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

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<title>Model - TAS Taipei iGEM Wiki</title>
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<title>Modeling - TAS Taipei iGEM Wiki</title>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/project#background">Background</a></h5>
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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/project/achievements">Achievements</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Achievements">Achievements</a></h5>
 
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<h4><b>Cataracts</b> - the leading cause of blindness. Find out how we can both <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 noninvasively <b>treat</b> and <b>prevent</b> cataract formation.</b></h4>
 
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<a href="https://2016.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://2015.igem.org/Team:TAS_Taipei/wetlab"><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/wetlab#construct">Construct</a></h5>
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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/wetlab#prototype">Proof of Construct</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/wetlab#safety">Prototype</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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<h4>We conduct science - and we are proud to show it. Follow along with our journey of discovery in the lab.</h4>
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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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<a href="https://2016.igem.org/Team:TAS_Taipei/Model"><h4 class='dropdown-toggle disabled' data-toggle="dropdown"><b>MODELING</b></h4></a>
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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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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Model#overview">Overview</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Model#crystallin">Cataract Damage</a></h5>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Model#gsr25hc">GSR/25HC</a></h5>
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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#eyedrop">Eyedrops</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">Nanoparticles</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Model#eyedrop">Eyedrop Model</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Model#geneexpression">Gene Expression</a></h5>
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<h4><b>Computational Biology</b> provides us models that we cannot easily test. Click to see the power of math.</h4>
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<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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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Practices#research">Research</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Human_Practices#research">Research</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Practices#change">Change</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Practices#outreach">Outreach</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Human_Practices#outreach">Outreach</a></h5>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Practices#entertainment">Entertainment</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Human_Practices#impact">Impact</a></h5>
 
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<a href="https://2016.igem.org/Team:TAS_Taipei/team"><h4 class='dropdown-toggle disabled' data-toggle="dropdown"><b>TEAM</b></h4></a>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/team#members">Members</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Team#members">Members</a></h5>
 
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Attributions">Attributions</a></h5>
 
<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Attributions">Attributions</a></h5>
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<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Standard_Pages">Wiki Standard Pages</a></h5>
 
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<h4>Behind every tough iGem project lies a tough, hard-working yet cheerful group of students. <b>Meet the team!</b></h4>
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<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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COUNTERACTS</b></h2>
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C&#9678;UNTERACTS</b></h2>
 
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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>
 
<li><a href="#overview">Overview</a></li>
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<li><a href="#crystallin">Crystallin</a></li>
 
<li><a href="#gsr25hc">GSR/25HC</a></li>
 
<li><a href="#gsr25hc">GSR/25HC</a></li>
<li><a href="#eyedrop">Eyedrop</a></li>
 
 
<li><a href="#nanoparticle">Nanoparticles</a></li>
 
<li><a href="#nanoparticle">Nanoparticles</a></li>
<li><a href="#geneexpression">Gene Expression</a></li>
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<li><a href="#eyedrop">Eyedrop</a></li>
 
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<h1 id='overview'>Modeling</h1>
 
<h1 id='overview'>Modeling</h1>
<p>Granzyme B (GzmB) activity is elevated during inflammation, which can lead to excess cleavage of extracellular matrix (ECM) proteins in human tissue. Aside from causing damage to healthy tissues, this also exacerbates chronic inflammatory conditions, which keeps producing more GzmB and creates a vicious cycle. Our project aims to selectively inhibit GzmB in the ECM in order to prevent damage during chronic inflammation. Since we do not have the means of working with GzmB and directly testing its interactions in human test subjects, we predicted these interactions using mathematical models and data from the literature.</p>
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<p>The Hill equation is used to model the interaction between a ligand and its binding partner, a macromolecule/enzyme – in our case, how well a GzmB inhibitor binds to GzmB. It is a function of free ligand concentration, and it returns the fraction of macromolecules that are bound. Two constants are involved in this equation: the dissociation constant and the Hill coefficient (Weiss, 1997). </p>
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<p>The Hill coefficient describes cooperativity of the binding. Positive cooperativity (n>1) means that a bound enzyme has higher affinity for other ligands; negative cooperativity (n<1) means the converse is true; and non-cooperative binding (n=0) means that whether or not the enzyme is bound has no bearing on further binding (Weiss, 1997).</p>
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<p>The Hill equation is shown below: <br><img src = "https://static.igem.org/mediawiki/2015/b/ba/Model_eqn1.gif">
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, where [L] is concentration of the ligand (in our case, the inhibitor), Kd is the dissociation constant, and n is the Hill coefficient.
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                                    <h3> Abstract </h4>
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                <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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                                    <h3>Achievements</h4>
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                                    <ul style="font-size:15px">
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                                        <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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                                        <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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<h3> Outline </h3>
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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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<h2 id = 'gsr25hc'>Mouse Inhibitor Serpina3n vs GzmB Activity</h2>
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<p>Our first dataset (Table 1), which measures Serpina3n concentration vs relative GzmB activity, came from research by Ang <i>et al.</i> at the University of British Columbia (2011). Serpina3n is a known mouse GzmB inhibitor, and the paper documented the effects of Serpina3n on GzmB activity. Given its specificity in mice, this inhibitor was not chosen as part of the final construct, but data from this paper was used because the relevant constants can be analyzed and compared to other inhibitor substitutes.<br></p>
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<h2 id = 'crystallin'>Model 1: Crystallin Damage</h2>
<caption style='caption-side:top;'><b>Table 1: Dataset obtained from Ang <i>et al.</i>,</b> showing Serpina3n Concentration vs Relative GzmB Activity </caption>
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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.
 +
                                        <ol>
 +
                                            <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>
 +
                                            <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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                        <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>
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 +
                        <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>
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                        <h3>Absorbance Equivalence to Crystallin Damage: Experimental Data</h3>
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                            <div class="col-sm-7">
 +
                                <div class="col-sm-12" >
 +
                                    <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.
 +
                                    </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>
 +
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 +
                                <div class="col-sm-12">
 +
                                    <p>
 +
                                        <table class="table table-bordered" style='width: 80%;margin-left:0%;'>
 +
                <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>
 +
                                </div>
 +
                            </div>
 +
                        </div>
 +
       
 +
<button class="accordion">Background, Method, Results, Discussion</button>
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<div class="panel">
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 +
<div class="accordionmenu1" class ="col-sm-12" >
 +
  <ul class="nav nav-tabs">
 +
  <li class="active"><a data-toggle="tab" href="#cryshome">Background</a></li>
 +
  <li><a data-toggle="tab" href="#crysmenu1">Assumptions</a></li>
 +
  <li><a data-toggle="tab" href="#crysmenu2">Procedure</a></li>
 +
  <li><a data-toggle="tab" href="#crysmenu3">Results</a></li>
 +
  <li><a data-toggle="tab" href="#crysmenu4">Discussion</a></li>
 +
</ul>
 +
 
 +
  <div class="tab-content">
 +
  <div id="cryshome" class="tab-pane fade in active">
 +
      <h3>Background</h3>
 +
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                    <div class="col-sm-8">
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                        <div class="col-sm-12" style="border:1px solid black">
 +
                            <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>
 +
                    </div>
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                        <div class="col-sm-12" style="border:1px solid black">
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                            <h3>LOCS Scale</h3><br> <br> <br><br> <br> <br> <br><br><br><br>
 +
                        </div>
 +
                    </div>
 +
                   
 +
                </div>                   
 +
 +
 
 +
 
 +
  </div>
 +
 
 +
    <div id="crysmenu1" class="tab-pane fade">
 +
    <h3>Assumptions</h3>
 +
                <div class="row">
 +
                    <div class="col-sm-12">
 +
                        <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>
 +
                        </div>
 +
                    </div>
 +
                   
 +
                </div>   
 +
               
 +
     
 +
 
 +
 
 +
  </div>
 +
  <div id="crysmenu2" class="tab-pane fade">
 +
      <h3>Procedure</h3>
 +
 
 +
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 +
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 +
                        <div class="col-sm-12" style="border:1px solid black">
 +
                            <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>
 +
                        </div>
 +
                    </div>
 +
               
 +
                    <div class="col-sm-4" style="background-color:lightpink;margin:0px">
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                        <div class="col-sm-12" style="border:1px solid black">
 +
                            <h3>LOCS Scale</h3><br> <br> <br><br> <br> <br> <br><br><br><br>
 +
                        </div>
 +
                    </div>
 +
                   
 +
                </div>                     
 +
 
 +
  </div>
 +
  <div id="crysmenu3" class="tab-pane fade">
 +
                <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>
 
<tbody>
 
<tr>
 
<tr>
<td>[Sa3n] (nM)</td>
+
<td>LOCS</td>
<td>0.4</td>
+
<td>0.0</td>
<td>1.4</td>
+
<td>0.5</td>
<td>2.8</td>
+
<td>1.0</td>
<td>3.8</td>
+
                                    <td>1.5</td>
<td>5</td>
+
<td>2.0</td>
<td>7.8</td>
+
                                    <td>2.5</td>
<td>10</td>
+
<td>3.0</td>
<td>16</td>
+
<td>4.0</td>
<td>21</td>
+
<td>5.0</td>
<td>40</td>
+
<td>80</td>
+
 
</tr>
 
</tr>
 
<tr>
 
<tr>
<td>Relative GzmB Activity (%)</td>
+
<td>Degree</td>
<td>118</td>
+
<td>None</td>
<td>110</td>
+
<td colspan="2">Trace</td>
<td>115</td>
+
<td colspan="3">Mild</td>
<td>102</td>
+
<td colspan="2">Moderate</td>
<td>78</td>
+
<td>Severe</td>
<td>76</td>
+
</tr>
<td>65</td>
+
<tr>
<td>56</td>
+
<td>Opacity (%)</td>
<td>39</td>
+
<td>0</td>
<td>15</td>
+
                                    <td>3.24</td>
<td>4</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>
 
</tr>
 
</tbody>
 
</tbody>
</table>
+
</table>
<p>Several adjustments were made to the equation and dataset so that we could have a meaningful model.  First, GzmB activity was shown as percentages ranging from 10% to 120% in the paper. This is likely because the control for the experiment was set at some point where the Serpina3n expression is not 0. Thus, we scaled down the data points by a factor of 1/120. This scaling is necessary since the Hill equation returns a fraction; the output is limited to between 0 and 1.</p>
+
                <br><br><br>
<p>More importantly, since the data was presented as the concentration of enzymes that remain free after binding, we needed to modify the Hill equation in order to model the fraction of unbound GzmB. Since <i>bound + unbound = 100%</i>, and the Hill equation models the bound component, it can be said that <img src = 'https://static.igem.org/mediawiki/2015/f/f8/Model_eqn2.gif'>, provided that the dataset is properly scaled to a range between 100%-0%.</p>
+
                <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
<p>The FindFit function of Mathematica was used to find the unknown constants Kd and n for the modified Hill equation above. Our model returned a Kd of ≈ 28.130 and n ≈ 1.3540. The final equation is <img src = 'https://static.igem.org/mediawiki/2015/7/72/Model_eqn3.gif'>, where θ<sub>free</sub> is GzmB activity and [L] stands for concentration of Serpina3n (Figure 1).</p>
+
                    <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>
<figure class = "col-sm-10">
+
<tbody>
<img src="https://static.igem.org/mediawiki/2015/6/6a/Model_fig1.png">
+
                                <thead>
<figcaption class='darkblue'><b>Figure 1. Model: Serpina3n Inhibition of GzmB.</b> Using data from the Ang <i>et al.</i> paper, we developed an equation that models relative GzmB Activity as a function of Serpina3n concentration</figcaption>
+
                                    <td>Trial</td>
</figure>
+
<td>H2O2 Concentration (M)</td>
</div>
+
<td>Exposure Time (h)</td>
</div>
+
<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>
 +
                               
 +
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    <h3>Discussion</h3>
<h2 id = 'eyedrop'>Human GzmB Inhibitor ACT3m</h2>
+
                <h4>Model Result</h4>
<button class="accordion">Section 1</button>
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                                <p>
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                                    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.
 +
                                </p>
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                <h4>Model Adjustment</h4>
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                                <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.
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                <h4>Error Analysis</h4>
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                                <p>
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                                    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.
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                                <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.
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    <h3> Conclusion</h3>
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                                <p>
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                                    <br><br><br><br><br>
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                                <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.
 +
                                    For future models, this value 0.9981 units of c.d. will be called the crystallin damage threshold for LOCS 2.5.
 +
 
 +
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<h2 id = 'gsr25hc'>Model 2: GSR/25HC Chemical Pathway</h2>
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                                        <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>
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 +
                                        <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>
 +
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 +
           
 +
                        <h3> Chemical Kinetics Model: Differential Equations </h3>
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 +
                                        <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>
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                                        <h3>Blackbox Approach: Testing GSR Impact </h3>
 +
                                        <p> Image</p>
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                                        <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>
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<button class="accordion">Background, Method, Results, Discussion</button>
 
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   <li><a data-toggle="tab" href="#gsrmenu1">Method</a></li>
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  <li><a data-toggle="tab" href="#gsrmenu2">Results Part 1</a></li>
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   <li><a data-toggle="tab" href="#gsrmenu2">Results Part 2</a></li>
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       <h3>HOME</h3>
+
       <h4>Background</h4>
    <p>Given our model of Serpina3n, we also wanted to create a model for the protein used in our device, ACT3m. The dataset obtained from the ACT3m paper (Marcet-Palacios <i>et al.</i>, 2014) is the result of a colorimetric assay. Data was presented as absorbance values (A<sub>405</sub>), which correspond to the concentration of free GzmB, at different inhibitor concentrations. The paper used this to prove that their novel ACT3m inhibitor was the strongest out of their entire pool of possible candidates: treatment with ACT3m resulted in the lowest A<sub>405</sub> values, which suggests the strongest inhibition of GzmB.</p>
+
                               
 +
<p> The following 6 reactions describe the antioxidant system inside the cortex and nucleus.</p>
  
 +
$$GP_{xr}+[H_2O_2]_{in}+H^+ \xrightarrow[]{k_1} GP_{xo}+H_2O ...(1)$$
 +
$$GP_{xo}+GSH+H^+ \xrightarrow[]{k_2} [GS-GP_x]+H_2O ...(2)$$
 +
$$[GS-GP_x] + GSH \xrightarrow[]{k_3} GP_{xr}+GSSG+H^+ ...(3)$$
 +
$$NADPH \xrightarrow[GSR]{k4, K_{4M}} NADP^+ ...(4)$$
 +
$$GSSG \xrightarrow[GSR']{k_5, K_{5M}} 2GSH ...(5)$$
 +
$$[H_2O_2]_{out} \xrightarrow[]{k_5} [H_2O_2]_{in} ...(6)$$
 +
 +
<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>
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     <h3>Menu 1</h3>
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      <p>To model this set of data, similar adjustments had to be made. First, the dataset was scaled so the numbers ranged between 0 and 1 (in this case, increased by a factor of 2). The same modified Hill equation was used from the Serpina3n analysis. Our model returned a Kd of ≈ 13.336 and n ≈ 0.605, so the equation looks like <img class = "col-sm-3" src = 'https://static.igem.org/mediawiki/2015/1/17/Model_eqn4.gif'>(Figure 2).</p>
+
     <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>
   <div id="menu2" class="tab-pane fade">
+
   <div id="gsrmenu2" class="tab-pane fade">
       <h3>Menu 2</h3>
+
       <h4>Part 1 Results</h4>
       <figure class = "col-sm-8">
+
 
<img src="https://static.igem.org/mediawiki/2015/0/0f/Model_fig2.png">
+
       <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
<figcaption class='darkblue'><b>Figure 2. Model: ACT3m Inhibition of GzmB.</b> Using data from the Marcet-Palacios <i>et al.</i> paper, we developed an equation that models relative GzmB activity as a function of ACT3m concentration.concentration.
+
<caption style='caption-side:top;'><b>Table 1: Data obtained from XXX<b> relating each value of the LOCS scale, to opacity values. </caption>
</figcaption>
+
<tbody>
</figure>
+
<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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   <div id="menu3" class="tab-pane fade">
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     <h3>Menu 3</h3>
+
     <h4>Menu 3</h4>
 
       <p>Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.</p>
 
       <p>Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.</p>
 
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</div>
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<div class = "row">
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                        <h3></h3>
<div class="col-sm-12">
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                        <div class="row">
<h2 id ="nanoparticle">Analysis</h2>
+
                            <div class="col-sm-6">
<table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+
                                <div class="col-sm-12" >
<caption style='caption-side:top;'><b>Table 2. Values Returned from Model:</b> the dissociation, association and Hill constants were calculated using Mathematica.</caption>
+
                                    <p>
<thead>
+
                                        <br><br><br><br><br>
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                                    </p>
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                            </div>
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                            <div class="col-sm-6" >
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                                <div class="col-sm-12">
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                                    <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>
 +
                       
 +
<h4> Conclusion</h4>
 +
<p> Conclusion</p>
 +
 
 +
 
 +
 
 +
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</div> <!-- Container -->
 +
 
 +
 
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<div class = "row">
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<div class="col-sm-12">
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<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>
 
<tr>
<th></th>
+
<td>LOCS</td>
<th>Kd (nM)</th>
+
<td>0.0</td>
<th>Ka (nM^-1)</th>
+
<td>0.5</td>
<th>n</th>
+
<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>
</thead>
 
<tbody>
 
 
<tr>
 
<tr>
<td>Sa3n</td>
+
<td>Degree</td>
<td>28.130</td>
+
<td>None</td>
<td>0.035549</td>
+
<td></td>
<td>1.3540</td>
+
<td>Trace</td>
 +
<td>Mild</td>
 +
<td>Surgery Suggested</td>
 +
<td>Moderate</td>
 +
<td>Severe</td>
 +
<td>Very Severe</td>
 
</tr>
 
</tr>
 
<tr>
 
<tr>
<td>ACT3m</td>
+
<td>Opacity (%)</td>
<td>13.336</td>
+
<td>0.34</td>
<td>0.074985</td>
+
<td>4.24</td>
<td>0.60462</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>
 
</tr>
 
</tbody>
 
</tbody>
 
</table>
 
</table>
<p class="col-sm-12">To interpret the above data, we first compare the constants of dissociation, Kd. In this context, Kd represents [Gzmb<sub>free</sub>][Inhibitor]/[Gzmb<sub>inhib</sub>-Inhibitor] at equilibrium (Bisswanger, 2008); therefore, a lower Kd would represent better inhibition: more bound GzmB compared to free GzmB.</p>
+
<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>
<p class="col-sm-12">We can also analyze the Ka, the association constant. Ka is the inverse of Kd, and can be found as [Gzmb<sub>inhib</sub>-Inhibitor]/ [Gzmb<sub>free</sub>][Inhibitor]. This represents the relative amount of bound molecules, so that a higher Ka represents stronger binding affinity. Compared to the mouse inhibitor Serpina3n, human ACT3m has a lower Kd and a higher Ka, which suggests stronger inhibition. This conclusion is in agreement with Marcet-Palacios <i>et al.</i>, where this novel inhibitor was also compared to mouse Serpina3n (2014).</p>
+
<p class="col-sm-12">The Hill constant may also be considered to analyze the nature of the inhibitor-GzmB complex. With n>1, Serpina3n is likely to bind to multiple sites on GzmB (Weiss <i>et al.</i>, 1997). ACT3m, in contrast, has a n<1, meaning that it likely binds competitively to selective and perhaps singular sites. This information is interesting; taking the association constants into account, this means that despite less opportunity to bind, ACT3m still acts as a better inhibitor than Serpina3n.</p>
+
</div>
+
</div>
+
</div>
+
  
<div class = "row">
+
 
<div class="col-sm-12">
+
 
<h2 id ="geneexpression">Inhibitor Concentration Calculator</h2>
+
  </div>
<p class = "col-sm-12"><br>The following equations were developed with a question in mind:</p>
+
  <div id="npmenu3" class="tab-pane fade">
<div class = "col-sm-2"></div>
+
 
<h3 class = "col-sm-8 purple" style = "color:white; padding: 20px">How much inhibitor is needed to bring GzmB levels back to normal?</h3>
+
  </div>
<p class = 'col-sm-12'><br>Since there are many diseases that cause inflammation, and thus increased levels of GzmB, we created a calculator to determine the amount of treatment needed for any GzmB-related diseases. The model can show the relative percent decrease of GzmB as the inhibitor concentration increases. A patient could obtain information regarding their condition and calculate the amount of treatment needed.</p>
+
 
<p class = 'col-sm-12'>Given that <img src = 'https://static.igem.org/mediawiki/2015/f/f8/Model_eqn2.gif'>, reversing the parameters yields the equivalent function of <img src = 'https://static.igem.org/mediawiki/2015/a/aa/Model_eqn5.gif'>, or <img src = 'https://static.igem.org/mediawiki/2015/9/95/Model_eqn6.gif'> . This equation calculates the inhibitor concentration that corresponds to a certain relative level of GzmB. </p>
+
  <div id="npmenu4" class="tab-pane fade">
<p class = 'col-sm-12'>Rheumatoid arthritis (RA) is one of the main chronic inflammatory diseases made worse by elevated GzmB activity. We will use this as an example to show how the calculator works. GzmB concentrations in synovial fluids (joint fluids) of arthritis patients were determined from Tak <i>et al.</i>, 2009 (summarized in Table 3). There is a significant GzmB concentration difference between the control group and RA patients. The equation that returns a concentration of inhibitor can be used here, as it takes in relative GzmB levels and returns the amount of inhibitor needed.</p>
+
    <h4>Menu 3</h4>
<table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+
      <p>Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.</p>
<caption style='caption-side:top;'><b>Table 3: GzmB Concentration in Synovial Fluids.</b> GzmB concentration in patients suffering from rheumatoid arthritis obtained from Tak <i>et al.</i>, 2009.</caption>
+
    </div>
<thead>
+
 
 +
</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>
 +
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 +
  <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>
 
<tr>
<th></th>
+
<td>LOCS</td>
<th>Rheumatoid arthritis (pg/mL)</th>
+
<td>0.0</td>
<th>Control (pg/mL)</th>
+
<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>
</thead>
 
<tbody>
 
 
<tr>
 
<tr>
<td>Mean +/- s.d.</td>
+
<td>Degree</td>
<td>3306 +/- 10311</td>
+
<td>None</td>
<td>34 +/- 32</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>
 
<tr>
 
<tr>
<td>Median</td>
+
<td>Opacity (%)</td>
<td>251</td>
+
<td>0.34</td>
<td>29</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>
 
</tr>
 
</tbody>
 
</tbody>
 
</table>
 
</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>
  
<p>If a patient has a GzmB level that is X times the amount of control (around 34 pg/mL), then proportionally, X/100% = 100%/Y, where Y is the factor we want to decrease the patient’s level by (relative to his original level). Therefore, <img src = "https://static.igem.org/mediawiki/2015/d/d2/Model_eqn7.gif"> , and the amount of inhibitor needed [L] can be calculated. For example, if an RA patient has a GzmB concentration of 3400 pg/mL, then the patient has about 100x the normal GzmB level. Therefore, the Y factor would be 1%, and [L] can be calculated to be around 130 uM.</p>
 
<p>It should be noted, however, that there is a large standard deviation for GzmB levels in RA patients, which means there are significant variations: if treatments are to be given, it would be better to conduct treatments on a case-by-case basis.</p>
 
  
  
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+
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<div class="panel">
+
    <h4>Menu 3</h4>
  <p>Lorem ipsum...</p>
+
      <p>Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.</p>
</div>
+
    </div>
  
<button class="accordion">Section 3</button>
+
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<div class="panel">
+
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  <p>Lorem ipsum...</p>
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</div>
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<h4> Conclusion</h4>
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<span>nM of ACT</span>
 
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<h3>Citations</h3>
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<h2 id ="X">Conclusion</h2>
<p>Weiss, J. (1997). The Hill equation revisited: Uses and misuses. Faseb J, 11(11), 835-841. Retrieved September 5, 2015, from Pubmed. <br><br>
+
  
Ang, L., Boivin, W., Williams, S., Zhao, H., Abraham, T., Carmine-Simmen, K., Granville, D. (2011). Serpina3n attenuates granzyme B-mediated decorin cleavage and rupture in a murine model of aortic aneurysm. Cell Death Dis Cell Death and Disease. <br><br>
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<p class="col-sm-12">Yay</p>
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</div>
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</div>
  
Marcet-Palacios, M., Ewen, C., Pittman, E., Duggan, B., Carmine-Simmen, K., Fahlman, R., & Bleackley, R. (2014). Design and characterization of a novel human Granzyme B inhibitor. Protein Engineering Design and Selection, 9-17. <br><br>
 
  
Bisswanger, H. (2008). Enzyme kinetics: Principles and methods (2nd rev. and updated ed.). Weinheim: Wiley-VCH. <br><br>
+
  
Tak PP, Spaeny-Dekking L, Kraan MC, Breedveld FC, Froelich CJ, Hack CE. The levels of soluble granzyme A and B are elevated in plasma and synovial fluid of patients with rheumatoid arthritis (RA). Clinical and Experimental Immunology. 1999;116(2):366-370. doi:10.1046/j.1365-2249.1999.00881.x.<br><br>
 
  
  
Vaughan, M. (1959). Cellulose Acetate Membranes suitable for Osmotic Measurements. Nature, 43-44.<br><br>
 
  
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<h3>Citations</h3>
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        <br> <br>  <br>  <br>  <br>  <br>  <br>  <br>          
 
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        <h3>Prevention</h3>
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        <h5>GSR Eyedrop</h5>
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Revision as of 14:13, 30 September 2016

Modeling - TAS Taipei iGEM Wiki





Modeling

Abstract

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.

Achievements

  • Designed a simple calculator to find amount of GSR or 25HC eyedrops needed for a patient's LOCS score.
  • Bridged the gap between the medical, biological, and chemical measurement of crystallin damage.
  • Predicted impact of adding GSR and 25HC on the amount of crystallin damage in the lens.
  • Created Nanoparticle Customizer for doctors to find a full treatment plan.
  • Generalized our Customizer to allow other iGEM teams who wish to use nanoparticle drug delivery
  • Analyzed sensitivity of prototype, and suggested insights into optimal manufacturing and clinical use of our prototype.
  • Used Experimental data to develop Models 1 and 3.

Outline

Introduction

Why Model?

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.

Focus

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.

Guiding Questions

  1. How much GSR do we want inside the lens?
  2. How do we use nanoparticles to control the amount of GSR in the lens?
  3. How do we synthesize GSR, package into NP, and send it into the eye?

Model 1: Crystallin Damage

Abstract

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.

Purpose

How much do we need to limit crystallin damage so surgery is not needed?

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. Opacity (%): This is the physical, quantitative property of the LOC scale.
  3. Absorbance at 397.5 nm: This is the experimental method, used by our team in the lab (c.d.).
  4. 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. 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.

<

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.

LOCS Equivalence to Absorbance: Literature Research

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.

Absorbance Equivalence to Crystallin Damage: Experimental Data

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.

With this relation in Figure 2, we calculate the equivalent crystallin damage to each LOCS rating and its equivalent absorbance.

Error Analysis

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.

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.

Table 2: Results of Model 1 – Equivalent values for LOCS, Opacity, Absorbance, and Crystallin Damage.
LOCS Opacity (%) Absorbance (@397.5 nm) Crystallin Damage (M-h)
0.0 0.00 0.0000 0.0000
0.5 3.24 0.0143 0.1327
1.0 6.65 0.0299 0.2774
1.5 10.81 0.0497 0.4610
2.0 15.88 0.0751 0.6966
2.5 21.95 0.1076 0.9981
3.0 29.07 0.1492 1.3840
4.0 46.37 0.2706 2.5101
5.0 66.05 0.4691 4.3514

Background

There are four ways to measure cataract severity (how blurred the lens is):

  1. Lens Optical Cataract Scale III (LOCS) - a scale from 0-6 used by physicians.
  2. Opacity (%) - used to calculate the LOC scale
  3. Absorbance at 397.5 nm - measurable in the lab.
  4. 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:
\[c.d.(t) = \int_{0}^{\infty} [H_2O_2]_t dt\]

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.

LOCS Scale











Assumptions

  1. 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.
  2. 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.
  3. 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.
  4. We assume that fish and human lens contain similar crystallin proteins.

Procedure

  1. 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.
  2. 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.
  3. 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.

LOCS Scale











Results

Table 1: Results of Model 1 - Equivalent values for LOCS, Opacity, Absorbance, and Crystallin Damage.
LOCS 0.0 0.5 1.0 1.5 2.0 2.5 3.0 4.0 5.0
Degree None Trace Mild Moderate Severe
Opacity (%) 0 3.24 6.65 10.81 15.88 21.95 29.07 46.37 66.05
Absorbance (a.u.) 0.0000 0.0143 0.0299 0.0497 0.0751 0.1076 0.1492 0.2706 0.4691
Crystallin Damage (c.d.) 0.0000 0.1327 0.2774 0.4610 0.6966 0.9981 1.3840 2.5101 4.3514



Table 2: Experimental Data used for Model 1 from Cataract Lens Model (TAS) - Absorbance vs. Crystallin Damage
Trial H2O2 Concentration (M) Exposure Time (h) Crystallin Damage (c.d.) Measured Absorbance (abs @400 nm)
1 0.100 24.0 2.40 0.105
2 0.100 46.5 4.65 0.451
3 0.100 72.0 7.20 0.0.695
4 0.100 20.0 2.00 0.089
5 0.100 42.0 4.20 0.392
6 0.100 15.0 1.50 0.093
7 0.100 42.0 0.340 0.340
8 0.100 67.0 6.70 0.563

Discussion

Model Result

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.






Model Adjustment






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.

Error Analysis

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.

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.

Conclusion






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. For future models, this value 0.9981 units of c.d. will be called the crystallin damage threshold for LOCS 2.5.

Model 2: GSR/25HC Chemical Pathway

Abstract

The key question: How much GSR to add? 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>

Purpose

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?

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

Image

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.

Background

The following 6 reactions describe the antioxidant system inside the cortex and nucleus.

$$GP_{xr}+[H_2O_2]_{in}+H^+ \xrightarrow[]{k_1} GP_{xo}+H_2O ...(1)$$ $$GP_{xo}+GSH+H^+ \xrightarrow[]{k_2} [GS-GP_x]+H_2O ...(2)$$ $$[GS-GP_x] + GSH \xrightarrow[]{k_3} GP_{xr}+GSSG+H^+ ...(3)$$ $$NADPH \xrightarrow[GSR]{k4, K_{4M}} NADP^+ ...(4)$$ $$GSSG \xrightarrow[GSR']{k_5, K_{5M}} 2GSH ...(5)$$ $$[H_2O_2]_{out} \xrightarrow[]{k_5} [H_2O_2]_{in} ...(6)$$

Each reaction will be discussed in detail, and we will derive rate equations.

Reaction 1:As hydrogen ions are numerous are negligible in the reaction, we will ignore it. By the law of mass action, the rate of this reaction is: $$r_1=k_1[GP_{xr}][H_2O_2]_{in}$$

Reaction 2: By the law of mass action, the rate of this reaction is: $$r_2=k_2[GP_{xo}][GSH]$$

Reaction 3: By the law of mass action, the rate of this reaction is: $$r_3=k_3[GS-GP_x][GSH]$$

Summary of Reaction 1-3: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.


Reaction 4: ByMichaelis-Menten kinetics and the Ping-Pong mechanism, the rate of this reaction, with rate constant k4, and Michaelis-Menten constant Km4, is: $$r_4=k_4\frac{[NADPH]}{K_{4M}+[NADPH]}$$

Reaction 5: ByMichaelis-Menten kinetics and the Ping-Pong mechanism, the rate of this reaction, with rate constant k5, and Michaelis-Menten constant Km5, is: $$r_5=k_5\frac{[GSSG]}{K_{4M}+[GSSG]}$$

Summary of Reaction 4-5: 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.


Reaction 6: By the Law of Passive Diffusion, the rate of diffusion into the cortex and lens is: is: $$r_6=k_6([H_2O_2]_{out}-[H_2O_2]_{in})$$

Differential Equations

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:

Substituting the rate of each reaction, we get the following system of differential equations.

$$\frac{d[GP_{xr}]}{dt}=k_3[GS-GP_x][GSH]-k_1[GP_{xr}][H_2O_2]_{in}$$ $$\frac{d[H_2O_2]}{dt}=k_6[[H_2O_2]_{out}-{H_2O_2]_{in}]-k_1[GP_{xr}][H_2O_2]_{in}$$ $$\frac{d[H_2O_2]}{dt}=k_1([H_2O_2]_{out} - [H_2O_2]_{in})-k_1[GP_{xr}][H_2O_2]_{in}$$ $$\frac{d[GP_{x0}]}{dt}=k_1[GP_{xr}][H_2O_2]_{in}-k_2[GP_{xo}][GSH]$$ $$\frac{d[H_2O]}{dt}=k_1[GP_{xr}][H_2O_2]_{in}+k_2[GP_{xo}][GSH]$$ $$\frac{d[GSH]}{dt}=2k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}-k_2[GP_{xo}][GSH]-k_3[GS-GP_x][GSH]$$ $$\frac{d[GS-GP_x]}{dt}=k_2[GP_{xo}][GSH]-k_3[GS-GP_x][GSH]$$ $$\frac{d[GSSG]}{dt}=k_3[GS-GP_x][GSH]-k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}$$ $$\frac{d[NADPH]}{dt}=-k_4[GSR]\frac{[NADPH]}{K_{4M}+[NADPH]}$$ $$\frac{d[GSR]}{dt}=k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}-k_4[GSR]\frac{[NADPH]}{K_{4M}+[NADPH]}$$ $$\frac{d[GSR']}{dt}=k_4[GSR]\frac{[NADPH]}{K_{4M}+[NADPH]}-k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}$$

Part 1 Results

Table 1: Data obtained from XXX relating each value of the LOCS scale, to opacity values.
LOCS 0.0 0.5 1.0 2.0 3.0 4.0 5.0 6.0
Degree None Trace Mild Surgery Suggested Moderate Severe Very Severe
Opacity (%) 0.34 4.24 5.80 18.88 23.60 49.14 65.61 90+
Absorbance (a.u.) 0.001 0.019 0.026 0.091 0.117 0.294 0.464 1.3+

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.

Menu 3

Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.






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.

Conclusion

Conclusion

Model 3: Nanoparticles

Abstract

Abstract

Purpose

Purpose

Background

There are three quantifiers of how severe cataract formation is, two are measurable, one is not.

  1. Absorbance @ 397.5 nm, which is measured with lab equipment.
  2. LOCS scale, subjectively measured by physicians on a scale from 0 - 6.
  3. Crystallin Damage, which we define as the following (for any time $t$)

\[c.d.(t) = \int_{0}^{\infty} [H_2O_2]_t dt\]

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.

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.

Method

We will relate the three by doing the following:

  1. Relate LOCS scale to opacity via literature research.
  2. Relate opacity to light transmittance via literature research.
  3. Relate light transmittance to absorbance via physical calculations.
  4. Relate absorbance to crystallin damage via experimental data.

Part 1 Results

Table 1: Data obtained from XXX relating each value of the LOCS scale, to opacity values.
LOCS 0.0 0.5 1.0 2.0 3.0 4.0 5.0 6.0
Degree None Trace Mild Surgery Suggested Moderate Severe Very Severe
Opacity (%) 0.34 4.24 5.80 18.88 23.60 49.14 65.61 90+
Absorbance (a.u.) 0.001 0.019 0.026 0.091 0.117 0.294 0.464 1.3+

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.

Menu 3

Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.

Conclusion

Conclusion

Model 4: Eyedrops

Abstract

Abstract

Purpose

Purpose

Background

There are three quantifiers of how severe cataract formation is, two are measurable, one is not.

  1. Absorbance @ 397.5 nm, which is measured with lab equipment.
  2. LOCS scale, subjectively measured by physicians on a scale from 0 - 6.
  3. Crystallin Damage, which we define as the following (for any time $t$)

\[c.d.(t) = \int_{0}^{\infty} [H_2O_2]_t dt\]

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.

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.

Method

We will relate the three by doing the following:

  1. Relate LOCS scale to opacity via literature research.
  2. Relate opacity to light transmittance via literature research.
  3. Relate light transmittance to absorbance via physical calculations.
  4. Relate absorbance to crystallin damage via experimental data.

Part 1 Results

Table 1: Data obtained from XXX relating each value of the LOCS scale, to opacity values.
LOCS 0.0 0.5 1.0 2.0 3.0 4.0 5.0 6.0
Degree None Trace Mild Surgery Suggested Moderate Severe Very Severe
Opacity (%) 0.34 4.24 5.80 18.88 23.60 49.14 65.61 90+
Absorbance (a.u.) 0.001 0.019 0.026 0.091 0.117 0.294 0.464 1.3+

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.

Menu 3

Eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.

Conclusion

Conclusion

Conclusion

Yay

Citations












Prevention

GSR Eyedrop

Treatment

25HC Eyedrop

LOCS: 0

Eyedrops