Difference between revisions of "Team:TAS Taipei/Model"

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<a href="https://2016.igem.org/Team:TAS_Taipei/project"><h4 class="dropdown-toggle disabled" data-toggle="dropdown"><b>PROJECT</b></h4></a>
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<a href="https://2016.igem.org/Team:TAS_Taipei/Description"><h4 class="dropdown-toggle disabled" data-toggle="dropdown"><b>PROJECT</b></h4></a>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Description#background">Background</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Description">Background</a></h5>
 
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<img src="https://static.igem.org/mediawiki/2016/1/11/T--TAS_Taipei--TAS_Icon_Project.png">
<h4><b>Cataracts</b> - the leading cause of blindness. Find out how we can noninvasively <b>treat</b> and <b>prevent</b> cataract formation.</b></h4>
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<h4><b>Cataracts</b> - the leading cause of blindness. Find out how we can non-invasively <b>treat</b> and <b>prevent</b> cataract formation.</b></h4>
 
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<a href="https://2015.igem.org/Team:TAS_Taipei/wetlab"><h4 class='dropdown-toggle disabled' data-toggle="dropdown"><b>EXPERIMENTAL</b></h4></a>
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<a href="https://2016.igem.org/Team:TAS_Taipei/Experimental_Summary"><h4 class='dropdown-toggle disabled' data-toggle="dropdown"><b>EXPERIMENTAL</b></h4></a>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Experiments#lensmodel">Lens Cataract Model</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Experimental_Summary#lensmodel">Lens Cataract Model</a></h5>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Experiments#construct">Prevention and Treatment Constructs </a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Experimental_Summary#construct">Prevention and Treatment Constructs </a></h5>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Experiments#prototype">Delivery Prototype</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Experimental_Summary#prototype">Delivery Prototype</a></h5>
 
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<h4>We don't just come up with great ideas. We show they work. Follow along our discovery of exciting science!</h4>
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                        <h4>We build <b>constructs</b> to make our great ideas become reality. Follow along our discovery of exciting science!</h4>
 
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<a href="https://2016.igem.org/Team:TAS_Taipei/Modeling"><h4 class='dropdown-toggle disabled' data-toggle="dropdown"><b>MODEL</b></h4></a>
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<a href="https://2016.igem.org/Team:TAS_Taipei/Model"><h4 class='dropdown-toggle disabled' data-toggle="dropdown"><b>MODEL</b></h4></a>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Model#gsr25hc">GSR/25HC Pathway</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Model#gsrch25h">GSR/CH25H Pathway</a></h5>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Model#nanoparticle">Nanoparticle Degradation</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Model#nanoparticle">Nanoparticle Delivery</a></h5>
 
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<img src="https://static.igem.org/mediawiki/2015/3/3e/Tas_icon_modeling.png">
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<img src="https://static.igem.org/mediawiki/2016/c/ca/T--TAS_Taipei--TAS_Icon_Model.png">
<h4><b>Computational Biology</b> provides us models that we cannot easily test. Click to find out the results of our modeling, and if you want, the math behind it!</h4>
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<h4><b>Computational Biology</b> provides us models that we cannot easily test experimentally. Click to find out the results of our modeling, and the math behind it!</h4>
 
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<img src="https://static.igem.org/mediawiki/2015/0/0f/Tas_icon_hp.png">
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<img src="https://static.igem.org/mediawiki/2016/b/b9/T--TAS_Taipei--TAS_Icon_HP.png">
 
<h4>We don't just grow cool bacteria. We make a <b>difference</b>. Find out how we tackled <b>social aspects</b> of this project.</h4>
 
<h4>We don't just grow cool bacteria. We make a <b>difference</b>. Find out how we tackled <b>social aspects</b> of this project.</h4>
 
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<img src="https://static.igem.org/mediawiki/2015/9/91/Tas_icon_safety.png">
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<img src="https://static.igem.org/mediawiki/2016/7/7e/T--TAS_Taipei--TAS_Icon_Safety.png">
 
<h4><b>Safety first.</b> Especially in a lab. Here's how we maintained and investigated the integrity and security of our work environment.</h4>
 
<h4><b>Safety first.</b> Especially in a lab. Here's how we maintained and investigated the integrity and security of our work environment.</h4>
 
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<img src="https://static.igem.org/mediawiki/2015/3/34/Tas_icon_team.png">
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<img src="https://static.igem.org/mediawiki/2016/c/c6/T--TAS_Taipei--TAS_Icon_Team.png">
<h4>Behind every tough iGem project lies a hard-working yet cheerful group of students. <b>Meet the team!</b></h4>
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<h4>Every iGEM project is the accumulation of an entire year's hard work by a group of cheerful students. <b>Meet the team!</b></h4>
 
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<a href="https://2016.igem.org/Team:TAS_Taipei" style='text-decoration: none'><img src="https://static.igem.org/mediawiki/2016/c/c6/T--TAS_Taipei--TAS_iGEM_Logo.png
 
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<h2 style="font-family:'Lato';letter-spacing:10px;color: white; font-size: 60px;  margin-top: 0;  margin-bottom: 0;"><b>
 
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C&#9678;UNTERACTS</b></h2>
 
C&#9678;UNTERACTS</b></h2>
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<a href="https://igem.org/HS"><img src="https://static.igem.org/mediawiki/2016/6/6e/T--TAS_Taipei--TAS_Icon_Logo2.png" alt="" style="width: 100px;"></a>
 
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<ul class="nav nav-list" data-spy="affix" data-offset-top="160" style='-webkit-transform: translateZ(0);width:160px;margin-left:0' >
<li><a href="#overview">Overview</a></li>
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<li><a href="#crystallin">Crystallin</a></li>
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<li><a href="#GSRConc">Prevention: GSR Concentration</a></li>
<li><a href="#gsr25hc">GSR/25HC</a></li>
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                        <ul>
<li><a href="#nanoparticle">Nanoparticles</a></li>
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                            <li> <a href="#model1">1. Crystallin Damage</a></li>
<li><a href="#eyedrop">Eyedrop</a></li>
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                            <li> <a href="#model2">2. GSR Pathway</a></li>
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                        </ul>
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                        <li><a href="#prototype">Prevention: Delivery Prototype</a></li>
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                        <ul>
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                            <li> <a href="#model3">3. Nanoparticles</a></li>
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                            <li> <a href="#model4">4. Eyedrops</a></li>
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                        </ul>
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                        <li><a href="#treatment">Treatment</a></li>
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                        <li><a href="#software">Calculator (Software)</a></li>
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<h1>Model</h1>
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<h1 id='overview'>Modeling</h1>
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                                <p>Cataract prevention occurs over 20 – 50 years, so we cannot perform experiments on the long-term impact of adding GSR or CH25H. However, computational biology allows us to predict cataract development in the long-term. These models allow our team to understand the impact of adding GSR-loaded nanoparticles into the lens over a 50 year period, and to design a full treatment plan on how to prevent and treat cataracts with our project. Therefore, the results of our model are essential in developing a functional prototype.</p>
                                                   
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                                <p>For sake of clarity, we will discuss each model in detail with respect to prevention (using GSR) only. At the end, we explain these results to treatment. In addition, we include collapsibles for interested readers and judges, in order to fully document our modeling work (eg. assumptions, mathematics) while keeping the main page clear with basic points only.
 
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                          <h2>Introduction</h2>
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                                     <h3> Abstract </h4>
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                                     <ol>
                <p>We answer two questions: How much GSR to maintain in the lens, and how to maintain that amount?  We find the amount of GSR needed in the lens (Model 2) to limit crystallin damage so the resulting cataract is less than LOCS 2.5 (Model 1). Then, we find the optimal design of eyedrops (Model 4) and nanoparticles that will maintain this amount of GSR in the lens (Model 3). These models allow our team to understand the impact of adding GSR-loaded nanoparticles into the lens, and to design a full treatment plan on how to prevent and treat cataracts. </p>
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                                        <li>How much GSR to maintain in the lens?</li>
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                                        <li>How to maintain that amount of GSR using nanoparticles and eyedrops?</li>
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                                    </ol>
 
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                                <h3>Focus of Models</h3>
 
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                                    <h3>Achievements</h4>
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                                <p>
                                     <ul style="font-size:15px">
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                                     Since our construct is not directly placed into the eyes, how our synthesized protein impacts the eye after it is separately transported into the lens is of greater importance. As a result, we create models with the intent on understanding how GSR and CH25H impacts the eye.
                                        <li>Designed a simple calculator to find amount of GSR or 25HC eyedrops needed for a patient's LOCS score.</li>
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                                </p>
                                        <li>Bridged the gap between the medical, biological, and chemical measurement of crystallin damage.</li>
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                                        <li>Predicted impact of adding GSR and 25HC on the amount of crystallin damage in the lens.</li>
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                                        <li>Created Nanoparticle Customizer for doctors to find a full treatment plan.</li>
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                                        <li>Generalized our Customizer to allow other iGEM teams who wish to use nanoparticle drug delivery </li>
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                                        <li>Analyzed sensitivity of prototype, and suggested insights into optimal manufacturing and clinical use of our prototype.</li>
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                                        <li>Used Experimental data to develop Models 1 and 3.</li>
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                                    </ul>
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                                <h3>Relation to Experiments</h3>
<h3> Outline </h3>
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                                     <p>We use measurements from the cataract lens experiment to create the first model, and extend the     results with the second model to find GSR concentrations, which our experiments could not find.
 
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<h2>Introduction</h2>
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  <h3> Why Model? </h3> 
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<p>In the lab, biologists are often unable to test everything experimentally. For example, in our cataracts project, cataract prevention occurs in the long-term, from 20-50 years. Obviously, although short experiments can provide us an idea of what prevention may look like, the power of computational biology allows us to model into the future. As a result, our modeling has been crucial in developing a prototype.</p>
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  <h3> Focus </h3> 
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<p>Most iGEM teams perform modeling on gene expression, which we accomplish in model 5. However, as our construct is not directly placed into the eyes, how our synthesized protein impacts the eyes after it is seperately transported is much more interesting. As a result, we spent the majority of our models on understanding the impacts on the eye.</p>
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<h3>Guiding Questions </h3>
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<ol>
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      <li>How much GSR do we want inside the lens?</li>
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      <li>How do we use nanoparticles to control the amount of GSR in the lens?</li>
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      <li>How do we synthesize GSR, package into NP, and send it into the eye?</li>
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        </ol>
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<h2 id = 'crystallin'>Model 1: Crystallin Damage</h2>
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                        <h3>Abstract</h3>
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                        <p>In our experiments, absorbance measurements are meaningless without understanding how severe a cataract that absorbance measurement means. We use literature research to relate LOCS, the physician's scale of cataract severity) to absorbance, which is how we quantified crystallin damage in experiments. We use experimental data to understand how crystallin damage can be quantified by measuring absorbance. With this model, we can calculate how much crystallin damage we have to limit to reduce LOCS to an acceptable level.</p>
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<h3> Purpose </h3>
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<p> How much do we need to limit crystallin damage so surgery is not needed? </p>
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                        <h3>Measurement of Cataract Severity</h3>
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                                     <p>
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                                        There are four ways of measuring cataract severity, each used for a different purpose.
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                                        <ol>
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                                            <li><b>Lens Optical Cataract Scale (LOCS):</b> Physicians use this scale, from 0 – 6, to grade the severity of cataracts.</li>
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                                            <li><b>Opacity (%):</b> This is the physical, quantitative property of the LOC scale.</li>
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                                            <li><b>Absorbance at 397.5 nm:</b> This is the experimental method, used by our team in the lab (c.d.).</li>
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                                            <li><b>Crystallin Damage: </b>This is a chemical definition. We quantify cataract severity as a function of how much oxidizing agents there are, as well as how long crystalline is exposed to oxidizing agents. We define 1 crystallin damage unit as the damage done to human crystallin when exposed to 1 M hydrogen peroxide, the main oxidizing agent, for 1 hour.</li>
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                                        </ol>
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                        <p>We use the unit of crystallin damage to connect cataract severity with the amount of GSR we add (in Model 2). We want to lower c.d. below so that the resulting cataract is of LOCS 2.5. For the rest of the model, our task is simple: relate each point of the LOCS scale to c.d., in order to connect to Model 2.</p>
 
   
 
                        <h3>LOCS Equivalence to Absorbance: Literature Research</h3>
 
                        <p>Past studies have done numerous studies on how absorbance measurements can be converted to the LOC scale that physicians end up using. With the results of ________ and ________, we construct the first three columns in Table 2.</p>
 
   
 
                        <h3>Absorbance Equivalence to Crystallin Damage: Experimental Data</h3>
 
                        <div class="row">
 
                            <div class="col-sm-7">
 
                                <div class="col-sm-12" >
 
 
                                     <p>
 
                                     <p>
                                         We use experimental data from our team’s Cataract Lens Model (link).  In each trial, they added H2O2 to crystallin, and measured the resulting absorbance. The data used are shown in Table 1. We can calculate the theoretical c.d., and graph absorbance vs. crystallin damage in Figure 2.  
+
                                         We modelled nanoparticle degradation before performing actual experiments, to estimate the optimal amount of protein to load into the nanoparticles. After performing the experiments, we can directly compare them to see the efficiency of our drug-loading. Although we could not experimentally test an eyedrop prototype, model 4 extends the results of the nanoparticle degradation to better understand how to use eyedrops to deliver nanoparticles.
 
                                     </p>
 
                                     </p>
                                    <p>With this relation in Figure 2, we calculate the equivalent crystallin damage to each LOCS rating and its equivalent absorbance.</p>
 
                                    <h3>Error Analysis</h3>
 
                                    <p>It may be surprising that only around 1 M-h is required to induce moderately severe cataracts. Remember that this is done in the absence of antioxidation systems (GSR) and at an extremely high oxidizing concentration of H2O2 (1M of H2O2). In the lens, H2O2 has a much lower concentration, so severe cataracts are induced over months to years.</p>
 
                                    <p>There are some limitations of the model that arise from our assumptions. We assume that fish and human lens contain similar crystallin proteins that are degraded in the similar manner (Assumption 4). In addition, we made a rough adjustment of data based our diluting procedure. For better results to create a human cataract model, experiments will need to be done on human lens, even better if done in vitro, without any dilutions.</p>
 
 
                                 </div>
 
                                 </div>
                            </div>
+
                          </div>
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+
                             <div class="row">
 +
                                <h3>Relation to Overall Project</h3>
 
                                 <div class="col-sm-12">
 
                                 <div class="col-sm-12">
 
                                     <p>
 
                                     <p>
                                         <table class="table table-bordered" style='width: 80%;margin-left:0%;'>
+
                                         Although experiments could validate a prototype, it is through modeling that we find the optimal designs for these prototypes. By building a full calculator, we can envision how the results of this project can be applied clinically. A patient finds his or her LOCS score from the physician, and then enters it into the calculator, which returns a full treatment plan, using standardized cataract prevention and treatment eyedrops. Our nanoparticles are fully customizable, to allow physicians to alter the design to best fit a patient’s specific cataract conditions.
                <caption style='caption-side:top;'><b>Table 2: Results of Model 1 – Equivalent values for LOCS, Opacity, Absorbance, and Crystallin Damage.</caption>
+
                <thead>
+
                <tr>
+
                                                    <th>LOCS</th>
+
                                                    <th>Opacity (%)</th>
+
                                                    <th>Absorbance (@397.5 nm)</th>
+
                                                    <th>Crystallin Damage (M-h)</th>
+
                                                </tr>
+
                                            </thead>
+
                                            <tr>
+
                                                <th>0.0</th>
+
                                                <th>0.00</th>
+
                                                <th>0.0000</th>
+
                                                <th>0.0000</th>
+
                                            </tr>
+
                                            <tr>
+
                                                <th>0.5</th>
+
                                                <th>3.24</th>
+
                                                <th>0.0143</th>
+
                                                <th>0.1327</th>
+
                                            </tr>
+
                                            <tr>
+
                                                <th>1.0</th>
+
                                                <th>6.65</th>
+
                                                <th>0.0299</th>
+
                                                <th>0.2774</th>
+
                                            </tr>
+
                                            <tr>
+
                                                <th>1.5</th>
+
                                                <th>10.81</th>
+
                                                <th>0.0497</th>
+
                                                <th>0.4610</th>
+
                                            </tr>
+
                                            <tr>
+
                                                <th>2.0</th>
+
                                                <th>15.88</th>
+
                                                <th>0.0751</th>
+
                                                <th>0.6966</th>
+
                                            </tr>
+
                                            <tr>
+
                                                <th>2.5</th>
+
                                                <th>21.95</th>
+
                                                <th>0.1076</th>
+
                                                <th>0.9981</th>
+
                                            </tr>
+
                                            <tr>
+
                                                <th>3.0</th>
+
                                                <th>29.07</th>
+
                                                <th>0.1492</th>
+
                                                <th>1.3840</th>
+
                                            </tr>
+
                                            <tr>
+
                                                <th>4.0</th>
+
                                                <th>46.37</th>
+
                                                <th>0.2706</th>
+
                                                <th>2.5101</th>
+
                                            </tr>
+
                                            <tr>
+
                                                <th>5.0</th>
+
                                                <th>66.05</th>
+
                                                <th>0.4691</th>
+
                                                <th>4.3514</th>
+
                                            </tr>
+
                                        </table>
+
 
+
 
                                     </p>
 
                                     </p>
 +
                                </div>
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                                </div>
 +
                                <figure class = "col-sm-8">
 +
        <img src="https://static.igem.org/mediawiki/2016/8/86/T--TAS_Taipei--Fish_Lens_Picture.jpg" style="align:center">
 +
                                    <figcaption class='darkblue'> <b>Figure 1 (left).</b> Priacanthus macracanthus purchased from the market. <b>(right)</b> The two spheres on the left are lens with cortex and nucleus and the two smaller spheres on the right are nucleus. </figcaption>
 +
      </figure>
 +
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                                 </div>
 
                                 </div>
 
                             </div>
 
                             </div>
                        </div>
+
                          <h2>Model 1: Crystallin Damage</h2>
       
+
                             <div class="row">
<button class="accordion">Background, Method, Results, Discussion</button>
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  <ul class="nav nav-tabs">
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  <li class="active"><a data-toggle="tab" href="#cryshome">Background</a></li>
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  <li><a data-toggle="tab" href="#crysmenu1">Assumptions</a></li>
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  <li><a data-toggle="tab" href="#crysmenu2">Procedure</a></li>
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  <li><a data-toggle="tab" href="#crysmenu3">Results</a></li>
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  <li><a data-toggle="tab" href="#crysmenu4">Discussion</a></li>
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</ul>
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      <h3>Background</h3>
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                            <p>There are four ways to measure cataract severity (how blurred the lens is):
+
          <ol>
+
          <li>Lens Optical Cataract Scale III (LOCS) - a scale from 0-6 used by physicians.</li>
+
          <li>Opacity (%) - used to calculate the LOC scale</li>
+
          <li>Absorbance at 397.5 nm - measurable in the lab. </li>
+
                                    <li>Crystallin Damage - used to quantify how much crystallin has been reacted with hydrogen peroxide to create insoluble, damaged crystallin. The following definition of crystallin damage is used:</li>
+
          </ol>
+
                                \[c.d.(t) = \int_{0}^{\infty} [H_2O_2]_t dt\]
+
            </p>
+
 
+
            <p> In other words, 1 unit of crystallin damage, in M-h,  is equal to the damage caused by 1 molar concentration of hydrogen peroxide reacting crystallin in the eyes for 1 hour.</p>
+
                        </div>
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                             <h3>LOCS Scale</h3><br> <br> <br><br> <br> <br> <br><br><br><br>
+
                        </div>
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                    </div>
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                </div>                   
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    <h3>Assumptions</h3>
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                        <div class="col-sm-12">
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                            <p>
+
                                 <ol>
+
                                      <li>Definition of crystallin damage: Crystallin damage is proportional to the concentration of hydrogen peroxide, and the time of exposure. This is a valid assumption, supported by the fact that the reaction between cysteine (molecules on crystallin) and hydrogen peroxide is linear. </li>
+
                                      <li>We assume that the amount of crystallin is far greater than the amount oxidized. Our product is meant for long-term cataract prevention and minor treatment, and is not suggested for patients with extremely severe cataracts. </li>
+
                                      <li>When the experiments diluted the cataract lens protein, the amount of crystallin is diluted. However, the final absorbance of degraded crystallin is also diluted, so we assume any errors in absorbance is canceled out.</li>
+
                                      <li>We assume that fish and human lens contain similar crystallin proteins.</li>
+
 
+
 
+
                                </ol>
+
                </p>
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                    </div>
+
                   
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                </div>   
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      <h3>Procedure</h3>
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                        <div class="col-sm-12" style="border:1px solid black">
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                            <p>
+
                                <ol>
+
                                    <li>In the first part, we find how the absorbance measurements in the lab are related to the severity of the cataracts. Through literature data, we can relate LOCS to the opacity of the lens. Then, via physical calculations, we can relate the opacity of the lens to the absorbance of the lens at 400 nm.</li>
+
                                    <li>Then, we use our team’s experimental data in the cataract model. For each trial, the concentration of H2O2 and the length of exposure are given, so we can calculate the theoretical crystallin damage using the definition above and the assumptions we made. In each trial we also measured the absorbance, so we have a relation between crystallin damage and absorbance. </li>
+
                                    <li>However, we need to make a minor adjustment, because absorbance is affected by dilution. When the fish lens was isolated, they were placed in Tris buffer and diluted. We calculate the ratio of volumes from diluted volume to the Tris buffer, and multiply each absorbance measurement by this value.</li>
+
                                </ol>
+
                </p>
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                            <h3>LOCS Scale</h3><br> <br> <br><br> <br> <br> <br><br><br><br>
+
                        </div>
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                    </div>
+
                   
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                </div>                     
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                <h3>Results</h3>
+
 
+
      <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+
                    <caption style='caption-side:top;'><b>Table 1: Results of Model 1 - Equivalent values for LOCS, Opacity, Absorbance, and Crystallin Damage. </b> </caption>
+
<tbody>
+
<tr>
+
<td>LOCS</td>
+
<td>0.0</td>
+
<td>0.5</td>
+
<td>1.0</td>
+
                                    <td>1.5</td>
+
<td>2.0</td>
+
                                    <td>2.5</td>
+
<td>3.0</td>
+
<td>4.0</td>
+
<td>5.0</td>
+
</tr>
+
<tr>
+
<td>Degree</td>
+
<td>None</td>
+
<td colspan="2">Trace</td>
+
<td colspan="3">Mild</td>
+
<td colspan="2">Moderate</td>
+
<td>Severe</td>
+
</tr>
+
<tr>
+
<td>Opacity (%)</td>
+
<td>0</td>
+
                                    <td>3.24</td>
+
<td>6.65</td>
+
<td>10.81</td>
+
<td>15.88</td>
+
<td>21.95</td>
+
<td>29.07</td>
+
<td>46.37</td>
+
<td>66.05</td>
+
</tr>
+
<tr>
+
<td>Absorbance (a.u.)</td>
+
<td>0.0000</td>
+
<td>0.0143</td>
+
<td>0.0299</td>
+
<td>0.0497</td>
+
<td>0.0751</td>
+
<td>0.1076</td>
+
<td>0.1492</td>
+
<td>0.2706</td>
+
                                    <td>0.4691</td>
+
</tr>
+
                                <tr>
+
<td>Crystallin Damage (c.d.)</td>
+
<td>0.0000</td>
+
<td>0.1327</td>
+
                                    <td>0.2774</td>
+
<td>0.4610</td>
+
<td>0.6966</td>
+
<td>0.9981</td>
+
<td>1.3840</td>
+
<td>2.5101</td>
+
<td>4.3514</td>
+
</tr>
+
</tbody>
+
</table>
+
                <br><br><br>
+
                <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+
                    <caption style='caption-side:top;'><b>Table 2: Experimental Data used for Model 1 from Cataract Lens Model (TAS) - Absorbance vs. Crystallin Damage </b></caption>
+
<tbody>
+
                                <thead>
+
                                    <td>Trial</td>
+
<td>H2O2 Concentration (M)</td>
+
<td>Exposure Time (h)</td>
+
<td>Crystallin Damage (c.d.)</td>
+
                                    <td>Measured Absorbance (abs @400 nm)</td>
+
                                </thead>
+
<tr>
+
                                    <td>1</td>
+
                                    <td>0.100</td>
+
                                    <td>24.0</td>
+
                                    <td>2.40</td>
+
                                    <td>0.105</td>
+
</tr>
+
                                <tr>
+
                                    <td>2</td>
+
                                    <td>0.100</td>
+
                                    <td>46.5</td>
+
                                    <td>4.65</td>
+
                                    <td>0.451</td>
+
</tr>
+
                                <tr>
+
                                    <td>3</td>
+
                                    <td>0.100</td>
+
                                    <td>72.0</td>
+
                                    <td>7.20</td>
+
                                    <td>0.0.695</td>
+
</tr>
+
                                <tr>
+
                                    <td>4</td>
+
                                    <td>0.100</td>
+
                                    <td>20.0</td>
+
                                    <td>2.00</td>
+
                                    <td>0.089</td>
+
</tr>
+
                                <tr>
+
                                    <td>5</td>
+
                                    <td>0.100</td>
+
                                    <td>42.0</td>
+
                                    <td>4.20</td>
+
                                    <td>0.392</td>
+
</tr>
+
                                <tr>
+
                                    <td>6</td>
+
                                    <td>0.100</td>
+
                                    <td>15.0</td>
+
                                    <td>1.50</td>
+
                                    <td>0.093</td>
+
</tr>
+
                                <tr>
+
                                    <td>7</td>
+
                                    <td>0.100</td>
+
                                    <td>42.0</td>
+
                                    <td>0.340</td>
+
                                    <td>0.340</td>
+
</tr>
+
                                <tr>
+
                                    <td>8</td>
+
                                    <td>0.100</td>
+
                                    <td>67.0</td>
+
                                    <td>6.70</td>
+
                                    <td>0.563</td>
+
</tr>
+
+
</tbody>
+
</table>
+
                               
+
  </div>
+
 
+
  <div id="crysmenu4" class="tab-pane fade">
+
    <h3>Discussion</h3>
+
                <h4>Model Result</h4>
+
          <div class="row">
+
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+
 
                                 <p>
 
                                 <p>
                                     The model successfully relates LOCS, opacity of lens, absorbance measurements, and the equivalent crystallin damage of the lens. The purpose of relating LOCS to crystallin damage, is that in Model 2, we will use chemical kinetics to determine how adding GSR to the lens will decrease the amount of crystallin damage. Exactly how much crystallin damage we need to decrease is determined by the desired LOCS. For example, if we want to have a LOCS rating of less than 2.5, then we must lower crystalline damage to only 0.9981 M-h.
+
                                     The amount of damage to crystallin by H2O2 determines the severity of a cataract. We relate the amount of crystallin damage to the corresponding rating on the LOCS scale, used by physicians to rate cataract severity. Our goal is to lower LOCS to below 2.5, the threshold for surgery. Through literature research as well as our own experimental data, we find the maximum allowable crystallin damage to prevent a LOCS 2.5 cataract from developing.  
 
                                 </p>
 
                                 </p>
 +
                                </div>
 
                             </div>
 
                             </div>
                        </div>
+
                          <h3>Measurement of Cataract Severity</h3>
                       
+
                            <div class="row">
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                                 <p>
 
                                 <p>
                                     <br><br><br><br><br>
+
                                    There are four ways of measuring cataract severity, each used for a different purpose.
 +
                                     <ol>
 +
                                        <li>Lens Optical Cataract Scale (LOCS): Physicians use this scale, from 0 – 6, to grade the severity of cataracts.
 +
                                        </li>
 +
                                        <li>Absorbance at 397.5 nm: This is the experimental method, used by our team in the lab (c.d.) </li>
 +
                                        <li>Crystallin Damage: This is a chemical definition. We quantify cataract severity as a function of how much oxidizing agents there are, as well as how long crystalline is exposed to oxidizing agents. </li>
 +
                                    </ol>
 +
                                    When we add GSR into the system, crystallin damage decreases. Our goal is to find the equivalent crystallin damage that leads to a LOCS 2.5 cataract, in order to know how much GSR to prevent this amount of crystallin damage in Model 2.
 
                                 </p>
 
                                 </p>
 +
                                </div>
 +
                         
 
                             </div>
 
                             </div>
                         </div>
+
                          
                   
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                            <div class="row">
                    </div>
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                                <div class="col-sm-8">
                <h4>Model Adjustment</h4>
+
                                    <h3>Measurement of Cataract Severity</h3>
                    <div class="row">
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                                 <p>
 
                                 <p>
                                     <br><br><br><br><br>
+
                                     Numerous studies show how absorbance measurements can be converted to the LOC scale that physicians use. With the results of ________ and ________, we construct the first two columns in Table 2.
 
                                 </p>
 
                                 </p>
                            </div>
+
                                    <h3>Absorbance Equivalence to Crystallin Damage: Experimental Data</h3>
                        </div>
+
                       
+
                        <div class="col-sm-6" >
+
                            <div class="col-sm-12">
+
 
                                 <p>
 
                                 <p>
                                     When determining the relationship between absorbance and crystallin, in Figure 1 the best fit line has a x – intercept that is nonzero. However, when converting each absorbance rating to equivalent crystallin damage in Table 2, we ignore the constant term. When doing the experiments, the fish lens may have contained GSH that is still active, so the fact that the crystallin is exposed to H2O2, the degradation reaction does not happen until all GSH is depleted, and crystallin damage begins to form. We subtract around 1 unit of crystallin damage from all values.  
+
                                     We use experimental data from our team’s Cataract Lens Model (link). They induced an amount of crystallin damage, and measured the resulting absorbance.  
 +
                                    With this relation in Figure 2, we calculate the equivalent crystallin damage of each LOCS rating and absorbance.
 
                                 </p>
 
                                 </p>
                            </div>
+
                                    <h3>Conclusion</h3>
                        </div>
+
                   
+
                    </div>
+
                <h4>Error Analysis</h4>
+
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+
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+
                            <div class="col-sm-12" >
+
 
                                 <p>
 
                                 <p>
                                     It may be surprising that only around 1 M-h is required to induce moderately severe cataracts. Remember that this is done in the absence of antioxidation systems (GSR) and at an extremely high oxidizing concentration of H2O2 (1M of H2O2). In the lens, H2O2 has a much lower concentration, so severe cataracts are induced over months to years.
+
                                     To guarantee that surgery is not needed for 50 years, we need to limit crystallin damage to 0.9981 units. If crystallin damage goes above this threshold, then surgery is needed. This is the crystallin damage threshold for a LOCS 2.5 cataract.
 
                                 </p>
 
                                 </p>
 +
                                </div>
 +
                         
 
                             </div>
 
                             </div>
                         </div>
+
                         <h2>Model 2: GSR Pathway</h2>
                       
+
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+
 
                                 <p>
 
                                 <p>
                                     There are some limitations of the model that arise from our assumptions. We assume that fish and human lens contain similar crystallin proteins that are degraded in the similar manner (Assumption 4). Also, to simplify the experiments, the lens were diluted in Tris buffer. Because of this dilution, the actual crystallin damage is much lower, but so is the actual absorbance. We assume that the decrease in crystallin damage and absorbance is the same, so no adjustments need to be made for the relation between crystallin damage and absorbance (Assumption 3). For better results to create a human cataract model, experiments will need to be done on human lens, even better if done in vitro, without any dilutions.
+
                                     Now that we know how much GSR we need to limit crystallin damage to LOCS 2.5, we model the naturally occurring GSR Pathway in the lens of a human eye. For prevention (2A), we calculate the necessary GSR concentration to be maintained over 50 years so that the resulting cataract is below LOCS 2.5.  
 
                                 </p>
 
                                 </p>
 +
                                </div>
 
                             </div>
 
                             </div>
                        </div>
+
                          <h3>Chemical Kinetics Model: Differential Equations</h3>
                       
+
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+
 
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</div>  <!-- End Menu -->
+
 
+
 
+
    <h3> Conclusion</h3>
+
<div class="row">
+
                        <div class="col-sm-6" style="background-color:lightpink;margin:0px">
+
                            <div class="col-sm-12" >
+
 
                                 <p>
 
                                 <p>
                                     <br><br><br><br><br>
+
                                     By the Law of Mass Action, Michaelis-Menten Enzyme kinetics, Ping-pong mechanism, and the Law of Passive Diffusion, we build a system of 10 differential equations based on 6 chemical reactions. All parameters, constants, and initial conditions are based off literature data. Estimates made are also shown with assumptions and reasoning. The details are shown in the collapsible for interested readers.
 
                                 </p>
 
                                 </p>
 +
                                </div>
 +
                         
 
                             </div>
 
                             </div>
                        </div>
 
 
                          
 
                          
                        <div class="col-sm-6">
+
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                            <div class="col-sm-12">
+
                                <div class="col-sm-8">
 +
                                    <h3>Blackbox Approach: Testing GSR Impact</h3>
 
                                 <p>
 
                                 <p>
                                     For surgery to not be needed, the LOCS value has to be below 2.5. This is equivalent to 21.95% in light opacity or 0.1076 abs units. Based on the results of our experiments, this is equivalent to 0.9981 units of crystallin damage, the damage done to crystallin if exposed to 0.9981 M of H2O2 for 1 hr.
+
                                     We vary the input, Initial GSR concentration, holding all other variables constant, and numerically solve for the amount of hydrogen peroxide over time. With this graph, we can find the amount of crystallin damage accumulated over 20 to 50 years if different levels of GSR is maintained.  
                                    For future models, this value 0.9981 units of c.d. will be called the crystallin damage threshold for LOCS 2.5.
+
                               
 
+
 
                                 </p>
 
                                 </p>
 +
                                <p>
 +
                                    From this graph, we can find the GSR concentration needed for the LOCS 2.5 threshold and the LOCS 1.0 threshold.
 +
                                </p>
 +
                                </div>
 +
                         
 
                             </div>
 
                             </div>
                        </div>
+
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+
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                    </div>
+
                                    <h3>Crystallin Damage vs. GSR Level</h3>
 
+
                                <p>
 
+
                                    According to literature data and our model, the naturally occurring GSR concentration is 10 uM. All curves show crystallin damage decreasing as GSR levels are increased, which supports both research and experimental data, and suggests that this prototype is effective in preventing crystallin damage. However, GSR levels need to be raised significantly, up to 40+ uM from the natural 10 uM of GSR in order to show long-term protection.  
 
+
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+
 
+
 
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+
 
+
<div class = "row">
+
<div class="col-sm-12">
+
<h2 id = 'gsr25hc'>Model 2: GSR/25HC Chemical Pathway</h2>
+
                       
+
                        <div class="row">
+
                                 <div class="col-sm-6" >
+
                                        <h3> Abstract </h3>
+
                                        <p> The key question: <b>How much GSR to add?</b> Now that we know how much we need to limit crystallin damage, we use systems of ordinary differential equation to model the GSR Pathway. We calculate the necessary GSR concentration to be maintained over 50 years so that the resulting cataract is below LOCS 2.5./p>
+
                                        </p>
+
                                </div>
+
                                <div class="col-sm-6" >
+
                                        <h3> Purpose </h3>
+
                                        <p> How much GSR do we need to maintain in the lens so that the crystallin damage recorded over 50 years is below the threshold for LOCS 2.5? </p>
+
                                </div>
+
                        </div>
+
+
           
+
                        <h3> Chemical Kinetics Model: Differential Equations </h3>
+
                        <div class="row">
+
                                <div class="col-sm-12" >
+
                                        <p> By the Law of Mass Action, Michaelis-Menten Enzyme kinetics, Ping-pong mechanism, and the Law of Passive Diffusion, we build a system of 10 differential equations based on 6 chemical reactions. All parameters, constants, and initial conditions are based off literature data. Estimates made are also shown with assumptions and reasoning. The details are shown in the collapsible for interested readers. </p>
+
                                </div>
+
                        </div>
+
           
+
                        <div class="row">
+
                                <div class="col-sm-6" >
+
                                        <h3>Blackbox Approach: Testing GSR Impact </h3>
+
                                        <p> Image</p>
+
                                </div>
+
                                <div class="col-sm-6" >
+
                                        <h3>  </h3>
+
                                        <p> We will vary the input, Initial GSR concentration, from 0 to 100 uM, holding all other variables constant, and numerically solve for the amount of hydrogen peroxide over time. With this graph, we can find the amount of crystallin damage accumulated over 20 to 50 years if different levels of GSR is maintained. </p>
+
                                </div>
+
                        </div>
+
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+
           
+
           
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<button class="accordion">Background, Method, Results, Discussion</button>
+
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+
 
+
<div class="accordionmenu1" class ="col-sm-12" >
+
  <ul class="nav nav-tabs">
+
  <li class="active"><a data-toggle="tab" href="#gsrhome">Background</a></li>
+
  <li><a data-toggle="tab" href="#gsrmenu1">Method</a></li>
+
  <li><a data-toggle="tab" href="#gsrmenu2">Results Part 1</a></li>
+
  <li><a data-toggle="tab" href="#gsrmenu2">Results Part 2</a></li>
+
  <li><a data-toggle="tab" href="#gsrmenu3">Discussion</a></li>
+
</ul>
+
 
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+
  <div id="gsrhome" class="tab-pane fade in active">
+
      <h4>Background</h4>
+
 
                                  
 
                                  
<p> The following 6 reactions describe the antioxidant system inside the cortex and nucleus.</p>
+
                                </p>
 
+
                                <p>
$$GP_{xr}+[H_2O_2]_{in}+H^+ \xrightarrow[]{k_1} GP_{xo}+H_2O ...(1)$$
+
                                    Table 3 shows the amount of GSR we need to maintain for 50 years in order to prevent a LOCS cataract of a certain severity. The row of interest is LOCS 2.5, the threshold for surgery. Notice that we say “maintain” the level of GSR. This level needs to be constant at all times for 50 years for full prevention. The delivery of GSR to maintain this level is discussed in Model 3.
$$GP_{xo}+GSH+H^+ \xrightarrow[]{k_2} [GS-GP_x]+H_2O ...(2)$$
+
                                 </p>
$$[GS-GP_x] + GSH \xrightarrow[]{k_3} GP_{xr}+GSSG+H^+ ...(3)$$
+
$$NADPH \xrightarrow[GSR]{k4, K_{4M}} NADP^+ ...(4)$$
+
$$GSSG \xrightarrow[GSR']{k_5, K_{5M}} 2GSH ...(5)$$
+
$$[H_2O_2]_{out} \xrightarrow[]{k_5} [H_2O_2]_{in} ...(6)$$
+
 
+
<p> Each reaction will be discussed in detail, and we will derive rate equations.</p>
+
 
+
                <p><b>Reaction 1:</b>As hydrogen ions are numerous are negligible in the reaction, we will ignore it. By the <b>law of mass</b> action, the rate of this reaction is: $$r_1=k_1[GP_{xr}][H_2O_2]_{in}$$</p>
+
               
+
                <p><b>Reaction 2:</b> By the <b>law of mass</b> action, the rate of this reaction is: $$r_2=k_2[GP_{xo}][GSH]$$</p>
+
               
+
                <p><b>Reaction 3:</b> By the <b>law of mass</b> action, the rate of this reaction is: $$r_3=k_3[GS-GP_x][GSH]$$</p> 
+
               
+
                <p><b>Summary of Reaction 1-3:</b>In these reactions, hydrogen peroxide is reduced to water. GSH is consumed to recycle the enzyme GPx back into reduced form, to neutralize more hydrogen peroxide.</p>
+
                <br>
+
               
+
                <p><b>Reaction 4:</b> By<b>Michaelis-Menten kinetics </b>and the <b>Ping-Pong mechanism</b>, the rate of this reaction, with rate constant k4, and Michaelis-Menten constant Km4, is: $$r_4=k_4\frac{[NADPH]}{K_{4M}+[NADPH]}$$</p> 
+
               
+
                <p><b>Reaction 5:</b> By<b>Michaelis-Menten kinetics </b>and the <b>Ping-Pong mechanism</b>, the rate of this reaction, with rate constant k5, and Michaelis-Menten constant Km5, is: $$r_5=k_5\frac{[GSSG]}{K_{4M}+[GSSG]}$$</p> 
+
 
+
                <p><b>Summary of Reaction 4-5</b>: In these, GSSG is reduced back to form GSH, using the enzyme GSR. This is necessary for antioxidation to continue as reaction 1 is constantly using GSH, converting them to GSSG.</p>
+
                <br>
+
               
+
                <p><b>Reaction 6:</b> By the <b>Law of Passive Diffusion</b>, the rate of diffusion into the cortex and lens is: is: $$r_6=k_6([H_2O_2]_{out}-[H_2O_2]_{in})$$</p>
+
               
+
  </div>
+
 
+
    <div id="gsrmenu1" class="tab-pane fade">
+
    <h4>Differential Equations</h4>
+
      <p>We have six reaction rates derived from above. Now, we will form differential equations, where every time a species is used as a reactant, the reaction rate will be subtracted from the species’ derivative, while each time it is formed as a product, the reaction rate will be added to the species’ derivative. We will go through each species in detail:</p>
+
                <p>Substituting the rate of each reaction, we get the following system of differential equations. </p>
+
    <p>
+
                    $$\frac{d[GP_{xr}]}{dt}=k_3[GS-GP_x][GSH]-k_1[GP_{xr}][H_2O_2]_{in}$$
+
                   
+
                    $$\frac{d[H_2O_2]}{dt}=k_6[[H_2O_2]_{out}-{H_2O_2]_{in}]-k_1[GP_{xr}][H_2O_2]_{in}$$
+
                   
+
                    $$\frac{d[H_2O_2]}{dt}=k_1([H_2O_2]_{out} - [H_2O_2]_{in})-k_1[GP_{xr}][H_2O_2]_{in}$$
+
                   
+
                    $$\frac{d[GP_{x0}]}{dt}=k_1[GP_{xr}][H_2O_2]_{in}-k_2[GP_{xo}][GSH]$$
+
                   
+
                    $$\frac{d[H_2O]}{dt}=k_1[GP_{xr}][H_2O_2]_{in}+k_2[GP_{xo}][GSH]$$
+
                   
+
                    $$\frac{d[GSH]}{dt}=2k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}-k_2[GP_{xo}][GSH]-k_3[GS-GP_x][GSH]$$
+
                   
+
                    $$\frac{d[GS-GP_x]}{dt}=k_2[GP_{xo}][GSH]-k_3[GS-GP_x][GSH]$$
+
                   
+
                    $$\frac{d[GSSG]}{dt}=k_3[GS-GP_x][GSH]-k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}$$
+
                   
+
                    $$\frac{d[NADPH]}{dt}=-k_4[GSR]\frac{[NADPH]}{K_{4M}+[NADPH]}$$
+
                   
+
                    $$\frac{d[GSR]}{dt}=k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}-k_4[GSR]\frac{[NADPH]}{K_{4M}+[NADPH]}$$
+
                   
+
                    $$\frac{d[GSR']}{dt}=k_4[GSR]\frac{[NADPH]}{K_{4M}+[NADPH]}-k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}$$
+
                   
+
      </p>
+
 
+
 
+
  </div>
+
  <div id="gsrmenu2" class="tab-pane fade">
+
      <h4>Part 1 Results</h4>
+
 
+
      <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+
<caption style='caption-side:top;'><b>Table 1: Data obtained from XXX<b> relating each value of the LOCS scale, to opacity values. </caption>
+
<tbody>
+
<tr>
+
<td>LOCS</td>
+
<td>0.0</td>
+
<td>0.5</td>
+
<td>1.0</td>
+
<td>2.0</td>
+
<td>3.0</td>
+
<td>4.0</td>
+
<td>5.0</td>
+
<td>6.0</td>
+
</tr>
+
<tr>
+
<td>Degree</td>
+
<td>None</td>
+
<td></td>
+
<td>Trace</td>
+
<td>Mild</td>
+
<td>Surgery Suggested</td>
+
<td>Moderate</td>
+
<td>Severe</td>
+
<td>Very Severe</td>
+
</tr>
+
<tr>
+
<td>Opacity (%)</td>
+
<td>0.34</td>
+
<td>4.24</td>
+
<td>5.80</td>
+
<td>18.88</td>
+
<td>23.60</td>
+
<td>49.14</td>
+
<td>65.61</td>
+
<td>90+</td>
+
</tr>
+
<tr>
+
<td>Absorbance (a.u.)</td>
+
<td>0.001</td>
+
<td>0.019</td>
+
<td>0.026</td>
+
<td>0.091</td>
+
<td>0.117</td>
+
<td>0.294</td>
+
<td>0.464</td>
+
<td>1.3+</td>
+
</tr>
+
</tbody>
+
</table>
+
<p> We wish to remain below clinically significant levels, so we will reach attempt to lower the  LOCS rating of a cataract to below grade 2.5, which means we want to control GSR such that the crystallin damage results in less than 0.108 a.u. at absorbance at 397.5 nm. </p>
+
 
+
 
+
 
+
  </div>
+
  <div id="gsrmenu3" class="tab-pane fade">
+
 
+
  </div>
+
 
+
  <div id="gsrmenu4" class="tab-pane fade">
+
    <h4>Menu 3</h4>
+
      <p>Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.</p>
+
    </div>
+
 
+
</div>
+
</div>
+
 
+
 
+
+
</div>  <!-- End Menu -->
+
 
+
                        <h3></h3>
+
                        <div class="row">
+
                            <div class="col-sm-6">
+
                                 <div class="col-sm-12" >
+
                                    <p>
+
                                        <br><br><br><br><br>
+
                                    </p>
+
 
                                 </div>
 
                                 </div>
 +
                         
 
                             </div>
 
                             </div>
 
+
                       
                             <div class="col-sm-6" >
+
                             <div class="row">
 +
                                <h3>Conclusion</h3>
 
                                 <div class="col-sm-12">
 
                                 <div class="col-sm-12">
                                     <p>
+
                                     <p>We need to maintain (NOT add) 43.5 uM of GSR in the lens so that the crystallin damage recorded over 50 years is below the LOCS 2.5 threshold. </p>
                                        When determining the relationship between absorbance and crystallin, in Figure 1 the best fit line has a x – intercept that is nonzero. However, when converting each absorbance rating to equivalent crystallin damage in Table 2, we ignore the constant term. When doing the experiments, the fish lens may have contained GSH that is still active, so the fact that the crystallin is exposed to H2O2, the degradation reaction does not happen until all GSH is depleted, and crystallin damage begins to form. We subtract around 1 unit of crystallin damage from all values.  
+
                                    </p>
+
 
                                 </div>
 
                                 </div>
 +
                         
 
                             </div>
 
                             </div>
 
                          
 
                          
<h4> Conclusion</h4>
+
                       
<p> Conclusion</p>
+
                       
  
 
+
                           
 
+
                         
</div> <!-- Container -->
+
                        </div> <!-- Container -->
</div> <!-- Container -->
+
                    </div> <!-- Container -->
 
+
               
 
+
               
 
+
               
<div class = "row">
+
                    <div class = "row">
<div class="col-sm-12">
+
  <div class="col-sm-12">
<h2 id = 'nanoparticle'>Model 3: Nanoparticles</h2>
+
<h4> Abstract </h4>
+
<p> Abstract </p>
+
+
<h4> Purpose </h4>
+
<p> Purpose </p>
+
 
+
 
+
 
+
<button class="accordion">Background, Method, Results, Discussion</button>
+
<div class="panel">
+
 
+
<div class="accordionmenu1" class ="col-sm-12" >
+
  <ul class="nav nav-tabs">
+
  <li class="active"><a data-toggle="tab" href="#nphome">Background</a></li>
+
  <li><a data-toggle="tab" href="#npmenu1">Method</a></li>
+
  <li><a data-toggle="tab" href="#npmenu2">Results Part 1</a></li>
+
  <li><a data-toggle="tab" href="#npmenu2">Results Part 2</a></li>
+
  <li><a data-toggle="tab" href="#npmenu3">Discussion</a></li>
+
</ul>
+
 
+
  <div class="tab-content">
+
  <div id="home" class="tab-pane fade in active">
+
      <h4>Background</h4>
+
                               
+
<p>There are three quantifiers of how severe cataract formation is, two are measurable, one is not.
+
<ol>
+
<li>Absorbance @ 397.5 nm, which is measured with lab equipment.</li>
+
<li>LOCS scale, subjectively measured by physicians on a scale from 0 - 6.
+
</li>
+
<li>Crystallin Damage, which we define as the following (for any time $t$)     </li>
+
</ol>
+
 
+
</p>
+
 
+
\[c.d.(t) = \int_{0}^{\infty} [H_2O_2]_t dt\]
+
 
+
<p> In other words, 1 unit of crystallin damage, in M-h,  is equal to the damage caused by 1 molar concentration of hydrogen peroxide reacting crystallin in the eyes for 1 hour.</p>
+
 
+
                              <p> In making this definition, we assume that crystallin damage is directly proportional to the amount of time crystallin is exposed to hydrogen peroxide. Hydrogen peroxide causes damage by forming disulfide bridges within cysteine molecules on crystallin. This changes the structure of crystallin, causing misfolding and cataract damage. Our linear assumption is valid because the rate for this reaction is first order with respect to hydrogen peroxide concentration. </p> 
+
 
+
  </div>
+
 
+
    <div id="npmenu1" class="tab-pane fade">
+
    <h4>Method</h4>
+
      <p>We will relate the three by doing the following:
+
    <ol>
+
                                      <li>Relate LOCS scale to opacity via literature research. </li>
+
                                      <li>Relate opacity to light transmittance via literature research. </li>
+
                                      <li>Relate light transmittance to absorbance via physical calculations. </li>
+
                                      <li>Relate absorbance to crystallin damage via experimental data. </li>
+
 
+
 
+
    </ol>
+
      </p>
+
 
+
 
+
  </div>
+
  <div id="npmenu2" class="tab-pane fade">
+
      <h4>Part 1 Results</h4>
+
 
+
      <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+
<caption style='caption-side:top;'><b>Table 1: Data obtained from XXX<b> relating each value of the LOCS scale, to opacity values. </caption>
+
<tbody>
+
<tr>
+
<td>LOCS</td>
+
<td>0.0</td>
+
<td>0.5</td>
+
<td>1.0</td>
+
<td>2.0</td>
+
<td>3.0</td>
+
<td>4.0</td>
+
<td>5.0</td>
+
<td>6.0</td>
+
</tr>
+
<tr>
+
<td>Degree</td>
+
<td>None</td>
+
<td></td>
+
<td>Trace</td>
+
<td>Mild</td>
+
<td>Surgery Suggested</td>
+
<td>Moderate</td>
+
<td>Severe</td>
+
<td>Very Severe</td>
+
</tr>
+
<tr>
+
<td>Opacity (%)</td>
+
<td>0.34</td>
+
<td>4.24</td>
+
<td>5.80</td>
+
<td>18.88</td>
+
<td>23.60</td>
+
<td>49.14</td>
+
<td>65.61</td>
+
<td>90+</td>
+
</tr>
+
<tr>
+
<td>Absorbance (a.u.)</td>
+
<td>0.001</td>
+
<td>0.019</td>
+
<td>0.026</td>
+
<td>0.091</td>
+
<td>0.117</td>
+
<td>0.294</td>
+
<td>0.464</td>
+
<td>1.3+</td>
+
</tr>
+
</tbody>
+
</table>
+
<p> We wish to remain below clinically significant levels, so we will reach attempt to lower the  LOCS rating of a cataract to below grade 2.5, which means we want to control GSR such that the crystallin damage results in less than 0.108 a.u. at absorbance at 397.5 nm. </p>
+
 
+
 
+
 
+
  </div>
+
  <div id="npmenu3" class="tab-pane fade">
+
 
+
  </div>
+
 
+
  <div id="npmenu4" class="tab-pane fade">
+
    <h4>Menu 3</h4>
+
      <p>Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.</p>
+
    </div>
+
 
+
</div>
+
</div>
+
 
+
 
+
+
</div>  <!-- End Menu -->
+
 
+
 
+
<h4> Conclusion</h4>
+
<p> Conclusion </p>
+
 
+
 
+
 
+
</div> <!-- Container -->
+
</div> <!-- Container -->
+
 
+
 
+
 
+
 
+
 
+
 
+
 
+
<div class = "row">
+
<div class="col-sm-12">
+
<h2 id = 'eyedrop'>Model 4: Eyedrops</h2>
+
<h4> Abstract </h4>
+
<p> Abstract </p>
+
+
<h4> Purpose </h4>
+
<p> Purpose </p>
+
 
+
 
+
 
+
<button class="accordion">Background, Method, Results, Discussion</button>
+
<div class="panel">
+
 
+
<div class="accordionmenu1" class ="col-sm-12" >
+
  <ul class="nav nav-tabs">
+
  <li class="active"><a data-toggle="tab" href="#eyehome">Background</a></li>
+
  <li><a data-toggle="tab" href="#eyemenu1">Method</a></li>
+
  <li><a data-toggle="tab" href="#eyemenu2">Results Part 1</a></li>
+
  <li><a data-toggle="tab" href="#eyemenu2">Results Part 2</a></li>
+
  <li><a data-toggle="tab" href="#eyemenu3">Discussion</a></li>
+
</ul>
+
 
+
  <div class="tab-content">
+
  <div id="eyehome" class="tab-pane fade in active">
+
      <h4>Background</h4>
+
                               
+
<p>There are three quantifiers of how severe cataract formation is, two are measurable, one is not.
+
<ol>
+
<li>Absorbance @ 397.5 nm, which is measured with lab equipment.</li>
+
<li>LOCS scale, subjectively measured by physicians on a scale from 0 - 6.
+
</li>
+
<li>Crystallin Damage, which we define as the following (for any time $t$)     </li>
+
</ol>
+
 
+
</p>
+
 
+
\[c.d.(t) = \int_{0}^{\infty} [H_2O_2]_t dt\]
+
 
+
<p> In other words, 1 unit of crystallin damage, in M-h,  is equal to the damage caused by 1 molar concentration of hydrogen peroxide reacting crystallin in the eyes for 1 hour.</p>
+
 
+
                              <p> In making this definition, we assume that crystallin damage is directly proportional to the amount of time crystallin is exposed to hydrogen peroxide. Hydrogen peroxide causes damage by forming disulfide bridges within cysteine molecules on crystallin. This changes the structure of crystallin, causing misfolding and cataract damage. Our linear assumption is valid because the rate for this reaction is first order with respect to hydrogen peroxide concentration. </p> 
+
 
+
  </div>
+
 
+
    <div id="eyemenu1" class="tab-pane fade">
+
    <h4>Method</h4>
+
      <p>We will relate the three by doing the following:
+
    <ol>
+
                                      <li>Relate LOCS scale to opacity via literature research. </li>
+
                                      <li>Relate opacity to light transmittance via literature research. </li>
+
                                      <li>Relate light transmittance to absorbance via physical calculations. </li>
+
                                      <li>Relate absorbance to crystallin damage via experimental data. </li>
+
 
+
 
+
    </ol>
+
      </p>
+
 
+
 
+
  </div>
+
  <div id="eyemenu2" class="tab-pane fade">
+
      <h4>Part 1 Results</h4>
+
 
+
      <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+
<caption style='caption-side:top;'><b>Table 1: Data obtained from XXX<b> relating each value of the LOCS scale, to opacity values. </caption>
+
<tbody>
+
<tr>
+
<td>LOCS</td>
+
<td>0.0</td>
+
<td>0.5</td>
+
<td>1.0</td>
+
<td>2.0</td>
+
<td>3.0</td>
+
<td>4.0</td>
+
<td>5.0</td>
+
<td>6.0</td>
+
</tr>
+
<tr>
+
<td>Degree</td>
+
<td>None</td>
+
<td></td>
+
<td>Trace</td>
+
<td>Mild</td>
+
<td>Surgery Suggested</td>
+
<td>Moderate</td>
+
<td>Severe</td>
+
<td>Very Severe</td>
+
</tr>
+
<tr>
+
<td>Opacity (%)</td>
+
<td>0.34</td>
+
<td>4.24</td>
+
<td>5.80</td>
+
<td>18.88</td>
+
<td>23.60</td>
+
<td>49.14</td>
+
<td>65.61</td>
+
<td>90+</td>
+
</tr>
+
<tr>
+
<td>Absorbance (a.u.)</td>
+
<td>0.001</td>
+
<td>0.019</td>
+
<td>0.026</td>
+
<td>0.091</td>
+
<td>0.117</td>
+
<td>0.294</td>
+
<td>0.464</td>
+
<td>1.3+</td>
+
</tr>
+
</tbody>
+
</table>
+
<p> We wish to remain below clinically significant levels, so we will reach attempt to lower the  LOCS rating of a cataract to below grade 2.5, which means we want to control GSR such that the crystallin damage results in less than 0.108 a.u. at absorbance at 397.5 nm. </p>
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    <h4>Menu 3</h4>
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      <p>Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.</p>
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<h2 id ="X">Conclusion</h2>
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<h3>Citations</h3>
 
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             nowRadius = this.blurRadius;
 
             nowRadius = this.blurRadius;
 
         var LOCSnum = Math.round(nowRadius*6/9);
 
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         $('#LOCS').text(LOCSnum+"");
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        /**if (NineLOCSnum > 20) switchMessage("YELLOW","<b> Oh no! </b> Cataracts are forming! Click on the Eyedrop Tab and get <b>TREATMENT</b> eyedrops!", currentColor()=="GREEN");
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                switchMessage("GREEN","<b>Your eyes are <i>pernamently</i> crystal clear!</b> Treatment is not needed, so don't forget to turn it off!. Click the question mark to learn more.", currentColor()=="BLUE")
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 +
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             else {startBlur(12000);}
 
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         $("#redbutton").removeClass("isOn"); }
 
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   else { $("#redbutton").addClass("isOn"); }
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         <h4><b> LOCS: <span id="LOCS">0 &#160;</span></b> &#160; &#160; <a href="https://2016.igem.org/Team:TAS_Taipei/Wiki_Standard_Pages#Animation"><button  type="button" class="btn btn-danger btn-md">?</button> </a>
  
 
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     <div id="clickme">
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             Eyedrops
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             <br> Eyedrops  
 
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            <p style="font-size:14px !important"><a href="#" class="close" data-dismiss="alert" aria-label="close">&times;</a>
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                <strong>The tutorial is disabled.</strong> &#160; &#160; &#160; &#160; &#160;<a href="https://2016.igem.org/Team:TAS_Taipei/Wiki_Standard_Pages#Animation"><button  type="button" class="btn btn-danger btn-sm">?</button> </a><span style="font-size:14px"><br>Turn off prevention eyedrops to activate the animation. For a full tutorial, click the question mark. </span></p>
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Revision as of 11:19, 8 October 2016

Model - TAS Taipei iGEM Wiki





Model

Cataract prevention occurs over 20 – 50 years, so we cannot perform experiments on the long-term impact of adding GSR or CH25H. However, computational biology allows us to predict cataract development in the long-term. These models allow our team to understand the impact of adding GSR-loaded nanoparticles into the lens over a 50 year period, and to design a full treatment plan on how to prevent and treat cataracts with our project. Therefore, the results of our model are essential in developing a functional prototype.

For sake of clarity, we will discuss each model in detail with respect to prevention (using GSR) only. At the end, we explain these results to treatment. In addition, we include collapsibles for interested readers and judges, in order to fully document our modeling work (eg. assumptions, mathematics) while keeping the main page clear with basic points only.

Introduction

  1. How much GSR to maintain in the lens?
  2. How to maintain that amount of GSR using nanoparticles and eyedrops?

Focus of Models

Since our construct is not directly placed into the eyes, how our synthesized protein impacts the eye after it is separately transported into the lens is of greater importance. As a result, we create models with the intent on understanding how GSR and CH25H impacts the eye.

Relation to Experiments

We use measurements from the cataract lens experiment to create the first model, and extend the results with the second model to find GSR concentrations, which our experiments could not find.

We modelled nanoparticle degradation before performing actual experiments, to estimate the optimal amount of protein to load into the nanoparticles. After performing the experiments, we can directly compare them to see the efficiency of our drug-loading. Although we could not experimentally test an eyedrop prototype, model 4 extends the results of the nanoparticle degradation to better understand how to use eyedrops to deliver nanoparticles.

Relation to Overall Project

Although experiments could validate a prototype, it is through modeling that we find the optimal designs for these prototypes. By building a full calculator, we can envision how the results of this project can be applied clinically. A patient finds his or her LOCS score from the physician, and then enters it into the calculator, which returns a full treatment plan, using standardized cataract prevention and treatment eyedrops. Our nanoparticles are fully customizable, to allow physicians to alter the design to best fit a patient’s specific cataract conditions.

Figure 1 (left). Priacanthus macracanthus purchased from the market. (right) The two spheres on the left are lens with cortex and nucleus and the two smaller spheres on the right are nucleus.

Model 1: Crystallin Damage

The amount of damage to crystallin by H2O2 determines the severity of a cataract. We relate the amount of crystallin damage to the corresponding rating on the LOCS scale, used by physicians to rate cataract severity. Our goal is to lower LOCS to below 2.5, the threshold for surgery. Through literature research as well as our own experimental data, we find the maximum allowable crystallin damage to prevent a LOCS 2.5 cataract from developing.

Measurement of Cataract Severity

There are four ways of measuring cataract severity, each used for a different purpose.

  1. Lens Optical Cataract Scale (LOCS): Physicians use this scale, from 0 – 6, to grade the severity of cataracts.
  2. Absorbance at 397.5 nm: This is the experimental method, used by our team in the lab (c.d.)
  3. Crystallin Damage: This is a chemical definition. We quantify cataract severity as a function of how much oxidizing agents there are, as well as how long crystalline is exposed to oxidizing agents.
When we add GSR into the system, crystallin damage decreases. Our goal is to find the equivalent crystallin damage that leads to a LOCS 2.5 cataract, in order to know how much GSR to prevent this amount of crystallin damage in Model 2.

Measurement of Cataract Severity

Numerous studies show how absorbance measurements can be converted to the LOC scale that physicians use. With the results of ________ and ________, we construct the first two columns in Table 2.

Absorbance Equivalence to Crystallin Damage: Experimental Data

We use experimental data from our team’s Cataract Lens Model (link). They induced an amount of crystallin damage, and measured the resulting absorbance. With this relation in Figure 2, we calculate the equivalent crystallin damage of each LOCS rating and absorbance.

Conclusion

To guarantee that surgery is not needed for 50 years, we need to limit crystallin damage to 0.9981 units. If crystallin damage goes above this threshold, then surgery is needed. This is the crystallin damage threshold for a LOCS 2.5 cataract.

Model 2: GSR Pathway

Now that we know how much GSR we need to limit crystallin damage to LOCS 2.5, we model the naturally occurring GSR Pathway in the lens of a human eye. For prevention (2A), we calculate the necessary GSR concentration to be maintained over 50 years so that the resulting cataract is below LOCS 2.5.

Chemical Kinetics Model: Differential Equations

By the Law of Mass Action, Michaelis-Menten Enzyme kinetics, Ping-pong mechanism, and the Law of Passive Diffusion, we build a system of 10 differential equations based on 6 chemical reactions. All parameters, constants, and initial conditions are based off literature data. Estimates made are also shown with assumptions and reasoning. The details are shown in the collapsible for interested readers.

Blackbox Approach: Testing GSR Impact

We vary the input, Initial GSR concentration, holding all other variables constant, and numerically solve for the amount of hydrogen peroxide over time. With this graph, we can find the amount of crystallin damage accumulated over 20 to 50 years if different levels of GSR is maintained.

From this graph, we can find the GSR concentration needed for the LOCS 2.5 threshold and the LOCS 1.0 threshold.

Crystallin Damage vs. GSR Level

According to literature data and our model, the naturally occurring GSR concentration is 10 uM. All curves show crystallin damage decreasing as GSR levels are increased, which supports both research and experimental data, and suggests that this prototype is effective in preventing crystallin damage. However, GSR levels need to be raised significantly, up to 40+ uM from the natural 10 uM of GSR in order to show long-term protection.

Table 3 shows the amount of GSR we need to maintain for 50 years in order to prevent a LOCS cataract of a certain severity. The row of interest is LOCS 2.5, the threshold for surgery. Notice that we say “maintain” the level of GSR. This level needs to be constant at all times for 50 years for full prevention. The delivery of GSR to maintain this level is discussed in Model 3.

Conclusion

We need to maintain (NOT add) 43.5 uM of GSR in the lens so that the crystallin damage recorded over 50 years is below the LOCS 2.5 threshold.

Citations












Prevention

GSR Eyedrop

Treatment

25HC Eyedrop

LOCS: 0      


Eyedrops




× The tutorial is disabled.          
Turn off prevention eyedrops to activate the animation. For a full tutorial, click the question mark.