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<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> | <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 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> | ||
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<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> | <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> | <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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<div id="gsrmenu1" class="tab-pane fade"> | <div id="gsrmenu1" class="tab-pane fade"> | ||
− | <h4> | + | <h4>Differential Equations</h4> |
− | <p>We will | + | <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> | |
− | + | $$\frac{d[GP_{xr}]}{dt}=k_3[GS-GP_x][GSH]-k_1[GP_{xr}][H_2O_2]_{in}$$ | |
− | + | ||
− | + | $$\frac{d[H_2O_2]}{dt}=k_6([H_2O_2]_{out}-{H_2O_2]_{out})-k_1[GP_{xr}][H_2O_2]_{in}$$ | |
− | + | ||
− | + | $$\frac{d[GP_{x0}]}{dt}=k_1[GP_{xr}][H_2O_2]_{in}-k_2[GP_{xo}][GSH]$$ | |
− | + | ||
+ | $$\frac{d[H_2O]}{dt}=k_1[GP_{xr}][H_2O_2]_{in}+k_2[GP_{xo}][GSH]$$ | ||
+ | |||
+ | $$\frac{d[GSH]}{dt}=2k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}-k_2[GP_{xo}][GSH]-k_3[GS-GP_x][GSH]$$ | ||
+ | |||
+ | $$\frac{d[GS-GP_x]}{dt}=k_2[GP_{xo}][GSH]-k_3[GS-GP_x][GSH]$$ | ||
+ | |||
+ | $$\frac{d[GSSG]}{dt}=k_3[GS-GP_x][GSH]-k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}$$ | ||
+ | |||
+ | $$\frac{d[NADPH]}{dt}=-k_4[GSR]\frac{[NADPH]}{K_{4M}+[NADPH]}$$ | ||
+ | |||
+ | $$\frac{d[GSR]}{dt}=k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}-k_4[GSR]\frac{[NADPH]}{K_{4M}+[NADPH]}$$ | ||
+ | |||
+ | $$\frac{d[GSR']}{dt}=k_4[GSR]\frac{[NADPH]}{K_{4M}+[NADPH]}-k_5[GSR']\frac{[GSSG]}{K_{5M}+[GSSG]}$$ | ||
+ | |||
</p> | </p> | ||
Revision as of 16:33, 17 September 2016
Modeling
Overall Modeling Abstract
Abstract
Our goal is simple: produce GSR/25HC, package it into nanoparticles, and transport into the lens. GSR/25HC is released over time, which decreases H2O2 concentration, reduces crystallin damage, and prevents cataracts. Our models approach these steps in reverse order, starting with our desired goal, and working backwards to understand the entire process.
Achievements
- 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 user to find a full treatment plan.
- Generalized Customizer to allow other iGEM teams to predict any nanoparticle drug delivery
- Analyzed sensitivity of prototype, and suggested insights into optimal manufacturing of prototype.
- Experimental data used 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
- How much GSR do we want inside the lens?
- How do we use nanoparticles to control the amount of GSR in the lens?
- 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?
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/H2O2
Abstract
Abstract
Purpose
Purpose
Conclusion
Conclusion
Model 3: Nanoparticles
Abstract
Abstract
Purpose
Purpose
Conclusion
Conclusion
Model 4: Eyedrops
Abstract
Abstract
Purpose
Purpose
Conclusion
Conclusion
Conclusion
Yay