Team:NTU-Singapore/Modeling

From 2008.igem.org

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[[Image:Blackboard.jpg|center|400px]]
=Introduction=
=Introduction=
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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.
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Dictionary Definitions : Model
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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)
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"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.)
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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.
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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.
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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.
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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>
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<br>
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<br>
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''"All models are wrong; Some are useful"'' <br>
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'''George P. Box.''' <br>
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<br><br>
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var tags_before_clock = "<b>It is now "
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var tags_middle_clock = "on"
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var tags_after_clock  = "</b>"
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=System=
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if(navigator.appName == "Netscape") {
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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).
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document.write('<layer id="clock"></layer><br>');
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}
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==Constructs of the system==
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if (navigator.appVersion.indexOf("MSIE") != -1){
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document.write('<span id="clock"></span>');
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}
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===Constitutive Protein Synthesis===
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DaysofWeek = new Array()
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{| align="center" border="1"
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  DaysofWeek[0]="Sunday"
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|[[Image:Protein production.JPG|300px|Constitutive transcription]]
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  DaysofWeek[1]="Monday"
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|[[Image:Protein_synthesis.jpg|650px|Constitutive transcription results]]
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  DaysofWeek[2]="Tuesday"
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|}
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  DaysofWeek[3]="Wednesday"
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  DaysofWeek[4]="Thursday"
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  DaysofWeek[5]="Friday"
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  DaysofWeek[6]="Saturday"
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The constitutive model allows us to understand how fast steady state can be achieved for basal transcription.
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Months = new Array()
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===AND Gate===
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  Months[0]="January"
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{| align="center" border="1"
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  Months[1]="February"
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|[[Image:Andgate.JPG|300px|AND gate]]
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  Months[2]="March"
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|[[Image:Andgate_results.jpg|650px|AND gate results]]
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  Months[3]="April"
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|}
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  Months[4]="May"
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  Months[5]="June"
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  Months[6]="July"
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  Months[7]="August"
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  Months[8]="September"
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  Months[9]="October"
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  Months[10]="November"
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  Months[11]="December"
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Addition of inputs was done at 250 minutes.
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var dte = new Date();
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var hrs = dte.getHours();
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var min = dte.getMinutes();
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var sec = dte.getSeconds();
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var day = DaysofWeek[dte.getDay()]
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var date = dte.getDate()
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var month = Months[dte.getMonth()]
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var year = dte.getFullYear()
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The AND gate model allows us to observe that even when there is no input, basal transcription still yields a certain amount of product. The difference is observed both inputs are applied and a sharp increase over the basal amount can be easily observed.
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var col = ":";
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var spc = " ";
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var com = ",";
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var apm;
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We can observe AND gate behaviour in this sense as it is impossible to have no protein production at all even in the most well-regulated system.
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if (date == 1 || date == 21 || date == 31)
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  {ender = "<sup>st</sup>"}
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else
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if (date == 2 || date == 22)
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  {ender = "<sup>nd</sup>"}
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else
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if (date == 3 || date == 23)
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  {ender = "<sup>rd</sup>"}
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===Complex Formation===
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else
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  {ender = "<sup>th</sup>"}
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[[Image:Complex.JPG|400px|Complex Formation]]<br>
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if (12 < hrs) {
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This is the Simulink Model Construct for Complex Formations. The model is tested by applying an input when time = 150 min.
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apm="<font size='-1'>pm</font>";
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[[Image:ComForm_Input.jpg|750px|Vary Input]]<br>
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hrs-=12;
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By increasing the input, we can see an increase in the amount of complex formed.
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}
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[[Image:ComForm_Rate.jpg|750px|Vary Rate]]<br>
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By changing the rate of Complex formation, we can also see a change in the amount of complex formed.
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Both results show that the model works fine and can be used in our modeling exercises later on.
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else {
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===Regulated Transcription===
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apm="<font size='-1'>am</font>";
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The model for regulated transcription is compared with the model used in Constitutive transcription. Input into both models was done when time = 150 min. This would allow us to see if there is a difference under two different conditions for the two models.
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}
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[[Image:R&C_150_1.jpg|600px|150 minutes]]<br>
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[[Image:R&C_300_1.jpg|600px|300 minutes]]<br>
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if (hrs == 0) hrs=12;
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if (hrs<=9) hrs="0"+hrs;
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if (min<=9) min="0"+min;
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if (sec<=9) sec="0"+sec;
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[[Image:R&C_150_2.jpg|600px|150 minutes]]<br>
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if(navigator.appName == "Netscape") {
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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);
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document.clock.document.close();
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}
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[[Image:R&C_300_2.jpg|600px|300 minutes]]<br>
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if (navigator.appVersion.indexOf("MSIE") != -1){
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===Lactose Induced GFP production===
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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;
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[[Image:GFP_LACTOSE.jpg|850px| GFP Production Model]]
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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.



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