Revision as of 12:20, 17 October 2018

Model Overview

1. Abstract

In modeling, we obtain mathematical relationships between quantities in the system. Then, one can easily obtain the initial conditions that would lead to the desired outcome. The main variation in the inital condition is variation in the initial concentration of the inducer (AHL - Acyl-Homoserine-lactone), which can (mainly) vary the total bacteria living time. Because of the complexity of our model, we use an ODE (Ordinary Differential Equations) numerical solver we’ve written in matlab for obtaining final and graphical results. We present our system briefly and reactions, and then we compare the model and the experimental results for validation and conclusions.

2.Introduction

Our model has 2 main aspects: 1. Gene expression; 2. Plasmid loss. For the first aspect, we obtained the equations by applying enzyme kinetics and mass action on our reactions. For the second aspect, we obtain the equations from a typcial bacterial population growth and plasmid loss models.

2.1. Why Do We Need a Model?

Our model is an integral part of our biological system. In order to use our kill switch properly, one needs to know exactly which initial conditions match the expected result. Using our model, one can easily obtain the initial concentrations to put in the kill switch activate it for the appropriate time.

The plasmid loss aspect of our model is an additional model that takes into account the fact that plasmid loss can occur and cause unexpected results. For example, Satellite Colonies (see “Plasmid Loss” page for more details), which can hurt the functioning of the kill switch.

2.2. Methods

In this model, we described all the reactions and processes by ODEs (Ordinary Differential Equations). This method is suitable for describing dynamic systems and for easy simulation. This is the common procedure for describing dynamic systems in science, especially in biology. It enables predicting the behaviour of very complex dynamic systems, as long as we can describe how the system change at any given time. Our system is for sure complex and dynamic, so we use a set of ODE to describe it.

In order to achive a quantitive description of the reactions and processes, we use mainly the Law of Mass Action. This law, or principle, states that the rate of a reaction is proportional to the product of the masses (hence the name) or concentrations of the reactant. This law holds for system in a steady state and since we assume that are system is in a quasi steady state, i.e. the changes in it are relatively slow, we can use it. There are a few reaction for which we use other kinetic laws.

2.3. Our System

2.3.1. In General

Our system consists of an inducer (AHL from the Homoserine-Lactones group) and the genetic circuit that is inserted in a plasmid. In the circuit, there is a “death protein” (in this case, ccdB) which is responsible for the actual death. The precence of the inducer in the bacteria represses the expression of the death protein. Therefore, after the inducer is degraded, there is nothing that can repress the expression of the death gene, and the bacteria die.

2.3.2. In Detail

The AHL (inducer) binds to the protein LuxR and they form a complex. This complex binds to the pLux promoter and activates it. Then, the tetR protein is expressed, binds to the pTet promoter and deactivates it. As a result, the ccdb (“death protein”) will not be expressed. When the AHL is fully degreaded, there will be not AHL-LuxR complex to activate the pLux promoter, thus no tetR will be expressed, thus ccdB will be expressed, which will kill the bacteria.

2.3.3. Note About Notations

In this page we’ll use the (relatively) full names for the substances and complexes. In the equations page we’ll use abbreviations which will be explained there. Please note that we sometime call the TetR repressor TRLV (TetR with tag LVA). It’s so because during the process of modelling our system we didn’t knew for sure which version of TetR we’ll finally use. In other words, for any purposes of the modelling TRLV and TetR are equivalent and are used interchangeably in this wiki. As you've seen in the description page, in the end we used TetR in our biological circuit.

Furthermore, the notations of in, out and sum are used in this page without much explanation, although they aren’t crucial for understanding our model. Thorough explanation of them available in the Documents section

3. Reactions

i. AHL self-degradation.

o Law: Mass action

o Explanation: Each molecule of AHL has a certain probability to degrade, hence the corresponding change rate in the amount of the AHL is proportional to the amount of AHL in all the cells. The coefficient is noted by C2 for cell internal AHL and C2' for cell external AHL.

o Results:

ii. Diffusion of AHL

o Law: Simple passive diffusion

o Explanation: Will be explained in the processes section.

o Results:
Change in external AHL concentration:

Change in total amount inside of AHL inside all the cells:

iii. AHL degradation by AiiA

o Law: Michaelis Menten

o Explanation: AiiA is an enzyme, and simple Mass Action doesn't work well for enzymatic reactions. The reason for it is the fact that the enzyme and the substrate form a complex, which is then converted to a product and the original enzyme. Therefore, two mass actions are required to describe this process, but under quasi-steady-state assumption we can derive a single equation, which is the Michaelis Menten law. It has two parameters, the maximal reaction rate and the turnover number.

o Results:

iv. Pairing of AHL and LuxR into AHL-LuxR complex

o Law: Mass action

o Explanation: The chance of a molecule of AHL to meet a molecule of LuxR is proportional to both the concentration of AHL and LuxR (the more AHL you have, the higher the chance for reaction between AHL and LuxR). We get that the reaction rate is proportional to the product of the concentrations of AHL and LuxR.

o Results:

v. Disassociation of the AHL-LuxR complex to its components

o Law: Mass action

o Explanation: Each AHL-LuxR complex has a certain probability to disassociate, hence the corresponding change rate in the amount of the AHL is proportional to the amount of AHL-LuxR. The coefficient is denoted by C4.

o Results:

vi. Pairing of 2 AHL-LuxR complexes into the dimer (AHL-LuxR)₂

o Law: Mass action

o Explanation: The chance of a molecule of AHL-LuxR complex to meet another one is proportional, again, to the product of their concentrations, (which this time are equal and we get [AHL-LuxR]^2).

o Results:

vii. Disassociation of (AHL-LuxR)₂ to its components

o Law: Mass action

o Explanation: Each (AHL-LuxR)₂ dimer has a certain probability to disassociate, hence the corresponding change rate in the amount of the AHL is proportional to the total amount of AHL-LuxR in the cells. The coefficient is denoted by C6.

o Results:

viii. (AHL-LuxR)₂ binds to the pLuxR promoter

o Law: Mass action

o Explanation: The activation rate is proportional to the product of the concentrations of the dimer and the number of plasmid plasmids with pLuxR promoters. It will be explained later in the processes section.

o Results:

ix. (AHL-LuxR)₂unbinds from the pLuxR promoter

o Law: Mass action

o Explanation: Each activated promoter has a certain probability to deactivate and to release its (AHL-LuxR)₂, and therefore the rate of this process is proportional to the number of activated promoters. It will be explained later in the processes section.

o Results:

x. Transcription of RNA_TRLV by pLuxR promoter without the complex

o Law: Mass action

o Explanation: Each inactivated promoter transcripts mRNA in a certain rate. This rate is called leakiness. We multiply it by the number of inactivated LuxR promoters to get the total rate. It will be explained further in the processes section.

o Results:

xi. Transcription of RNA_TRLV by pLuxR promoter with the complex

o Law: Mass action

o Explanation: Each activated promoter transcripts mRNA in a certain rate. We multiply it by the number of activated LuxR promoters to get the total rate. It will be explained further in the processes section.

o Results:

xii. Translation of TRLV from RNA_TRLV

o Law: Mass action

o Explanation: mRNA of TetR translates to the protein TetR in a certain rate. We multiply it by the concentration of RNA to get the total rate. It will be explained further in the processes section.

o Results:

xiii. TRLV self-degradation

o Law: Mass action

o Explanation: Each molecule of TRLV has a certain probability to degrade, hence the corresponding change rate in the amount of the TRLV is proportional to the amount of TRLV all the cells.

o Results:

xiv. TRLV binds to the pTetR repressor

o Law: Mass action

o Explanation: The activation rate is proportional to the product of the concentrations of the dimer and the number of plasmid plasmids with pTetR promoters. It will be explained later in the processes section.

o Results:

xv. TRLV unbinds from the pLuxR repressor

o Law: Mass action

o Explanation: Each activated promoter has a certain probability to deactivate and to release its TRLV, and therefore the rate of this process is proportional to the number of activated promoters. It will be explained later in the processes section.

o Results:

xvi. Transcription of RNA_ccdB by ptetR promoter without the TRLV

o Law: Mass action

o Explanation: For each inactivated repressor there is transcription to mRNA in a certain rate. We multiply it by the number of inactivated ptetR promoters to get the total rate. It will be explained further in the processes section.

o Results:

xvii. Transcription of RNA_ccdB by ptetR promoter with the TRLV

o Law: Mass action

o Explanation: For each activated repressor there is still transcription to mRNA in a certain rate. We multiply it by the number of activated ptetR promoters to get the total rate. It will be explained further in the processes section.

o Results:

xviii. Translation of ccdB from RNA_ccdB

o Law: Mass action

o Explanation: mRNA of ccdb translates to the protein ccdb in a certain rate. We multiply it by the concentration of RNA to get the total rate. It will be explained further in the processes section.

o Results:

xix. ccdB self-degradation

o Law: Mass action

o Explanation: Each molecule of ccdB has a certain probability to degrade, hence the corresponding change rate in the amount of the ccdB is proportional to the amount of ccdB all the cells.

o Results:

xx. producing of the desired protein x by the pCONST promoter

o Law: Mass Action

o Explanation: Each plasmid with our circuit produces the desired enzyme, X, in a certain amount.

o Results:

xxi. producing of LuxR by the pCONST promoter

o Law: Mass Action

o Explanation: Each plasmid with our circuit produces LuxR in a certain amount.

o Results:

xxii. producing of AiiA by the pCONST promoter

o Law: Mass Action

o Explanation: Each plasmid with our circuit produces AiiA in a certain amount.

o Results:

xxiii. plasmid loss

o We model the effect of plasmid loss on the system. It affects the equations by having both bacteria with plasmids (N+) and without plasmid (N-).

o Further explanation is here.

o Results:

4. Processes

4.1. AHL Diffusion

Our system is based on controlling the initial amount of AHL inside the cells in order to control the life span of the bacteria. However, we can’t put the AHL directly inside the cells. We put it in the test tube together with the bacteria. Therefore, it’s important to model how this process, of AHL entering the cell, accure and how it affects our system. It is part of seeing our system as an integrated complex, whose parts interect with each other and affect the result: the external AHL diffuse inside the cells, inside the cells the AHL is degraded by the AiiA, and as AHL is decreasing inside the cells, the external AHL diffuses accordingly into the cells in order to maintain equilibrium.

As AHL diffuse rather quickly through the membrane of E. Coli, we use a rather simplified model. We assume that each seperated part of our system (external environment, inside each cell, etc) is homogenous, which is quite true as AHL diffuses quickly, and it’s suffeciant to our needs.

We base our diffusion model on this document. Essentially, it says that the rate of the diffusion is proportional to the concetration gradient.

4.2. Transcription and Translation

We have two proteins whose production is a part of our biological circuit: the TetR and the ccdb (or the RFP in the experiments). In our model, each of this processes is described using 4 equations. The first two describe the number of plasmids with an activated promoter (or repressor, depends on the processes) using regular Mass Action. In the third we assume that RNA is transcripted in a certain constant rate for each actiivated binding site and the same for unactivated, and get an expression for the change in the concentration of RNA strands. In the last one we desscribe the translation rate of the protein, using the Mass Action law, as a function of the RNA. We assume that the translation rate is proportional to the concentration of the RNA.

4.3. Plasmid Loss

Read the full explanation and description of the plasmid loss model here.

5. Documents

During our work, we’ve made a documents describing different aspects and parts of our model. We put them here in hope that whomever want to dive into our model will be able to do so and will find these documents interesting.

6. Simulation

We simulated our system a few times using our numerical solver. Description and documentation of our solver can be found here. The results we’ve got are in the Modelling Results page.

Parameters

In order to describe our biological system, we need the right parameters. We looked up in literature and in iGEM projects from previous years (using our Constant Database!) and found almost all the 40 required parameters and constants, and estimated the rest. Check our parameter table here

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+<h1><font color="#008080">Model Overview</font> </h1></font></h1>
+<h2>1. Abstract</h2>
+<div class="Unindented">
+<p>In modeling, we obtain mathematical relationships between quantities in the system. Then, one can easily obtain the initial conditions that would lead to the desired outcome. The main variation in the inital condition is variation in the initial concentration of the inducer (AHL - Acyl-Homoserine-lactone), which can (mainly) vary the total bacteria living time. Because of the complexity of our model, we use an ODE (Ordinary Differential Equations) numerical solver we’ve written in matlab for obtaining final and graphical results. We present our system briefly and reactions, and then we compare the model and the experimental results for validation and conclusions.</p>
+</div>
+<h2>2.Introduction</h2>
+<div class="Unindented"><p>
+Our model has 2 main aspects: 1. Gene expression; 2. Plasmid loss. For the first aspect, we obtained the equations by applying enzyme kinetics and mass action on our reactions. For the second aspect, we obtain the equations from a typcial bacterial population growth and plasmid loss models.</p>
+</div>
+<h3 class="Subsection">
+.1. Why Do We Need a Model?
+</h3>
+<div class="Unindented"><p>
+Our model is an integral part of our biological system. In order to use our kill switch properly, one needs to know exactly which initial conditions match the expected result. Using our model, one can easily obtain the initial concentrations to put in the kill switch activate it for the appropriate time. </p>
+</div>
+<div class="Indented"><p>
+The plasmid loss aspect of our model is an additional model that takes into account the fact that plasmid loss can occur and cause unexpected results. For example, Satellite Colonies (see &ldquo;Plasmid Loss&rdquo; page for more details), which can hurt the functioning of the kill switch.</p>
+</div>
+<h3 class="Subsection">
+.2. Methods
+</h3>
+<div class="Unindented"><p>
+In this model, we described all the reactions and processes by ODEs (Ordinary Differential Equations). This method is suitable for describing dynamic systems and for easy simulation. This is the common procedure for describing dynamic systems in science, especially in biology. It enables predicting the behaviour of very complex dynamic systems, as long as we can describe how the system change at any given time. Our system is for sure complex and dynamic, so we use a set of ODE to describe it.</p>
+</div>
+<div class="Indented"><p>
+In order to achive a quantitive description of the reactions and processes, we use mainly the Law of Mass Action. This law, or principle, states that the rate of a reaction is proportional to the product of the masses (hence the name) or concentrations of the reactant. This law holds for system in a steady state and since we assume that are system is in a quasi steady state, i.e. the changes in it are relatively slow, we can use it. There are a few reaction for which we use other kinetic laws.</p>
+</div>
+<h3 class="Subsection">
+.3. Our System
+</h3>
+<h4>
+.3.1. In General
+</h4>
+<div class="Unindented"><p>
+Our system consists of an inducer (AHL from the Homoserine-Lactones group) and the genetic circuit that is inserted in a plasmid. In the circuit, there is a &ldquo;death protein&rdquo; (in this case, ccdB) which is responsible for the actual death. The precence of the inducer in the bacteria represses the expression of the death protein. Therefore, after the inducer is degraded, there is nothing that can repress the expression of the death gene, and the bacteria die.</p>
+</div>
+<h4>
+.3.2. In Detail
+</h4>
+<div class="Unindented"><p>
+The AHL (inducer) binds to the protein LuxR and they form a complex. This complex binds to the pLux promoter and activates it. Then, the tetR protein is expressed, binds to the pTet promoter and deactivates it. As a result, the ccdb (&ldquo;death protein&rdquo;) will not be expressed. When the AHL is fully degreaded, there will be not AHL-LuxR complex to activate the pLux promoter, thus no tetR will be expressed, thus ccdB will be expressed, which will kill the bacteria.</p>
+</div>
+<h4>
+.3.3. Note About Notations
+</h4>
+<div class="Unindented"><p>
+In this page we’ll use the (relatively) full  names for the substances and complexes. In the equations page we’ll use abbreviations which will be explained there. Please note that we sometime call the TetR repressor TRLV (TetR with tag LVA). It’s so because during the process of modelling our system we didn’t knew for sure which version of TetR we’ll finally use. In other words, for any purposes of the modelling TRLV and TetR are equivalent and are used interchangeably in this wiki. As you've seen in the description page, in the end we used TetR in our biological circuit.</p>
+</div>
+<div class="Indented"><p>
+Furthermore, the notations of in, out and sum are used in this page without much explanation, although they aren’t crucial for understanding our model. Thorough explanation of them available in the Documents section</p>
+</div>
+<h3 class="Subsection">
+. Reactions
+</h3>
+<img src="https://static.igem.org/mediawiki/2015/7/70/Technion_HS_2015_reactions.png" style="width:80%">
+<p class=MsoListParagraphCxSpFirst dir=LTR style='margin-top:0cm;margin-right:
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+%'>i.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>AHL self-degradation. </span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
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+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
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+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: Each molecule of AHL has a certain probability to degrade,
+hence the corresponding change rate in the amount of the AHL is proportional to
+the amount of AHL in all the cells. The coefficient is noted by C2 for cell
+internal AHL and C2' for cell external AHL. </span></p>
-    /*GOOGLE FONTS*/
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
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+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/1/1d/Technion_HS_2015_Reaction_1.png" class="term"><br/><img src="https://static.igem.org/mediawiki/2015/0/04/Technion_HS_2015_Reaction_2.png
+" class="term"></span></p>
-/* latin */
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
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+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
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+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
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+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-  src: local('Raleway'), local('Raleway-Regular'),  url(https://static.igem.org/mediawiki/2018/5/59/T--MIT--raleway2.woff) format('woff');
+%'>Law: Simple passive diffusion</span></p>
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-}
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
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+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: Will be explained in the processes section.</span></p>
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+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+Change in external AHL concentration:<br>
+<img src="https://static.igem.org/mediawiki/2015/1/16/Technion_HS_2015_Reaction_3.png" class="term"><br>
+Change in total amount inside of AHL inside all the cells:<br>
+<img src="https://static.igem.org/mediawiki/2015/7/7d/Technion_HS_2015_Reaction_4.png" class="term"> </span></p>
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+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
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+%'>AHL degradation by AiiA</span></p>
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+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
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+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Michaelis Menten</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
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+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: AiiA is an enzyme, and simple Mass Action doesn't work well
+for enzymatic reactions. The reason for it is the fact that the enzyme and the
+substrate form a complex, which is then converted to a product and the original
+enzyme. Therefore, two mass actions are required to describe this process, but
+under quasi-steady-state assumption we can derive a single equation, which is
+the Michaelis Menten law. It has two parameters, the maximal reaction rate and
+the turnover number.</span></p>
-    .sub {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        font-family: 'Dosis', sans-serif;;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        font-size: 1.5vw;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        float: left;
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-    }
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/4/40/Technion_HS_2015_Reaction_5.png" class="term"></span></p>
-    .sub a {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        display: block;
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-        color: white;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        text-align: center;
+%'>iv.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-        padding: 15px 30px;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        text-decoration: none;
+%'>Pairing of AHL and LuxR into AHL-LuxR complex</span></p>
-    }
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
-    .activemenu {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        background-color: #9055ff;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-    }
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: The chance of a molecule of AHL to meet a molecule of LuxR
+is proportional to both the concentration of AHL and LuxR (the more AHL you
+have, the higher the chance for reaction between AHL and LuxR). We get that the
+reaction rate is proportional to the product of the concentrations of AHL and
+LuxR.</span></p>
-    .dropdown {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        position: relative;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        display: inline-block;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-    }
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/d/d4/Technion_HS_2015_Reaction_6.png" class="term"></span></p>
-    .dropdown-content {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        font-family: 'Raleway', sans-serif;;
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-        font-size: 1.2vw;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        display: none;
+%'>v.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-        position: absolute;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        top: 4.2vw;
+%'>Disassociation of the AHL-LuxR complex to its components</span></p>
-        background-color: #2c2c2c;
-        min-width: 160px;
-        box-shadow: 0px 8px 16px 0px rgba(0,0,0,0.2);
-        z-index: 1;
-    }
-    .dropdown-content a {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        color: white;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        padding: 12px 16px;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        text-decoration: none;
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-        display: block;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-    }
+%'>Law: Mass action</span></p>
-    .dropdown-content a:hover {background-color: #474747;}
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: Each AHL-LuxR complex has a certain probability to
+disassociate, hence the corresponding change rate in the amount of the AHL is
+proportional to the amount of AHL-LuxR. The coefficient is denoted by C4.</span></p>
-    .dropdown:hover .dropdown-content {display: block;}
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/8/8a/Technion_HS_2015_Reaction_7.png" class="term"></span></p>
-body{
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        margin:0;
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-    }
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>vi.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Pairing of 2 AHL-LuxR complexes into the dimer (AHL-LuxR)<sub>2</sub></span></p>
-     </style>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-     <style>
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
-          .MIT-content {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-               font-family: "Times New Roman", Times, serif;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-               padding: 14px 16px;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-          }
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: The chance of a molecule of AHL-LuxR complex to meet another
+one is proportional, again, to the product of their concentrations, (which this
+time are equal and we get [AHL-LuxR]^2).</span></p>
-          #project-overview {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-               text-indent: 50px;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-          }
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/8/8e/Technion_HS_2015_Reaction_8.png" class="term"></span></p>
-        /* end css.sty */
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        h4{
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-            font-family: 'Raleway', sans-serif;;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-            font-size: 1.3vw;
+%'>vii.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-        }
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        span{
+%'>Disassociation of (AHL-LuxR)<sub>2</sub> to its components</span></p>
-            font-family: 'Raleway', sans-serif;;
-            font-size: 1.3vw;
-        }
-        .panel{
-            font-family: 'Raleway', sans-serif;;
-            font-size: 1.3vw;
-        }
-        body{
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        margin-top: 4.2vw;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
-    }
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-.accordion {
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        font-family: 'Dosis', sans-serif;;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        font-size: 1.5vw;
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-        background-color: #2c2c2c;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        color: #e8e8e8;
+%'>Explanation: Each (AHL-LuxR)<sub>2</sub> dimer has a certain probability
-        cursor: pointer;
+to disassociate, hence the corresponding change rate in the amount of the AHL
-        padding: 18px;
+is proportional to the total amount of AHL-LuxR in the cells. The coefficient
-        width: 100%;
+is denoted by C6.</span></p>
-        border: none;
-        text-align: left;
-        outline: none;
-        transition: 0.4s;
-    }
-    .active, .accordion:hover {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        background-color: #202020;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-    }
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/0/0b/Technion_HS_2015_Reaction_9.png" class="term"></span></p>
-    .accordion:after {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        content: '\002B';
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-        color: #777;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        font-weight: bold;
+%'>viii.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-        float: right;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        margin-left: 5px;
+%'>(AHL-LuxR)<sub>2</sub> binds to the pLuxR promoter</span></p>
-    }
-    .active:after {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        content: "\2212";
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-    }
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
-    .panel {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        padding: 0 18px;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        background-color: white;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        max-height: 0;
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-        overflow: hidden;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        transition: max-height 0.2s ease-out;
+%'>Explanation: The activation rate is proportional to the product of the
-    }
+concentrations of the dimer and the number of plasmid plasmids with pLuxR
-        .h3{
+promoters. It will be explained later in the processes section.</span></p>
-            color: white;
-            font-family: 'Dosis', sans-serif;;
-            font-size: 8vw;
-position: absolute;
-            left: 2vw;
-top: 3vw;
-            z-index: 5;
-        }
-     </style>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-</head>
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-<body >
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/c/c3/Technion_HS_2015_Reaction_10.png" class="term"></span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>ix.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>(AHL-LuxR)<sub>2 </sub>unbinds from the pLuxR promoter</span></p>
-<div style="position: absolute; top: 65vw">
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-    <button class="accordion">1. List of Constants and Variables Used in the Model</button>
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-    <div class="panel">
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
-        <div class="tabular"> <table id="TBL-2" class="tabular"
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-                                     cellspacing="0" cellpadding="0"
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        ><colgroup id="TBL-2-1g"><col
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-                id="TBL-2-1"></colgroup><colgroup id="TBL-2-2g"><col
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-                id="TBL-2-2"></colgroup><colgroup id="TBL-2-3g"><col
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-                id="TBL-2-3"></colgroup><colgroup id="TBL-2-4g"><col
+%'>Explanation: Each activated promoter has a certain probability to
-                id="TBL-2-4"></colgroup><tr
+deactivate and to release its (AHL-LuxR)<sub>2</sub>, and therefore the rate of
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
+this process is proportional to the number of activated promoters. It will be
-                style="vertical-align:baseline;" id="TBL-2-1-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-1-1"
+explained later in the processes section.</span></p>
-                                                                    class="td11">  Symbol   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-1-2"
-                                                                                                      class="td11">                     Meaning                                  </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-1-3"
-                                                                                                                                                                                           class="td11">  Value   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-1-4"
-                                                                                                                                                                                                                            class="td11">                     Units                                  </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-2-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-2-1"
-                                                                    class="td11">    <span
-                class="cmmi-10">k</span><sub><span
-                class="cmmi-7">tx</span></sub>      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-2-2"
-                                                              class="td11">             Transcription Rate of a Gene                    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-2-3"
-                                                                                                                                                  class="td11">    <img
-                src="https://static.igem.org/mediawiki/2018/2/2a/T--MIT--MITMorpheqs0x.png" alt="13"  class="frac" align="middle">       </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-2-4"
-                                                                                            class="td11">           transcripts per gene per second                 </td></tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-3-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-3-1"
-                                                                    class="td11"> <span
-                class="cmmi-10">k</span><sub>
-<span
-        class="cmmi-7">tf</span></sub>      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-3-2"
-                                                      class="td11">  Transcription Factor Activity of Phosphorylated ComE   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-3-3"
-                                                                                                                                      class="td11">   0.15    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-3-4"
-                                                                                                                                                                        class="td11">     transcripts per ComEP per gene per second        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-4-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-4-1"
-                                                                    class="td11">  <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">mCSP</span></sub>    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-4-2"
-                                                              class="td11">              Decay Rate of CSP mRNA                      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-4-3"
-                                                                                                                                               class="td11">   <img
-                src="https://static.igem.org/mediawiki/2018/4/45/T--MIT--MITMorpheqs1x.png" alt="1--
-"  class="frac" align="middle">      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-4-4"
-                                                  class="td11">              transcripts per second                       </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-5-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-5-1"
-                                                                    class="td11">  <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">mComD</span></sub>   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-5-2"
-                                                              class="td11">             Decay Rate of ComD mRNA                    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-5-3"
-                                                                                                                                             class="td11">   <img
-                src="https://static.igem.org/mediawiki/2018/c/c1/T--MIT--MITMorpheqs2x.png" alt="1--
-"  class="frac" align="middle">      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-5-4"
-                                                  class="td11">              transcripts per second                       </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-6-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-6-1"
-                                                                    class="td11">  <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">mComE</span></sub>   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-6-2"
-                                                              class="td11">             Decay Rate of ComE mRNA                    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-6-3"
-                                                                                                                                             class="td11">   <img
-                src="https://static.igem.org/mediawiki/2018/1/19/T--MIT--MITMorpheqs3x.png" alt="1--
-"  class="frac" align="middle">      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-6-4"
-                                                  class="td11">              transcripts per second                       </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-7-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-7-1"
-                                                                    class="td11">  <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">mGTFC</span></sub>   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-7-2"
-                                                              class="td11">            Decay Rate of mGTFC mRNA                   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-7-3"
-                                                                                                                                            class="td11">   <img
-                src="https://static.igem.org/mediawiki/2018/e/eb/T--MIT--MITMorpheqs4x.png" alt="1--
-"  class="frac" align="middle">      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-7-4"
-                                                  class="td11">              transcripts per second                       </td></tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-8-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-8-1"
-                                                                    class="td11"> <span
-                class="cmmi-10">pComC </span></td> <td  style="white-space:nowrap; text-align:center;" id="TBL-2-8-2"
-                                                        class="td11"> Number of ComC genes </td> <td  style="white-space:nowrap; text-align:center;" id="TBL-2-8-3"
-                                                                                                      class="td11"> 1 </td> <td  style="white-space:nowrap; text-align:center;" id="TBL-2-8-4"
-                                                                                                                                 class="td11"> genes</td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-9-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-9-1"
-                                                                    class="td11">  <span
-                class="cmmi-10">pComD  </span></td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-9-2"
-                                                        class="td11">               Number of ComD genes                        </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-9-3"
-                                                                                                                                          class="td11">    1      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-9-4"
-                                                                                                                                                                            class="td11">                     genes                                  </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-10-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-10-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">pComE   </span></td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-10-2"
-                                                         class="td11">               Number of ComE genes                        </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-10-3"
-                                                                                                                                           class="td11">    1      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-10-4"
-                                                                                                                                                                             class="td11">                     genes                                  </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-11-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-11-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">pGTFC  </span></td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-11-2"
-                                                        class="td11">               Number of GTFC genes                        </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-11-3"
-                                                                                                                                          class="td11">    1      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-11-4"
-                                                                                                                                                                            class="td11">                     genes                                  </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-12-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-12-1"
-                                                                     class="td11">   <span
-                class="cmmi-10">&#x03B1;</span><sub><span
-                class="cmmi-7">CSP</span></sub>    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-12-2"
-                                                             class="td11">               Translation Rate of CSP                       </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-12-3"
-                                                                                                                                                 class="td11">  <img
-                src="https://static.igem.org/mediawiki/2018/0/06/T--MIT--MITMorpheqs5x.png" alt="-22-
-"  class="frac" align="middle">    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-12-4"
-                                                  class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-13-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-13-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">&#x03B1;</span><sub><span
-                class="cmmi-7">ComD</span></sub>   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-13-2"
-                                                             class="td11">              Translation Rate of ComD                      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-13-3"
-                                                                                                                                                class="td11">  <img
-                src="https://static.igem.org/mediawiki/2018/0/0d/T--MIT--MITMorpheqs6x.png" alt="-22-
-"  class="frac" align="middle">    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-13-4"
-                                                  class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-14-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-14-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">&#x03B1;</span><sub><span
-                class="cmmi-7">ComE</span></sub>   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-14-2"
-                                                             class="td11">              Translation Rate of ComE                      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-14-3"
-                                                                                                                                                class="td11">  <img
-                src="https://static.igem.org/mediawiki/2018/9/9c/T--MIT--MITMorpheqs7x.png" alt="-22-
-"  class="frac" align="middle">    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-14-4"
-                                                  class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-15-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-15-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">&#x03B1;</span><sub><span
-                class="cmmi-7">GTFC</span></sub>   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-15-2"
-                                                             class="td11">              Translation Rate of GTFC                      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-15-3"
-                                                                                                                                                class="td11">  <img
-                src="https://static.igem.org/mediawiki/2018/3/3b/T--MIT--MITMorpheqs8x.png" alt="-22-
-"  class="frac" align="middle">    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-15-4"
-                                                  class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-16-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-16-1"
-                                                                     class="td11">   <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">CSP</span></sub>     </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-16-2"
-                                                              class="td11">                 Decay Rate of CSP                           </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-16-3"
-                                                                                                                                                  class="td11"> <span
-                class="cmsy-10">&#x2223;</span><img
-                src="https://static.igem.org/mediawiki/2018/e/e1/T--MIT--MITMorpheqs9x.png" alt="ln(1&#x2215;2)-
-"  class="frac" align="middle"><span
-                class="cmsy-10">&#x2223;</span> </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-16-4"
-                                                          class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-17-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-17-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">ComE</span></sub>    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-17-2"
-                                                              class="td11">                Decay Rate of ComE                          </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-17-3"
-                                                                                                                                                 class="td11"> <span
-                class="cmsy-10">&#x2223;</span><img
-                src="https://static.igem.org/mediawiki/2018/7/7a/T--MIT--MITMorpheqs10x.png" alt=" ln(1&#x2215;2)
-"  class="frac" align="middle"><span
-                class="cmsy-10">&#x2223;</span> </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-17-4"
-                                                          class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-18-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-18-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">ComD</span></sub>    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-18-2"
-                                                              class="td11">                Decay Rate of ComD                         </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-18-3"
-                                                                                                                                                class="td11"><span
-                class="cmr-10">1</span><span
-                class="cmmi-10">.</span><span class="overline"><span
-                class="cmr-10">5</span></span> <span
-                class="cmsy-10">&#x00D7; </span><span
-                class="cmr-10">10</span><sup><span
-                class="cmsy-7">-</span><span
-                class="cmr-7">5</span></sup></td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-18-4"
-                                                      class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-19-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-19-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">GTFC</span></sub>    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-19-2"
-                                                              class="td11">                Decay Rate of GTFC                         </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-19-3"
-                                                                                                                                                class="td11"> <span
-                class="cmsy-10">&#x2223;</span><img
-                src="https://static.igem.org/mediawiki/2018/1/1d/T--MIT--MITMorpheqs11x.png" alt="ln(1&#x2215;2)
--"  class="frac" align="middle"><span
-                class="cmsy-10">&#x2223;</span> </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-19-4"
-                                                          class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-20-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-20-1"
-                                                                     class="td11"><span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">CSPComDP</span></sub></td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-20-2"
-                                                              class="td11">              Decay Rate of CSPComDP                     </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-20-3"
-                                                                                                                                              class="td11"><span
-                class="cmr-10">1</span><span
-                class="cmmi-10">.</span><span class="overline"><span
-                class="cmr-10">5</span></span> <span
-                class="cmsy-10">&#x00D7; </span><span
-                class="cmr-10">10</span><sup><span
-                class="cmsy-7">-</span><span
-                class="cmr-7">5</span></sup></td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-20-4"
-                                                      class="td11">               complexes per second                       </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-21-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-21-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">ComEP</span></sub>   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-21-2"
-                                                              class="td11">         Decay Rate of Phosphorylated ComE               </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-21-3"
-                                                                                                                                              class="td11">  <img
-                src="https://static.igem.org/mediawiki/2018/c/c3/T--MIT--MITMorpheqs12x.png" alt="--1--
-"  class="frac" align="middle">    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-21-4"
-                                                   class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-22-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-22-1"
-                                                                     class="td11">    <span
-                class="cmmi-10">k</span><sub><span
-                class="cmmi-7">b</span></sub>       </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-22-2"
-                                                              class="td11">           Binding Activity of CSP to ComD                 </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-22-3"
-                                                                                                                                                class="td11"> <img
-                src="https://static.igem.org/mediawiki/2018/0/0e/T--MIT--MITMorpheqs13x.png" alt="--2----
-10000000"  class="frac" align="middle">  </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-22-4"
-                                                   class="td11">      complexes per CSP per ComD per second          </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-23-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-23-1"
-                                                                     class="td11">    <span
-                class="cmmi-10">k</span><sub><span
-                class="cmmi-7">ub</span></sub>      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-23-2"
-                                                              class="td11">Unbinding Activity of CSP:Phosphorylated ComD Complex</td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-23-3"
-                                                                                                                                          class="td11"> <img
-                src="https://static.igem.org/mediawiki/2018/9/9c/T--MIT--MITMorpheqs14x.png" alt="---5---
-100000000"  class="frac" align="middle"> </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-23-4"
-                                                   class="td11">      dissasociations per CSPComDP per second         </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-24-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-24-1"
-                                                                     class="td11">    <span
-                class="cmmi-10">k</span><sub><span
-                class="cmmi-7">k</span></sub>       </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-24-2"
-                                                              class="td11">        Kinase Activity of Phosphorylated ComD            </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-24-3"
-                                                                                                                                               class="td11"> <img
-                src="https://static.igem.org/mediawiki/2018/9/98/T--MIT--MITMorpheqs15x.png" alt="---5---
-100000000"  class="frac" align="middle"> </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-24-4"
-                                                   class="td11">phosphorylations per CSPComDP per ComE per second</td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-25-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-25-1"
-                                                                     class="td11">    <span
-                class="cmmi-10">k</span><sub><span
-                class="cmmi-7">e</span></sub>       </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-25-2"
-                                                              class="td11">              Enzyme Activity of GTFC                      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-25-3"
-                                                                                                                                                class="td11"> <img
-                src="https://static.igem.org/mediawiki/2018/7/7c/T--MIT--MITMorpheqs16x.png" alt="--1----
-10000000"  class="frac" align="middle">  </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-25-4"
-                                                   class="td11">    glucans formed per GTFC per Sugar per second      </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-26-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-26-1"
-                                                                     class="td11">   <span
-                class="cmmi-10">&#x03D5;</span><sub><span
-                class="cmmi-7">CSP</span></sub>    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-26-2"
-                                                             class="td11">            Export Rate of CSP from a Cell                  </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-26-3"
-                                                                                                                                                class="td11">   <img
-                src="https://static.igem.org/mediawiki/2018/7/7c/T--MIT--MITMorpheqs17x.png" alt="1--
-"  class="frac" align="middle">      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-26-4"
-                                                  class="td11">                 <sup class="nicefrac"><span
-                class="cmr-10">1</span></sup><span
-                class="cmmi-10">&#x2215;</span><sub class="nicefrac"><span
-                class="cmmi-10">CSP </span><span
-                class="cmsy-10">&#x00D7; </span><span
-                class="cmmi-10">second</span></sub>                      </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-27-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-27-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">&#x03D5;</span><sub><span
-                class="cmmi-7">Glucan</span></sub>   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-27-2"
-                                                               class="td11">          Export Rate of Glucans from a Cell                </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-27-3"
-                                                                                                                                                  class="td11">    <img
-                src="https://static.igem.org/mediawiki/2018/3/30/T--MIT--MITMorpheqs18x.png" alt="1
-"  class="frac" align="middle">       </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-27-4"
-                                                 class="td11">                <sup class="nicefrac"><span
-                class="cmr-10">1</span></sup><span
-                class="cmmi-10">&#x2215;</span><sub class="nicefrac"><span
-                class="cmmi-10">Glucan </span><span
-                class="cmsy-10">&#x00D7; </span><span
-                class="cmmi-10">second</span></sub>                     </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-28-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-28-1"
-                                                                     class="td11">    <span
-                class="cmmi-10">k</span><sub><span
-                class="cmmi-7">ab</span></sub>      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-28-2"
-                                                              class="td11">           Binding Activity of ScFv to GTFC                 </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-28-3"
-                                                                                                                                                 class="td11">  <img
-                src="https://static.igem.org/mediawiki/2018/b/b4/T--MIT--MITMorpheqs19x.png" alt="-4--
-"  class="frac" align="middle">    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-28-4"
-                                                  class="td11">      Complexes per ScFv per GTFC per second         </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-29-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-29-1"
-                                                                     class="td11"> <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">GTFCScFv</span></sub> </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-29-2"
-                                                               class="td11">          Decay Rate of GTFC:ScFv Complex                </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-29-3"
-                                                                                                                                               class="td11"> <span
-                class="cmsy-10">&#x2223;</span><img
-                src="https://static.igem.org/mediawiki/2018/3/37/T--MIT--MITMorpheqs20x.png" alt="ln(1&#x2215;2)-
-"  class="frac" align="middle"><span
-                class="cmsy-10">&#x2223;</span> </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-29-4"
-                                                          class="td11">               complexes per second                       </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-30-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-30-1"
-                                                                     class="td11">  <span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">ScFv</span><sub><span
-                class="cmmi-5">cell</span></sub></sub>   </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-30-2"
-                                                                   class="td11">                 Decay Rate of ScFv                           </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-30-3"
-                                                                                                                                                        class="td11"> <span
-                class="cmsy-10">&#x2223;</span><img
-                src="https://static.igem.org/mediawiki/2018/9/97/T--MIT--MITMorpheqs21x.png" alt="ln(1&#x2215;2)
---"  class="frac" align="middle"><span
-                class="cmsy-10">&#x2223;</span> </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-30-4"
-                                                          class="td11">                proteins per second                        </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-31-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-31-1"
-                                                                     class="td11">    <span
-                class="cmmi-10">k</span><sub><span
-                class="cmmi-7">kc</span></sub>      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-31-2"
-                                                              class="td11">           Binding Activity of Kappa-Casein                 </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-31-3"
-                                                                                                                                                 class="td11">    1      </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-31-4"
-                                                                                                                                                                                   class="td11">          <sup class="nicefrac"><span
-                class="cmr-10">1</span></sup><span
-                class="cmmi-10">&#x2215;</span><sub class="nicefrac"><span
-                class="cmmi-10">KCasein </span><span
-                class="cmsy-10">&#x00D7; </span><span
-                class="cmmi-10">Glucan </span><span
-                class="cmsy-10">&#x00D7; </span><span
-                class="cmmi-10">second</span></sub>              </td>
-        </tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-32-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-32-1"
-                                                                     class="td11"><span
-                class="cmmi-10">&#x03B4;</span><sub><span
-                class="cmmi-7">KCasein</span><sub><span
-                class="cmmi-5">cell</span></sub></sub></td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-32-2"
-                                                                class="td11">             Decay Rate of Kappa-Casein                    </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-32-3"
-                                                                                                                                                  class="td11"> <span
-                class="cmsy-10">&#x2223;</span><img
-                src="https://static.igem.org/mediawiki/2018/4/48/T--MIT--MITMorpheqs22x.png" alt=" ln(1&#x2215;2)
-"  class="frac" align="middle"><span
-                class="cmsy-10">&#x2223;</span> </td><td  style="white-space:nowrap; text-align:center;" id="TBL-2-32-4"
-                                                          class="td11">                proteins per second                        </td></tr><tr
-                class="hline"><td><hr></td><td><hr></td><td><hr></td><td><hr></td></tr><tr
-                style="vertical-align:baseline;" id="TBL-2-33-"><td  style="white-space:nowrap; text-align:center;" id="TBL-2-33-1"
-                                                                     class="td11"> </td> </tr></table>
-        </div>
-    </div>
-    <button class="accordion">2. Morpheus and the Cellular Potts Model</button>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-    <div class="panel">
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        <p class="noindent" >
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        <!--l. 217--><p class="noindent" >
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-        <h4 class="subsectionHead"><span class="titlemark">2.1   </span> <a
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-                id="x1-30002.1"></a>Cell Energy and Migration</h4>
+%'>Results:<br>
-        <!--l. 219--><p class="noindent" ><div class="eqnarray">
+<img src="https://static.igem.org/mediawiki/2015/0/01/Technion_HS_2015_Reaction_11.png" class="term"></span></p>
-        <center class="math-display" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-            <img
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-                    src="https://static.igem.org/mediawiki/2018/e/ea/T--MIT--MITMorpheqs23x.png" alt="P (&#x03C3; &#x2032;  &#x2192;   &#x03C3; ) = { 1-i(f&#x0394; &#x0394;HH+Y)+ Y &#x003E; 0              (1)
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-    x       x     e---T---otherwise
+%'>x.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-" class="math-display" ></center>
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-    </div>
+%'>Transcription of RNA<sub>TRLV</sub> by pLuxR promoter without the complex</span></p>
-        <table
-                class="equation"><tr><td><a
-                id="x1-3002r2"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/1/1b/T--MIT--MITMorpheqs24x.png" alt="     &#x2211;
-H  =    &#x03BB;V(&#x03BD;&#x03C3; - Vt)2
-     &#x03C3;&#x003E;0
-" class="math-display" ></center></td><td class="equation-label">(2)</td></tr></table>
-        <!--l. 228--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-3003r3"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/4/4d/T--MIT--MITMorpheqs25x.png" alt="     &#x2211;
-H  =    [&#x03BB;V (&#x03BD;&#x03C3; - Vt)2 + &#x03BB;P (&#x03C1;&#x03C3; - Pt)2]
-     &#x03C3;&#x003E;0
-" class="math-display" ></center></td><td class="equation-label">(3)</td></tr></table>
-        <!--l. 232--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-3004r4"></a>
-            <center class="math-display" >
-                <img
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-                        src="https://static.igem.org/mediawiki/2018/b/b4/T--MIT--MITMorpheqs26x.png" alt="    &#x2211;
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-H =    J[&#x03C4;(&#x03C3;i),&#x03C4;(&#x03C3;j)](1- &#x03B4;&#x03C3;i&#x03C3;j)
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-    i,j
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-" class="math-display" ></center></td><td class="equation-label">(4)</td></tr></table>
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        <!--l. 236--><p class="nopar" >
+%'>Law: Mass action</span></p>
-        <table
-                class="equation"><tr><td><a
-                id="x1-3005r5"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/7/70/T--MIT--MITMorpheqs27x.png" alt="&#x03B4;&#x03C3;i&#x03C3;j = {1,&#x03C3;i = &#x03C3;j;0,&#x03C3;i &#x2044;= &#x03C3;j}
-" class="math-display" ></center></td><td class="equation-label">(5)</td></tr></table>
-        <!--l. 240--><p class="nopar" >
-        <!--l. 242--><p> </p>Morpheus is based on the Cellular Potts Model, which defines cells as spaces in a two
-        or three dimensional lattice (our model used a hexagonal lattice in 2d) and
-        determines changes to cell shape and size by using the Hamiltonian (Equations
--4). Equation 2 determines changes to the volume of a cell <span
-                class="grmn-1000">&#x03C3; </span>with current
-        volume v<span
-                class="grmn-1000">&#x03C3; </span>in lattice sites and intended volume <span
-                class="cmmi-10">V</span> <sub><span
-                class="cmmi-7">t</span></sub> where <span
-                class="cmmi-10">&#x03BB;</span><sub><span
-                class="cmmi-7">V</span> </sub> is a constant
-        parameter of elasticity governing the extent to which the difference between
-        the cell&#8217;s immediate and intended volume contributes to a rise in its free
-        energy <span
-                class="ecti-1000">H</span>. Equation 3 incorporates a similar system for cell perimeter into the
-        equation.
-        <!--l. 254--><p> </p> In addition to modelling adjustments to cells&#8217; shape and size as they migrate, the
-        Cellular Potts Model also uses the Hamiltonian to model the interactions between
-        cells. Equation 4 determines the interaction energies between different cell types
-        where <span
-                class="cmmi-10">&#x03C4;</span><span
-                class="cmr-10">(</span><span
-                class="cmmi-10">&#x03C3;</span><sub><span
-                class="cmmi-7">i</span></sub><span
-                class="cmmi-10">,&#x03C3;</span><sub><span
-                class="cmmi-7">j</span></sub><span
-                class="cmr-10">) </span>represents the cell types of two cells <span
-                class="cmmi-10">&#x03C3;</span><sub><span
-                class="cmmi-7">i</span></sub> and <span
-                class="cmmi-10">&#x03C3;</span><sub><span
-                class="cmmi-7">j</span></sub> and <span
-                class="ecti-1000">J </span>specifies
-        said energies in matrix form. In order to prevent cells from returning values
-        for interactions with themselves, the term known as the Kronecker Delta
-        defined in Equation 5 is included. Each update to the configuration of cells in
-        the lattice as a result of equations 2-4 only occurs with a certain likelihood
-        governed by the Boltzmann probability in Equation 1. This equation states
-        that the cell&#8217;s chance of changing state is 100% if its change in energy <span
-                class="grmn-1000">&#x0394;</span><span
-                class="ecti-1000">H</span>
-        added to its resistance to change <span
-                class="ecti-1000">Y </span>is favorable (<span
-                class="grmn-1000">&#x0394;</span><span
-                class="ecti-1000">H</span>+<span
-                class="ecti-1000">Y </span>&#x003C; 0) and decreases
-        exponentially with a rate of <img
-                src="https://static.igem.org/mediawiki/2018/9/9d/T--MIT--MITMorpheqs28x.png" alt="1T-"  class="frac" align="middle"> where <span
-                class="ecti-1000">T </span>represents the amount of unfavorable
-        updates to the cell lattice, defined as modifications to the cell&#8217;s perimeter or
-        volume.
-        <p class="noindent" >
-        <h4 class="subsectionHead"><span class="titlemark">2.2   </span> <a
-                id="x1-40002.2"></a>Diffusion and the Cell Lattice Space</h4>
-        <table
-                class="equation"><tr><td><a
-                id="x1-4001r6"></a>
-            <center class="math-display" >
-                <img
-src="https://static.igem.org/mediawiki/2018/f/f4/T--MIT--MITMorpheqs29x.png" alt="-&#x2202;c    -&#x2202;2c
-&#x2202;T = D &#x2202;X2
-" class="math-display" ></center></td><td class="equation-label">(6)</td></tr></table>
-        <!--l. 277--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-4002r7"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/b/b9/T--MIT--MITMorpheqs30x.png" alt="    X-    T-
-x = L ,t = &#x03C4;
-" class="math-display" ></center></td><td class="equation-label">(7)</td></tr></table>
-        <!--l. 281--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-4003r8"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/4/4d/T--MIT--MITMorpheqs31x.png" alt="&#x2202;c   &#x03C4;D-&#x2202;2c-
-&#x2202;t = L2 &#x2202;x2
-" class="math-display" ></center></td><td class="equation-label">(8)</td></tr></table>
-        <!--l. 285--><p class="nopar" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        <table
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-                class="equation"><tr><td><a
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-                id="x1-4004r9"></a>
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-            <center class="math-display" >
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-                <img
+%'>Explanation: Each inactivated promoter transcripts mRNA in a certain rate.
-                        src="https://static.igem.org/mediawiki/2018/f/fb/T--MIT--MITMorpheqs32x.png" alt="c(x,t) &#xE306; ci,j &#x2261; c(xi,tj),xi &#x2261; i&#x03B4;x,tj &#x2261; j&#x03B4;t
+This rate is called leakiness. We multiply it by the number of inactivated LuxR
-" class="math-display" ></center></td><td class="equation-label">(9)</td></tr></table>
+promoters to get the total rate. It will be explained further in the processes
-        <!--l. 289--><p class="nopar" >
+section.</span></p>
-        <!--l. 291--><p class="noindent" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-4005r10"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/2/21/T--MIT--MITMorpheqs33x.png" alt="&#x2202;c-|xi,tj&#xE306; ci+1,j --ci--1,j= ci+1,j---ci-1,j-
-&#x2202;x         xi - xi-1        2&#x03B4;x
-" class="math-display" ></center></td><td class="equation-label">(10)</td></tr></table>
-        <!--l. 295--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-4006r11"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/b/b4/T--MIT--MITMorpheqs34x.png" alt="         &#x2202;c       &#x2202;c
-&#x2202;2c-| &#xE306; -&#x2202;x |xi+-12 --&#x2202;x |xi--12= ci+1,j---2ci,j-+ci-1,j
-&#x2202;x2  xi     xi+12 - xi- 12            (&#x03B4;x)2
-" class="math-display" ></center></td><td class="equation-label">(11)</td></tr></table>
-        <!--l. 299--><p class="nopar" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        <table
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-                class="equation"><tr><td><a
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-                id="x1-4007r12"></a>
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-            <center class="math-display" >
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-                <img
+%'>Results:<br>
-                        src="https://static.igem.org/mediawiki/2018/f/f8/T--MIT--MITMorpheqs35x.png" alt="c    = c  + -&#x03B4;t--(c    - 2c  + c    )
+<img src="https://static.igem.org/mediawiki/2015/a/a0/Technion_HS_2015_Reaction_13.png" class="term"></span></p>
- i,j+1    i,j  (&#x03B4;x)2 i+1,j    i,j   i-1,j
-" class="math-display" ></center></td><td class="equation-label">(12)</td></tr></table>
-        <!--l. 303--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-4008r13"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/a/af/T--MIT--MITMorpheqs36x.png" alt="(  2     2 )
-  &#x2202;-c+ &#x2202;-c   &#xE306; ci+1,j --2ci,j-+-ci-1,j-+ ck+1,j --2ck,j +-ck-1,j
-  &#x2202;x2  &#x2202;y2           (&#x03B4;x)2                (&#x03B4;y)2
-" class="math-display" ></center></td><td class="equation-label">(13)</td></tr></table>
-        <!--l. 307--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-4009r14"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/6/63/T--MIT--MITMorpheqs37x.png" alt="ci,k,j+1 = ci,j +-&#x03B4;t2(ci+1,j - 2ci,j +ci-1,j)+ --&#x03B4;t2(ck+1,j - 2ck,j + ck-1,j)
-             (&#x03B4;x)                      (&#x03B4;y)
-" class="math-display" ></center></td><td class="equation-label">(14)</td></tr></table>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        <!--l. 311--><p class="nopar" >
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-        <table
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-                class="equation"><tr><td><a
+%'>xi.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-                id="x1-4010r15"></a>
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-            <center class="math-display" >
+%'>Transcription of RNA<sub>TRLV</sub> by pLuxR promoter with the complex</span></p>
-                <img
-                        src="https://static.igem.org/mediawiki/2018/0/04/T--MIT--MITMorpheqs38x.png" alt="        4  &#x2211;&#x221E;    sin[(n-+-1)&#x03B8;]sin[(m-+-1)&#x03B8;]--sin-(n&#x03B8;)sin[(m---1)&#x03B8;]
-h2(2s) = 3                  [(n+ 12m )2 + 3(12m)2]s
-         m,n=-&#x221E;
-" class="math-display" ></center></td><td class="equation-label">(15)</td></tr></table>
-        <!--l. 315--><p class="nopar" >
-        <!--l. 317--><p> </p>   Another important component of our model was treating sugar, CSP, and our
-        potential outputs not simply as cell-associated values but as scalar fields representing
-        the concentration of said molecules. Fortunately Morpheus also incorporates the
-        ability to overlay fields like these on simulated cell populations and allows the field to
-        be updated locally based on cell activity at a specific lattice site (cells can also report
-        on fields or other cells surrounding them, a function which is explained in the
-        next section). Diffusion Fields were evaluated using the Central Difference
-        Method to solve the 2-D Diffusion Equation (Equations 6-14). Equation 6 is a
-        differential equation modelling diffusion in one dimension where the concentration
-        c is a function of the X-coordinate and time T. D signifies the diffusion
-        coefficient and L represents the length between nodes in (X, T) space where
-        the domain of solutions is 0<span
-                class="cmsy-10">&#x2264;</span>X<span
-                class="cmsy-10">&#x2264;</span>L. By making the change of variables in
-        Equation 7, the Diffusion Equation can be rewritten in the form of Equation
-.
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: Each activated promoter transcripts mRNA in a certain rate.
+We multiply it by the number of activated LuxR promoters to get the total rate.
+It will be explained further in the processes section.</span></p>
-        <!--l. 334--><p class="indent" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        <video src="https://static.igem.org/mediawiki/2018/7/7c/T--MIT--MITvid1.mp4" controls muted replay autoplay style="width: 30vw; position: relative; left: 32vw;"></video>
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        <p> </p>Next, a set of approximations are made in order to solve for the first and second
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        derivatives of concentration with respect to x (Equation 9). The central difference
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-        method is a version of the finite difference method of approximations to solve the
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        Diffusion Equation, which assumes that there is a minimum distance in both
+%'>Results:<br>
-        dimensions, <span
+<img src="https://static.igem.org/mediawiki/2015/f/f8/Technion_HS_2015_Reaction_14.png" class="term"></span></p>
-                class="cmmi-10">&#x03B4;</span>x and <span
-                class="cmmi-10">&#x03B4;</span>t, for which the concentration changes. This creates
-        a grid in (x, t) space as shown in Figure . The central difference method
-        approximates the x-derivative of concentration based on concentration values on
-        either side of a point (i, j), one for each of the smallest change in x from
-        the starting point: (i+1, j) and (i-1, j) (Equation 10). This is more precise
-        than the forwards or backwards difference methods which only take into
-        account one direction of incrementation in x. Next, the second derivative of
-        concentration with respect to x is approximated using the values of the first
-        derivative on a range half as large as in the previous approximation (Equation
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-).
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-        <!--l. 350--><p> </p>Using these results, an approximation of the concentration at a point 1 time step
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        in the future can be obtained based on the concentrations at the surrounding points
+%'>xii.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-        at the initial time (Equation 12), which can be appended with terms based on the
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        approximations for the first and second derivatives in Equations 10 and 11 in order to
+%'>Translation of TRLV from RNA<sub>TRLV</sub></span></p>
-        obtain a more accurate approximation. Of course, in our model this was done in two
-        dimensions, but the steps for the second dimension y are the same as those above and
-        can be combined into Equations 13 and 14 in order to obtain values for a 2-D
-        diffusion model.
-        <!--l. 360--><p> </p>  In order to sense nearby concentrations or cells in Morpheus, each cell can take
-        advantage of the NeighborhoodReporter function, which maps values within a
-        specified node length from a cell to an average, variance, or sum specific to that cell.
-        In our model, cells employed the sum function of the NeighborhoodReporter to
-        interact with the various diffusion fields. Equation 15 is the equation for a lattice sum
-        in a 2-dimensional hexagonal lattice, which Morpheus approximates to write field
-        values to individual cells.
-        <!--l. 369--><p class="noindent" >
-    </div>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
-    <button class="accordion">3. Model Specifics</button>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-    <div class="panel">
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        <p> </p>The first objective of accurately modelling a bacterial population was to model
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-            population growth over time. We chose to define our time step in the model as one
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-            second, and used the canonical doubling time of around 3800 seconds to
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-            determine a probability of cell division at each time step. Next, in order to reflect
+%'>Explanation: mRNA of TetR translates to the protein TetR in a certain
-            the constantly shifting environment of saliva on teeth, we programmed the
+rate. We multiply it by the concentration of RNA to get the total rate. It will
-            cells with random motion defined within a realistic range for cell velocity in
+be explained further in the processes section.</span></p>
-            the salivary microbiome. This ensured that the cells would interact so that
-            they would be affected by the modified adhesion associated with biofilm
-            initiation.
-            <!--l. 382--><p class="noindent" >
-        <image src="https://static.igem.org/mediawiki/2018/4/4f/T--MIT--MITpic1.png" style="width: 60%; position: relative; left: 20vw;">
-        <h4 class="subsectionHead"><span class="titlemark">3.1   </span> <a
-                id="x1-60003.1"></a>Transcription and Translation of the Relevant Genes</h4>
-        <table
-                class="equation"><tr><td><a
-                id="x1-6001r16"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/c/c1/T--MIT--MITMorpheqs39x.png" alt="dmCSP-- = ktx &#x00D7; pComC + ktf &#x00D7; ComEP  &#x00D7; pComC  - &#x03B4;mCSP &#x00D7; mCSP
-   dt
-" class="math-display" ></center></td><td class="equation-label">(16)</td></tr></table>
-        <!--l. 386--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-6002r17"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/b/bd/T--MIT--MITMorpheqs40x.png" alt="dmComD---= ktx &#x00D7; pComD - &#x03B4;mComD &#x00D7; mComD
-   dt
-" class="math-display" ></center></td><td class="equation-label">(17)</td></tr></table>
-        <!--l. 390--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-6003r18"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/4/46/T--MIT--MITMorpheqs41x.png" alt="dmComE---= ktx &#x00D7; pComE - &#x03B4;mComE &#x00D7; mComE
-   dt
-" class="math-display" ></center></td><td class="equation-label">(18)</td></tr></table>
-        <!--l. 394--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-6004r19"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/c/c5/T--MIT--MITMorpheqs42x.png" alt="dmGT--FC-= k  &#x00D7; ComEP   &#x00D7; pGTF C - &#x03B4;      &#x00D7; mGT  FC
-   dt       tf                      mGTFC
-" class="math-display" ></center></td><td class="equation-label">(19)</td></tr></table>
-        <!--l. 398--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-6005r20"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/f/f3/T--MIT--MITMorpheqs43x.png" alt="dCSPin- = &#x03B1;    &#x00D7; mCSP  - &#x03B4;    &#x00D7; CSP
-   dt      CSP            CSP       in
-" class="math-display" ></center></td><td class="equation-label">(20)</td></tr></table>
-        <!--l. 402--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-6006r21"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/b/b6/T--MIT--MITMorpheqs44x.png" alt="dComD--= &#x03B1;ComD &#x00D7;mComD   - &#x03B4;ComD&#x00D7;ComD+kub   &#x00D7;CSP ComDP   - kb&#x00D7;CSPout &#x00D7;ComD
-   dt
-" class="math-display" ></center></td><td class="equation-label">(21)</td></tr></table>
-        <!--l. 406--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-6007r22"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/1/1f/T--MIT--MITMorpheqs45x.png" alt="dComE--= &#x03B1;ComE &#x00D7;mComE   - &#x03B4;ComE &#x00D7;ComE - kk&#x00D7;CSP ComDP  &#x00D7;ComE+ktf  &#x00D7;pComC  &#x00D7;ComEP   +ktf&#x00D7;pGT F C&#x00D7;ComEP
-  dt
-" class="math-display" ></center></td><td class="equation-label">(22)</td></tr></table>
-        <!--l. 410--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-6008r23"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/e/e3/T--MIT--MITMorpheqs46x.png" alt="dGT-FC- = &#x03B1;GTFC &#x00D7; mGT F C - &#x03B4;GTFC &#x00D7; GT FC
-   dt
-" class="math-display" ></center></td><td class="equation-label">(23)</td></tr></table>
-        <!--l. 414--><p class="nopar" >
-        <!--l. 416--><p> </p>The biggest hurdle in creating an accurate model of biofilm formation in S. mutans
-        was simulating the two-component signaling system known as ComCDE. We began
-        by creating differential equations for the transcription and translation of the ComC,
-        ComD, and ComE genes based on transcription rates, translation rates and decay
-        rates for mRNAs and proteins from the literature. We also researched the genome
-        size and operon structure of the bacteria in order to better reflect its production of
-        the relevant proteins in our model. Equations 16-18 represent the transcription of
-        mRNAs for the three genes we chose to study, and the first four terms in each of
-        Equations 20-22 represent the translation of those mRNAs. All terms and
-        constants are defined in the table at the beginning of this section. Now that we
-        had the cells generating values for these variables at each time step, we
-        could add terms to model the kinetics of the two-component sensing system
-        itself.
-        <!--l. 432--><p class="noindent" >
-        <h4 class="subsectionHead"><span class="titlemark">3.2   </span> <a
-                id="x1-70003.2"></a>Two-Component Sensing System: Ligand Binding, Response Regulator
-            Phosphorylation and DNA Binding</h4>
-        <table
-                class="equation"><tr><td><a
-                id="x1-7001r24"></a>
-            <center class="math-display" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-                <img
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-                        src="https://static.igem.org/mediawiki/2018/1/17/T--MIT--MITMorpheqs47x.png" alt="dCSPout
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
----dt---= kub&#x00D7;CSP ComDP   - kb&#x00D7;CSPout &#x00D7;ComD+kk &#x00D7;CSP  ComDP  &#x00D7;ComE
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-" class="math-display" ></center></td><td class="equation-label">(24)</td></tr></table>
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        <!--l. 436--><p class="nopar" >
+%'>Results:<br>
-        <table
+<img src="https://static.igem.org/mediawiki/2015/b/b3/Technion_HS_2015_Reaction_15.png" class="term"></span></p>
-                class="equation"><tr><td><a
-                id="x1-7002r25"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/5/52/T--MIT--MITMorpheqs48x.png" alt="dCSP-ComD--
-     dt     = kb&#x00D7;CSPout&#x00D7;ComD   - kub&#x00D7;CSP ComDP  - kk&#x00D7;CSP ComDP  &#x00D7;ComE  - &#x03B4;CSP ComDP &#x00D7;CSP comDP
-" class="math-display" ></center></td><td class="equation-label">(25)</td></tr></table>
-        <!--l. 440--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-7003r26"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/c/c5/T--MIT--MITMorpheqs49x.png" alt="dComEP---= kk&#x00D7;CSP  ComD &#x00D7;ComEP   - ktf&#x00D7;pComC &#x00D7;ComEP  - ktf&#x00D7;pGT FC &#x00D7;ComEP  - &#x03B4;ComEP&#x00D7;ComEP
-   dt
-" class="math-display" ></center></td><td class="equation-label">(26)</td></tr></table>
-        <!--l. 444--><p class="nopar" >
-        <!--l. 446--><p> </p>We used the Law of Mass Action to create differential equations reflecting the
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        kinetics of ComD binding its ligand CSP, the autophosphorylation of ComD, the
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-        phosphorylation of ComE by ComD, and finally the DNA binding and transcription
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        factor activity of phosphorylated ComE. For a full explanation of the way the
+%'>xiii.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-        two-component signalling system works in live bacteria, please refer to our project
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        page, as this section assumes knowledge of the relevant components and their
+%'>TRLV self-degradation</span></p>
-        functions. The first step in the signalling system is the binding of CSP to
-        ComD. In order to initiate this activity, we used the NeighborhoodReporter
-        function to update the variable CSPout at each time step. ComD binds
-        CSP at the rate kb, at which point the two are considered one complex,
-        CSPComDP for autophosphorylated ComD:CSP, and the amount of CSP and
-        ComD decrease accordingly (Equations 21 and 24). CSPComDP has an
-        unbinding rate kub which decreases the amount of ComD:CSP complexes while
-        increasing both CSPout and ComD by the same amount. In order to simplify
-        the system of equations, the assumption was made that once CSPComDP
-        phosphorylates its response regulator ComE, the complex dissociates and
-        returns to separate ComD and CSPout. kk represents the rate of the complex
-        phosphorylating ComE (Equation 25). Once ComE is phosphorylated, it is considered
-        a different variable, ComEP for phosphorylated ComE. Phosphorylated ComE
-        upregulates the ComC and Glycosyltransferase genes with the rate ktf in order
-        to create a positive feedback loop within the population characteristic of
-        quorum-sensing systems and produce the necessary enzymes for biofilm formation.
-        Once again, the assumption was made that after ComEP binds DNA it is
-        dephosphorylated by available phosphatases and returns to its initial state,
-        hence the amount of ComEP decreases with the rate ktf for each gene it
-        upregulates and ComE increases by the same amount (Equations 22 and
-).
-        <!--l. 475--><p class="noindent" >
-        <h4 class="subsectionHead"><span class="titlemark">3.3   </span> <a
-                id="x1-80003.3"></a>Water-Insoluble Glucan Synthesis via Glucosyltransferase Activity</h4>
-        <table
-                class="equation"><tr><td><a
-                id="x1-8001r27"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/f/ff/T--MIT--MITMorpheqs50x.png" alt="dGlucan
----dt---= ke &#x00D7; GT F C &#x00D7;Sugarcell - &#x03D5;Glucan &#x00D7; Glucan
-" class="math-display" ></center></td><td class="equation-label">(27)</td></tr></table>
-        <!--l. 479--><p class="nopar" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        <!--l. 481--><p> </p>Biofilm formation in the model depends on two main factors: Sugar available to the
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        cell and the amount of Glycosyltransferase enzymes a cell possesses (GTFC). mRNAs
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        for GTFC (Equation 19) are only transcribed when ComEP binds the gene to
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-        upregulate it, and GTFC proteins are translated according to Equation 23.
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        Sugar concentration (<span
+%'>Law: Mass action</span></p>
-                class="cmmi-10">Sugar</span><sub><span
-                class="cmmi-7">field</span></sub>) is given an initial value as a diffusion field
-        in the model, which was defined as a homogeneous diffusion field due to
-        sugar&#8217;s high solubility in saliva. <span
-                class="cmmi-10">Sugar</span><sub><span
-                class="cmmi-7">cell</span></sub> is defined at each time step via the
-        NeighborhoodReporter function based on the current concentration of the
-        <span
-                class="cmmi-10">Sugar</span><sub><span
-                class="cmmi-7">cell</span></sub>.
-        <!--l. 492--><p> </p> The final differential equation based on the Law of Mass Action in the most basic
-        form of the model, Equation 27, governs the production of water-insoluble
-        glucans from available sugar. The enzymatic activity of GTFC is denoted
-        ke, and the glucans become the basis of the extracellular biofilm by being
-        incorporated into the extracellular field of the same name at the rate <span
-                class="cmmi-10">&#x03D5;</span><sub><span
-                class="cmmi-7">Glucan</span></sub>. In
-        order to simulate the transition of S. mutans from free-floating planktonic
-        cells to biofilm-bound immobilized cells which grow in localized colonies,
-        each cell was programmed to also use the NeighborhoodReporter to return
-        a constantly updated value for how concentrated biofilm-forming glucans
-        are around that cell. Once the local biofilm reaches a threshold value of
-arbitrary units, cells are considered to be adhered and their movement
-        ceases.
-        <!--l. 505--><p class="noindent" >
-        <h4 class="subsectionHead"><span class="titlemark">3.4   </span> <a
-                id="x1-90003.4"></a>Extracellular Diffusion Fields</h4>
-        <table
-                class="equation"><tr><td><a
-                id="x1-9001r28"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/c/cb/T--MIT--MITMorpheqs51x.png" alt="dCSP
---dt-- = &#x03D5;CSP &#x00D7;CSPin
-" class="math-display" ></center></td><td class="equation-label">(28)</td></tr></table>
-        <!--l. 509--><p class="nopar" >
-        <table
-                class="equation"><tr><td><a
-                id="x1-9002r29"></a>
-            <center class="math-display" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-                <img
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-                        src="https://static.igem.org/mediawiki/2018/1/1a/T--MIT--MITMorpheqs52x.png" alt="dBiofilm
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
----------= &#x03D5;Glucan &#x00D7;Glucan
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-   dt
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-" class="math-display" ></center></td><td class="equation-label">(29)</td></tr></table>
+%'>Explanation: Each molecule of TRLV has a certain probability to degrade,
-        <!--l. 513--><p class="nopar" >
+hence the corresponding change rate in the amount of the TRLV is proportional
-        <table
+to the amount of TRLV all the cells.</span></p>
-                class="equation"><tr><td><a
-                id="x1-9003r30"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/4/4c/T--MIT--MITMorpheqs53x.png" alt="dSugarfield
-----dt----= - ke &#x00D7; GT FC &#x00D7; Sugarcell
-" class="math-display" ></center></td><td class="equation-label">(30)</td></tr></table>
-        <!--l. 517--><p class="nopar" >
-        <!--l. 519--><p> </p>Equations 28-30 are evaluated at each time step at each point in the lattice in order
-        to affect the changes individual cells make to field values. Both the biofilm and CSP
-        field equations increase at an export rate times the number of proteins a cell at a
-        given point has, and the Sugar decreases as GTFC transforms it into glucans. Sugar
-        undergoes homogeneous or well-mixed diffusion, CSP was given a diffusion
-        constant of <span
-                class="ecti-1000">D </span>= 1, and the Biofilm was given the diffusion constant <span
-                class="ecti-1000">D </span>=
-.001, both in as employed in Equation 6 and its subsequent approximate
-        solutions.
-        <!--l. 529--><p class="noindent" >
-       </div>
-    <button class="accordion">4. Results</button>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-    <div class="panel">
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        <p> </p>Our model proved quite successful in qualitatively reproducing multiple aspects of
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        the formation of live <span
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-                class="ecti-1000">S. mutans </span>biofilms. The simulated cells form clear microcolonies
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        in the locations where glucan concentration is the highest which expand
+%'>Results:<br>
-        from there. CSP increases everywhere throughout the simulation as the
+<img src="https://static.igem.org/mediawiki/2015/d/d3/Technion_HS_2015_Reaction_16.png" class="term"></span></p>
-        time steps modelled only encompass the phase of growth when that is the
-        case.
-        <!--l. 537--><p class="noindent" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        <h4 class="subsectionHead"><span class="titlemark">4.1   </span> <a
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-                id="x1-110004.1"></a>Effect of Sugar Concentration on Biofilm Formation</h4>
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        <img src="https://static.igem.org/mediawiki/2018/0/07/T--MIT--MITpic2.png">
+%'>xiv.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-        <!--l. 539--><p> </p>The first parameter we varied was sugar by modifying the initial value of the
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        diffusion field. After fifteen thousand time steps, there is a clear difference in biofilm
+%'>TRLV binds to the pTetR repressor </span></p>
-        density in plots of the cells themselves. Graphs of data collected from a
-        representative cell in each condition show a clear distinction in glucan production
-        between sugar concentrations. For the time period simulated, limiting sugar
-        concentration was between 10 and 25 arbitrary units, at which point the cells were
-        unable to generate enough glucans to adhere and create microcolonies in a
-        biofilm. These results reflect our experiments with live <span
-                class="ecti-1000">S. mutans </span>in which
-        we varied sucrose concentration and measured its effect on biofilm growth
-        through image analysis of of colony-forming units as well as crystal violet
-        staining. As expected based on our differential equations, the concentration
-        of sugar decreases exponentially over time, whereas the total amount of
-        glucans produced increases exponentially over time. The rates of exponential
-        growth and decay also depend on the sugar available, with the difference
-        in glucans produced by the end of the simulation being around one order
-        of magnitude less than the difference in sugar available in all cases. This
-        data was useful in helping us match the arbitrary units in the model to real
-        experiments.
-        <!--l. 559--><p class="noindent" >
-        <h4 class="subsectionHead"><span class="titlemark">4.2   </span> <a
-                id="x1-120004.2"></a>Inhibition of GTFC Activity by Single-Chain Variable Fragments</h4>
-        <!--l. 561--><p class="noindent" >
-        <h5 class="subsubsectionHead"><span class="titlemark">4.2.1   </span> <a
-                id="x1-130004.2.1"></a>Additional Cellular Equations Governing ScFv Activity</h5>
-        <table
-                class="equation"><tr><td><a
-                id="x1-13001r31"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/8/89/T--MIT--MITMorpheqs54x.png" alt="dGT-F-CScF-v = kab &#x00D7; ScFvcell &#x00D7; GT FC - &#x03B4;GTFCScFv &#x00D7; GT FCScF v
-     dt
-" class="math-display" ></center></td><td class="equation-label">(31)</td></tr></table>
-        <!--l. 565--><p class="nopar" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        <table
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-                class="equation"><tr><td><a
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-                id="x1-13002r32"></a>
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-            <center class="math-display" >
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-                <img
+%'>Law: Mass action</span></p>
-                        src="https://static.igem.org/mediawiki/2018/f/f0/T--MIT--MITMorpheqs55x.png" alt="dScF-vcell= - k  &#x00D7;ScF v   &#x00D7; GT FC - &#x03B4;      &#x00D7; ScF v
-   dt         ab       cell           ScFvcell       cell
-" class="math-display" ></center></td><td class="equation-label">(32)</td></tr></table>
-        <!--l. 569--><p class="nopar" >
-        <!--l. 572--><p class="noindent" >
-        <h5 class="subsubsectionHead"><span class="titlemark">4.2.2   </span> <a
-                id="x1-140004.2.2"></a>Additional Field Equations Governing ScFv Activity</h5>
-        <table
-                class="equation"><tr><td><a
-                id="x1-14001r33"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/9/93/T--MIT--MITMorpheqs56x.png" alt="dScF-vfield-= (- k &#x00D7; ScF v   &#x00D7;GT F C - &#x03B4;      &#x00D7; ScFv   ) ÷100
-    dt         ab       cell          ScFvcell      cell
-" class="math-display" ></center></td><td class="equation-label">(33)</td></tr></table>
-        <!--l. 576--><p class="nopar" >
-        <!--l. 579--><p class="noindent" >
-        <h5 class="subsubsectionHead"><span class="titlemark">4.2.3   </span> <a
-                id="x1-150004.2.3"></a>Modified Equations Integating ScFv Activity</h5>
-        <table
-                class="equation"><tr><td><a
-                id="x1-15001r34"></a>
-            <center class="math-display" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-                <img
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-                        src="https://static.igem.org/mediawiki/2018/5/5a/T--MIT--MITMorpheqs57x.png" alt="dGT FC
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
---dt---= &#x03B1;GT FC &#x00D7; mGT F C - &#x03B4;GT FC &#x00D7;GT F C - kab &#x00D7; ScFvcell &#x00D7; GT FC
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-" class="math-display" ></center></td><td class="equation-label">(34)</td></tr></table>
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        <!--l. 583--><p class="nopar" >
+%'>Explanation: The activation rate is proportional to the product of the
+concentrations of the dimer and the number of plasmid plasmids with pTetR promoters.
+It will be explained later in the processes section.</span></p>
-        <img src="https://static.igem.org/mediawiki/2018/1/1a/T--MIT--MITpic3.png">
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-        <!--l. 585--><p> </p>The primary purpose of our model was to preemptively compare the effectiveness of
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-        our potential outputs by modelling their inhibition of different parts of the pathway
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-        and its effects on overall biofilm growth. We began by implementing the above
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-        differential equations (Equations 31-33), and modifying Equation 23 into equation 34.
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        The amount of ScFvs affecting the cell is determined via the NeighborhoodReporter
+%'>Results:<br>
-        function, and the ScFvs bind GTFC at the rate kab. Once the ScFv binds a GTFC, it
+<img src="https://static.igem.org/mediawiki/2015/6/67/Technion_HS_2015_Reaction_17.png" class="term"></span></p>
-        forms a GTFC:ScFv complex represented in Equation 31, decreasing both
-        the cell&#8217;s GTFC and ScFv count accordingly (Equations 32 and 34). The
-        complex degrades quickly based on a rate from the literature, and once it has
-        degraded both the ScFv and GTFC bound have been eliminated from the
-        simulation.
-        <!--l. 598--><p> </p> The effects of the ScFv on biofilm formation are immediately obvious from plots
-        of the cells at the end of the simulation, with only 0.075 arbitrary units of
-        concentration to start with being enough to prevent the bacteria from forming
-        adherent microcolonies throughout the time modelled. The critical point
-        at which the amount of GTFC: ScFv complexes goes from increasing to
-        decreasing determines how soon the cells are able to begin initiating biofilm
-        formation, assuming they are still in the logarithmic growth phase where CSP
-        production is increasing. Since GTFC production is decreased, everything
-        downstream of it is also affected: cells consume less sugar, produce fewer
-        glucans, and create less of a biofilm field in the presence of ScFvs, as shown
-        in the following figures. In equation 33, the decrease of the ScFv field is
-        divided by 100 due to the membrane resolution being set to 100 for the
-        simulation.
-        <!--l. 613--><p class="noindent" >
-        <h4 class="subsectionHead"><span class="titlemark">4.3   </span> <a
-                id="x1-160004.3"></a>Inhibition of Glucan Activity by Kappa-Casein</h4>
-        <!--l. 615--><p class="noindent" >
-        <h5 class="subsubsectionHead"><span class="titlemark">4.3.1   </span> <a
-                id="x1-170004.3.1"></a>Additional Cellular Equations Governing K-Casein Activity</h5>
-        <table
-                class="equation"><tr><td><a
-                id="x1-17001r35"></a>
-            <center class="math-display" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-                <img
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
-                        src="https://static.igem.org/mediawiki/2018/f/f9/T--MIT--MITMorpheqs58x.png" alt="dKCaseincell
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
------dt-----= - kkc &#x00D7; KCaseincell &#x00D7; Glucan - &#x03B4;KCaseincell &#x00D7; KCaseincell
+%'>xv.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-" class="math-display" ></center></td><td class="equation-label">(35)</td></tr></table>
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        <!--l. 619--><p class="nopar" >
+%'>TRLV unbinds from the pLuxR repressor</span></p>
-        <!--l. 622--><p class="noindent" >
-        <h5 class="subsubsectionHead"><span class="titlemark">4.3.2   </span> <a
-                id="x1-180004.3.2"></a>Additional Fiels Equations Governing K-Casein Activity</h5>
-        <table
-                class="equation"><tr><td><a
-                id="x1-18001r36"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/2/2c/T--MIT--MITMorpheqs59x.png" alt="dKCaseinfield
------dt------= (- kkc&#x00D7;KCaseincell&#x00D7;Glucan- &#x03B4;KCaseincell&#x00D7;KCaseincell)÷100
-" class="math-display" ></center></td><td class="equation-label">(36)</td></tr></table>
-        <!--l. 626--><p class="nopar" >
-        <!--l. 629--><p class="noindent" >
-        <h5 class="subsubsectionHead"><span class="titlemark">4.3.3   </span> <a
-                id="x1-190004.3.3"></a>Modified Equations Integating K-Casein Activity</h5>
-        <table
-                class="equation"><tr><td><a
-                id="x1-19001r37"></a>
-            <center class="math-display" >
-                <img
-                        src="https://static.igem.org/mediawiki/2018/f/f7/T--MIT--MITMorpheqs60x.png" alt="dGlucan-= ke&#x00D7;GT F C&#x00D7;Sugarcell- &#x03D5;Glucan&#x00D7;Glucan - kkc&#x00D7;KCaseincell&#x00D7;Glucan
-   dt
-" class="math-display" ></center></td><td class="equation-label">(37)</td></tr></table>
-        <!--l. 633--><p class="nopar" >
-        <img src="https://static.igem.org/mediawiki/2018/0/08/T--MIT--MITpic4.png">
-        <!--l. 635--><p> </p>Next, we sought to create a similar set of equations to model the effect of
-        Kappa-Casein on biofilm formation. Equation 35 governs the effect of K-Casein on
-        an individual cell. Cells use the NeighborhoodReporter to determine the
-        amount of K-Casein molecules affecting it, and those molecules bind glucans
-        at a rate of kkc. Rather than creating a new variable for the complex of
-        K-Casein and a glucan, both are removed from the simulation immediately.
-        Due to being outside the cell, the binding rate of K-Casein was set to 1.
-        Equation 37 is a modification of equation 27 integrating the decrease in
-        glucans.
-        <!--l. 645--><p> </p> It became clear from varying the initial K-Casein concentration that the
-        equations were successful in modelling the decrease in biofilm formation due to a
-        decrease in effective adherent glucans surrounding the cells. However, despite the
-        K-Casein being given a dramatically higher binding rate than the ScFvs, a much
-        higher concentration of K-Casein was required to limit the formation of a biofilm
-        during the time simulated. In fact, ten times as high a concentration of
-        K-Casein was required to achieve the same effects as ScFvs. The K-Casein
-        also affected fewer aspects of the overall system of equations because its
-        influence was only effective on one of the most downstream components of the
-        simulation.
-        <!--l. 657--><p class="noindent" >
-        </div>
-    <button class="accordion">5. Conclusions</button>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-    <div class="panel">
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-       <p> </p>The most obvious takeaway from the results of our computational model was that
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-            ScFvs were more effective than K-Casein at inhibiting biofilm formation, or, more
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-            broadly, inhibiting GTFC is a better method for limiting the virulence of S. mutans
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-            than reducing the glucans themselves. This result had a profound effect on our
+%'>Law: Mass action</span></p>
-            experimental design and our project as a whole. While Kappa-Casein can be readily
-            purchased and implemented in live experiments, the ScFvs we planned to
-            express and implement were not available for purchase anywhere, would be
-            very expensive to get synthesized, and would require additional training
-            and lab techniques to isolate from mammalian cells expressing the protein
-            itself. However, thanks to data from the model, we were able to confirm the
-            superiority of the ScFvs for our purposes. Based on these results, we decided to
-            move further ahead with characterization experiments for GTFC-inhibiting
-            ScFvs.
-            <!--l. 674--><p class="noindent" >
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-    </div>
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-</div>
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-    <script>
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-        var acc = document.getElementsByClassName("accordion");
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-        var i;
+%'>Explanation: Each activated promoter has a certain probability to
+deactivate and to release its TRLV, and therefore the rate of this process is proportional
+to the number of activated promoters. It will be explained later in the
+processes section.</span></p>
-        for (i = 0; i < acc.length; i++) {
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
-            acc[i].addEventListener("click", function() {
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
-                this.classList.toggle("active");
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
-                var panel = this.nextElementSibling;
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
-                if (panel.style.maxHeight){
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
-                    panel.style.maxHeight = null;
+%'>Results:<br>
-                } else {
+<img src="https://static.igem.org/mediawiki/2015/e/e0/Technion_HS_2015_Reaction_18.png" class="term"></span></p>
-                    panel.style.maxHeight = panel.scrollHeight + "px";
-                }
-            });
-        }
-    </script>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>xvi.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Transcription of RNA<sub>ccdB</sub> by ptetR promoter without the TRLV</span></p>
-</body>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: For each inactivated repressor there is transcription to mRNA
+in a certain rate. We multiply it by the number of inactivated ptetR promoters
+to get the total rate. It will be explained further in the processes section.</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/7/74/Technion_HS_2015_Reaction_19.png" class="term"></span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>xvii.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Transcription of RNA<sub>ccdB</sub> by ptetR promoter with the TRLV</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: For each activated repressor there is still transcription to
+mRNA in a certain rate. We multiply it by the number of activated ptetR promoters
+to get the total rate. It will be explained further in the processes section.</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/d/d6/Technion_HS_2015_Reaction_20.png" class="term"></span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>xviii.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Translation of ccdB from RNA<sub>ccdB</sub></span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: mRNA of ccdb translates to the protein ccdb in a certain
+rate. We multiply it by the concentration of RNA to get the total rate. It will
+be explained further in the processes section.</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/d/d1/Technion_HS_2015_Reaction_21.png" class="term"></span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>xix.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>ccdB self-degradation</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass action</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: Each molecule of ccdB has a certain probability to degrade,
+hence the corresponding change rate in the amount of the ccdB is proportional
+to the amount of ccdB all the cells.</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/3/3e/Technion_HS_2015_Reaction_22.png" class="term"></span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>xx.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>producing of the desired protein x by the pCONST promoter</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass Action</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: Each plasmid with our circuit produces the desired enzyme, X,
+in a certain amount.</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/a/a8/Technion_HS_2015_Reaction_23.png" class="term"></span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>xxi.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>producing of LuxR by the pCONST promoter</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass Action</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: Each plasmid with our circuit produces LuxR in a certain amount.</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/3/35/Technion_HS_2015_Reaction_24.png" class="term"></span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>xxii.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>producing of AiiA by the pCONST promoter</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Law: Mass Action</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Explanation: Each plasmid with our circuit produces AiiA in a certain amount.</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/2/20/Technion_HS_2015_Reaction_25.png" class="term"></span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:54.0pt;text-align:left;text-indent:-36.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%'>xxiii.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>plasmid loss</span></p>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>We model the effect of plasmid loss on the system. It affects the
+equations by having both bacteria with plasmids (N+) and without plasmid (N-).</span></p>
+<p class=MsoListParagraphCxSpLast dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Further explanation is <a
+href="https://2015.igem.org/Team:Technion_HS_Israel/PlasmidLoss">here</a>. </span>
+<span dir=LTR></span>
+<p class=MsoListParagraphCxSpMiddle dir=LTR style='margin-top:0cm;margin-right:
+cm;margin-bottom:10.0pt;margin-left:72.0pt;text-align:left;text-indent:-18.0pt;
+direction:ltr;unicode-bidi:embed'><span style='font-size:16.0pt;line-height:
+%;font-family:"Courier New"'>o<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;
+</span></span><span dir=LTR></span><span style='font-size:16.0pt;line-height:
+%'>Results:<br>
+<img src="https://static.igem.org/mediawiki/2015/9/97/Technion_HS_2015_Reaction_26.png" class="term"></span></p>
+</p>
+</p>
+<h2>
+. Processes
+</h2>
+<h3 class="Subsection">
+.1. AHL Diffusion
+</h3>
+<div class="Unindented"><p>
+Our system is based on controlling the initial amount of AHL inside the cells in order to control the life span of the bacteria. However, we can’t put the AHL directly inside the cells. We put it in the test tube together with the bacteria. Therefore, it’s important to model how this process, of AHL entering the cell, accure and how it affects our system. It is part of seeing our system as an integrated complex, whose parts interect with each other and affect the result: the external AHL diffuse inside the cells, inside the cells the AHL is degraded by the AiiA, and as AHL is decreasing inside the cells, the external AHL diffuses accordingly into the cells in order to maintain equilibrium.</p>
+</div>
+<div class="Indented"><p>
+As AHL diffuse rather quickly through the membrane of E. Coli, we use a rather simplified model. We assume that each seperated part of our system (external environment, inside each cell, etc) is homogenous, which is quite true as AHL diffuses quickly, and it’s suffeciant to our needs.</p>
+</div>
+<div class="Indented"><p>
+We base our diffusion model on <a class="URL" href="http://www.tiem.utk.edu/~gross/bioed/webmodules/diffusion.htm">this document</a>. Essentially, it says that the rate of the diffusion is proportional to the concetration gradient.</p>
+</div>
+<h3 class="Subsection">
+.2. Transcription and Translation
+</h3>
+<div class="Unindented"><p>
+We have two proteins whose production is a part of our biological circuit: the TetR and the ccdb (or the RFP in the experiments). In our model, each of this processes is described using 4 equations. The first two describe the number of plasmids with an activated promoter (or repressor, depends on the processes) using regular Mass Action. In the third we assume that RNA is transcripted in a certain constant rate for each actiivated binding site and the same for unactivated, and get an expression for the change in the concentration of RNA strands. In the last one we desscribe the translation rate of the protein, using the Mass Action law, as a function of the RNA. We assume that the translation rate is proportional to the concentration of the RNA. </p>
+</div>
+<h3 class="Subsection">
+.3. Plasmid Loss
+</h3>
+<div class="Unindented"><p>
+Read the full explanation and description of the plasmid loss model <a class="URL" href="https://2015.igem.org/Team:Technion_HS_Israel/PlasmidLoss">here</a>.</p>
+</div>
+<h2 class="Section">
+. Documents
+</h2>
+<div class="Unindented"><p>
+During our work, we’ve made a documents describing different aspects and parts of our model. We put them here in hope that whomever want to dive into our model will be able to do so and will find these documents interesting.</p>
+</div>
+<ul>
+<li>
+<a class="URL" href="https://static.igem.org/mediawiki/2015/8/8c/Technion_HS_2015_Scopes_ofModelling.pdf">Scopes in biological systems modelling.</a>
+</li>
+<li>
+<a class="URL" href="https://static.igem.org/mediawiki/2015/9/9b/Simulation.pdf">Solving dynamic systems numerically</a>
+</li>
+<li>
+Partial modelling notebook: <a class="URL" href="https://static.igem.org/mediawiki/2015/9/9c/Technion_HS_2015_Summary_Modelling1.pdf">1</a> <a class="URL" href="https://static.igem.org/mediawiki/2015/2/2c/Technion_HS_2015_Summary_Modelling2.pdf">2</a> <a class="URL" href="https://static.igem.org/mediawiki/2015/8/84/Technion_HS_2015_Summary_Modelling3.pdf">3</a>.
+</li>
+</ul>
+<h2 class="Section">
+. Simulation
+</h2>
+<div class="Unindented"><p>
+We simulated our system a few times using our numerical solver. Description and documentation of our solver can be found <a class="URL" href="https://2015.igem.org/Team:Technion_HS_Israel/Software/Simulation">here</a>. The results we’ve got are in the <a class="URL" href="https://2015.igem.org/Team:Technion_HS_Israel/Modelling/Results">Modelling Results page</a>.</p>
+<h3>Parameters</h3>
+<p>In order to describe our biological system, we need the right parameters. We looked up in literature and in iGEM projects from previous years (using our <a href="https://2015.igem.org/Team:Technion_HS_Israel/Constants_Database"> Constant Database</a>!) and found almost all the 40 required parameters and constants, and estimated the rest. Check our parameter table <a href="https://2015.igem.org/Team:Technion_HS_Israel/Modelling/Parameters">here</a></p>
+</div>
+</body>
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Difference between revisions of "Team:IIT Kanpur/TestPage"

Revision as of 12:20, 17 October 2018

Model Overview

1. Abstract

2.Introduction

2.1. Why Do We Need a Model?

2.2. Methods

2.3. Our System

2.3.1. In General

2.3.2. In Detail

2.3.3. Note About Notations

3. Reactions

4. Processes

4.1. AHL Diffusion

4.2. Transcription and Translation

4.3. Plasmid Loss

5. Documents

6. Simulation

Parameters