological, or social system to which it is analogous in some way" (McGraw-Hill dictionary of Scientific and Technical Terms.)
 +
-----------------------------------------------------------------------------------------------------------------
 +
The use of models to describe synthetic biology has its merits. Synthetic biology investigates the use of different biological parts to put together and assemble devices that carry out specific functions. Good mathematical models to describe each part would greatly help not only in the characterization of a part but also facilitate the use of the part by other people when they choose to use the part within their devices or systems.
The use of models to describe synthetic biology has its merits. Synthetic biology investigates the use of different biological parts to put together and assemble devices that carry out specific functions. Good mathematical models to describe each part would greatly help not only in the characterization of a part but also facilitate the use of the part by other people when they choose to use the part within their devices or systems.
Simulations based on modeling can give a first insight on how the system would turn out and provide a rough guide of the system’s behaviour.
Simulations based on modeling can give a first insight on how the system would turn out and provide a rough guide of the system’s behaviour.
 +
We hope to use a control engineering approach in this project, and we hope that by understanding the transient behaviours of the systems can we better design our system to suit their purpose.
-
=System=
+
The models that are created and found in the subsequent sections can still be improved by comparing the modeling results against actual wet lab results. SIMULINK has proved to be an immensely useful tool for Deterministic modeling and solving ODEs. Cellware had its own limitations when dealing with Stochastic models. As the system got more complicated, the shorter the time span the program was able to simulate and produce useful results.  
-
The system can be viewed as two parts. The first part comprises of lactose induced production of colicin E7 and the immunity protein. The second part comprises of a detection mechanism that produces the lysis protein upon the detection of both Iron ions and Ai-2 ( Autoinducer 2).
+
-
=ODEs used in modeling=
+
We had seen from our models that our AND gate system should have the shorter SupD gene attached to the Fe promoter. This was because in our assumptions, Fe ions would be ion lower concentration in the intestinal environment compared to Ai-2 and to have a similar response rate at the AND gate, the choice of AND gate inputs is critical.
-
The following equations shows the break down of the different equations that will be used in this modeling exercise. By understanding this section, it would make the understanding of the system of ODEs used
+
 +
We also realised that differing inputs of Lactose or Ai-2 would have an impact on the system via the models and this would be explored in greater detail in our wet lab experiments to see if the models are predicting the outcome correctly. <br>
 +
<br>
 +
<br>
 +
''"All models are wrong; Some are useful"'' <br>
 +
'''George P. Box.''' <br>
 +
<br><br>
 +
<html>
 +
<script language=Javascript1.2>
 +
<!--
-
==Constant synthesis & Linear Synthesis==
+
var tags_before_clock = "<b>It is now "
-
*Simple ode to describe constant synthesis
+
var tags_middle_clock = "on"
-
*Gives an explicit analytical solution
+
var tags_after_clock  = "</b>"
-
*Unique solution once a IC is posed
+
-
==Linear Degradation==
+
if(navigator.appName == "Netscape") {
-
*Rate of degradation is proportional to how much of the molecule is present
+
document.write('<layer id="clock"></layer><br>');
-
*Gives an explicit analytical solution
+
}
-
*Constant half life
+
-
==Simple Forward Reaction==
+
if (navigator.appVersion.indexOf("MSIE") != -1){
-
This equation ignores the fact that dissociation of the complex occurs.  
+
document.write('<span id="clock"></span>');
-
We can do so if the dissociation is much slower than the formation.
+
}
-
*Single solvable equation for the unknown C
+
DaysofWeek = new Array()
-
*Simple, unique solution available with I.C
+
  DaysofWeek[0]="Sunday"
 +
  DaysofWeek[1]="Monday"
 +
  DaysofWeek[2]="Tuesday"
 +
  DaysofWeek[3]="Wednesday"
 +
  DaysofWeek[4]="Thursday"
 +
  DaysofWeek[5]="Friday"
 +
  DaysofWeek[6]="Saturday"
-
==Phosphorylation and Dephosphorylation==
+
Months = new Array()
-
Assumptions:
+
  Months[0]="January"
-
*Linear kintic rate laws apply only if XT is much less than the Michaelis constants of both kinase and phosphotase
+
  Months[1]="February"
 +
  Months[2]="March"
 +
  Months[3]="April"
 +
  Months[4]="May"
 +
  Months[5]="June"
 +
  Months[6]="July"
 +
  Months[7]="August"
 +
  Months[8]="September"
 +
  Months[9]="October"
 +
  Months[10]="November"
 +
  Months[11]="December"
 +
function upclock(){
 +
var dte = new Date();
 +
var hrs = dte.getHours();
 +
var min = dte.getMinutes();
 +
var sec = dte.getSeconds();
 +
var day = DaysofWeek[dte.getDay()]
 +
var date = dte.getDate()
 +
var month = Months[dte.getMonth()]
 +
var year = dte.getFullYear()
-
*Modeled after simple linear kinetics
+
var col = ":";
-
*Gives a hyperbolic signal response curve when X plotted vs S
+
var spc = " ";
 +
var com = ",";
 +
var apm;
 +
if (date == 1 || date == 21 || date == 31)
 +
  {ender = "<sup>st</sup>"}
 +
else
 +
if (date == 2 || date == 22)
 +
  {ender = "<sup>nd</sup>"}
 +
else
 +
if (date == 3 || date == 23)
 +
  {ender = "<sup>rd</sup>"}
 +
 +
else
 +
  {ender = "<sup>th</sup>"}
 +
 +
if (12 < hrs) {
 +
apm="<font size='-1'>pm</font>";
 +
hrs-=12;
 +
}
 +
 +
else {
 +
apm="<font size='-1'>am</font>";
 +
}
 +
 +
if (hrs == 0) hrs=12;
 +
if (hrs<=9) hrs="0"+hrs;
 +
if (min<=9) min="0"+min;
 +
if (sec<=9) sec="0"+sec;
 +
 +
if(navigator.appName == "Netscape") {
 +
document.clock.document.write(tags_before_clock+hrs+col+min+col+sec+apm+spc+tags_middle_clock+spc+day+com+spc+date+ender+spc+month+com+spc+year+tags_after_clock);
 +
document.clock.document.close();
 +
}
 +
 +
if (navigator.appVersion.indexOf("MSIE") != -1){
 +
clock.innerHTML = tags_before_clock+hrs+col+min+col+sec+apm+spc+tags_middle_clock+spc+day+com+spc+date+ender+spc+month+com+spc+year+tags_after_clock;
 +
}
 +
}
 +
 +
setInterval("upclock()",1000);
 +
//-->
 +
</script>
 +
</html>
-
</div>
 
<!---End of main content--->
<!---End of main content--->
-
</div>
+
 
<!---End of body--->
<!---End of body--->

Latest revision as of 05:42, 27 October 2008

Blackboard.jpg

Introduction

The primary objective of this section is to assist us in developing an understanding of the dynamic behaviour of the systems that we would create in our iGEM project. A requirement for assessing the dynamic behaviour is a time-dependent mathematical model of the bio-chemical processes that take place.


Dictionary Definitions : Model

Model is derived from the Latin word modus, which stands for measure. As a noun it means, " a small representation of a planned or exiting object" (Webster's New World Dictionary)

"A mathematical or physical system, obeying certain specified conditions, whose behaviour is used to understand a physical, biological, or social system to which it is analogous in some way" (McGraw-Hill dictionary of Scientific and Technical Terms.)

The use of models to describe synthetic biology has its merits. Synthetic biology investigates the use of different biological parts to put together and assemble devices that carry out specific functions. Good mathematical models to describe each part would greatly help not only in the characterization of a part but also facilitate the use of the part by other people when they choose to use the part within their devices or systems.

Simulations based on modeling can give a first insight on how the system would turn out and provide a rough guide of the system’s behaviour.

We hope to use a control engineering approach in this project, and we hope that by understanding the transient behaviours of the systems can we better design our system to suit their purpose.

The models that are created and found in the subsequent sections can still be improved by comparing the modeling results against actual wet lab results. SIMULINK has proved to be an immensely useful tool for Deterministic modeling and solving ODEs. Cellware had its own limitations when dealing with Stochastic models. As the system got more complicated, the shorter the time span the program was able to simulate and produce useful results.

We had seen from our models that our AND gate system should have the shorter SupD gene attached to the Fe promoter. This was because in our assumptions, Fe ions would be ion lower concentration in the intestinal environment compared to Ai-2 and to have a similar response rate at the AND gate, the choice of AND gate inputs is critical.

We also realised that differing inputs of Lactose or Ai-2 would have an impact on the system via the models and this would be explored in greater detail in our wet lab experiments to see if the models are predicting the outcome correctly.


"All models are wrong; Some are useful"
George P. Box.



Retrieved from "http://2008.igem.org/Team:NTU-Singapore/Modeling"