Difference between revisions of "Team:GreatBay SCIE/Model"

 
(48 intermediate revisions by 6 users not shown)
Line 1: Line 1:
−
{{GreatBay_SCIE/HTML/navbar}}
+
{{GreatBay_SCIE/HTML/loader}}
−
<!DOCTYPE html>
+
 
<html>
 
<html>
 
<head>
 
<head>
 
<link rel="stylesheet" href="https://2021.igem.org/wiki/index.php?title=Template:GreatBay_SCIE/CSS_new&action=raw&ctype=text/css">
 
<link rel="stylesheet" href="https://2021.igem.org/wiki/index.php?title=Template:GreatBay_SCIE/CSS_new&action=raw&ctype=text/css">
−
<script src=“https://2021.igem.org/wiki/index.php?title=Template:GreatBay_SCIE/jquery.js&action=raw&ctype=text/javascript”></script>
+
<link rel="stylesheet" type="text/css" href="https://2021.igem.org/wiki/index.php?title=Template:GreatBay_SCIE/CSS/movable_navbar_new&action=raw&ctype=text/css&action=raw&ctype=text/css" />
 +
<script src=“https://2021.igem.org/wiki/index.php?title=Template:GreatBay_SCIE/jquery.js&action=raw&ctype=text/javascript”>
 +
</script>
 +
</head>
  
 +
<style>
 +
#sideMenu, #top_title, .patrollink, #firstHeading, #home_logo, #sideMenu { display:none; }
 +
#content { padding:0px; width:100%; margin-top:-7px; margin-left:0px; border:none;}
 +
body, html {width: 100%; height: 100%;}
 +
#bodyContent h1, #bodyContent h2, #bodyContent h3, #bodyContent h4, #bodyContent h5 { margin-bottom: 0px; }
 +
#bodyContent a[href ^="https://"], .link-https {padding-right:25px;}
  
−
<meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>
+
</style>
−
<title>Maximum Drug Loading Amount(Markdown)</title>
+
−
</head>
+
 
<body>
 
<body>
 +
 +
 +
<div class="navbarsticker" id="nb" style="margin-top:10px;"></div>
 +
<img src="https://static.igem.org/mediawiki/2021/2/28/T--GreatBay_SCIE--Model_HeadPic.png" class="header" style="margin-top:-8px">
 +
<div class="navbarsticker" id="navbarsticker" style="margin-top:10px;"></div>
 +
<div class="navbar" id="navbar">
 +
 +
<a href="https://2021.igem.org/Team:GreatBay_SCIE" style="padding-right:0px">
 +
<img class="plogo" id="project_logo" src="https://static.igem.org/mediawiki/2021/6/6a/T--GreatBay_SCIE--Project_Logo.png" alt="logo" height="46" style="position:absolute; margin-left:50px; margin-top:10px; left:0px;">
 +
<img class="tlogo" id="team_logo" src="https://static.igem.org/mediawiki/2021/0/06/T--GreatBay_SCIE--Team_Logo.png" alt="logo" height="46" style="position:absolute; left:0; margin-top:13px!important; left:0px;">
 +
</a>
 +
<ul style="margin-left: -11px"> 
 +
        <li>
 +
            <a href="https://2021.igem.org/Team:GreatBay_SCIE">Home</a>
 +
        </li>
 +
        <li>
 +
            <a href="https://2021.igem.org/Team:GreatBay_SCIE/Team">About Us</a>
 +
            <ul>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Team">Members</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Attributions">Attributions</a></li>
 +
            </ul>
 +
        </li>
 +
        <li>
 +
            <a href="https://2021.igem.org/Team:GreatBay_SCIE/Description">Project</a>
 +
            <ul>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Description">Description</a></li>                 
 +
               
 +
             
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Design">Design</a></li>
 +
        <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Proof_Of_Concept">Proof of Concept</a></li> 
 +
        <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Results">Results</a></li>   
 +
        <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Engineering">Engineering</a></li>
 +
        <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Parts">Parts</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Implementation">Implementation</a></li> 
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Contribution">Contribution</a></li> 
 +
            </ul>
 +
        </li>
 +
        <li>
 +
            <a href="https://2021.igem.org/Team:GreatBay_SCIE/Experiments">Lab</a>
 +
            <ul>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Experiments">Experimental Design</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Results">Results</a></li> 
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Safety">Safety</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Notebook">Lab Notes</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Protocol">Protocol</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Measurement">Measurement</a></li>
 +
 +
            </ul>
 +
        </li>
 +
        <li>
 +
            <a href="https://2021.igem.org/Team:GreatBay_SCIE/Model">Modeling</a>
 +
            <ul>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Model">Overview</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Optimum_Aptamer_Concentration" >Optimum Liposome-Aptamer Ratio</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Drug_Loading">Drug Loading</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Dissociation_constant">Dissociation Constant</a></li>
 +
<li><a href="https://2021.igem.org/Team:GreatBay_SCIE/3D_Model">3D Models</a></li>
 +
 +
            </ul>
 +
        </li>
 +
        <li>
 +
            <a href="https://2021.igem.org/Team:GreatBay_SCIE/Human_Practices">Human Practices</a>
 +
            <ul>
 +
<li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Human_Practices">Integrated Human Practices</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Communication">Public Engagement & Education</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/BreastCancerInChina">GreatBay_SCIE X Pink Ribbon</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Collaborations">Collaborations</a></li>
 +
                <li><a href="https://2021.igem.org/Team:GreatBay_SCIE/Partnership">Partnership with SMS_Shenzhen</a></li>
 +
            </ul>
 +
        </li>
 +
 +
    </ul>
 +
</div>
 +
<script type="text/javascript" src="https://2021.igem.org/wiki/index.php?title=Template:GreatBay_SCIE/JS/navbar&action=raw&ctype=text/javascript"></script>
 +
 +
 
<div class="sidebarsticker" id="sidebarsticker"></div>
 
<div class="sidebarsticker" id="sidebarsticker"></div>
−
<div class="sidebar_outer" id="sidebar_inner">
+
<div class="sidebar_outer" id="sidebar_inner" style="width: 20%;height: auto!important;margin-left: 3%;border-radius:10px;">
 +
<img src="https://static.igem.org/mediawiki/2021/9/9c/T--GreatBay_SCIE--Cat.gif" id="cat">
 
   <ul>
 
   <ul>
 
         <li class="top1">  
 
         <li class="top1">  
−
             <a href = "#sec1" id = "nav1">Project Description</a>
+
             <a href = "#introduction" id = "nav1">Introduction</a>
 
         </li>       
 
         </li>       
 
         <li>  
 
         <li>  
−
             <a href = "#sec2" id = "nav2">Background</a>
+
             <a href = "#mathematical" id = "nav2">Mathematical Modelling</a>
 
         </li>   
 
         </li>   
−
         <li>
+
         <li class="btm1">  
−
            <a href = "#sec3" id = "nav3">Breast Cancer in China</a>
+
             <a href = "#Structural" id = "nav3">Structural Modelling</a>
−
        </li>
+
−
        <li>  
+
−
             <a href = "#sec4" id = "nav4">Our Project</a>
+
 
         </li>  
 
         </li>  
 
     </ul>
 
     </ul>
 +
<div class="top_bt">
 +
<img  onclick="backtotop()" src="https://static.igem.org/mediawiki/2021/9/94/T--GreatBay_SCIE--Button.png"></img>
 +
</div>
 +
 
</div>
 
</div>
 
</div>
 
</div>
−
<div class="content">
 
  
 +
<div class="content" style="margin-top:42.5px;">
 +
<body>
 +
<div class="title"style="font-size:500% !important; text-align:center;">Modeling Overview</div>
 +
<br>
 +
<body><h1 id='introduction'>Introduction</h1>
  
 +
<p>Mathematical modeling is a useful tool in synthetic biology, as it allows us to describe the relationship between different parameters and variables during biochemical processes using a set of mathematical equations. In our project, we used mathematical modeling to obtain quantitative solutions to several problems we encounter in our project.</p>
 +
<p>&nbsp;</p>
 +
<h1 id="mathematical">Mathematical Modeling</h1>
  
 +
<p>In our first model, we have predicted the optimum concentration of the aptamer used for the nanoparticle-aptamer conjugation, to improve the aptamers&#39; binding affinity by mainly applying the principles and theories of calculus. By doing so, the efficiency of the drug we use can be substantially increased.</p>
 +
<p>To get more information on this model, you can click
 +
<a href="./Optimum_Aptamer_Concentration" class="bton">here</a> to visit a page with more detailed information.</p>
 +
 +
<p>&nbsp;</p>
 +
<p>In our second model, in order to predict the effectiveness of our drug, we have predicted the drug loading amount in a liposome by using Fick&#39;s Laws, which can assist the manufacturing of the drug and help predict the usage amount of the drug better.</p>
 +
<p>To get more information on this model, you can click <a href="./Drug_Loading" class="bton">here</a> to visit a page with more detailed information.</p>
 +
<p>&nbsp;</p>
 +
<p>Besides, we also construct an additional modeling of binding constant to see the binding affinity of our aptamer to the HER2</p>
 +
<p>To get more information on this additional model, you can click <a href="./Dissociation_constant" class="bton">here</a> to visit a page with more detailed information.</p>
  
−
<body><h1 id='maximum-drug-loading-amount'>Maximum Drug Loading Amount</h1>
 
−
<p>Because the doxorubicin is loaded onto the liposomes via diffusion, it must follow the pattern of the Fick&#39;s First Law, which is :</p>
 
−
<div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n3" cid="n3" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"  style="text-align: center;"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="12.819ex" height="2.081ex" role="img" focusable="false" viewBox="0 -705 5666 920" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.486ex; text-align:center;"><defs><path id="MJX-4-TEX-I-1D43D" d="M447 625Q447 637 354 637H329Q323 642 323 645T325 664Q329 677 335 683H352Q393 681 498 681Q541 681 568 681T605 682T619 682Q633 682 633 672Q633 670 630 658Q626 642 623 640T604 637Q552 637 545 623Q541 610 483 376Q420 128 419 127Q397 64 333 21T195 -22Q137 -22 97 8T57 88Q57 130 80 152T132 174Q177 174 182 130Q182 98 164 80T123 56Q115 54 115 53T122 44Q148 15 197 15Q235 15 271 47T324 130Q328 142 387 380T447 625Z"></path><path id="MJX-4-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-4-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-4-TEX-I-1D437" d="M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z"></path><path id="MJX-4-TEX-N-25BD" d="M59 480Q59 485 61 489T66 495T72 498L75 500H814Q828 493 828 480V474L644 132Q458 -210 455 -212Q451 -215 444 -215T433 -212Q429 -210 342 -49T164 282T64 466Q59 478 59 480ZM775 460H113Q113 459 278 153T444 -153T610 153T775 460Z"></path><path id="MJX-4-TEX-I-1D436" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D43D" xlink:href="#MJX-4-TEX-I-1D43D"></use></g><g data-mml-node="mo" transform="translate(910.8,0)"><use data-c="3D" xlink:href="#MJX-4-TEX-N-3D"></use></g><g data-mml-node="mo" transform="translate(1966.6,0)"><use data-c="2212" xlink:href="#MJX-4-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(2744.6,0)"><use data-c="1D437" xlink:href="#MJX-4-TEX-I-1D437"></use></g><g data-mml-node="mo" transform="translate(3794.8,0)"><use data-c="25BD" xlink:href="#MJX-4-TEX-N-25BD"></use></g><g data-mml-node="mi" transform="translate(4906,0)"><use data-c="1D436" xlink:href="#MJX-4-TEX-I-1D436"></use></g></g></g></svg></mjx-container></div></div>
 
−
<p>In this formula, J represents the diffusion flux, D represents the diffusion coefficient, ▽ represents the gradient operator and C represents the concentration. We can work out the value of J and ▽C by carrying out experiments, which can help us work out the value of D. Which is:</p>
 
−
<div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n5" cid="n5" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"  style="text-align: center;"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="12.819ex" height="2.081ex" role="img" focusable="false" viewBox="0 -705 5666 920" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.486ex; text-align:center;"><defs><path id="MJX-5-TEX-I-1D437" d="M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z"></path><path id="MJX-5-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-5-TEX-N-25BD" d="M59 480Q59 485 61 489T66 495T72 498L75 500H814Q828 493 828 480V474L644 132Q458 -210 455 -212Q451 -215 444 -215T433 -212Q429 -210 342 -49T164 282T64 466Q59 478 59 480ZM775 460H113Q113 459 278 153T444 -153T610 153T775 460Z"></path><path id="MJX-5-TEX-I-1D436" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path><path id="MJX-5-TEX-N-2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path><path id="MJX-5-TEX-I-1D43D" d="M447 625Q447 637 354 637H329Q323 642 323 645T325 664Q329 677 335 683H352Q393 681 498 681Q541 681 568 681T605 682T619 682Q633 682 633 672Q633 670 630 658Q626 642 623 640T604 637Q552 637 545 623Q541 610 483 376Q420 128 419 127Q397 64 333 21T195 -22Q137 -22 97 8T57 88Q57 130 80 152T132 174Q177 174 182 130Q182 98 164 80T123 56Q115 54 115 53T122 44Q148 15 197 15Q235 15 271 47T324 130Q328 142 387 380T447 625Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D437" xlink:href="#MJX-5-TEX-I-1D437"></use></g><g data-mml-node="mo" transform="translate(1105.8,0)"><use data-c="3D" xlink:href="#MJX-5-TEX-N-3D"></use></g><g data-mml-node="mo" transform="translate(2161.6,0)"><use data-c="25BD" xlink:href="#MJX-5-TEX-N-25BD"></use></g><g data-mml-node="mi" transform="translate(3050.6,0)"><use data-c="1D436" xlink:href="#MJX-5-TEX-I-1D436"></use></g><g data-mml-node="mo" transform="translate(4032.8,0)"><use data-c="2212" xlink:href="#MJX-5-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(5033,0)"><use data-c="1D43D" xlink:href="#MJX-5-TEX-I-1D43D"></use></g></g></g></svg></mjx-container></div></div>
 
−
<p>And the D value can be used in the Fick&#39;s Second Law, and because the diffusion is taken place on liposome which can be considered as a perfect sphere, the formula can be inferred as is:</p>
 
−
<div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n7" cid="n7" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"  style="text-align: center;"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="24.634ex" height="5.095ex" role="img" focusable="false" viewBox="0 -1509.9 10888.3 2251.9" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.679ex; text-align:center;"><defs><path id="MJX-6-TEX-N-2202" d="M202 508Q179 508 169 520T158 547Q158 557 164 577T185 624T230 675T301 710L333 715H345Q378 715 384 714Q447 703 489 661T549 568T566 457Q566 362 519 240T402 53Q321 -22 223 -22Q123 -22 73 56Q42 102 42 148V159Q42 276 129 370T322 465Q383 465 414 434T455 367L458 378Q478 461 478 515Q478 603 437 639T344 676Q266 676 223 612Q264 606 264 572Q264 547 246 528T202 508ZM430 306Q430 372 401 400T333 428Q270 428 222 382Q197 354 183 323T150 221Q132 149 132 116Q132 21 232 21Q244 21 250 22Q327 35 374 112Q389 137 409 196T430 306Z"></path><path id="MJX-6-TEX-I-1D436" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path><path id="MJX-6-TEX-I-1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path><path id="MJX-6-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-6-TEX-I-1D437" d="M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z"></path><path id="MJX-6-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-6-TEX-N-32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path><path id="MJX-6-TEX-I-1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path><path id="MJX-6-TEX-N-2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path><path id="MJX-6-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mfrac"><g data-mml-node="mrow" transform="translate(220,676)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mo"><use data-c="2202" xlink:href="#MJX-6-TEX-N-2202"></use></g></g><g data-mml-node="mi" transform="translate(566,0)"><use data-c="1D436" xlink:href="#MJX-6-TEX-I-1D436"></use></g></g><g data-mml-node="mrow" transform="translate(419.5,-686)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mo"><use data-c="2202" xlink:href="#MJX-6-TEX-N-2202"></use></g></g><g data-mml-node="mi" transform="translate(566,0)"><use data-c="1D461" xlink:href="#MJX-6-TEX-I-1D461"></use></g></g><rect width="1526" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(2043.8,0)"><use data-c="3D" xlink:href="#MJX-6-TEX-N-3D"></use></g><g data-mml-node="mi" transform="translate(3099.6,0)"><use data-c="1D437" xlink:href="#MJX-6-TEX-I-1D437"></use></g><g data-mml-node="mo" transform="translate(3927.6,0)"><use data-c="28" xlink:href="#MJX-6-TEX-N-28"></use></g><g data-mml-node="mfrac" transform="translate(4316.6,0)"><g data-mml-node="mrow" transform="translate(220,676)"><g data-mml-node="msup"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mo"><use data-c="2202" xlink:href="#MJX-6-TEX-N-2202"></use></g></g><g data-mml-node="mn" transform="translate(650.8,363) scale(0.707)"><use data-c="32" xlink:href="#MJX-6-TEX-N-32"></use></g></g><g data-mml-node="mi" transform="translate(1054.3,0)"><use data-c="1D436" xlink:href="#MJX-6-TEX-I-1D436"></use></g></g><g data-mml-node="mrow" transform="translate(400.4,-719.9)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mo"><use data-c="2202" xlink:href="#MJX-6-TEX-N-2202"></use></g></g><g data-mml-node="msup" transform="translate(566,0)"><g data-mml-node="mi"><use data-c="1D45F" xlink:href="#MJX-6-TEX-I-1D45F"></use></g><g data-mml-node="mn" transform="translate(484,289) scale(0.707)"><use data-c="32" xlink:href="#MJX-6-TEX-N-32"></use></g></g></g><rect width="2014.3" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(6793.1,0)"><use data-c="2B" xlink:href="#MJX-6-TEX-N-2B"></use></g><g data-mml-node="mfrac" transform="translate(7793.3,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="32" xlink:href="#MJX-6-TEX-N-32"></use></g><g data-mml-node="mi" transform="translate(244.5,-686)"><use data-c="1D45F" xlink:href="#MJX-6-TEX-I-1D45F"></use></g><rect width="700" height="60" x="120" y="220"></rect></g><g data-mml-node="mfrac" transform="translate(8733.3,0)"><g data-mml-node="mrow" transform="translate(220,676)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mo"><use data-c="2202" xlink:href="#MJX-6-TEX-N-2202"></use></g></g><g data-mml-node="mi" transform="translate(566,0)"><use data-c="1D436" xlink:href="#MJX-6-TEX-I-1D436"></use></g></g><g data-mml-node="mrow" transform="translate(374.5,-686)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mo"><use data-c="2202" xlink:href="#MJX-6-TEX-N-2202"></use></g></g><g data-mml-node="mi" transform="translate(566,0)"><use data-c="1D45F" xlink:href="#MJX-6-TEX-I-1D45F"></use></g></g><rect width="1526" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(10499.3,0)"><use data-c="29" xlink:href="#MJX-6-TEX-N-29"></use></g></g></g></svg></mjx-container></div></div>
 
−
<p>And through this formula, we can work out the relationship between the concentration of the doxorubicin, change in time and the change in position. Through which, we can indicate the maximum drug loading amount by the maximum concentration of doxorubicin in the liposome.</p>
 
 
<p>&nbsp;</p>
 
<p>&nbsp;</p>
 +
<h1 id="Structural">Structural Modeling</h1>
  
 +
<p>In order to help us view the structure of our aptamer and the binding model of our aptamer and the HER-II protein, we have used several software and algorithms (eg: Matlab, Mfold, RNA Composer......) to predict the structure of them. This has helped us to see how effective our drug is by knowing what is the epitope when binding.</p>
 +
<p>To get more information on these models, you can click
 +
<a href="./3D_Model" class="bton">here</a> to visit a page with more detailed information.</p>
 +
 +
<center>
 +
<p style="text-align: center;">
 +
<img src="https://static.igem.org/mediawiki/2021/f/f7/T--GreatBay_SCIE--Binding.gif"/width="70%"/>
 +
<div class="image_text"> <strong>Figure 1.1: This is the predicted figure of the HER-II protein binding with the HER-II positive aptamer</Strong></div><br/>
 +
</center>
 +
 +
<br></br>
 +
<br></br>
 
<script src="https://2021.igem.org/wiki/index.php?title=Template:GreatBay_SCIE/JS/sidebar&action=raw&ctype=text/javascript">
 
<script src="https://2021.igem.org/wiki/index.php?title=Template:GreatBay_SCIE/JS/sidebar&action=raw&ctype=text/javascript">
 
</script>
 
</script>
 +
</div>
 +
 
</body>
 
</body>
 
</html>
 
</html>

Latest revision as of 14:17, 21 October 2021

Modeling Overview

Introduction

Mathematical modeling is a useful tool in synthetic biology, as it allows us to describe the relationship between different parameters and variables during biochemical processes using a set of mathematical equations. In our project, we used mathematical modeling to obtain quantitative solutions to several problems we encounter in our project.

 

Mathematical Modeling

In our first model, we have predicted the optimum concentration of the aptamer used for the nanoparticle-aptamer conjugation, to improve the aptamers' binding affinity by mainly applying the principles and theories of calculus. By doing so, the efficiency of the drug we use can be substantially increased.

To get more information on this model, you can click here to visit a page with more detailed information.

 

In our second model, in order to predict the effectiveness of our drug, we have predicted the drug loading amount in a liposome by using Fick's Laws, which can assist the manufacturing of the drug and help predict the usage amount of the drug better.

To get more information on this model, you can click here to visit a page with more detailed information.

 

Besides, we also construct an additional modeling of binding constant to see the binding affinity of our aptamer to the HER2

To get more information on this additional model, you can click here to visit a page with more detailed information.

 

Structural Modeling

In order to help us view the structure of our aptamer and the binding model of our aptamer and the HER-II protein, we have used several software and algorithms (eg: Matlab, Mfold, RNA Composer......) to predict the structure of them. This has helped us to see how effective our drug is by knowing what is the epitope when binding.

To get more information on these models, you can click here to visit a page with more detailed information.

Figure 1.1: This is the predicted figure of the HER-II protein binding with the HER-II positive aptamer