Difference between revisions of "Team:NYU Abu Dhabi/Model"

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<html>
 +
 +
 +
<script>
 +
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 +
$(document).ready(function() {
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$("#HQ_page").attr('id','');
 +
//mobile menu access
 +
$(".igem_2018_team_mobile_bar").click(function(){
 +
$(this).next().toggleClass("displaying_menu");
 +
});
 +
});
 +
 +
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 +
</script>
 +
 +
<head>
 +
<link href="https://fonts.googleapis.com/css?family=IBM+Plex+Sans" rel="stylesheet">
 +
<meta name="viewport" content="width=device-width, initial-scale=1">
 +
  <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
 +
  <meta name="viewport" content="width=device-width, initial-scale=1">
 +
<!-- Bootstrap -->
 +
        <link rel="stylesheet" href="https://2018.igem.org/Template:NYU_Abu_Dhabi/BootstrapCSSV4?action=raw&amp;ctype=text/css" />
 +
        <script type="text/javascript" src="https://2018.igem.org/Template:NYU_Abu_Dhabi/BootstrapJSV4?action=raw&amp;ctype=text/javascript"></script>
 +
<style>
 +
/**************************************************************************************************************************************************************************************************/
 +
/**************************************************************************************************************************************************************************************************/
 +
/* DEFAULT WIKI SETTINGS */
 +
/**************************************************************************************************************************************************************************************************/
 +
#home_logo, #sideMenu { display:none; }
 +
#sideMenu, #top_title, .patrollink  {display:none;}
 +
#content { margin-left:0px; margin-top:-7px; padding:0px; width:100%;}
 +
/* body {background-color:white;
 +
width: 960px; */
 +
    /* width: 80%; */
 +
      /* margin: auto;} */
 +
#bodyContent h1, #bodyContent h2, #bodyContent h3, #bodyContent h4, #bodyContent h5 { margin-bottom: 0px; }
 +
/**************************************************************************************************************************************************************************************************/
 +
/* MENU */
 +
/**************************************************************************************************************************************************************************************************/
 +
.igem_2018_team_menu .submenu{
 +
background-color: white;
 +
clear:both;
 +
display:none;
 +
float: left;
 +
width:100%;
 +
}
 +
/* Styling the menu */
 +
/*this wraps the whole of the menu*/
 +
.igem_2018_team_menu {
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background-color:white;
 +
border-left: 1px solid white;
 +
display:block;
 +
float:right;
 +
height:100vh;
 +
max-width: 270px;
 +
overflow-y: auto;
 +
overflow-x: hidden;
 +
padding:0px;
 +
position:fixed;
 +
right:0%;
 +
text-align:left;
 +
width: 15%;
 +
}
 +
.igem_2018_team_menu.displaying_menu{
 +
display:block;
 +
}
 +
.igem_2018_team_menu  a {
 +
color: white;
 +
text-decoration:none;
 +
text-align: center;
 +
}
 +
.igem_2018_team_menu img {
 +
width:100%;
 +
}
 +
.igem_2018_team_menu .menu_item {
 +
background-color: white;
 +
border-bottom: 1px solid white;
 +
clear: both;
 +
color: white;
 +
cursor: pointer;
 +
float: left;
 +
font-size: 120%;
 +
font-weight: bold;
 +
padding: 15px 0px 15px 5%;
 +
width: 100%;
 +
}
 +
.igem_2018_team_menu .menu_item.direct_link {
 +
color: white;
 +
padding-left: 15%;
 +
}
 +
.igem_2018_team_menu .menu_item:hover {
 +
background-color: white;
 +
}
 +
.igem_2018_team_menu .menu_item .submenu_control_icon {
 +
color: white;
 +
float: left;
 +
width: 10%;
 +
}
 +
/* submenu icon "+"  "-"*/
 +
.igem_2018_team_menu .menu_item .submenu_control_icon::before {
 +
content:"-";
 +
}
 +
/* submenu icon "+"  "-"*/
 +
.igem_2018_team_menu .menu_item .submenu_control_icon.open::before {
 +
content:"+";
 +
}
 +
/* styling for a submenu item */
 +
.igem_2018_team_menu .submenu .submenu_item {
 +
border-bottom: 1px solid white;
 +
color: white;
 +
height: 30px;
 +
float: left;
 +
font-size: 110%;
 +
font-weight: bold;
 +
padding: 12px 0px 0px 15%;
 +
width: 100%;
 +
}
 +
.igem_2018_team_menu .submenu .submenu_item:hover {
 +
background-color: white;
 +
}
 +
.igem_2018_team_menu .submenu .submenu_item.current_page,
 +
.igem_2018_team_menu .menu_item.current_page,
 +
.igem_2018_team_menu .menu_item.direct_link.current_page {
 +
background-color:white;
 +
}
 +
/* NAVBAR STYLES */
 +
.navbar {
 +
    background-color: white;
 +
    font-size: 1rem;
 +
}
 +
.navbar-brand>img {
 +
    width: 120px;
 +
    height: 33px;
 +
    position: relative;
 +
}
 +
.navbar a:visited {
 +
    color: #000;
 +
}
 +
/*Styling Buttons*/
 +
.fa {
 +
font-size: 20px;
 +
padding:17px;
 +
width: 54px;
 +
text-align: center;
 +
text-decoration: none;
 +
/* margin: 5px 2px; */
 +
border-radius: 50%;
 +
}
 +
.fa:hover {
 +
opacity: 0.7;
 +
}
 +
.fa-facebook {
 +
background: #7E5BD3;
 +
color: white;
 +
}
 +
.fa-twitter {
 +
background: #7E5BD3;
 +
color: white;
 +
}
 +
.fa-google {
 +
background: #7E5BD3;
 +
color: white;
 +
}
 +
.fa-youtube {
 +
background: #7E5BD3;
 +
color: white;
 +
}
 +
.fa-instagram {
 +
background: #7E5BD3;
 +
color: white;
 +
}
 +
/* end of styling buttons */
 +
/* Styling the footer */
 +
.footer>.container-fluid {
 +
padding: 10px 10px;
 +
}
 +
.footer>.container-fluid>.row {
 +
display: flex;
 +
}
 +
.footer-section {
 +
text-align: center !important;
 +
/* padding: 0px 25px; */
 +
display: flex;
 +
flex-wrap: wrap;
 +
flex-direction: row;
 +
align-items: center;
 +
align-content: center;
 +
justify-content: center;
 +
font-family: 'IBM Plex Sans', sans-serif;
 +
}
 +
.footer-text {
 +
text-align: center !important;
 +
font-family: 'IBM Plex Sans', sans-serif;
 +
}
 +
.footer-logo {
 +
width: 80%;
 +
padding-right: 10px;
 +
display: inline-block;
 +
}
 +
.footer-logo2 {
 +
width: 100%;
 +
padding-right: 15px;
 +
display: inline-block;
 +
}
 +
.footer {
 +
font-family: 'IBM Plex Sans', sans-serif;
 +
width:100%;
 +
}
 +
/*end of styling the footer */
 +
/*mobile menu bar styling*/
 +
/**************************************************************************************************************************************************************************************************/
 +
.igem_2018_team_mobile_bar {
 +
background-color:#e4dede;
 +
border-bottom: 1px solid #c4baba;
 +
cursor:pointer;
 +
display:none;
 +
float:left;
 +
margin-top: 0;
 +
padding: 5px 0;
 +
position:fixed;
 +
width:100%;
 +
}
 +
.igem_logo_mobile img {
 +
width:70px;
 +
}
 +
.igem_logo_mobile {
 +
float:left;
 +
padding-left: 5%;
 +
width: 30%;
 +
}
 +
.igem_menu_control_mobile img {
 +
width:25px;
 +
}
 +
.igem_menu_control_mobile {
 +
float:right;
 +
padding-right:5%;
 +
padding-top:5px;
 +
text-align:right;
 +
width: 30%;
 +
}
 +
/**************************************************************************************************************************************************************************************************/
 +
/* CONTENT OF THE PAGE */
 +
/**************************************************************************************************************************************************************************************************/
 +
/* general wrapper for the content */
 +
.igem_2018_team_content {
 +
background-color: white;
 +
display:block;
 +
width: 87%;
 +
}
 +
/* subwrapper to center content */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper {
 +
margin:auto;
 +
max-width: 1400px;
 +
width:90%;
 +
}
 +
/*general styling*/
 +
/**************************************************************************************************************************************************************************************************/
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h1 { font-size: 210%;}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h2 { font-size: 190%;}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h3 { font-size: 170%;}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h4 { font-size: 150%;}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h5 { font-size: 140%;}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h6 { font-size: 130%;}
 +
/* styling for the titles h1, h2*/
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h1, .igem_2018_team_content .igem_2018_team_column_wrapper h2 {
 +
border-bottom:0px;
 +
color: #2A4C44;
 +
font-family: 'IBM Plex Sans', sans-serif;
 +
padding: 10px 0px;
 +
}
 +
/* styling for the titles h3, h3, h5, h6 */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h3,
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.igem_2018_team_content .igem_2018_team_column_wrapper h4,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h5,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper h6 {
 +
border-bottom:0px;
 +
color: #2A4C44;
 +
font-family: 'IBM Plex Sans', sans-serif;
 +
padding: 5px 0px;
 +
}
 +
/* text */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper p {
 +
font-size: 130%;
 +
font-family: 'IBM Plex Sans', sans-serif;
 +
padding: 5px 0px;
 +
text-align: left;
 +
color: #2A4C44;
 +
}
 +
/* Links */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper a {
 +
color: #2A4C44;
 +
font-weight: bold;
 +
text-decoration: underline;
 +
text-decoration-color:#772C7F;
 +
transition: all 0.4s ease;
 +
-webkit-transition: all 0.4s ease;
 +
-moz-transition: all 0.4s ease;
 +
-ms-transition: all 0.4s ease;
 +
-o-transition: all 0.4s ease;
 +
}
 +
/* hover for the links */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper a:hover {
 +
color: #2A4C44;
 +
text-decoration:none;
 +
}
 +
/* Table */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper table {
 +
border: 1px solid #2A4C44;
 +
border-collapse: collapse;
 +
font-size: 130%;
 +
width: 100%;
 +
}
 +
/* table cells */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper td {
 +
border: 1px solid #2A4C44;
 +
border-collapse: collapse;
 +
font-size: 105%;
 +
padding: 10px;
 +
vertical-align: text-top;
 +
}
 +
/* table headers */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper th {
 +
background-color:white;
 +
border: 1px solid #2A4C44;
 +
border-collapse: collapse;
 +
font-size: 110%;
 +
padding: 10px;
 +
vertical-align: text-top;
 +
}
 +
/* non numbered lists */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper ul, .igem_2018_team_content .igem_2018_team_column_wrapper ol {
 +
font-size: 130%;
 +
font-family: 'IBM Plex Sans', sans-serif;
 +
padding:0px 20px;
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper ul ul li, .igem_2018_team_content .igem_2018_team_column_wrapper ul ul ul li,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper ul ol li, .igem_2018_team_content .igem_2018_team_column_wrapper ul ul ol li,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper ol ol li, .igem_2018_team_content .igem_2018_team_column_wrapper ul ol ul li,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper ol ul li, .igem_2018_team_content .igem_2018_team_column_wrapper ul ol ol li,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper ol ul ul li, .igem_2018_team_content .igem_2018_team_column_wrapper ol ol ul li,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper ol ol ol li, .igem_2018_team_content .igem_2018_team_column_wrapper ol ul ol li{ font-size: 76%; }
 +
/*layout classes*/
 +
/**************************************************************************************************************************************************************************************************/
 +
/*main layout class */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .column  {
 +
float:left;
 +
margin: 1% 2%;
 +
padding: 0px;
 +
}
 +
/* 100% */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .column.full_size { width:96%; }
 +
/* 66% */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .column.two_thirds_size { width: 62.6%; }
 +
/* 33% */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .column.third_size { width: 29.3%; }
 +
/*styling for all images*/
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .column.full_size img,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .column.two_thirds_size img,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .column.third_size img {
 +
margin-bottom: 15px;
 +
width: 100%;
 +
}
 +
/* page break */
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .clear {
 +
clear:both;
 +
}
 +
/*add extra space to page break with clear class*/
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .clear.extra_space {
 +
height: 30px;
 +
}
 +
/* horizontal line to divide the page*/
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .line_divider {
 +
    border-top: 1px solid #6FCCB5;
 +
  margin: auto;
 +
  width: 98%;
 +
}
 +
/*support classes*/
 +
/**************************************************************************************************************************************************************************************************/
 +
/*Button  */
 +
/************************************************/
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .button_link {
 +
font-size: 130%;
 +
margin: 30px auto;
 +
text-align: center;
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .button_link a  {
 +
background-color: white;
 +
color: #6FCCB5 !important;
 +
font-weight: bold;
 +
margin: auto;
 +
text-decoration: none !important;
 +
padding: 10px 15px;
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .button_link a:hover {
 +
background-color: white !important;
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight {
 +
padding: 15px 20px;
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight p,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight h1,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight h2,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight h3,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight h4,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight h5,
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight h6 {
 +
padding: 5px 15px;
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight.decoration_background {
 +
background-color: #F6A4FF;
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight.decoration_A_top {
 +
    border-top: 4px solid #F6A4FF;
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight.decoration_A_full {
 +
    border: 4px solid #F6A4FF;
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight.decoration_B_top {
 +
    border-top: 4px solid #F6A4FF
 +
}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .highlight.decoration_B_full {
 +
    border: 4px solid #f8b732;
 +
}
 +
/*mobile*/
 +
/**************************************************************************************************************************************************************************************************/
 +
/* 1800px  */
 +
/************************************************/
 +
@media only screen and (max-width: 1800px) {
 +
.igem_2018_team_content { width: 85%;}
 +
.igem_2018_team_menu {display:block;}
 +
}
 +
/* 1400px  */
 +
/************************************************/
 +
@media only screen and (max-width: 1400px) {
 +
.igem_2018_team_menu .menu_item { font-size:100%;}
 +
.igem_2018_team_menu .submenu .submenu_item { font-size:90%;}
 +
.igem_2018_team_menu {display:block;}
 +
}
 +
@media only screen and (max-width: 1001px) {
 +
.igem_2018_team_menu {display:block;}
 +
}
 +
/* 1000px  */
 +
/************************************************/
 +
@media only screen and (max-width: 1000px) {
 +
.igem_2018_team_content {width:100%; margin-left:0px;}
 +
.igem_2018_team_menu {display:none; margin-top: 45px; min-width:50%; width:50%;}
 +
.igem_2018_team_mobile_bar {display:block;}
 +
.igem_2018_team_content .igem_2018_team_column_wrapper .column.full_size, .igem_2018_team_content .igem_2018_team_column_wrapper .column.two_thirds_size,.igem_2018_team_content .igem_2018_team_column_wrapper .column.third_size {width:96%; }
 +
}
 +
@media only screen and (max-width: 500px) {
 +
.igem_2018_team_menu {min-width:100%; width:100%; }
 +
}
 +
/**************************************************************************************************************************************************************************************************/
 +
</style>
 +
</head>
 +
 +
<!------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------->
 +
<!--- THIS IS WHERE THE HTML BEGINS --->
 +
<!------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------->
 +
 +
<head>
 +
 +
<!-- This tells the browser that your page is responsive -->
 +
<meta name="viewport" content="width=device-width, initial-scale=1">
 +
<script src='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML' async></script>
 +
 +
 +
</head>
 +
 +
<!-- ADDING PRELIMINARY DESCRIPTION -->
 +
<style>
 +
* {
 +
    box-sizing: border-box;
 +
}
 +
/* Create two equal columns that floats next to each other */
 +
.column {
 +
    float: left;
 +
    width: 50%;
 +
    padding: 10px;
 +
}
 +
/* Clear floats after the columns */
 +
.row:after {
 +
    content: "";
 +
    display: table;
 +
    clear: both;
 +
}
 +
/* USE THIS FOR PAGE HEADINGS */
 +
h6 {
 +
font-family: 'IBM Plex Sans', serif;
 +
color: #0BB4C1;
 +
  font-size: 31px;
 +
  text-align: center;
 +
}
 +
/* USE THIS FOR PARAGRAPH TEXT */
 +
h2 {
 +
font-family: 'IBM Plex Sans', serif;
 +
color: black;
 +
font-size: 16px;
 +
text-align: justify;
 +
margin-right: 90px;
 +
margin-left: 90px;
 +
}
 +
/* USE THIS FOR ANYTHING UNDER SUBHEADING TO BE IN A DIFFERENT COLOUR*/
 +
h3 {
 +
font-family: 'IBM Plex Sans', serif;
 +
color: white;
 +
  font-size: 16px;
 +
  /* text-align: left; */
 +
  /* margin-right: 90px;
 +
  margin-left: 90px; */
 +
}
 +
/* USE THIS FOR SUBHEADINGS */
 +
h4 {
 +
  font-family: 'IBM Plex Sans', serif;
 +
color: #274F96;
 +
  font-size: 16px;
 +
  text-align: left;
 +
  margin-right: 90px;
 +
  margin-left: 90px;
 +
}
 +
h5 {
 +
  font-family: 'IBM Plex Sans', serif;
 +
color: #0085B6;
 +
  font-size: 16px;
 +
  text-align: left;
 +
  margin-right: 90px;
 +
  margin-left: 90px;
 +
}
 +
body {
 +
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<h6><b>Mathematical Modelling</b></h6>
 +
 +
<!-- <hr style="width:25%"> -->
 +
 +
<h2>As part of out project, we sought to understand the molecular reactions in more depth and thereby improve our results. We set out to model RPA, that has only been modeled once before. We found that the model in the given paper is insufficient and does not yield the generally correct responses. Accordingly, we built our model, but found that there is a lack of rate constants available for many of the reactions of binding happening during Recombinase Polymerase Amplification. We believe, however, that as our model helped us understand our project better, so it will provide researchers with a new way to look at modelling RPA and hopefully produce more reliable models.
 +
</h2>
 +
 +
<h2>Firstly, we identified the components of RPA, as supplied by both the foremost supplier, TwistDX, and other research papers. We have then researched and agreed upon a sequence of events that occurs in RPA based on the one used by the majority of researchers in the field. We must point out, however, that there is disagreement about the particularities of the individual binding reactions as well as to what complexities they should be modeled since many of the proteins involved are multimeric with their own respective association reactions. We felt that a general model could be agreed upon and be accepted and that is what we provide here. Realizing based on the equations that possible limiting reagents could be the SSB protein, and that decreasing its binding affinity could help rapidify the amplification.
 +
</h2>
 +
 +
<h2>Furthermore, what was of essential importance to our project was that the commonly identified constant stirring conditions necessary for the RPA model to hold place can be supported by our microfluidics. At the microfluidic level, the reagents have been lyophilized and put into close proximity to each other in the microfluidic channel. With the small amount of reagents used, this approach justifies the approximations made in the model, and we can say that the well-stirred state’s results are provided by the microfluidic system.
 +
</h2>
 +
 +
<h2>Before we continue with the mathematical modelling, some helpful synonyms and symbolics.
 +
</h2>
 +
 +
<br>  <h2>The following species were used throughout our modelling:</h2>
 +
<br>
 +
    <table id="species-table" class="table table-hover">
 +
        <thead>
 +
            <tr>
 +
                <th><h4><b>Species Name</b></h4></th>
 +
                <th><h4><b>Symbol Used</b></h4></th>
 +
            </tr>
 +
        </thead>
 +
        <tbody>
 +
            <tr>
 +
                <td><h2>Recombinase</h2></td>
 +
                <td><h2>\(R\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Primer</h2></td>
 +
                <td><h2>\(Pr\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>DNA</h2></td>
 +
                <td><h2>\(D\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>DNA Polymerase</h2></td>
 +
                <td><h2>\(P = 1.34 X 10^{-6} M\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Single Strand Binding Protein (SSB)</h2></td>
 +
                <td><h2>\(S = 9.4 X 10^{-7} M\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>A specific binding of recombinase to a primer to form a closed complex</h2></td>
 +
                <td><h2>\(R:Pr\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>A specific binding of recombinase and primer to the DNA to form a closed complex</h2></td>
 +
                <td><h2>\(R:Pr:D\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>A specific binding of recombinase, primer, SSB protein to the DNA to form a closed complex</h2></td>
 +
                <td><h2>\(R:Pr:D:S\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>A specific binding of recombinase, primer, SSB protein, DNA Polymerase to the DNA to form a closed complex</h2></td>
 +
                <td><h2>\(R:Pr:D:S:P\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>A specific binding of primer, SSB protein, DNA Polymerase to the DNA to form a closed complex</h2></td>
 +
                <td><h2>\(Pr:D:S:P\)</h2></td>
 +
            </tr>
 +
        </tbody>
 +
    </table>
 +
 +
<br>
 +
<h2>The following rate constants were deduced from the reactions below the table. An important note we must raise is that most of the rate constants here identified have not been measured for empirical values. It is for this reason that our model could not have been used to provide simulations which is common practice. We think, though, that our identification of the errors in the only RPA model provided, as well as our proposal of a different view into the RPA world, from which we drew important conclusions as well as microfluidic deductions is more than enough to state the contribution of this model to our project.
 +
</h2>
 +
    <h2>The following parameters were used:</h2>
 +
<br>
 +
    <table id="parameters-table" class="table table-hover">
 +
        <thead>
 +
            <tr>
 +
                <th><h4><b>Parameter</b></h4></th>
 +
                <th><h4><b>Variable Name</b></h4></th>
 +
            </tr>
 +
        </thead>
 +
        <tbody>
 +
            <tr>
 +
                <td><h2>Forward rate constant for the binding of Recombinase and Primer</h2></td>
 +
                <td><h2>\(k1f\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Reverse rate constant for the binding of Recombinase and Primer</h2></td>
 +
                <td><h2>\(k1r\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Forward rate constant for the binding of Recombinase, Primer to DNA</h2></td>
 +
                <td><h2>\(k2f\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Reverse rate constant for the binding of Recombinase, Primer to DNA</h2></td>
 +
                <td><h2>\(k2r\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Forward rate constant for the binding of Recombinase, Primer, DNA to SSB protein</h2></td>
 +
                <td><h2>\(k3f\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Reverse rate constant for the binding of Recombinase, Primer, DNA to SSB protein</h2></td>
 +
                <td><h2>\(k3r\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Forward rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase</h2></td>
 +
                <td><h2>\(k4f\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Reverse rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase</h2></td>
 +
                <td><h2>\(k4r\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Forward rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex</h2></td>
 +
                <td><h2>\(k5f\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Reverse rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex</h2></td>
 +
                <td><h2>\(k5r\)</h2></td>
 +
            </tr>
 +
            <tr>
 +
                <td><h2>Rate constant for the replication of DNA with the complex consists of Primer, DNA, SSB Protein, DNA Polymerase</h2></td>
 +
                <td><h2>\(kf\)</h2></td>
 +
            </tr>
 +
        </tbody>
 +
    </table>
 +
 +
<br>
 +
 +
<h2>Please note that in the reactions written below, we assumed steady supply of ATP and no limiting effect thereby. The double colons represent binding nature between the molecules, while the only non-reversible reaction is DNA replication in the 6th reaction.
 +
</h2>
 +
 +
<br>
 +
$$ 1. R + Pr \leftrightharpoons R:Pr $$
 +
$$ 2. R:Pr + D \leftrightharpoons R:Pr:D $$
 +
$$ 3. R:Pr:D + S \leftrightharpoons R:Pr:D:S $$
 +
$$ 4. R:Pr:D:S + P \leftrightharpoons R:Pr:D:S:P $$
 +
$$ 5. R:Pr:D:S:P \leftrightharpoons R + Pr:D:S:P $$
 +
$$ 6. Pr:D:S:P \to 2D + S + P + Pr $$
 +
 +
<br>
 +
 +
<h2>It is important to note that we assumed both the polymerase and single-strand binding protein concentrations to be of fixed value, which is a responsible assumption to make given higher concentrations in the provided RPA kits. Another note to take is that the below equations have a factor of 2 due to the very nature of RPA. Each DNA strand is being amplified at the same time, due to the flipped nature of the DNA sequences and ends. The recombinase and other mechanisms of RPA can equally likely start amplification at both ends of the DNA. Based on the reaction model above, the following equations could be deduced:
 +
</h2>
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<br>
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<br>
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<img src="https://static.igem.org/mediawiki/2018/2/2a/T--NYU_Abu_Dhabi--equations2.JPG"class="center">
 +
<br><br>
 +
 +
<h5><u>References:</u></h5>
 +
<h2>1. Moody C, Newell H, & Viljoen H (2016) A mathematical model of recombinase polymerase amplification under continuously stirred conditions. Biochemical engineering journal 112:193-201.</h2>
 +
<h2>2. Liu J, Berger CL, & Morrical SW (2013) Kinetics of presynaptic filament assembly in the presence of single-stranded DNA binding protein and recombination mediator protein. Biochemistry 52(45):7878-7889.</h2>
 +
<h2>3. Kuchta R, Mizrahi V, Benkovic P, Johnson K, & Benkovic S (1987) Kinetic mechanism of DNA polymerase I (Klenow). Biochemistry 26(25):8410-8417.</h2>
 +
<h2>4. Piepenburg O, Williams CH, Stemple DL, & Armes NA (2006) DNA detection using recombination proteins. PLoS biology 4(7):e204.</h2>
 +
<h2>5. Daher RK, Stewart G, Boissinot M, & Bergeron MG (2016) Recombinase polymerase amplification for diagnostic applications. Clinical chemistry:clinchem. 2015.245829.</h2>
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Latest revision as of 22:04, 17 October 2018

Mathematical Modelling

As part of out project, we sought to understand the molecular reactions in more depth and thereby improve our results. We set out to model RPA, that has only been modeled once before. We found that the model in the given paper is insufficient and does not yield the generally correct responses. Accordingly, we built our model, but found that there is a lack of rate constants available for many of the reactions of binding happening during Recombinase Polymerase Amplification. We believe, however, that as our model helped us understand our project better, so it will provide researchers with a new way to look at modelling RPA and hopefully produce more reliable models.

Firstly, we identified the components of RPA, as supplied by both the foremost supplier, TwistDX, and other research papers. We have then researched and agreed upon a sequence of events that occurs in RPA based on the one used by the majority of researchers in the field. We must point out, however, that there is disagreement about the particularities of the individual binding reactions as well as to what complexities they should be modeled since many of the proteins involved are multimeric with their own respective association reactions. We felt that a general model could be agreed upon and be accepted and that is what we provide here. Realizing based on the equations that possible limiting reagents could be the SSB protein, and that decreasing its binding affinity could help rapidify the amplification.

Furthermore, what was of essential importance to our project was that the commonly identified constant stirring conditions necessary for the RPA model to hold place can be supported by our microfluidics. At the microfluidic level, the reagents have been lyophilized and put into close proximity to each other in the microfluidic channel. With the small amount of reagents used, this approach justifies the approximations made in the model, and we can say that the well-stirred state’s results are provided by the microfluidic system.

Before we continue with the mathematical modelling, some helpful synonyms and symbolics.


The following species were used throughout our modelling:


Species Name

Symbol Used

Recombinase

\(R\)

Primer

\(Pr\)

DNA

\(D\)

DNA Polymerase

\(P = 1.34 X 10^{-6} M\)

Single Strand Binding Protein (SSB)

\(S = 9.4 X 10^{-7} M\)

A specific binding of recombinase to a primer to form a closed complex

\(R:Pr\)

A specific binding of recombinase and primer to the DNA to form a closed complex

\(R:Pr:D\)

A specific binding of recombinase, primer, SSB protein to the DNA to form a closed complex

\(R:Pr:D:S\)

A specific binding of recombinase, primer, SSB protein, DNA Polymerase to the DNA to form a closed complex

\(R:Pr:D:S:P\)

A specific binding of primer, SSB protein, DNA Polymerase to the DNA to form a closed complex

\(Pr:D:S:P\)

The following rate constants were deduced from the reactions below the table. An important note we must raise is that most of the rate constants here identified have not been measured for empirical values. It is for this reason that our model could not have been used to provide simulations which is common practice. We think, though, that our identification of the errors in the only RPA model provided, as well as our proposal of a different view into the RPA world, from which we drew important conclusions as well as microfluidic deductions is more than enough to state the contribution of this model to our project.

The following parameters were used:


Parameter

Variable Name

Forward rate constant for the binding of Recombinase and Primer

\(k1f\)

Reverse rate constant for the binding of Recombinase and Primer

\(k1r\)

Forward rate constant for the binding of Recombinase, Primer to DNA

\(k2f\)

Reverse rate constant for the binding of Recombinase, Primer to DNA

\(k2r\)

Forward rate constant for the binding of Recombinase, Primer, DNA to SSB protein

\(k3f\)

Reverse rate constant for the binding of Recombinase, Primer, DNA to SSB protein

\(k3r\)

Forward rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase

\(k4f\)

Reverse rate constant for the binding of Recombinase, Primer, DNA, SSB protein to DNA Polymerase

\(k4r\)

Forward rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex

\(k5f\)

Reverse rate constant for the unbinding of Recombinase from the Recombinase, Primer, DNA, SSB protein, DNA Polymerase complex

\(k5r\)

Rate constant for the replication of DNA with the complex consists of Primer, DNA, SSB Protein, DNA Polymerase

\(kf\)

Please note that in the reactions written below, we assumed steady supply of ATP and no limiting effect thereby. The double colons represent binding nature between the molecules, while the only non-reversible reaction is DNA replication in the 6th reaction.


$$ 1. R + Pr \leftrightharpoons R:Pr $$ $$ 2. R:Pr + D \leftrightharpoons R:Pr:D $$ $$ 3. R:Pr:D + S \leftrightharpoons R:Pr:D:S $$ $$ 4. R:Pr:D:S + P \leftrightharpoons R:Pr:D:S:P $$ $$ 5. R:Pr:D:S:P \leftrightharpoons R + Pr:D:S:P $$ $$ 6. Pr:D:S:P \to 2D + S + P + Pr $$

It is important to note that we assumed both the polymerase and single-strand binding protein concentrations to be of fixed value, which is a responsible assumption to make given higher concentrations in the provided RPA kits. Another note to take is that the below equations have a factor of 2 due to the very nature of RPA. Each DNA strand is being amplified at the same time, due to the flipped nature of the DNA sequences and ends. The recombinase and other mechanisms of RPA can equally likely start amplification at both ends of the DNA. Based on the reaction model above, the following equations could be deduced:





References:

1. Moody C, Newell H, & Viljoen H (2016) A mathematical model of recombinase polymerase amplification under continuously stirred conditions. Biochemical engineering journal 112:193-201.

2. Liu J, Berger CL, & Morrical SW (2013) Kinetics of presynaptic filament assembly in the presence of single-stranded DNA binding protein and recombination mediator protein. Biochemistry 52(45):7878-7889.

3. Kuchta R, Mizrahi V, Benkovic P, Johnson K, & Benkovic S (1987) Kinetic mechanism of DNA polymerase I (Klenow). Biochemistry 26(25):8410-8417.

4. Piepenburg O, Williams CH, Stemple DL, & Armes NA (2006) DNA detection using recombination proteins. PLoS biology 4(7):e204.

5. Daher RK, Stewart G, Boissinot M, & Bergeron MG (2016) Recombinase polymerase amplification for diagnostic applications. Clinical chemistry:clinchem. 2015.245829.



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