Team:NTU-Singapore/Modeling

From 2008.igem.org

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<div id="header">{{User:Greenbear/sandbox/header}}</div>
<div id="header">{{User:Greenbear/sandbox/header}}</div>
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<div id="maincontent" style="margin-top:200px;">
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[[Image:Blackboard.jpg|center|400px]]
=Introduction=
=Introduction=
-
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.
+
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.  
-
=System=
 
-
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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=ODEs used in modeling=
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-----------------------------------------------------------------------------------------------------------------
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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
+
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.)
 +
-----------------------------------------------------------------------------------------------------------------
-
==Constant synthesis & Linear Synthesis==
+
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.
-
*Simple ode to describe constant synthesis
+
-
*Gives an explicit analytical solution
+
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*Unique solution once a IC is posed
+
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==Linear Degradation==
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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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*Rate of degradation is proportional to how much of the molecule is present
+
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*Gives an explicit analytical solution
+
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*Constant half life
+
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==Simple Forward Reaction==
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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.  
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This equation ignores the fact that dissociation of the complex occurs.
+
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We can do so if the dissociation is much slower than the formation.  
+
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*Single solvable equation for the unknown C
+
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.  
-
*Simple, unique solution available with I.C
+
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==Phosphorylation and Dephosphorylation==
+
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.
-
Assumptions:
+
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*Linear kintic rate laws apply only if XT is much less than the Michaelis constants of both kinase and phosphotase
+
 +
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>
-
*Modeled after simple linear kinetics
+
''"All models are wrong; Some are useful"'' <br>
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*Gives a hyperbolic signal response curve when X plotted vs S
+
'''George P. Box.''' <br>
 +
<br><br>
 +
<html>
 +
<script language=Javascript1.2>
 +
<!--
-
==Regulated Transcription==
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var tags_before_clock = "<b>It is now "
 +
var tags_middle_clock = "on"
 +
var tags_after_clock  = "</b>"
-
=ODE system used in model=
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if(navigator.appName == "Netscape") {
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==Lactose controlled production of E7 + Imm==
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document.write('<layer id="clock"></layer><br>');
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===Variables===
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}
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#LacI = A
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#Lactose =B
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#E7 = C
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==Iron and Ai2 controlled production of Lysis==
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if (navigator.appVersion.indexOf("MSIE") != -1){
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===Variables===
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document.write('<span id="clock"></span>');
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Variables
+
}
-
#Ai-2 : A
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#ai-2-phos : B
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#LsrR : C
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#SupD derivatives : D
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#T7ptag : E
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#Lysis : F
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=Parameter Estimation=
+
DaysofWeek = new Array()
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Estimation of different parameters
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  DaysofWeek[0]="Sunday"
-
# Transcription         : 70nt/s
+
  DaysofWeek[1]="Monday"
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# Translation : 40aa/s
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  DaysofWeek[2]="Tuesday"
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# Number of Essential Genes : 297
+
  DaysofWeek[3]="Wednesday"
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# Number of mRNA per cell : 4000
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  DaysofWeek[4]="Thursday"
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# Average mRNA half life : 5min
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  DaysofWeek[5]="Friday"
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# Average mRNA length         : 1100
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  DaysofWeek[6]="Saturday"
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Assumptions
+
Months = new Array()
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#Rate of transcription is dependent on length of gene
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  Months[0]="January"
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#Number of amino acids is 1/3 of the number of nucleotides in a gene
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  Months[1]="February"
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#Rate of Translation is dependent on number of nucleotides
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  Months[2]="March"
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#For each gene mRNA = 10 at steady state
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  Months[3]="April"
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#Rate of degradation of average mRNA = 1100/ 5 min
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  Months[4]="May"
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#Rate of degradation of protein is equivalent to time for cell division i.e. 40 min
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  Months[5]="June"
 +
  Months[6]="July"
 +
  Months[7]="August"
 +
  Months[8]="September"
 +
  Months[9]="October"
 +
  Months[10]="November"
 +
  Months[11]="December"
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[[Image:Parameter_Estimation.JPG|450px|Results]]
+
function upclock(){
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==E7 production system==
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var dte = new Date();
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{| align="center" border="1"
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var hrs = dte.getHours();
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|Type
+
var min = dte.getMinutes();
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|Parameter
+
var sec = dte.getSeconds();
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|Values
+
var day = DaysofWeek[dte.getDay()]
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|Comments
+
var date = dte.getDate()
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|-
+
var month = Months[dte.getMonth()]
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|Transcription Rate of Lac I gene
+
var year = dte.getFullYear()
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|k1A
+
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|21
+
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|Made using Earlier assumptions
+
-
|-
+
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|Transcription Rate of E7 + Imm gene
+
-
|k1C
+
-
|2.470588
+
-
|Made using Earlier assumptions
+
-
|-
+
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|Degradation Rate of Lac I mRNA
+
-
|d1A
+
-
|0.76246
+
-
|Made using Earlier assumptions
+
-
|-
+
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|Transcription Rate of E7 + Imm mRNA
+
-
|d1C
+
-
|0.0897
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Translation Rate of Lac I mRNA
+
-
|k2A
+
-
|36
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Translation Rate of E7 + Imm mRNA
+
-
|k2C
+
-
|4.23539
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Protein Degradation Rate
+
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|d2A,d2C
+
-
|0.03465
+
-
|Made using Earlier assumptions
+
-
|-
+
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|Hill coefficeint for E7 + Imm
+
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|nC
+
-
|1
+
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|This is obtained on the assumption that one Repressor <br>Protein binds to one Lactose molecule complex
+
-
|-
+
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|Dissociation Constant for E7 + Imm
+
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|KC
+
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|0.8
+
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|[3]
+
-
|-
+
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|Constitutive Portion for E7 + Imm
+
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|aC
+
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|0.5
+
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|Estimate since a is between 0 and 1<br> Implication that Lactose may not be <br> a very strongly Regulated Promoter
+
-
|-
+
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|Complex Formation Rate Between <br> Lac I Repressor and Lactose
+
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|k3AB
+
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|1
+
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|Estimate
+
-
|}
+
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==E7 production system==
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var col = ":";
-
{| align="center" border="1"
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var spc = " ";
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|Type
+
var com = ",";
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|Parameter
+
var apm;
-
|Values
+
-
|Comments
+
-
|-
+
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|Phosphorylation Rate of Ai-2
+
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|kPF
+
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|1
+
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|Estimate
+
-
|-
+
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|Dephosphorylation Rate of Ai-2
+
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|kPB
+
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|1
+
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|Estimate
+
-
|-
+
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|Transcription Rate of LsrR gene
+
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|k1C
+
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|4.402517
+
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|Made using Earlier assumptions
+
-
|-
+
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|Transcription Rate of SupD gene
+
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|k1D
+
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|46.667
+
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|Made using Earlier assumptions
+
-
|-
+
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|Transcription Rate of t7pTag gene
+
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|k1E
+
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|1.5556
+
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|Made using Earlier assumptions
+
-
|-
+
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|Transcription Rate of Lysis gene
+
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|k1F
+
-
|28
+
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|Made using Earlier assumptions
+
-
|-
+
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|Degradation Rate of LsrR mRNA
+
-
|d1C
+
-
|0.159845
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Degradation Rate of SupD mRNA
+
-
|d1D
+
-
|1.694359
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Degradation Rate of t7pTag mRNA
+
-
|d1E
+
-
|0.056478
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Degradation Rate of Lysis mRNA
+
-
|d1F
+
-
|1.0166
+
-
|Made using Earlier assumptions
+
-
|-
+
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|Translation Rate of LsrR Protein
+
-
|k2C
+
-
|7.54716
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Translation Rate of t7 pTag Protein
+
-
|k2E
+
-
|2.6667
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Translation Rate of Lysis Protein
+
-
|k2F
+
-
|48
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Protein Degradation Rate
+
-
|d2C,d2E,d2F
+
-
|0.03465
+
-
|Made using Earlier assumptions
+
-
|-
+
-
|Hill coefficeint for SupD
+
-
|nD
+
-
|50
+
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|Trial And Error
+
-
|-
+
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|Hill coefficeint for t7 pTag
+
-
|nE
+
-
|1
+
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|Trial And Error
+
-
|-
+
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|Hill coefficeint for Lysis
+
-
|nF
+
-
|1
+
-
|Estimate
+
-
|-
+
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|Dissociation Constant for SupD
+
-
|KD
+
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|15
+
-
|[5]
+
-
|-
+
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|Dissociation Constant for t7 pTag
+
-
|KE
+
-
|1
+
-
|Estimate
+
-
|-
+
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|Dissociation Constant for Lysis
+
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|KF
+
-
|0.8
+
-
|Estimate
+
-
|-
+
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|Constitutive Portion for SupD
+
-
|aD
+
-
|0.01
+
-
|Estimate
+
-
|-
+
-
|Constitutive Portion for t7 pTag
+
-
|aE
+
-
|0.01
+
-
|Estimate
+
-
|-
+
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|Constitutive Portion for Lysis
+
-
|aF
+
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|0.0001
+
-
|Estimate
+
-
|-
+
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|Complex Formation Rate Between <br> LsrR Repressor and Ai-2-Phosphorylated
+
-
|k3BC
+
-
|0.01
+
-
|Estimate
+
-
|-
+
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|Complex Formation Rate Between <br> SupD tRNA and t7 pTag mRNA
+
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|k3DE
+
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|0.000000001
+
-
|Estimate
+
-
|-
+
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|Amount of Protein Kinase
+
-
|S
+
-
|28.747
+
-
|From Earlier Assumptions
+
-
|-
+
-
|}
+
-
=Results of Modeling=
+
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>"}
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==E7 production system==
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else
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[[Image:Varying_lactose_input.jpg|850px| E7 Production Modeling Results]]
+
  {ender = "<sup>th</sup>"}
-
Modeling of the System shows that Lactose induction is essential to produce E7 and a variation of Lactose input can result in different yields of E7
+
if (12 < hrs) {
 +
apm="<font size='-1'>pm</font>";
 +
hrs-=12;
 +
}
-
==Lysis Production system==
+
else {
-
[[Image:Varying_Lysis.jpg|850px|Lysis Prodcution Modeling Results]]
+
apm="<font size='-1'>am</font>";
 +
}
-
Here we define 1 as a certain threshold e.g. (<250 µM) that when the lysis protein reaches it, lysis in the cell definitely occurs.
+
if (hrs == 0) hrs=12;
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Although we wish for an absolute AND gate, where 0 will have no lysis production at all, simulation on biological systems shows that such results are impossible. Both addition Fe ions and Ai-2 alone would induce a certain level of lysis production. However when both are available, the lysis protein production would be higher.
+
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();
 +
}
-
In the presence of Ai-2 alone, Lysis will most likely still occur albeit at a slower rate compared to situation when both Fe and Ai-2 are present.
+
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;
 +
}
 +
}
-
With the addition of iron and Ai-2 together the rate of lysis production is still significantly much higher compared to Ai-2 alone.
+
setInterval("upclock()",1000);
 +
//-->
 +
</script>
 +
</html>
-
Therefore, by giving the logical output ‘1’ as a suitable threshold value of Lysis protein production higher than that of Ai-2 induction alone, we would still be able to obtain an AND gate based on our definition.
 
 +
<!---End of main content--->
-
 
-
 
-
 
-
</div>
 
-
<!---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"