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<div class="col-sm-12"> | <div class="col-sm-12"> | ||
<div class="row"> | <div class="row"> | ||
− | <div class="col-sm- | + | <div class="col-sm-9"> |
<p>Cataract prevention occurs over 50 years, so we cannot perform experiments directly on the long-term impact of adding GSR or CH25H. Computational biology allows us to predict cataract development in the long-term. <b>These models allow our team to: (1) understand the impact of adding GSR-loaded nanoparticles into the lens over a 50 year period and (2) design a full treatment plan on how to prevent and treat cataracts with our project. Therefore, the results of our model are essential in developing a functional prototype. </b></p> | <p>Cataract prevention occurs over 50 years, so we cannot perform experiments directly on the long-term impact of adding GSR or CH25H. Computational biology allows us to predict cataract development in the long-term. <b>These models allow our team to: (1) understand the impact of adding GSR-loaded nanoparticles into the lens over a 50 year period and (2) design a full treatment plan on how to prevent and treat cataracts with our project. Therefore, the results of our model are essential in developing a functional prototype. </b></p> | ||
<p>For clarity, we will discuss each model in detail with respect to prevention (using GSR) only. At the end, we extend these results to treatment. In addition, we include collapsibles for interested readers and judges, in order to fully document our modeling work (eg. assumptions, mathematics, and full analysis) while keeping the main page clear with basic points only. | <p>For clarity, we will discuss each model in detail with respect to prevention (using GSR) only. At the end, we extend these results to treatment. In addition, we include collapsibles for interested readers and judges, in order to fully document our modeling work (eg. assumptions, mathematics, and full analysis) while keeping the main page clear with basic points only. | ||
</p> | </p> | ||
+ | |||
+ | <p>If you are interested in the programming/source codes of these computational models, please contact <b>Avery Wang</b>, at averyw17113532@tas.tw or averyw09521@gmail.com.</p> | ||
+ | </div> | ||
+ | <div class="col-sm-3"> | ||
+ | <img src="https://static.igem.org/mediawiki/2016/8/80/T--TAS_Taipei--Best_Model.png"/> | ||
</div> | </div> | ||
</div> | </div> | ||
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<div class="col-sm-12"> | <div class="col-sm-12"> | ||
<h3>Motivation</h3> | <h3>Motivation</h3> | ||
− | <p>Crystallin damage is the chemically significant way | + | <p>Crystallin damage is the chemically significant way to quantify cataract severity (Cui X.L. 1993). |
Physicians grade cataracts on a LOCS scale from 0 to 6, with 2.5 usually being the threshold for surgery. This standard method to determine cataract severity is through optical analysis, which is not applicable for chemical analysis. (Chylack)</p> | Physicians grade cataracts on a LOCS scale from 0 to 6, with 2.5 usually being the threshold for surgery. This standard method to determine cataract severity is through optical analysis, which is not applicable for chemical analysis. (Chylack)</p> | ||
<p>The purpose of this model is simple. In Model 2, we find the amount of GSR to maintain in order to ensure a cataract remains below a certain severity. <b>Before we can do that, we must find a way to relate the physical definition of cataract severity (LOCS) to the chemical definition (crystallin damage) in Model 1.</b></p> | <p>The purpose of this model is simple. In Model 2, we find the amount of GSR to maintain in order to ensure a cataract remains below a certain severity. <b>Before we can do that, we must find a way to relate the physical definition of cataract severity (LOCS) to the chemical definition (crystallin damage) in Model 1.</b></p> | ||
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<div class="col-sm-12"> | <div class="col-sm-12"> | ||
<h3>Quantification of Crystallin Damage</h3> | <h3>Quantification of Crystallin Damage</h3> | ||
− | <p>Crystallin damage is difficult to quantify, as few literature sources | + | <p>Crystallin damage is difficult to quantify, as few literature sources attempt to quantify it. We propose a mathematical way to measure crystallin damage based on how complete the degradation reaction of crystallin is complete depending on the amount of H<sub>2</sub>O<sub>2</sub>. |
</p> | </p> | ||
<p>Crystallin damage depends on two factors: (1) the <b>amount</b> of H<sub>2</sub>O<sub>2</sub> crystallin is exposed to, and (2) the <b>time</b> crystallin is exposed to H<sub>2</sub>O<sub>2</sub>. Therefore, we can mathematically quantify this by integrating the amount of H<sub>2</sub>O<sub>2</sub> in the crystallin over time: | <p>Crystallin damage depends on two factors: (1) the <b>amount</b> of H<sub>2</sub>O<sub>2</sub> crystallin is exposed to, and (2) the <b>time</b> crystallin is exposed to H<sub>2</sub>O<sub>2</sub>. Therefore, we can mathematically quantify this by integrating the amount of H<sub>2</sub>O<sub>2</sub> in the crystallin over time: | ||
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</p> | </p> | ||
− | <p>We define one unit of crystallin damage to be the equivalent damage caused by exposing the amount of crystallin in the human eyes 1 M of | + | <p>We define one unit of crystallin damage to be the equivalent damage caused by exposing the amount of crystallin in the human eyes 1 M of H<sub>2</sub>O<sub>2</sub> for 1 hour, with units M-h. We make an assumption here, described fully in “Assumptions” #1.</p> |
− | <p>Note that 1 M-h is a significant amount of crystallin damage, because the concentration of crystallin in the eyes is extremely small, in the neighborhood of 10 uM (Fraunfelder 2008). In addition, the eyes have a naturally occurring antioxidant system that lowers the concentration of | + | <p>Note that 1 M-h is a significant amount of crystallin damage, because the concentration of crystallin in the eyes is extremely small, in the neighborhood of 10 uM (Fraunfelder 2008). In addition, the eyes have a naturally occurring antioxidant system that lowers the concentration of H<sub>2</sub>O<sub>2</sub>, so it will take much longer than an hour of exposure until 1 M-h of crystallin damage is reached.</p> |
</div> | </div> | ||
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<thead> | <thead> | ||
<td>Trial</td> | <td>Trial</td> | ||
− | <td> | + | <td>H<sub>2</sub>O<sub>2</sub> Concentration (M)</td> |
<td>Exposure Time (h)</td> | <td>Exposure Time (h)</td> | ||
<td>Crystallin Damage (c.d.)</td> | <td>Crystallin Damage (c.d.)</td> | ||
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<p>We are about to use experimental data from experiments we performed. As we cannot perfectly simulate a human cataract in our lab, we have to make the following assumptions:</p> | <p>We are about to use experimental data from experiments we performed. As we cannot perfectly simulate a human cataract in our lab, we have to make the following assumptions:</p> | ||
<ol> | <ol> | ||
− | <li><b>Cataract damage is directly proportional to | + | <li><b>Cataract damage is directly proportional to H<sub>2</sub>O<sub>2</sub> concentration and time.</b> Crystallin damage is mainly caused by H<sub>2</sub>O<sub>2</sub> interacting the cysteine on crystallin. The reaction between H<sub>2</sub>O<sub>2</sub> and cysteine is first-order (Domínguez-Vicent 2016), supporting this assumption. This allows us to make the quantification of crystallin damage.</li> |
− | <li>We assume that the <b>amount of crystallin in the lens is far greater than the amount of crystallin degraded.</b> Therefore, a change in the amount of crystallin does not impact crystallin damage, as | + | <li>We assume that the <b>amount of crystallin in the lens is far greater than the amount of crystallin degraded.</b> Therefore, a change in the amount of crystallin does not impact crystallin damage, as H<sub>2</sub>O<sub>2</sub> only degrades a small portion of crystallin that causes blurred lens. (Cui X.L 1993)</li> |
<li>The <b>crystallin in humans is similar in function as crystallin in fish.</b> This allows us to use experimental data on fish into this model.</li> | <li>The <b>crystallin in humans is similar in function as crystallin in fish.</b> This allows us to use experimental data on fish into this model.</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 <b>any errors in absorbance is canceled out.</b></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 <b>any errors in absorbance is canceled out.</b></li> | ||
− | <li><b>In the fish used, we assume there is there is no GSR.</b> GSR decreases the amount of | + | <li><b>In the fish used, we assume there is there is no GSR.</b> GSR decreases the amount of H<sub>2</sub>O<sub>2</sub> in the fish, but since we could not find the amount of GSR in the fish, we must make this assumption.</li> |
</ol> | </ol> | ||
</p> | </p> | ||
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<div class="col-sm-6"> | <div class="col-sm-6"> | ||
<h3>Using Experimental Data for Model</h3> | <h3>Using Experimental Data for Model</h3> | ||
− | <p>In each trial (see Data Documentation), we added | + | <p>In each trial (see Data Documentation), we added H<sub>2</sub>O<sub>2</sub> of a known concentration to fish lens, and allowed crystallin to degrade for some set time. With all four assumptions, we can calculate the theoretical crystallin damage that occurred. Meanwhile, experimentally we found the absorbance of the degraded crystallin. We find a link between crystallin damage and absorbance. </p> |
</div> | </div> | ||
<figure class="col-sm-6"> | <figure class="col-sm-6"> | ||
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<h3>Model Adjustment</h3> | <h3>Model Adjustment</h3> | ||
<p> | <p> | ||
− | When determining the relationship between absorbance and crystallin, in Figure 4.A the best fit line has a x – intercept that is nonzero. However, when converting each absorbance rating to equivalent crystallin damage in Table 1, 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 | + | When determining the relationship between absorbance and crystallin, in Figure 4.A the best fit line has a x – intercept that is nonzero. However, when converting each absorbance rating to equivalent crystallin damage in Table 1, 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 H<sub>2</sub>O<sub>2</sub>, 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, as shown in Figure 4.B. |
</p> | </p> | ||
</div> | </div> | ||
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<tr> | <tr> | ||
<td>k1</td> | <td>k1</td> | ||
− | <td>$2.1 | + | <td>$2.1\cdot10^7$</td> |
<td>Rate constant for Reaction 1</td> | <td>Rate constant for Reaction 1</td> | ||
<td>(Ng 2007)</td> | <td>(Ng 2007)</td> | ||
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<tr> | <tr> | ||
<td>k2</td> | <td>k2</td> | ||
− | <td>$4 | + | <td>$4\cdot10^4$</td> |
<td>Rate constant for Reaction 2</td> | <td>Rate constant for Reaction 2</td> | ||
<td>(Ng 2007)</td> | <td>(Ng 2007)</td> | ||
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<tr> | <tr> | ||
<td>k3</td> | <td>k3</td> | ||
− | <td>$1 | + | <td>$1\cdot10^7$</td> |
<td>Rate constant for Reaction 3</td> | <td>Rate constant for Reaction 3</td> | ||
<td>(Ng 2007)</td> | <td>(Ng 2007)</td> | ||
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<tr> | <tr> | ||
<td>K4m</td> | <td>K4m</td> | ||
− | <td>$0.063 | + | <td>$0.063\cdot10^{-3}$</td> |
<td>Michaelis constant for NADPH</td> | <td>Michaelis constant for NADPH</td> | ||
<td>(Salvador 2005)</td> | <td>(Salvador 2005)</td> | ||
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<tr> | <tr> | ||
<td>K5m</td> | <td>K5m</td> | ||
− | <td>$0.154 | + | <td>$0.154\cdot10^{-3}$</td> |
<td>Michaelis constant for GSR</td> | <td>Michaelis constant for GSR</td> | ||
<td>(Saravanakumar 2015) | <td>(Saravanakumar 2015) | ||
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<tr> | <tr> | ||
<td>K4c</td> | <td>K4c</td> | ||
− | <td>$0.219 | + | <td>$0.219\cdot10^{-3}$</td> |
<td>Michaelis constant for NADPH</td> | <td>Michaelis constant for NADPH</td> | ||
<td>(Salvador 2005)</td> | <td>(Salvador 2005)</td> | ||
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<tr> | <tr> | ||
<td>K5c</td> | <td>K5c</td> | ||
− | <td>$7.985 | + | <td>$7.985\cdot10^{-3}$</td> |
<td>Michaelis constant for GSR</td> | <td>Michaelis constant for GSR</td> | ||
<td>(Saravanakumar 2015)</td> | <td>(Saravanakumar 2015)</td> | ||
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<tbody> | <tbody> | ||
<tr> | <tr> | ||
− | <td> | + | <td>H<sub>2</sub>O<sub>2</sub> (in)</td> |
− | <td>$0.5 | + | <td>$0.5\cdot10^{-3}$</td> |
<td>(Adimora 2010)</td> | <td>(Adimora 2010)</td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
− | <td> | + | <td>H<sub>2</sub>O<sub>2</sub> (out)</td> |
− | <td>$0.5 | + | <td>$0.5\cdot10^{-3}$</td> |
− | <td>Estimate, assuming | + | <td>Estimate, assuming H<sub>2</sub>O<sub>2</sub> in and otu are in dynamic equilibrium.</td> |
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>GPxr</td> | <td>GPxr</td> | ||
− | <td>$5 | + | <td>$5\cdot10^{-5}$</td> |
<td>(Ng 2007)</td> | <td>(Ng 2007)</td> | ||
</tr> | </tr> | ||
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<tr> | <tr> | ||
<td>GSH</td> | <td>GSH</td> | ||
− | <td>$3.68 | + | <td>$3.68\cdot10^{-5}$</td> |
<td>(Jones 2005)</td> | <td>(Jones 2005)</td> | ||
</tr> | </tr> | ||
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<tr> | <tr> | ||
<td>GSSG</td> | <td>GSSG</td> | ||
− | <td>$1.78 | + | <td>$1.78\cdot10^{-6}$</td> |
<td>(Ng 2007)</td> | <td>(Ng 2007)</td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>NADPH</td> | <td>NADPH</td> | ||
− | <td>$3.0 | + | <td>$3.0\cdot10^{-3}$</td> |
<td>(Martinovich 2005)</td> | <td>(Martinovich 2005)</td> | ||
</tr> | </tr> | ||
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<p>1. After building this differential equation model in Mathematica, we change the initial starting concentration of GSR, and numerically solve the equations. </p> | <p>1. After building this differential equation model in Mathematica, we change the initial starting concentration of GSR, and numerically solve the equations. </p> | ||
− | <p>2. The output will be a the concentration of | + | <p>2. The output will be a the concentration of H<sub>2</sub>O<sub>2</sub> as a function of time. Integrating this function over 50 years using the definition in Model 1 returns the total crystallin damage. </p> |
<p>3. We repeat this procedure from 0 to 100 uM of initial GSR, and graph the resulting crystallin damage against the initial GSR inputted (Figure 4.3).</p> | <p>3. We repeat this procedure from 0 to 100 uM of initial GSR, and graph the resulting crystallin damage against the initial GSR inputted (Figure 4.3).</p> | ||
<h3>Assumptions</h3> | <h3>Assumptions</h3> | ||
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<li><b>The amount of total GSR (in both forms) is constant.</b> In reality, for the first days of the treatment the GSR level is being increased, so GSR levels will not be constant until 30 days of the treatment have passed (see Model 3). As we will discuss in Model 3, a one-time treatment will be made as soon as prevention is fully effective.</li> | <li><b>The amount of total GSR (in both forms) is constant.</b> In reality, for the first days of the treatment the GSR level is being increased, so GSR levels will not be constant until 30 days of the treatment have passed (see Model 3). As we will discuss in Model 3, a one-time treatment will be made as soon as prevention is fully effective.</li> | ||
<li><b>The cortex and nucleus of the eyes are indistinguishable and regarded as a single entity.</b> As cataract damage can occur in both areas, we simplify the model by combining them to form a single system.</li> | <li><b>The cortex and nucleus of the eyes are indistinguishable and regarded as a single entity.</b> As cataract damage can occur in both areas, we simplify the model by combining them to form a single system.</li> | ||
− | <li><b>The amount of | + | <li><b>The amount of H<sub>2</sub>O<sub>2</sub> in the aqueous humor (but the amount in the nucleus changes).</b> As cellular respiration is constantly regenerating ROS and forming H<sub>2</sub>O<sub>2</sub>, there will constantly be H<sub>2</sub>O<sub>2</sub> diffusing into the lens.</li> |
− | <li><b>The amount of | + | <li><b>The amount of H<sub>2</sub>O<sub>2</sub> in the aqueous humor is equal to the initial value of H<sub>2</sub>O<sub>2</sub> in the cortex.</b> The rationale is that initially dynamic equilibrium exists between the lens and the aqueous humor.</li> |
</ol> | </ol> | ||
</p> | </p> | ||
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<th>LOCS</th> | <th>LOCS</th> | ||
<th>Crystallin Damage (c.d.)</th> | <th>Crystallin Damage (c.d.)</th> | ||
− | <th>GSR needed to maintain LOCS for 1 year</th> | + | <th>GSR needed to maintain LOCS for 1 year (uM)</th> |
− | <th>GSR needed to maintain LOCS for 20 years</th> | + | <th>GSR needed to maintain LOCS for 20 years (uM)</th> |
− | <th>GSR needed to maintain LOCS for 50 years</th> | + | <th>GSR needed to maintain LOCS for 50 years (uM)</th> |
</tr> | </tr> | ||
</thead> | </thead> | ||
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<div id="gsrmenu5" class="tab-pane fade"> | <div id="gsrmenu5" class="tab-pane fade"> | ||
<h3>Confirmation of Initial Value of GSR</h3> | <h3>Confirmation of Initial Value of GSR</h3> | ||
− | <p>We expect the lens to have some GSR in the lens naturally as part of the antioxidizing system. There will not be enough GSR to fully prevent cataract damage, however. Based on research, if | + | <p>We expect the lens to have some GSR in the lens naturally as part of the antioxidizing system. There will not be enough GSR to fully prevent cataract damage, however. Based on research, if H<sub>2</sub>O<sub>2</sub> levels remain at 10 uM for 1 year, which is common after traumatic accidents affecting the eye, a moderately severe cataract will develop, expected at around the LOCS 4-4.5 level (Fraunfelder 2008). </p> |
<p>Literature data estimates that the natural concentration is around 10 uM (Fraunfelder 2008). This corresponds to roughly a LOCS 4 cataract after a year, which confirms that our initial value of GSR in the cortex before any treatment. We will consider this as our starting point, and add GSR to reach this point.</p> | <p>Literature data estimates that the natural concentration is around 10 uM (Fraunfelder 2008). This corresponds to roughly a LOCS 4 cataract after a year, which confirms that our initial value of GSR in the cortex before any treatment. We will consider this as our starting point, and add GSR to reach this point.</p> | ||
</div> | </div> | ||
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<h4>Protein Degradation</h4> | <h4>Protein Degradation</h4> | ||
<p>All protein degrade over time, and the amount of degradation is proportional to an decreasing exponential function of time. Outside the nanoparticle, protein are degrading. We can apply a decay function on the outside concentration function from the differential equation, to estimate degradation. The turnover rate of the aqueous humor is about 16% per minute, so we expect the degradation factor to be on the order of -5. We define a new function, concentration of GSR outside nanoparticles adjusted for degradation, as a function of time.</p> | <p>All protein degrade over time, and the amount of degradation is proportional to an decreasing exponential function of time. Outside the nanoparticle, protein are degrading. We can apply a decay function on the outside concentration function from the differential equation, to estimate degradation. The turnover rate of the aqueous humor is about 16% per minute, so we expect the degradation factor to be on the order of -5. We define a new function, concentration of GSR outside nanoparticles adjusted for degradation, as a function of time.</p> | ||
− | $$C_{oa}(t)=C_{out} | + | $$C_{oa}(t)=C_{out}\cdot e^{-k_dt}$$ |
Line 1,235: | Line 1,240: | ||
<tr> | <tr> | ||
<td>Boltzmann Constant (kb)</td> | <td>Boltzmann Constant (kb)</td> | ||
− | <td>$1.3806 | + | <td>$1.3806 \cdot 10^{23} \cdot m^2 \cdot kg \cdot s^{-2} \cdot K^{-1}$</td> |
<td>Physical Constant</td> | <td>Physical Constant</td> | ||
<td></td> | <td></td> | ||
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<tr> | <tr> | ||
<td>Viscosity (u)</td> | <td>Viscosity (u)</td> | ||
− | <td>$1.0 | + | <td>$1.0 \cdot 10^{-4} Pa \cdot S $</td> |
<td></td> | <td></td> | ||
<td>Medicalopedia</td> | <td>Medicalopedia</td> | ||
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<tr> | <tr> | ||
<td>Volume of Aqueous Humor (V1)</td> | <td>Volume of Aqueous Humor (V1)</td> | ||
− | <td>$2.5 | + | <td>$2.5\cdot 10^{-4} L$</td> |
<td>Constant</td> | <td>Constant</td> | ||
<td>Medicalopedia</td> | <td>Medicalopedia</td> | ||
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<tr> | <tr> | ||
<td>Diffusion Layer</td> | <td>Diffusion Layer</td> | ||
− | <td>(1)$10^{-11} m$<br>(2)$2.5 | + | <td>(1)$10^{-11} m$<br>(2)$2.5\cdot10^{-11} m$</td> |
<td>Estimate, then revised upon experiments</td> | <td>Estimate, then revised upon experiments</td> | ||
<td>(Fraunfelder 2008)</td> | <td>(Fraunfelder 2008)</td> | ||
Line 1,278: | Line 1,283: | ||
<tr> | <tr> | ||
<td>Surface Area</td> | <td>Surface Area</td> | ||
− | <td>$4 | + | <td>$4 \pi r^2$</td> |
<td>Depends on radius</td> | <td>Depends on radius</td> | ||
<td></td> | <td></td> | ||
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<tr> | <tr> | ||
<td>Degradation (kd)</td> | <td>Degradation (kd)</td> | ||
− | <td>$1.0 | + | <td>$1.0\cdot10^{-5}$</td> |
<td>Estimate, based on turnover rate of lacrimal fluids, in order of -5.</td> | <td>Estimate, based on turnover rate of lacrimal fluids, in order of -5.</td> | ||
<td>(Fraunfelder 2008)</td> | <td>(Fraunfelder 2008)</td> | ||
Line 1,295: | Line 1,300: | ||
<div id="nanomenu3" class="tab-pane fade"> | <div id="nanomenu3" class="tab-pane fade"> | ||
<h3>Multiple Dose</h3> | <h3>Multiple Dose</h3> | ||
− | <p>Each dose of nanoparticles are released periodically. The function $C_{oa} (t)$ models the GSR increase after a dose given at $t = 0$. If we apply doses periodically, we can apply a time shift to this function by $n | + | <p>Each dose of nanoparticles are released periodically. The function $C_{oa} (t)$ models the GSR increase after a dose given at $t = 0$. If we apply doses periodically, we can apply a time shift to this function by $n\cdot p$, the number of periods multiplied by the period length, to create the graphs shown in Figure C. We also apply a unit step function, so the function value is 0 before the eyedrop is applied. <b>By summing up the contribution of each dose, we get the resulting concentration of GSR outside the nanoparticles over time.</b> Remember that our aim is to maintain 43.5 uM of GSR.</p> |
− | $$C_{total}(t)=\sum_{n=0}^\infty {C_{oa} (t-np \cdot)e^-k_d(t-np) \cdot u(t-np)}$$ | + | $$C_{total}(t)=\sum_{n=0}^\infty {C_{oa} (t-np \cdot)e^{-k_d(t-np)} \cdot u(t-np)}$$ |
<p>An example of the resulting $C_{total}(t)$ is shown in Figure D. </p> | <p>An example of the resulting $C_{total}(t)$ is shown in Figure D. </p> | ||
Line 1,342: | Line 1,347: | ||
<figure class = "col-sm-8"> | <figure class = "col-sm-8"> | ||
− | <img src="https://static.igem.org/mediawiki/2016/ | + | <img src="https://static.igem.org/mediawiki/2016/9/94/T--TAS_Taipei--FrequencyCorrected.png"> |
<figcaption class='darkblue'><b>Figure 4.F: Changing Frequency. </b>The equilibrium concentration is unaffected, although lower frequencies (greater periods between dose), with a higher concentration each time, results in an unstable graph. </figcaption> | <figcaption class='darkblue'><b>Figure 4.F: Changing Frequency. </b>The equilibrium concentration is unaffected, although lower frequencies (greater periods between dose), with a higher concentration each time, results in an unstable graph. </figcaption> | ||
</figure> | </figure> | ||
Line 1,473: | Line 1,478: | ||
</p> | </p> | ||
<p> | <p> | ||
− | <b>The results show that the bioavailability of nanoparticles is about 1.404 x 10-3%,</b> which means that for every gram of GSR (or any drug) we place into nanoparticles, approximately 14.04 ug of the drug reach the aqueous humor. <b>The variance is 2.34 ug/g.</b> (Calvo 1996) | + | <b>The results show that the bioavailability of nanoparticles is about 1.404 x 10 <sup>-3</sup>%,</b> which means that for every gram of GSR (or any drug) we place into nanoparticles, approximately 14.04 ug of the drug reach the aqueous humor. <b>The variance is 2.34 ug/g.</b> (Calvo 1996) |
</p> | </p> | ||
</div> | </div> |
Latest revision as of 03:49, 3 December 2016
Model
Cataract prevention occurs over 50 years, so we cannot perform experiments directly on the long-term impact of adding GSR or CH25H. Computational biology allows us to predict cataract development in the long-term. These models allow our team to: (1) understand the impact of adding GSR-loaded nanoparticles into the lens over a 50 year period and (2) design a full treatment plan on how to prevent and treat cataracts with our project. Therefore, the results of our model are essential in developing a functional prototype.
For clarity, we will discuss each model in detail with respect to prevention (using GSR) only. At the end, we extend these results to treatment. In addition, we include collapsibles for interested readers and judges, in order to fully document our modeling work (eg. assumptions, mathematics, and full analysis) while keeping the main page clear with basic points only.
If you are interested in the programming/source codes of these computational models, please contact Avery Wang, at averyw17113532@tas.tw or averyw09521@gmail.com.
Introduction
Guiding Questions
How much GSR to maintain in the lens? (GSR Function)
How to maintain that amount of GSR using nanoparticles and eyedrops? (Delivery Prototype)
Focus of Models
Since our construct is not directly placed into the eyes, how our synthesized protein impacts the eye after it is separately transported into the lens is of greater importance. As a result, we create models with the intent on understanding how GSR and CH25H impacts the eye, and how we can control its impact with a well-designed delivery prototype.
Prevention: GSR Function
Model 1: Crystallin Damage
The amount of damage to crystallin by H2O2 determines the severity of a cataract (Spector 1993). We relate the amount of crystallin damage to the corresponding rating on the LOCS scale, used by physicians to rate cataract severity. Our goal is to lower LOCS to below 2.5, the threshold for surgery. Through literature research as well as our own experimental data, we find the maximum allowable crystallin damage to prevent a LOCS 2.5 cataract from developing.
Measurement of Cataract Severity
There are three ways of measuring cataract severity, each used for a different purpose.
- Lens Optical Cataract Scale (LOCS): Physicians use this scale, from 0 – 6, to grade the severity of cataracts (Domínguez-Vicent 2016).
- Absorbance at 397.5 nm: This is the experimental method, used by our team in the lab (c.d.)
- 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 crystallin is exposed to oxidizing agents. (Cui X.L. 1993)
LOCS to Absorbance: Literature Data
Numerous studies show how absorbance measurements can be converted to the LOC scale that physicians use. With the results of Chylack, we construct the first two columns in Table 1 (Chylack 1993).
Absorbance Equivalence to Crystallin Damage: Experimental Data
We use experimental measurements from our team’s Cataract Lens Model (Link). They induced an amount of crystallin damage, and measured the resulting absorbance. The experimental results are listed in Table A, and Figure 4.A, we calculate the equivalent crystallin damage of each LOCS rating and absorbance, and create the third column of Table 1.
LOCS | Absorbance (@397.5 nm abs units) |
Crystallin Damage (M-h) |
---|---|---|
0.0 | 0.0000 | 0.0000 |
0.5 | 0.0143 | 0.1243 |
1.0 | 0.0299 | 0.2878 |
1.5 | 0.0497 | 0.4697 |
2.0 | 0.0751 | 0.6949 |
2.5 | 0.1076 | 0.9883 |
3.0 | 0.1492 | 1.3747 |
4.0 | 0.2706 | 2.5259 |
5.0 | 0.4691 | 4.3472 |
Conclusion
To guarantee that surgery is not needed for 50 years, we need to limit crystallin damage to 0.9883 units. If crystallin damage goes above this threshold, then surgery is needed. This is the crystallin damage threshold for a LOCS 2.5 cataract.
Model 2: GSR Pathway
Now that we know how much we need to limit crystallin damage to LOCS 2.5, we model the naturally occurring GSR Pathway in the lens of a human eye. We calculate the necessary GSR concentration to be maintained over 50 years so that the resulting cataract is below LOCS 2.5.
Chemical Kinetics Model: Differential Equations
By various enzyme kinetics laws, fully documented in the collapsible, we build a system of 10 differential equations based on 6 chemical reactions (Ault 1974, Pi 2004). All parameters, constants (Table B), and initial conditions (Table C) are based off literature data (Ng 2007, Melissa 2012, Saravanakumar 2015, Salvador 2005, Adimora 2010, Jones 2008, Martinovich 2005). Estimates made are also shown with assumptions and reasoning. The details are shown in the collapsible for interested readers.
Blackbox Approach: Testing GSR Impact
Our modeling approach is seen in Figure 4.2, where vary the input, Initial GSR concentration, holding all other variables constant, and numerically solve for the amount of hydrogen peroxide over time. We can find the amount of crystallin damage accumulated over 50 years if different levels of GSR is maintained, which we graph in Figure 4.3.
From this graph, we can find the GSR concentration needed for the LOCS 2.5 threshold.
Crystallin Damage vs. GSR Level
According to literature data and our model, the naturally occurring GSR concentration is 10 uM (Fraunfelder 2008). All curves show crystallin damage decreasing as GSR levels are increased, which supports both research and experimental data, and suggests that this prototype is effective in preventing crystallin damage. However, GSR levels need to be raised significantly, up to 40+ uM from the natural 10 uM of GSR in order to show long-term protection.
Figure 4.3 shows the amount of GSR we need to maintain for 50 years in order to prevent a LOCS cataract of a certain severity. The row of interest is LOCS 2.5, the threshold for surgery. Notice that we say “maintain” the level of GSR. This level needs to be constant at all times for 50 years for full prevention. The delivery of GSR to maintain this level is discussed in Model 3.
Conclusion
We need to maintain (NOT add) 43.5 uM of GSR in the lens so that the crystallin damage recorded over 50 years is below the LOCS 2.5 threshold.
Prevention: Prototype Function
Model 3: Nanoparticle Protein Delivery
To maximize delivery efficiency to the lens, we encapsulate GSR in chitosan nanoparticles (Wang 2011, Tajmir-Riahi 2014). From Models 1-2, we have found the necessary concentration of GSR that needs to be maintained in the lens. Now we design nanoparticles that will maintain those amounts. We build a model find how nanoparticles release GSR at appropriate rates to control the amount of GSR in the lens, and find the best engineered design for nanoparticles.
Single Dose: Change in GSR Concentration
In finding the best engineered design, we take into account variables such as nanoparticle radius and concentration. We build a differential equation model for the impact of a single dose of nanoparticles over time. To generalize the model, instead of using absolute concentrations, we use relative concentration, with respect to the natural amount, or initial amount of GSR in the lens. The full mathematics and details can be found in the collapsible.
We get two curves, the concentration of GSR outside nanoparticles subjected to degradation (Figure 4.4), and the release of GSR from nanoparticles (Figure 4.5), over time. This allows us to predict nanoparticle delivery rates before we perform the actual experiments (Link)
Comparison with Experimental Data
Yet in our model, we do not know the thickness of the nanoparticle diffusion layer. After performing experiments, we can use measurements of our prototype device to find this thickness, and refine our model. A direct comparison of our model with our experiment data is shown in Figure 4.5.
Multiple Dose: Change in GSR Concentration
Each dose of nanoparticles, represented in the Single Dose model, can be repeated to create the Multiple Dose model. Below is a graph of GSR concentration over time when multiple doses of nanoparticles are added.
In Figure 4.6, all curves approach equilibrium, after which the concentration oscillates about equilibrium. We have three goals, in order of importance for best nanoparticle design:
- GSR equilibrium concentration equal to amount we desire (i.e. 43.5 uM from Model 2)
- Stability of concentration at equilibrium (Model 4 goes into deeper depth regarding sensitivity)
- Time to reach equilibrium (time for full prevention to come into effect)
To do so, we can alter different variables: GSR concentration in nanoparticles, nanoparticle radius, and dose frequency. For a full analysis of how each variable impacts the concentration function, see the collapsible. Below is a summary of the results:
Independent Variable | Time to Reach Equilibrium | Equilibrium Concentration | Stability |
---|---|---|---|
Concentration | No impact | Proportional Increase | Slight Decrease |
Radius | No impact | Very Slight Decrease | Very Slight Decrease |
Dose Frequency | No impact | No impact | Increase |
We find the optimal combination of parameters is daily doses (high frequency) of 200 nm nanoparticles (small), with a concentration of 76.88 uM of GSR in the nanoparticles (concentration).
The calculator at the end of the page can be altered, so if the LOCS threshold is not 2.5, a new concentration can be calculated.
A Two Stage Eyedrop Approach
As shown in Table 2, we cannot alter the time to reach equilibrium, or reach full prevention. As supported by literature research, the time to reach equilibrium is a property of the lens that we cannot change (Fraunfelder 2008). However, we propose a two-stage eyedrop approach, of two differing nanoparticle concentrations, to decrease the time needed for full prevention. A full explanation is found in the collapsible.
Generalized Nanoparticles: Customizer
We built a full nanoparticle customizer, which generalizes the model to beyond delivery into the eye, found at the end of the page (Software). We hope that other iGEM teams who are interested in nanoparticle drug delivery can utilize this customizer to help them develop their own prototype.
Conclusion
We find the optimal combination of parameters is daily doses (high frequency) of 200 nm nanoparticles (small), with a concentration of 76.88 uM of GSR in the nanoparticles (concentration).
Model 4: Eyedrop Prototype
We have found a nanoparticle design to deliver GSR. We also need to model the function of eyedrops, to determine the concentration of GSR-loaded nanoparticles to put in eyedrops, and analyze how sensitive the resulting system is.
Bioavailability of GSR Delivery
The eye is well protected from foreign material attempting to enter the eye. The corneal epithelium is the most essential barrier against topical drugs in eyedrops, and as a result, much of drugs in eyedrops are lost in tear drainage (Lux 2003).
Bioavailability describes the proportion of the drug that reaches the site of action, regardless of the route of administration. For example, it is estimated that only 1-5% of an active drug with small solutes in an eyedrop penetrates the cornea (Bonate 2005). In the case of nanoparticles, which are much larger than chemical molecules, more is lost (Fraunfelder 2008).
The results show that the bioavailability of nanoparticles is about 1.404 x 10 -3%, which means that for every gram of GSR (or any drug) we place into nanoparticles, approximately 14.04 ug of the drug reach the aqueous humor. The variance is 2.34 ug/g. (Calvo 1996)
Necessary Adjustments in Eyedrops
To ensure that sufficient concentrations of GSR are delivered, we must place an excess of GSR. To determine how much, we simply divide the concentration of GSR in nanoparticles we found in Model 3 by the fraction of GSR that reaches the aqueous humor. This result is programmed in our calculator below.
We conclude that we need 5.48 mM of GSR in nanoparticles in our final eyedrop to maintain 43.5 uM GSR and thus 2.5 LOCS.
Sensitivity Analysis: Revisiting Nanoparticles Model
The mechanism for eyedrop delivery is complex, and there are variances in the bioavailability depending on the conditions of the eye (Fraunfelder 2008). The thickness of the cornea, lens, other eye diseases, age, and even time of day may impact the bioavailability of the drug (Gaudana 2010). We use a stochastic model to simulate Model 3 again, but this time, add a degree of variance. The result is shown in Figure 4.10.
The variance is impacted by the frequency of eyedrops. By giving eyedrops more frequently with less amounts given each time, the variance is decreased.
Ideally, we wish to deliver 100% of the GSR concentration of the amount found in Model 2 (43.5 uM). Because of variance, the actual amount maintained in the lens is different, shown in Figure 5. The full details and mathematics of the stochastic model can be found in the collapsible.
Insights into Manufacturing & Clinical Use
Using the details from Models 1-4, we offer the following suggestions for manufacturing our eyedrops, as well as prescribing them to patients.
- Frequent doses of low concentration eyedrops are more stable than occasional doses of high concentration eyedrops. (Model 3)
- Cataract severity is extremely sensitive to the amount of GSR concentration maintained. If this value falls below 43.5 uM even by a little, as shown in Model 2, cataracts may develop. (Model 2)
- When manufacturing, there should be a necessary upward adjustment, because even with daily eyedrops, some simulated trials resulted in less than 90% of GSR delivered. (Model 4)
- Cataract prevention is only fully effective after around 28 days of using the prevention eyedrop. (Model 3) During that time, further cataract damage may take place. The suggested order of treatment should be: start with GSR eyedrops until full prevention is in effect, the use 25HC eyedrops to reverse any existing cataract. Finally, stop 25HC eyedrop use, while continuing GSR eyedrops. (Model 1)
- To speed up the time for full prevention to take place, a two eyedrop approach to quickly deliver sufficient GSR should be used. (Model 4)
Treatment
We use the results from our previous models, and apply them to treatment. The process is almost the exact same as that of Prevention. The only difference is that our treatment protein, CH25H, reverses cataract damage (Griffiths 2016). We find the exact concentration of CH25H to reverse a cataract of a given LOCS score. The delivery models are unchanged, with the exception that the concentration of protein delivery will be different.
We use the results of Model 1 to calculate the LOCS equivalent crystallin damage we need to reverse (“negative crystallin damage”). Then we use experimental results to calculate the concentration of CH25H needed to reverse the cataract. We do not use Model 3, as this is a one-time treatment. After applying the results of Model 4, we can find the final concentration needed in CH25H eyedrops.
We propose eyedrops with 0.8 mg/mL CH25H. The number of drops needed for treatment depends on a patient's current LOCS score, and is calculated in the software tool below.
We use the results from our previous models, and apply them to treatment. The process is almost the exact same as that of Prevention. The only difference is that our treatment protein, CH25H, reverses cataract damage (Griffiths 2016). We find the exact concentration of CH25H to reverse a cataract of a given LOCS score. The delivery models are unchanged, with the exception that the concentration of protein delivery will be different.
We use the results of Model 1 to calculate the LOCS equivalent crystallin damage we need to reverse (“negative crystallin damage”). Then we use experimental results to calculate the concentration of CH25H needed to reverse the cataract. We do not use Model 3, as this is a one-time treatment. After applying the results of Model 4, we can find the final concentration needed in CH25H eyedrops.
We propose eyedrops with 0.8 mg/mL CH25H. The number of drops needed for treatment depends on a patient's current LOCS score, and is calculated in the software tool below.
CALCULATOR
Prevention
LOCS Score Threshold:We guarentee that by applying this prevention eyedrop daily, your LOCS score will remain below your threshold for 50 years.
Prevention Results
Variable | Value | Source |
---|---|---|
Allowable LOCS | ||
Crystallin Damage | c.d. | Model 1 |
GSR Maintained | uM | Model 2 |
Nanoparticle Conc. | uM | Model 3 |
Eyedrop Conc. | mM | Model 4 |
Eyedrop Result | mg/mL |
Treatment
Your current LOCS Score:By applying the following treatment, leaving an hour before each dose of eyedrops, we guarentee that it will lower your LOCS score to essentially 0.
Treatment Results
Variable | Value | Source |
---|---|---|
Allowable LOCS | ||
Crystallin Damage | c.d. | Model 2 |
Absorbance | a.u. | Model 1 |
CH25H | uM | Model 5 |
Eyedrop Conc. | uM | Model 4 |
Eyedrop Result | mg/mL | Model 4 |
# of Eyedrops | drops | (of 0.8 mg/mL eyedrop) |
Software
We built a nanoparticle customizer, which allows you to track the concentration and rates of drug delivery to any part of the body using nanoparticles. You can customize your own design of nanoparticles, and analyze its function inside the body.
This computational software can be used by future iGEM teams who are interested in using nanoparticles to efficiently deliver their synthesized proteins. The calculational tool is programmed on a Google Spreadsheet. Click the button below to visit the spreadsheet. Please make a copy of the spreadsheet to freely use it.
Conclusion
The models allowed us to extrapolate short-term experimental data to the long-term, to over 50 years, the duration for cataracts to form. In Models 1-2, with the Cataract Lens Experiments on our synthesized protein GSR (and CH25H), we found the amount of synthesized protein needed in the lens over 50 years. In Models 3-4, with the experimental results of a single dose of nanoparticle release, we simulate multiple doses to see the overall change in GSR concentration in the lens over 50 years. We calculate the exact concentrations of our eyedrop prototype, to prevent a LOCS 2.5 cataract from developing so surgery is not needed. With our predictions and simulations of cataract treatment, we offered insights into how the product should be manufactured and used in clinics. We also programmed a nanoparticle customizer to allow the results of these models to be generalized to all drug delivery iGEM projects.Citation
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