Latest revision as of 03:49, 3 December 2016

Model - TAS Taipei iGEM Wiki

PROJECT

Background

Achievements

Collaborations

Parts

Cataracts - the leading cause of blindness. Find out how we can non-invasively treat and prevent cataract formation.
EXPERIMENTAL

Lens Cataract Model

Prevention and Treatment Constructs

Delivery Prototype

Notebook

We build constructs to make our great ideas become reality. Follow along our discovery of exciting science!
MODEL

GSR Function

Prototype Delivery

CH25H Treatment

Calculator

Computational Biology provides us models that we cannot easily test experimentally. Click to find out the results of our modeling, and the math behind it!
HUMAN PRACTICE

Research

Outreach

Impact

We don't just grow cool bacteria. We make a difference. Find out how we tackled social aspects of this project.
SAFETY

Overview

Biosafety

Risk Reduction Methods

Further Questions

Safety first. Especially in a lab. Here's how we maintained and investigated the integrity and security of our work environment.
TEAM

Members

About

Attributions

Wiki Standard Pages

Every iGEM project is the accumulation of an entire year's hard work by a group of cheerful students. Meet the team!

C◎UNTERACTS

Prevention: GSR Function

1. Crystallin Damage
2. GSR Pathway

Prevention: Prototype

3. Nanoparticles
4. Eyedrops

Treatment
Calculator (Software)

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.

**Figure 4.0: Overall Modeling Approach.** We go in reverse order, starting with our final goal, to lower LOCS, and go backwards to find the amount of GSR needed, then to find the delivery prototype to deliver this amount of GSR.

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)

When we add GSR into the system, crystallin damage decreases (Cui X.L. 1993). Our goal is to find the equivalent crystallin damage that leads to a LOCS 2.5 cataract, in order to know how much GSR to prevent this amount of crystallin damage in Model 2.

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.

Table 1: Results of Model 1 – Equivalent values for LOCS, Absorbance, and Crystallin Damage. First two columns come from *Chylack*, the third column uses data from our team's Lens Model experiment (see collapsible)
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.

**Figure 4.1: Cataract Threshold.** The results show that if we must limit crystallin damage to below 0.9883 units, so surgery is not needed.

Motivation

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)

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. 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.

We use literature data to relate LOCS to absorbance, which is still a physical property, but is frequently used in the lab. Then, with experimental data, we relate crystallin damage to absorbance, thus completing the link between the chemical and the physical definitions.

Quantification of Crystallin Damage

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 H₂O₂.

Crystallin damage depends on two factors: (1) the amount of H₂O₂ crystallin is exposed to, and (2) the time crystallin is exposed to H₂O₂. Therefore, we can mathematically quantify this by integrating the amount of H₂O₂ in the crystallin over time: \[c.d.(t) = \int_{0}^{\infty} [H_2O_2]_t dt\]

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 H₂O₂ for 1 hour, with units M-h. We make an assumption here, described fully in “Assumptions” #1.

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 H₂O₂, so it will take much longer than an hour of exposure until 1 M-h of crystallin damage is reached.

Data Documentation

LOCS to Absorbance

The results of Chylack et. Al. relate LOCS to opacity. Opacity (%) is physically related to absorbance at 397.5 nm, and can be calculated with the following equation.

As a result, we can find the equivalent absorbance of each point on the LOCS scale, shown in Table 1 (outside collapsible).

Absorbance to Crystallin Damage

**Table A: 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	0.695
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

Assumptions of Model 1

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:

Cataract damage is directly proportional to H₂O₂ concentration and time. Crystallin damage is mainly caused by H₂O₂ interacting the cysteine on crystallin. The reaction between H₂O₂ and cysteine is first-order (Domínguez-Vicent 2016), supporting this assumption. This allows us to make the quantification of crystallin damage.
We assume that the amount of crystallin in the lens is far greater than the amount of crystallin degraded. Therefore, a change in the amount of crystallin does not impact crystallin damage, as H₂O₂ only degrades a small portion of crystallin that causes blurred lens. (Cui X.L 1993)
The crystallin in humans is similar in function as crystallin in fish. This allows us to use experimental data on fish into this model.
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.
In the fish used, we assume there is there is no GSR. GSR decreases the amount of H₂O₂ in the fish, but since we could not find the amount of GSR in the fish, we must make this assumption.

Data Analysis

Using Experimental Data for Model

In each trial (see Data Documentation), we added H₂O₂ 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.

**Figure 4.A: Absorbance vs. Crystallin Damage.** This is experimental data, comparing observations (absorbance) with the theoretical crystallin damage. With this graph, we can find the equivalence between absorbance and crystallin damage.

Model Adjustment

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 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, as shown in Figure 4.B.

Discussion

Error Analysis

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. 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.

Significance of Model

With the results of this experiment, we create Table 1, which equates each LOCS value with the equivalent absorbance.When we experiment with the cataract lens model, we measure the absorbance. However, the absorbance values are meaningless to physicians and patients. This model allows them to translate absorbance into LOCS, which tells them exactly whether they need surgery, or into crystallin damage, which tells them how much GSR they need.

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.

**Figure 4.2: Blackbox Approach.** Model 2 is a complex system. We vary the input, GSR concentration, to get the outputs, crystallin damage over 50 years. We then connect the result to Model 1.

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.

**Figure 4.3: Crystallin Damage vs. GSR.** The graphed results from Model 2 allows us to find the GSR concentration for the LOCS 2.5 threshold. The yellow area above 2.5 indicates surgery is needed, while blue means it is not needed.

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.

Introduction

We have already found the threshold for crystallin damage, in a unit that is related to hydrogen peroxide concentration. Now, we find how much GSR would limit hydrogen peroxide enough so crystallin damage falls below the threshold.

Because of our definition of crystallin damage, by integrating a hydrogen peroxide vs. time graph, we effectively calculate crystallin damage. We build our model, with the goal of finding the hydrogen peroxide over a period of 50 years.

We chose 50 years, because we assume prevention would start at an early age, such as the 30s to 40s, when cataracts may start developing. Then, our prototype will prevent cataracts for one’s entire lifetime.

Enzyme Kinetics

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 (Ault 1974,Pi 2004) .

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.

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

Parameters & Initial Conditions

**Table B: Parameters for Model 2, and their sources/estimates.**
Variable	Value	Notes	Source
k1	$2.1\cdot10^7$	Rate constant for Reaction 1	(Ng 2007)
k2	$4\cdot10^4$	Rate constant for Reaction 2	(Ng 2007)
k3	$1\cdot10^7$	Rate constant for Reaction 3	(Ng 2007)
K4m	$0.063\cdot10^{-3}$	Michaelis constant for NADPH	(Salvador 2005)
K5m	$0.154\cdot10^{-3}$	Michaelis constant for GSR	(Saravanakumar 2015)
K4c	$0.219\cdot10^{-3}$	Michaelis constant for NADPH	(Salvador 2005)
K5c	$7.985\cdot10^{-3}$	Michaelis constant for GSR	(Saravanakumar 2015)
K6	$10^{-5}$	Diffusion constant	Estimate, derived from (Adimora 2010,) estimate

**Table C: Initial Conditions of Model 2**
Chemmical	Initial Condition (M)	Source
H₂O₂ (in)	$0.5\cdot10^{-3}$	(Adimora 2010)
H₂O₂ (out)	$0.5\cdot10^{-3}$	Estimate, assuming H₂O₂ in and otu are in dynamic equilibrium.
GPxr	$5\cdot10^{-5}$	(Ng 2007)
GPxo	$10^{-14}$	(Ng 2007)
H2O	$0$	Ignored, does not impact system
GSH	$3.68\cdot10^{-5}$	(Jones 2005)
GSGPx	$10^{-14}$	Estimate, similar to GPxo
GSSG	$1.78\cdot10^{-6}$	(Ng 2007)
NADPH	$3.0\cdot10^{-3}$	(Martinovich 2005)
GSR1	Varied	We change this as an input in our Model
GSR2	$0$	Assuming no reaction has taken place yet.

Procedure

1. After building this differential equation model in Mathematica, we change the initial starting concentration of GSR, and numerically solve the equations.

2. The output will be a the concentration of H₂O₂ as a function of time. Integrating this function over 50 years using the definition in Model 1 returns the total crystallin damage.

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).

Assumptions

In this experiment, we made the following assumptions:

Crystallin damage is linear with respect to both concentration and time, as evidenced by cysteine’s first order reaction with hydrogen peroxide (Domínguez-Vicent 2016). (see Model 1 for full explanation).
The amount of total GSR (in both forms) is constant. 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.
The cortex and nucleus of the eyes are indistinguishable and regarded as a single entity. As cataract damage can occur in both areas, we simplify the model by combining them to form a single system.
The amount of H₂O₂ in the aqueous humor (but the amount in the nucleus changes). As cellular respiration is constantly regenerating ROS and forming H₂O₂, there will constantly be H₂O₂ diffusing into the lens.
The amount of H₂O₂ in the aqueous humor is equal to the initial value of H₂O₂ in the cortex. The rationale is that initially dynamic equilibrium exists between the lens and the aqueous humor.

Results

**Table D: Results of Model 2 - Necessary GSR to prevent cataract from exceeding LOCS for an amount of time.**
LOCS	Crystallin Damage (c.d.)	GSR needed to maintain LOCS for 1 year (uM)	GSR needed to maintain LOCS for 20 years (uM)	GSR needed to maintain LOCS for 50 years (uM)
0.0	0	N/A	N/A	N/A
0.5	0.1327	25.9	N/A	N/A
1	0.2774	23.4	52.49	96.1
1.5	0.4610	21.8	40.79	67.0
2.0	0.6966	20.4	34.78	52.3
2.5	0.9883	18.5	31.19	43.5
3.0	1.3840	16.5	28.83	37.8
4.0	2.5101	10.0	25.90	31.1
5.0	4.3514	0.00	24.05	27.5

Confirmation of Initial Value of GSR

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 H₂O₂ 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).

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.

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)

**Figure 4.4: Single Dose of Nanoparticles Concentration Graph.** Model of how GSR concentration in the lens is increased as a result of one dose of nanoparticles releasing GSR. Each curve represents a different concentration of GSR encapsulated in the nanoparticle. The GSR concentration in the lens increases, then decreases back to the initial, due to degradation.

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.

**Figure 4.5: Nanoparticle Release - Experiments vs. Model.**This is a graph of the amount of GSR left in nanoparticles as a function of time when placed in 37 degrees Celsius. As GSR is released, the amount of GSR in the nanoparticle falls as a decay exponential. We create a model to guide our experiments, and then use experimental data to refine our model.

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.

**Figure 4.6: Multiple Dose of Nanoparticles Concentration Graph.** When patients are given GSR-loaded nanoparticles daily, the resulting change in GSR concentrations in their lens is shown. Each curve represents a different amount of nanoparticle concentration in the eyedrop.

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)

**Figure 4.7: Procedure of Model 3.** We will change our inputs, radius, concentration, and frequency, which will change the design of nanoparticles. This will impact the concentration graph shown in Figure 4.6. We alter the inputs until the concentration graph satisfies our three goals.

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:

**Table 2: Results of Analysis, where we varied one independent variable at a time, and keeping the other two constant. The effect on the dependent variable is described in the table.**
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.

**Figure 4.8: Two Stage Eyedrop Approach.** Two nanoparticle designs are shown above, with high and low concentration. By applying high conc. eyedrops first until [GSR] reaches Low Eq, then switching to low conc. eyedrops to maintain Low Eq, this approach reaches equilibrium faster.

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).

Introduction

We do not put GSR directly into eyedrops, because the high turnover rate of the aqueous humor results in a lot of GSR being washed away. Instead, we encapsulate GSR into chitosan nanoparticles, which results in a greater amount of GSR delivered to the lens. This model will quantify the amount of GSR delivered to the lens over time, as new eyedrops are periodically applied.

Single Dose

Noyes-Whitney Equation

The Noyes-Whitney equation models the rate of diffusion over time through a diffusion layer, which will be the nanoparticle surrounding the drug, GSR. The following is the Noyes-Whitney equation. If chambers x and y are separated by diffusion layer z, then

$$\frac{dC_x}{dt}=\frac{DS}{V_y h} (C_y - C_x)$$

where Cx is the concentration of the drug in chamber x, Cy is the concentration of the drug in chamber y (assume our drug is 100% soluble), which is across the diffusion layer z from chamber x. Vx is the volume in chamber x, h is the thickness of the diffusion layer z, D is the diffusion coefficient, S is the surface area of the diffusion layer z.

The diffusion constant is defined as follow:

$$D = \frac{k_b T}{6 \pi \mu r}$$

where $k_b$ is the Boltzmann constant, T is the temperature, $\mu$ is the viscosity of the surrounding solution, and r is the radius of the nanoparticle (Fraunfelder 2008).

Differential Equations

$$\frac{dC_{in}}{dt}=\frac{DS}{V_{out} h} (C_{out} - C_{in})$$ $$\frac{dC_{out}}{dt}=-\frac{DS}{V_{in} h} (C_{out} - C_{in})$$

From these equations, we get the change in GSR concentration both inside and outside the nanoparticle.

Protein Degradation

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.

$$C_{oa}(t)=C_{out}\cdot e^{-k_dt}$$

Parameters

We know all components of the diffusion constant (temperature, viscosity, natural constants) except for nanoparticle radius. In addition, we find the volume of the aqueous humor by literature data. Other parameters, such as surface area and volume, are determined by the radius.

Determination of Diffusion Layer Dependence

From literature research, we estimate that the diffusion layer is on the order of -11, based on details on turnover rates in the aqueous humor and lens (Toxic). After creating our initial model to guide the experiments, we then used the experimental data to revise our initial model, by altering this constant to -2.5*10^-11

For initial conditions, the concentration inside the nanoparticles start at an initial value, while the concentration outside the nanoparticles start at the natural concentration of GSR (see Model 2 collapsible).

Parameters

**Table E: Parameters used for Differential Equations in Model 3**
Variable	Value	Notes	Source
Boltzmann Constant (kb)	$1.3806 \cdot 10^{23} \cdot m^2 \cdot kg \cdot s^{-2} \cdot K^{-1}$	Physical Constant
Temperature (T)	$273+37 K$	Body Temperature	Assumed
Viscosity (u)	$1.0 \cdot 10^{-4} Pa \cdot S $		Medicalopedia
Nanoparticle Radius	$200-400 nm$	Analyzed in model	Determined by SEM
Volume of Aqueous Humor (V1)	$2.5\cdot 10^{-4} L$	Constant	Medicalopedia
Volume of Nanoparticle (V2)	$10^{-7} L$		Estimate with Experimental Data from our experiments
Diffusion Layer	(1)$10^{-11} m$ (2)$2.5\cdot10^{-11} m$	Estimate, then revised upon experiments	(Fraunfelder 2008)
Surface Area	$4 \pi r^2$	Depends on radius
Degradation (kd)	$1.0\cdot10^{-5}$	Estimate, based on turnover rate of lacrimal fluids, in order of -5.	(Fraunfelder 2008)

Multiple Dose

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. By summing up the contribution of each dose, we get the resulting concentration of GSR outside the nanoparticles over time. Remember that our aim is to maintain 43.5 uM of GSR.

$$C_{total}(t)=\sum_{n=0}^\infty {C_{oa} (t-np \cdot)e^{-k_d(t-np)} \cdot u(t-np)}$$

An example of the resulting $C_{total}(t)$ is shown in Figure D.

Our modeling equation bares a resemblence to Fourier series, but instead we use exponentials to model the concentration function. The analysis we take later is similar to how Fourier series are analyzed.

Assumptions

In this model, we made the following assumptions:

All nanoparticles are uniform. All nanoparticle doses that are manufactured will be uniform.
GSR is delivered directly into the lens.It is difficult to model the function of the lens or diffusion inside the eyes, so we assume almost all GSR that is delivered
There is no limit to the concentration of GSR that can be placed into a nanoparticle.This would be an issue of manufacturing, although the concentrations we use are reasonably low to ensure that manufacturing is not a problem.

Analysis of Changing Variables

We vary each variable, nanoparticle radius, concentration, and dose frequency, one at a time, while keeping the other two variables constant.

Changing Radius

We find that changing the radius has little impact on the resulting graph, shown in Figure 4.D. Equilibrium is slightly decreased when radius is increased. We will ignore nanoparticle radius. We will use whatever range that is most convienient for manufacturers. For our purposes, we will use r = 200 nm.

Although we disregard nanoparticle radius, this simplification is only true in our desired range of 200 to 400 nm. Extremely small or large nanoparticles will show a difference in release.

**Figure 4.D: Changing Radius.** As shown in this graph, when concentration and dose frequency are kept constant, changing nanoparticle radius results in essentially no change in the concentration graph.

Changing Concentration

We find that changing the concentration impacts the equilibrium concentration. There is a direct relationship between GSR concentration inside the nanoparticles, and the equilibrium outside. Higher concentrations also make the graph more unstable, however, shown in a greater amplitude of oscillation in Figure 4.E sample graph is shown above.

Changing Frequency

We find that changing the frequency does not impact equilibrium concentration, but does change the stability at equilibrium, as shown in Figure 4.F. The concentration oscillates at a greater amplitude about the equilibrium, which is undesirable, when frequency is too low. Therefore, daily doses are definitely preferred.

We graphed each of the three dependent variables as a function of the three independent variables, and found the quantitative relationship between them. This engineering technique allows us to find an equation for the equilibrium concentration as a function of the three independent variables.

Notice that the time to reach equilibrium (related to the time constant) cannot be altered. See the two eyedrop appraoch to overcome this problem.

Two Stage Eyedrop Approach

Explanation

Problem: We cannot decrease the amount of time until the concentration reaches equilibrium, where full prevention is effective.

Solution: We propose the two stage eyedrop approach. For the first days of treatment, a higher concentration of eyedrop will be used before using a lower concentration. This will speed up the time to reach equilibrium.

In the diagram, we wish to reach the low equilibrium (in blue) as soon as possible. Using the higher concentrated nanoparticles results in the red curve. By applying the higher concentrated nanoparticles in the first days, then switching to the lower concentrated nanoparticles afterwards, we follow the highlighted path. This allows us to reach equilibrium faster.

We need to figure out the concentration of GSR in naoparticles for the blue and red curves. The blue curve (eyedrop 2) requires the original results of our model (outside collapsible). The red curve (eyedrop 1) requires some calculations.

Finding the Concentration of Eyedrop 1

We cannot change the shape of the concentration graphs, because we cannot change the amount of time to reach equilibrium. This means we can find a formula for the percent of GSR delivered. At equilibrium, the value is 1. By curve fitting an exponential to the graph, we find our "percent delivered" function.

The concentration depends on the desired amount of time to reach equilibriu, which we will call "time limit". By plugging the time limit into our percent function, we will know the percentage delivered at the time limit. We divide our goal concentration by this percentage, to find the equilibrium concentration of the red curve. Using the results our model, we can find the concentration of GSR in nanoparticles of eyedrop 1.

We built a functional calculator to find the concentrations of both eyedrops. This is an extention of the eyedrop provided at the bottom of the Model page.

Prevention

LOCS Score Threshold:
Time Limit (Days)
We guarentee that by applying this prevention eyedrop daily, your LOCS score will remain below your threshold for 50 years.

Variable	Eyedrop 1	Eyedrop 2
Nanoparticle Conc.	uM	uM
Eyedrop Result	mg/mL	mg/mL

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)

**Figure 4.9: Bioavailability.** For every 1 g of nanoparticles in the eyedrops, only 14.04 ug of them get through the cornea and into the lens.

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.

**Figure 4.10: Stochastic Model.** This model takes into account randomness and uncertainty related to the conditions of the eye. The average case (deterministic) is shown in blue, while each test trial is shown in various colors. Clearly, daily eyedrops is superior as this decreases the sensitivity of our model.

Stochastic Analysis

Mathematica provides a built-in process for stochastic analysis. We try to model our percent function (from Model 3), which calculates the ratio of current GSR versus final equilibrium GSR. Our percent function is: $$P(t)=1-1.027*e^{-0.1717t}$$ where t is in days.

Our stochastic model is based off the following differential equation, written in differential form: $$dC_R=dP + \sigma \frac{dP}{dt} dw(t)$$ where $C_R$ is the concentration ratio of current to final at equilibrium (like $P$, ranges from 0 to 1), $P$ is the percent function, $\sigma$ is the standard deviation of delivery, and $w(t)$ approximates the stochastic Wiener stochastic process.

The standard deviation is found from the square root of the variance divided by the equilibrium to get a number between 0 and 1, multiplied by a factor related to the frequency. The greater the frequency, the less GSR there is to every dose of eyedrop, so the standard deviation would decrease, and vice versa.

For full details, please see the research paper: Hanson, F.B. (2007).Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis and Computation. Chicago, IL:The Society for Industrial and Applied Mathematics.

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.

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

Adimora, N.J., Jones, D.P., & Kemp, M.L. (2010). A model of redox kinetics implicates the thiol proteome in cellular hydrogen peroxide responses. Antioxidants & Redox Signaling, 13(6), 731-43

Ault, A. (1974). An introduction to enzyme kinetics. Journal of Chemical Education,51(6), 381, DOI: 10.1021/ed051p381

Bonate, P.L., & Howard, D.R. (2005) Pharmacokinetics in Drug Development Volume 2: Regulatory and Development Paradigms. American Association of Pharmaceutical Scientists

CALVO, P., ALONSO, M. J., VILA‐JATO, J. L., & ROBINSON, J. R. (1996). Improved ocular bioavailability of indomethacin by novel ocular drug carriers. Journal of Pharmacy and Pharmacology, 48(11), 1147-1152.

Chylack, L.T., Wolfe, J.K., Singer, D, M., Leske, C., Bullimore, M, A., Bailey, I.L., Friend, J., McCarthy, D., & Wu, S. (1993). The Lens Opacities Classification System III. The Longitudinal Study of Cataract Study Group. American Medical Association. 111(6), 831-36.

Cui, X. L., & Lou, M. F. (1993). The effect and recovery of long-term H 2 O 2 exposure on lens morphology and biochemistry. Experimental eye research, 57(2), 157-167.

Dominguez-Vincent, A., Birkeldh, U., Carl-Gustaf, L., Nilson, M., Brautaset, R., & Al-Ghoul. K.J. (2016).Objective Assessment of Nuclear and Cortical Cataracts through Scheimpflug Images: Agreement with the LOCS III Scale. PLoS One.11(2), doi: 10.1371/journal.pone.0149249

Fraunfelder, F.T., Fraunfelder F.W., & Chambers, W.A.(2008) Clinical Ocular Toxicology: Drug-Induced Ocular Side Effects. Saunders

Gaudana, R., Ananthula, H.K., Parenky, A., Mitra, A.K. (2010). Ocular Drug Delivery. AAPS Journals, 12(3), 348-360 doi: 10.1208/s12248-010-9183-3

Griffiths, W.J., Khalik, J.A., Crick, P.J., Yutuc, E., & Wang, Y. (2016). New methods for analysis of oxysterols and related compounds by LC–MS. Journal of Steroid Biochemistry and Molecular Biology, 162, 4-26, http://dx.doi.ordg/10.1016/j.jsbmb.2015.11.017

Jones, D.P. (2008). Radical-free biology of oxidative stress. American Journal of Physiology. Cell Physiology, 295(4), 849-68

Lux, A., Maier, S., Dinslage, S., Suverkrup, R., & Diestelhorst, M.(2003). A comparative bioavailability study of three conventional eye drops versus a single lyophilisate. British Journal of Ophthalmology, 87(4), 436-440.

Martinovich, G.G., Cherenkevich, & S.N., Sauer. (2005). Intracellular redox state: towards quantitative description. European Biophysics Journal, 34(7), 937-42

Ng, C.F., Schafer, F.Q., Buettner, G.R., & Rodger, V.G.(2007).The rate of cellular hydrogen peroxide removal shows dependency on GSH: mathematical insight into in vivo H2O2 and GPx concentrations. Free Radical Research, 41(11), 1201-11

Norlin, M., Andersson, U., Bjorkhem, I., & Wikvall, Kjell. (2000). Oxysterol 7α-Hydroxylase Activity by Cholesterol 7α-Hydroxylase (CYP7A)*. The American Society for Biochemistry and Molecular Biology, J. Biol. Chem. 34046-34053. doi:10.1074/jbc.M002663200

Salvador, A., Savageau, M.A. (2005). Evolution of enzymes in a series is driven by dissimilar functional demands. National Academy of Sciences of the USA, 103(7), 2226-2231.

Saravanakumar, S., Eswari, A., & Rajendran, L. (2015). Mathematical analysis of immobilized enzyme with reaction-generated pH change on the kinetics using Asymptotic methods.International Journal of Advanced Multidisciplinary Research, 2(8), 98-119

Spector, A., Wang, G.M., Wang, R.R., Garner, W.H., & Moll, H. (1993). The prevention of cataract caused by oxidative stress in cultured rat lenses. I. H2O2 and photochemically induced cataract.Current Eye Research, 12(2), 163-79

Pi, N. A., Yu, Y., Mougous, J. D., & Leary, J. A. (2004). Observation of a hybrid random ping‐pong mechanism of catalysis for NodST: A mass spectrometry approach. Protein science, 13(4), 903-912.

Tajmir-Riahi, H.A., Nafisi, Sh., Sanyakamdhorn, S., Agudelo, D., & Chanphai, P. (2014). Applications of chitosan nanoparticles in drug delivery. Methods in Molecular Biology, 165-84, doi: 10.1007/978-1-4939-0363-4_11

Torchilin, V.P.(2006). Nanoparticles as Drug Carriers. Imperial College Press

Wang, J.J., Zeng, Z.W., Xiao, R.Z., Xie, T., Zhou, G.L., Zhan, X.R., & Wang, S.L. (2011). Recent advances of chitosan nanoparticles as drug carriers. Int J Nanomedicine, 6, 765-774 doi: 10.2147/IJN.S17296

Wong, M.M., Shukla, A.N., & Munir, W.M.(2012). Correlation of corneal thickness and volume with intraoperative phacoemulsification parameters using Scheimpflug imaging and optical coherence tomography. Journal of Cataract & Refractive Surgery, 40(12), 2067-75 doi: 10.1089/ars.2009.2968.

Prevention

GSR Eyedrop

Treatment

25HC Eyedrop

LOCS: 0

Eyedrops

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-								<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Description">Background</a></h5>
+								<h5><a href="https://2016.igem.org/Team:TAS_Taipei/Background">Background</a></h5>
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-                              <div class="col-sm-12">
+                              <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>For sake of 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>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"/>
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                                      Since our construct is not directly placed into the eyes, how our synthesized protein impacts the eye after it is separately transported into the lens is of greater importance.  As a result, we create models with the intent on understanding how GSR and CH25H impacts the eye, and how we can control its impact with a well-designed delivery prototype.
                                  </p>
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+                                <figure class = "col-sm-12">
+                                     <img src="https://static.igem.org/mediawiki/2016/b/b7/T--TAS_Taipei--Fig7.jpg">
+                                    <figcaption class='darkblue'><b>Figure 4.0: Overall Modeling Approach. </b> We go in reverse order, starting with our final goal, to lower LOCS, and go backwards to find the amount of GSR needed, then to find the delivery prototype to deliver this amount of GSR. </figcaption>
+                                </figure>
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                          <h1 id="GSRFunc">Prevention: GSR Function</h1>
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                                  <p>
-                                     The amount of damage to crystallin by H2O2 determines the severity of a cataract. We relate the amount of crystallin damage to the corresponding rating on the LOCS scale, used by physicians to rate cataract severity. Our goal is to lower LOCS to below 2.5, the threshold for surgery. Through literature research as well as our own experimental data, <b>we find the maximum allowable crystallin damage to prevent a LOCS 2.5 cataract from developing. </b>
+                                     The amount of damage to crystallin by H<sub>2</sub>O<sub>2</sub> 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, <b>we find the maximum allowable crystallin damage to prevent a LOCS 2.5 cataract from developing. </b>
                                  </p>
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                            <h3>Measurement of Cataract Severity</h3>
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                                      There are three 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><b>Lens Optical Cataract Scale (LOCS)</b>: Physicians use this scale, from 0 – 6, to grade the severity of cataracts (Domínguez-Vicent 2016).
                                          </li>
                                          <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 crystallin is exposed to oxidizing agents. </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 crystallin is exposed to oxidizing agents. (Cui X.L. 1993) </li>
                                      </ol>
-                                     When we add GSR into the system, crystallin damage decreases. Our goal is to find the <b>equivalent crystallin damage that leads to a LOCS 2.5 cataract</b>, in order to know <b>how much GSR</b> to prevent this amount of crystallin damage in Model 2.
+                                     When we add GSR into the system, crystallin damage decreases (Cui X.L. 1993). Our goal is to find the <b>equivalent crystallin damage that leads to a LOCS 2.5 cataract</b>, in order to know <b>how much GSR</b> to prevent this amount of crystallin damage in Model 2.
                                  </p>
                                  </div>
                              </div>
-                         <button class="accordion">Background, Method, Results, Discussion</button>
+                            <div class="row">
+                                <div class="col-sm-8">
+                                    <br><br>
+                                    <h3>LOCS to Absorbance: Literature Data</h3>
+                                <p>
+                                    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).
+                                </p>
+                                    <br><br>
+                                    <h3>Absorbance Equivalence to Crystallin Damage: Experimental Data</h3>
+                                <p>
+                                    We use experimental measurements from our team’s Cataract Lens Model (<a href="https://2016.igem.org/Team:TAS_Taipei/Experimental_Summary">Link</a>). 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 <b>equivalent crystallin damage of each LOCS rating and absorbance, and create the third column of Table 1.</b>
+                                </p>
+                                </div>
+                                <div class="col-sm-4">
+                                    <table class="table table-bordered" style='width: 90%;margin-left:0%;'>
+                                        <caption style='caption-side:top;'><b>Table 1: Results of Model 1 – Equivalent values for LOCS, Absorbance, and Crystallin Damage. First two columns come from <i>Chylack</i>, the third column uses data from our team's Lens Model experiment (see collapsible)</caption>
+							                 <thead>
+								                <tr>
+                                                    <th>LOCS</th>
+                                                    <th>Absorbance (@397.5 nm <br>abs units)</th>
+                                                    <th>Crystallin Damage <br>(M-h)</th>
+                                                </tr>
+                                            </thead>
+                                            <tr>
+                                                <th>0.0</th>
+                                                <th>0.0000</th>
+                                                <th>0.0000</th>
+                                            </tr>
+                                            <tr>
+                                                <th>0.5</th>
+                                                <th>0.0143</th>
+                                                <th>0.1243</th>
+                                            </tr>
+                                            <tr>
+                                                <th>1.0</th>
+                                                <th>0.0299</th>
+                                                <th>0.2878</th>
+                                            </tr>
+                                            <tr>
+                                                <th>1.5</th>
+                                                <th>0.0497</th>
+                                                <th>0.4697</th>
+                                            </tr>
+                                            <tr>
+                                                <th>2.0</th>
+                                                <th>0.0751</th>
+                                                <th>0.6949</th>
+                                            </tr>
+                                            <tr>
+                                                <th style="background:#FFFF66">2.5</th>
+                                                <th style="background:#FFFF66">0.1076</th>
+                                                <th style="background:#FFFF66;color:#FF0000">0.9883</th>
+                                            </tr>
+                                            <tr>
+                                                <th>3.0</th>
+                                                <th>0.1492</th>
+                                                <th>1.3747</th>
+                                            </tr>
+                                            <tr>
+                                                <th>4.0</th>
+                                                <th>0.2706</th>
+                                                <th>2.5259</th>
+                                            </tr>
+                                            <tr>
+                                                <th>5.0</th>
+                                                <th>0.4691</th>
+                                                <th>4.3472</th>
+                                            </tr>
+                                        </table>
+                                </div>
+                            </div>
+                                <div class="row">
+                                    <div class="col-sm-8">
+                                        <h3>Conclusion</h3>
+                                            <p>
+                                            To guarantee that surgery is not needed for 50 years, we need to <b>limit crystallin damage to 0.9883 units.</b> If crystallin damage goes above this threshold, then surgery is needed. This is the crystallin damage threshold for a LOCS 2.5 cataract.
+                                            </p>
+                                    </div>
+                                    <figure class = "col-sm-4">
+                                     <img src="https://static.igem.org/mediawiki/2016/f/fe/T--TAS_Taipei--Figure2_Model.jpg">
+                                    <figcaption class='darkblue'><b>Figure 4.1: Cataract Threshold. </b> The results show that if we must limit crystallin damage to below 0.9883 units, so surgery is not needed.
+                                    </figure>
+                                </div>
+                                    <br>
+                              <button class="accordion"><img src ="https://static.igem.org/mediawiki/2016/d/d2/T--TAS_Taipei--clickmeorange.gif" width:"75%" height:"75%"> Model 1 Details: Motivation, Data Documentation, Assumptions, Full Analysis and Discussion</button>
 <div class="panel">
@@ Line 323: / Line 424: @@
                      <div class="col-sm-12">
                          <h3>Motivation</h3>
-                         <p>Crystallin damage is the chemically significant way quantifying cataract severity.
+                         <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. </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>We use literature data to relate LOCS to absorbance, which is still a physical property, but is frequently used in the lab. Then, with experimental data, we relate crystallin damage to absorbance, thus completing the link between the chemical and the physical definitions.</p>
@@ Line 331: / Line 432: @@
                      <div class="col-sm-12">
                              <h3>Quantification of Crystallin Damage</h3>
-                             <p>Crystallin damage is rarely measured chemically. 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 H2O2. The chemical equation is as follow:
+                             <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>Crystallin damage depends on two factors: (1) the <b>amount</b> of H2O2 crystallin is exposed to, and (2) the <b>time</b> crystallin is exposed to H2O2. Therefore, we can mathematically quantify this by integrating the amount of H2O2 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:
                                  \[c.d.(t) = \int_{0}^{\infty} [H_2O_2]_t dt\]
                              </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 H2O2 for 1 hour, with units M-h. We make an assumption here, described fully in “Assumptions” #1.</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 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. In addition, the eyes have a naturally occurring antioxidant system that lowers the concentration of H2O2, so it will take much longer than an hour of exposure until 1 M-h of crystallin damage is reached.</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 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>
@@ Line 346: / Line 447: @@
       			 <h3>Data Documentation</h3>
                  <div class="col-sm-12">
-                        <h3>Data Documentation</h3>
                          <h4>LOCS to Absorbance</h4>
-                         <p>The results of <i>Domínguez-Vicent et. Al. </i> relate LOCS to opacity. Opacity (%) is physically related to absorbance at 397.5 nm, and can be calculated with the following equation.</p>
+                         <p>The results of <i>Chylack et. Al. </i> relate LOCS to opacity. Opacity (%) is physically related to absorbance at 397.5 nm, and can be calculated with the following equation.</p>
                          <p>As a result, we can find the equivalent absorbance of each point on the LOCS scale, shown in Table 1 (outside collapsible).</p>
                          <h4>Absorbance to Crystallin Damage</h4>
                           <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
-                     <caption style='caption-side:top;'><b>Table 2: Experimental Data used for Model 1 from Cataract Lens Model (TAS) - Absorbance vs. Crystallin Damage </b></caption>
+                     <caption style='caption-side:top;'><b>Table A: Experimental Data used for Model 1 from Cataract Lens Model (TAS) - Absorbance vs. Crystallin Damage </b></caption>
 							<tbody>
                                  <thead>
                                      <td>Trial</td>
-									<td>H2O2 Concentration (M)</td>
+									<td>H<sub>2</sub>O<sub>2</sub> Concentration (M)</td>
 									<td>Exposure Time (h)</td>
 									<td>Crystallin Damage (c.d.)</td>
@@ Line 380: / Line 480: @@
                                      <td>72.0</td>
                                      <td>7.20</td>
-                                     <td>0.0.695</td>
+                                     <td>0.695</td>
 								</tr>
                                  <tr>
@@ Line 423: / Line 523: @@
              </div>
              <div id="crysmenu2" class="tab-pane fade">
-      			 <h3>Assumptions</h3>
+      			 <h3>Assumptions of Model 1</h3>
                  <div class="col-sm-12">
-                         <h3>Assumptions of Model</h3>
                          <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>
-                                 <li><b>Cataract damage is directly proportional to H2O2 concentration and time.</b> Crystallin damage is mainly caused by H2O2 interacting the cysteine on crystallin. The reaction between H2O2 and cysteine is first-order (Domínguez-Vicent,), supporting this assumption. This allows us to make the quantification of crystallin damage.</li>
+                                 <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 H2O2 only degrades a small portion of crystallin that causes blurred lens.</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 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>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 H2O2 in the fish, but since we could not find the amount of GSR in the fish, we must make this assumption.</li>
+                                 <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>
                          </p>
@@ Line 447: / Line 547: @@
                      <div class="col-sm-6">
                          <h3>Using Experimental Data for Model</h3>
-                         <p>In each trial (see Data Documentation), we added H2O2 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>
+                         <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 class="col-sm-12">
+                  <figure class="col-sm-6">
+                   <img src=" https://static.igem.org/mediawiki/2016/8/83/T--TAS_Taipei--Model1AbsExp.png">
+                                    <figcaption class='darkblue'><b>Figure 4.A: Absorbance vs. Crystallin Damage. </b> This is experimental data, comparing observations (absorbance) with the theoretical crystallin damage. With this graph, we can find the equivalence between absorbance and crystallin damage.
+                                    </figure>
+                </div>
+                   <br>
+                <div class="row">
+                     <div class="col-sm-6">
                          <h3>Model Adjustment</h3>
                          <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.
+                             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>
                      </div>
+                    <figure class="col-sm-6">
+                   <img src="https://static.igem.org/mediawiki/2016/f/f2/T--TAS_Taipei--Twolines.jpg">
+                                    <figcaption class='darkblue'><b>Figure 4.B: Model Adjustment. </b> Theoretically, this should be a direct relation, so we assume that the remaining GSH inside the fish lens is being used in the first unit of crystallin damage, so no increase in absorbance is found at this range.
+                                    </figure>
                  </div>
+                   </div>
-</div>
              <div id="crysmenu4" class="tab-pane fade">
-                 <h3>Analysis</h3>
+                 <h3>Discussion</h3>
        			<div class="row">
@@ Line 480: / Line 591: @@
 </div>  <!-- End Menu -->
-                             <div class="row">
-                                <div class="col-sm-8">
-                                    <h3>Measurement of Cataract Severity</h3>
-                                <p>
-                                    Numerous studies show how absorbance measurements can be converted to the LOC scale that physicians use. With the results of ________ and ________, we construct the first two columns in Table 2.
-                                </p>
-                                    <h3>Absorbance Equivalence to Crystallin Damage: Experimental Data</h3>
-                                <p>
-                                    We use experimental measurements from our team’s Cataract Lens Model (link). They induced an amount of crystallin damage, and measured the resulting absorbance.
-                                    With this relation graphed in Figure 2, we calculate the <b>equivalent crystallin damage of each LOCS rating and absorbance, and create the third column of Table 2.</b>
-                                </p>
-                                </div>
-                                 <div class="col-sm-4">
+                                 <br><br>
-                                    <table class="table table-bordered" style='width: 90%;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>Absorbance (@397.5 nm <br>abs units)</th>
-                                                    <th>Crystallin Damage <br>(M-h)</th>
-                                                </tr>
-                                            </thead>
-                                            <tr>
-                                                <th>0.0</th>
-                                                <th>0.0000</th>
-                                                <th>0.0000</th>
-                                            </tr>
-                                            <tr>
-                                                <th>0.5</th>
-                                                <th>0.0143</th>
-                                                <th>0.1243</th>
-                                            </tr>
-                                            <tr>
-                                                <th>1.0</th>
-                                                <th>0.0299</th>
-                                                <th>0.2878</th>
-                                            </tr>
-                                            <tr>
-                                                <th>1.5</th>
-                                                <th>0.0497</th>
-                                                <th>0.4697</th>
-                                            </tr>
-                                            <tr>
-                                                <th>2.0</th>
-                                                <th>0.0751</th>
-                                                <th>0.6949</th>
-                                            </tr>
-                                            <tr>
-                                                <th style="background:#FFFF66">2.5</th>
-                                                <th style="background:#FFFF66">0.1076</th>
-                                                <th style="background:#FFFF66;color:#FF0000">0.9883</th>
-                                            </tr>
-                                            <tr>
-                                                <th>3.0</th>
-                                                <th>0.1492</th>
-                                                <th>1.3747</th>
-                                            </tr>
-                                            <tr>
-                                                <th>4.0</th>
-                                                <th>0.2706</th>
-                                                <th>2.5259</th>
-                                            </tr>
-                                            <tr>
-                                                <th>5.0</th>
-                                                <th>0.4691</th>
-                                                <th>4.3472</th>
-                                            </tr>
-                                        </table>
-                                </div>
-                            </div>
-                            <div class="row">
-                                <div class="col-sm-6">
-                                        <h3>Conclusion</h3>
-                                            <p>
-                                            To guarantee that surgery is not needed for 50 years, we need to <b>limit crystallin damage to 0.9883 units.</b> If crystallin damage goes above this threshold, then surgery is needed. This is the crystallin damage threshold for a LOCS 2.5 cataract.
-                                            </p>
-                                </div>
-                                <figure class = "col-sm-6">
-                                    <br><br><br>
-                                     <img src="https://static.igem.org/mediawiki/2016/f/fe/T--TAS_Taipei--Figure2_Model.jpg">
-                                    <figcaption class='darkblue'><b>Figure 2: Cataract Threshold </b> </figcaption>
-                                </figure>
-                            </div>
                          <h2 id="model2">Model 2: GSR Pathway</h2>
                              <div class="row">
@@ Line 580: / Line 606: @@
                                  <div class="col-sm-12">
                                  <p>
-                                     By various enzyme kinetics laws, fully documented in the collapsible, 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.
+                                     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.
                                  </p>
                                  </div>
@@ Line 590: / Line 616: @@
                                      <h3>Blackbox Approach: Testing GSR Impact</h3>
                                  <p>
-                                     We 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 2.
+                                     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.
                                  </p>
@@ Line 604: / Line 630: @@
                                      <br><br><br>
                                       <img src="https://static.igem.org/mediawiki/2016/8/88/T--TAS_Taipei--Figure3_Model.jpg">
-                                     <figcaption class='darkblue'><b>Figure 2: Cataract Threshold </b> </figcaption>
+                                     <figcaption class='darkblue'><b>Figure 4.2: Blackbox Approach. </b> Model 2 is a complex system. We vary the input, GSR concentration, to get the outputs, crystallin damage over 50 years. We then connect the result to Model 1. </figcaption>
                                  </figure>
                              </div>
+                                <br><br>
                              <div class="row">
                                  <div class="col-sm-12">
                                      <h3>Crystallin Damage vs. GSR Level</h3>
                                  <p>
-                                     According to literature data and our model, the naturally occurring GSR concentration is 10 uM. All curves show crystallin damage decreasing as GSR levels are increased, which supports both research and experimental data, and suggests that this prototype is effective in preventing crystallin damage. <b>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. </b>
+                                     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. <b>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. </b>
                                  </p>
                                  <p>
-                                     Table 3 shows the amount of GSR we need to maintain for 50 years in order to prevent a LOCS cataract of a certain severity. The row of interest is LOCS 2.5, the threshold for surgery. Notice that we say <i>“maintain”</i> 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.
+                                     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 <i>“maintain”</i> 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.
                                  </p>
@@ Line 623: / Line 650: @@
                                  <div class="col-sm-1"></div>
                                  <figure class = "col-sm-10">
-                                     <br><br><br>
 							         <img src="https://static.igem.org/mediawiki/2016/c/cc/T--TAS_Taipei--FinalGSRGraph.png">
-                                     <figcaption class='darkblue'><b>Figure 2. </b>Graph - more to be written.</figcaption>
+                                     <figcaption class='darkblue'><b>Figure 4.3: Crystallin Damage vs. GSR. </b>The graphed results from Model 2 allows us to find the GSR concentration for the LOCS 2.5 threshold. The yellow area above 2.5 indicates surgery is needed, while blue means it is not needed. </figcaption>
                                  </figure>
+                                <br><br>
                                  <div class="col-sm-1"></div>
                              </div>
+                               <br>
-                                 <button class="accordion">Background, Method, Results, Discussion</button>
+                        <br>
+                            <div class="row">
+                                <div class="col-sm-12">
+                                <h3>Conclusion</h3>
+                                    <p>We need to <b>maintain</b> (NOT add) <b>43.5 uM of GSR</b> in the lens so that the crystallin damage recorded over 50 years is below the LOCS 2.5 threshold. </p>
+                                </div>
+                                 <button class="accordion"><img src ="https://static.igem.org/mediawiki/2016/d/d2/T--TAS_Taipei--clickmeorange.gif" width:"75%" height:"75%">Model 2 Details: Enzymes & Differential Equations, Parameter Table, Procedure, Results, Discussion</button>
@@ Line 639: / Line 675: @@
                                           <li class="active"><a data-toggle="tab" href="#gsrhome">Introduction</a></li>
                                           <li><a data-toggle="tab" href="#gsrmenu1">Enzyme Kinetics</a></li>
-                                          <li><a data-toggle="tab" href="#gsrmenu2">Differential Equations & Paramters</a></li>
+                                          <li><a data-toggle="tab" href="#gsrmenu2">Equations</a></li>
                                           <li><a data-toggle="tab" href="#gsrmenu3">Procedure & Assumptions</a></li>
                                           <li><a data-toggle="tab" href="#gsrmenu4">Results</a></li>
@@ Line 648: / Line 684: @@
                                           <div id="gsrhome" class="tab-pane fade in active">
                                               <h3>Introduction</h3>
+                                             <p>We have already found the threshold for crystallin damage, in a unit that is related to hydrogen peroxide concentration. Now, we find how much GSR would limit hydrogen peroxide enough so crystallin damage falls below the threshold. </p>
+                                             <p>Because of our definition of crystallin damage, by integrating a hydrogen peroxide vs. time graph, we effectively calculate crystallin damage. We build our model, with the goal of finding the hydrogen peroxide over a period of 50 years.</p>
+                                             <p> We chose 50 years, because we assume prevention would start at an early age, such as the 30s to 40s, when cataracts may start developing. Then, our prototype will prevent cataracts for one’s entire lifetime. </p>
                                          </div>
                                           <div id="gsrmenu1" class="tab-pane fade">
@@ Line 661: / Line 700: @@
                              $$[H_2O_2]_{out} \xrightarrow[]{k_5} [H_2O_2]_{in} ...(6)$$
-                                             <p> Each reaction will be discussed in detail, and we will derive rate equations.</p>
+                                             <p> Each reaction will be discussed in detail, and we will derive rate equations (Ault 1974,Pi 2004) .</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>
@@ Line 684: / Line 723: @@
                                          </div>
                                           <div id="gsrmenu2" class="tab-pane fade">
-                                             <h4>Differential Equations</h4>
+                                             <h3>Differential Equations</h3>
                                              <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>
@@ Line 709: / Line 748: @@
                                              </p>
+                                             <h3>Parameters & Initial Conditions</h3>
+                                             <div class="row">
+                                                 <div class="col-sm-6">
+                                                     <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+							             <caption style='caption-side:top;'><b>Table B: Parameters for Model 2, and their sources/estimates.</caption>
+                                         <thead>
+                                                    <th>Variable</th><th>Value</th>
+                                                    <th>Notes</th>
+                                                    <th>Source</th>
+                                        </thead>
+                                             <tbody>
+                                            <tr>
+                                                <td>k1</td>
+                                                <td>$2.1\cdot10^7$</td>
+                                                <td>Rate constant for Reaction 1</td>
+                                                <td>(Ng 2007)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>k2</td>
+                                                <td>$4\cdot10^4$</td>
+                                                <td>Rate constant for Reaction 2</td>
+                                                <td>(Ng 2007)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>k3</td>
+                                                <td>$1\cdot10^7$</td>
+                                                <td>Rate constant for Reaction 3</td>
+                                                <td>(Ng 2007)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>K4m</td>
+                                                <td>$0.063\cdot10^{-3}$</td>
+                                                <td>Michaelis constant for NADPH</td>
+                                                <td>(Salvador 2005)</td>
+                                            </tr>
+                                                 <tr>
+                                                <td>K5m</td>
+                                                <td>$0.154\cdot10^{-3}$</td>
+                                                <td>Michaelis constant for GSR</td>
+                                                     <td>(Saravanakumar 2015)
+                                                 </tr>
+                                                <tr>
+                                                <td>K4c</td>
+                                                <td>$0.219\cdot10^{-3}$</td>
+                                                <td>Michaelis constant for NADPH</td>
+                                                <td>(Salvador 2005)</td>
+                                            </tr>
+                                                 <tr>
+                                                <td>K5c</td>
+                                                <td>$7.985\cdot10^{-3}$</td>
+                                                <td>Michaelis constant for GSR</td>
+                                                <td>(Saravanakumar 2015)</td>
+                                            </tr>
+                                                 <tr>
+                                                <td>K6</td>
+                                                <td>$10^{-5}$</td>
+                                                <td>Diffusion constant</td>
+                                                <td>Estimate, derived from (Adimora 2010,) estimate</td>
+                                            </tr>
+                                        </tbody>
+						          </table>
+                                                 </div>
+                                                 <div class="col-sm-6">
+                                                     <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+							             <caption style='caption-side:top;'><b>Table C: Initial Conditions of Model 2</caption>
+                                         <thead>
+                                                    <th>Chemmical</th><th>Initial Condition (M)</th>
+                                                    <th>Source</th>
+                                        </thead>
+                                             <tbody>
+                                            <tr>
+                                                <td>H<sub>2</sub>O<sub>2</sub> (in)</td>
+                                                <td>$0.5\cdot10^{-3}$</td>
+                                                <td>(Adimora 2010)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>H<sub>2</sub>O<sub>2</sub> (out)</td>
+                                                <td>$0.5\cdot10^{-3}$</td>
+                                                <td>Estimate, assuming H<sub>2</sub>O<sub>2</sub> in and otu are in dynamic equilibrium.</td>
+                                            </tr>
+                                            <tr>
+                                                <td>GPxr</td>
+                                                <td>$5\cdot10^{-5}$</td>
+                                                <td>(Ng 2007)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>GPxo</td>
+                                                <td>$10^{-14}$</td>
+                                                <td>(Ng 2007)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>H2O</td>
+                                                <td>$0$</td>
+                                                <td>Ignored, does not impact system</td>
+                                            </tr>
+                                                 <tr>
+                                                <td>GSH</td>
+                                                <td>$3.68\cdot10^{-5}$</td>
+                                                <td>(Jones 2005)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>GSGPx</td>
+                                                <td>$10^{-14}$</td>
+                                                <td>Estimate, similar to GPxo</td>
+                                            </tr>
+                                            <tr>
+                                                <td>GSSG</td>
+                                                <td>$1.78\cdot10^{-6}$</td>
+                                                <td>(Ng 2007)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>NADPH</td>
+                                                <td>$3.0\cdot10^{-3}$</td>
+                                                <td>(Martinovich 2005)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>GSR1</td>
+                                                <td>Varied</td>
+                                                <td>We change this as an input in our Model</td>
+                                            </tr>
+                                                 <tr>
+                                                <td>GSR2</td>
+                                                <td>$0$</td>
+                                                <td>Assuming no reaction has taken place yet.</td>
+                                            </tr>
+                                        </tbody>
+						          </table>
+                                                 </div>
+                                             </div>
                                          </div>
                                           <div id="gsrmenu3" class="tab-pane fade">
                                                 <h3>Procedure</h3>
-                                                 <p>Listed outside collapsible</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 H2O2 as a function of time. Integrating this function over 50 years using the definition in Model 1 returns the total crystallin damage. </p>
+                                                 <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).</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>
                                              <p>In this experiment, we made the following assumptions:
                                              <ol>
-                                                 <li><b>Crystallin damage is linear with respect to both concentration and time,</b> as evidenced by cysteine’s first order reaction with hydrogen peroxide (Domínguez-Vicent). (see Model 1 for full explanation).</li>
+                                                 <li><b>Crystallin damage is linear with respect to both concentration and time,</b> as evidenced by cysteine’s first order reaction with hydrogen peroxide (Domínguez-Vicent 2016). (see Model 1 for full explanation).</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 100 days of the treatment have passed. 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 amount of H2O2 in the aqueous humor (but the amount in the nucleus changes).</b> As cellular respiration is constantly regenerating ROS and forming H2O2, there will constantly be H2O2 diffusing into the lens.</li>
+                                                 <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 H2O2 in the aqueous humor is equal to the initial value of H2O2 in the cortex.</b> The rationale is that initially dynamic equilibrium exists between the lens and the aqueous humor.</li>
+                                                 <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>
                                               </p>
@@ Line 731: / Line 911: @@
                                               <h3>Results</h3>
                                                <table class="table table-bordered" style='background-color:none;width: 90%;margin-left:0%;'>
-							                 <caption style='caption-side:top;'><b>Table 4: Results of Model 2 - Necessary GSR to prevent cataract from exceeding LOCS for an amount of time.</caption>
+							                 <caption style='caption-side:top;'><b>Table D: Results of Model 2 - Necessary GSR to prevent cataract from exceeding LOCS for an amount of time.</caption>
 							                 <thead>
 								                <tr>
                                                      <th>LOCS</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>
                                              </thead>
@@ Line 778: / Line 958: @@
                                              <tr>
                                                  <th>2.5</th>
-                                                 <th>0.9981</th>
+                                                 <th>0.9883</th>
                                                  <th>18.5</th>
                                                  <th>31.19</th>
@@ Line 808: / Line 988: @@
                                          <div id="gsrmenu5" class="tab-pane fade">
                                              <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 H2O2 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.</p>
+                                             <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 10uM. 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>
@@ Line 817: / Line 997: @@
                                  </div>
-                            <div class="row">
-                                <div class="col-sm-12">
-                                <h3>Conclusion</h3>
-                                    <p>We need to <b>maintain</b> (NOT add) <b>43.5 uM of GSR</b> in the lens so that the crystallin damage recorded over 50 years is below the LOCS 2.5 threshold. </p>
-                                </div>
@@ Line 835: / Line 1,008: @@
                                  <div class="col-sm-12">
                                  <p>
-                                     To maximize delivery efficiency to the lens, we encapsulate GSR in chitosan nanoparticles. 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.  <b>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.</b>
+                                     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.  <b>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.</b>
                                  </p>
                                  </div>
                              </div>
                              <div class="row">
                                  <div class="col-sm-12">
@@ Line 847: / Line 1,021: @@
                                  </p>
                                  <p>
-                                     We get two curves, concentration of GSR in the nanoparticles, and GSR release from nanoparticles, over time. <b>This allows us to predict nanoparticle delivery rates before we perform the actual experiments.</b>
+                                     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. <b>This allows us to predict nanoparticle delivery rates before we perform the actual experiments<a href="https://2016.igem.org/Team:TAS_Taipei/Experimental_Summary#prototype">&nbsp; (Link)</a></b>
                                  </p>
                                  </div>
@@ Line 856: / Line 1,030: @@
                                      <br><br><br>
 							         <img src="https://static.igem.org/mediawiki/2016/6/6b/T--TAS_Taipei--GSR_SingleDose_Model.png">
-                                     <figcaption class='darkblue'><b>Figure 3. Single Dose of Nanoparticles </b>Model of how GSR concentration in the lens is increased as a result of one dose of nanoparticles releasing GSR. Each line represents a different concentration of GSR in the nanoparticle. The GSR concentration in the lens increases, then decreases back to the initial, due to degradation.</figcaption>
+                                     <figcaption class='darkblue'><b>Figure 4.4: Single Dose of Nanoparticles Concentration Graph. </b>Model of how GSR concentration in the lens is increased as a result of one dose of nanoparticles releasing GSR. Each curve represents a different concentration of GSR encapsulated in the nanoparticle. The GSR concentration in the lens increases, then decreases back to the initial, due to degradation.</figcaption>
                                      </figure>
+                                <br>
                                  <div class="col-sm-1"></div>
                              </div>
                              <div class="row">
+                                 <div class="col-sm-12">
                                      <h3>Comparison with Experimental Data</h3>
                                  <p>
-                                     Yet in our model, we do not know the thickness of the nanoparticle diffusion layer. <b>After performing experiments, we can use measurements of our prototype device to find this thickness, and refine our model.</b> A direct comparison of our model with our experiment data is shown in Figure ___.
+                                     Yet in our model, we do not know the thickness of the nanoparticle diffusion layer. <b>After performing experiments, we can use measurements of our prototype device to find this thickness, and refine our model.</b> A direct comparison of our model with our experiment data is shown in Figure 4.5.
                                  </p>
+                                </div>
                              </div>
-                             <div class="rol-sm-12">
+                             <div class="row">
                                  <div class="col-sm-1"></div>
                                      <figure class = "col-sm-10">
                                      <br><br><br>
 							         <img src="https://static.igem.org/mediawiki/2016/5/5e/T--TAS_Taipei--Nanoparticle_Release_Model_final.png">
-                                     <figcaption class='darkblue'><b>Figure 4. Nanoparticle Release: Experiments vs. Model</b>This is a graph of the amount of GSR left in nanoparticles as a function of time. As GSR is released, the amount of GSR in the nanoparticle falls as a decay exponential. We create a model to guide our experiments, and then use experimental data to refine our model. </figcaption>
+                                     <figcaption class='darkblue'><b>Figure 4.5: Nanoparticle Release - Experiments vs. Model.</b>This is a graph of the amount of GSR left in nanoparticles as a function of time when placed in 37 degrees Celsius. As GSR is released, the amount of GSR in the nanoparticle falls as a decay exponential. We create a model to guide our experiments, and then use experimental data to refine our model. </figcaption>
                                  </figure>
                                  <div class="col-sm-1"></div>
@@ Line 883: / Line 1,059: @@
                                      <h3>Multiple Dose: Change in GSR Concentration</h3>
-                                <p>
+                                    <p>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.</p>
-                                    In Figure ____, all curves approach equilibrium, after which the concentration oscillates about equilibrium. We have three goals, in order of importance for best nanoparticle design:
+                                     <br><br>
-                                </p>
+                                    <div class="row">
-                                     <figure class = "col-sm-10">
+                                <div class="col-sm-1"></div>
-                                    <br><br><br>
+                                <div class="col-sm-10">
-							         <img src="https://static.igem.org/mediawiki/2016/d/db/T--TAS_Taipei--Figure4_Model.jpg">
+                                    <figure class = "col-sm-12">
-                                    <figcaption class='darkblue'><b>Figure 4. Nanoparticle Release: Experiments vs. Model</b> </figcaption>
-                                </figure>
+                                         <img src="https://static.igem.org/mediawiki/2016/f/ff/T--TAS_Taipei--MultipleDose_ConcChange.png">
+                                        <figcaption class='darkblue'><b>Figure 4.6: Multiple Dose of Nanoparticles Concentration Graph.   </b> When patients are given GSR-loaded nanoparticles daily, the resulting change in GSR concentrations in their lens is shown. Each curve represents a different amount of nanoparticle concentration in the eyedrop. </figcaption>
+                                    </figure>
+                                    </div>
+                                <br><br><br><br><br>
+                                <div class="col-sm-1"></div>
+                                </div>
+                                <p>
+<br><br>
+                                    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:
+                                </p>
                                  <ol>
                                      <li>GSR equilibrium concentration equal to amount we desire (i.e. 43.5 uM from Model 2)</li>
@@ Line 897: / Line 1,084: @@
                                      <li>Time to reach equilibrium (time for full prevention to come into effect)</li>
                                  </ol>
+                                </div>
+                             </div>
+                                    <br><br><br>
+                            <div class="row">
+                                    <div class="col-sm-1"></div>
+                                    <figure class = "col-sm-10">
+                                         <img src="https://static.igem.org/mediawiki/2016/d/db/T--TAS_Taipei--Figure4_Model.jpg">
+                                        <figcaption class='darkblue'><b>Figure 4.7: Procedure of Model 3. </b> We will change our inputs, radius, concentration, and frequency, which will change the design of nanoparticles. This will impact the concentration graph shown in Figure 4.6. We alter the inputs until the concentration graph satisfies our three goals. </figcaption>
+                                    </figure>
+                                    <div class="col-sm-1"></div>
+                            </div>
+                                <br><br>
+                            <div class="row">
+                                <div class="col-sm-12">
                                  <p>
                                      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:
                                  </p>
                                  </div>
                              </div>
                              <div class="row">
                                  <div class="col-sm-12">
                                      <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
-							             <caption style='caption-side:top;'><b>Table ___</caption>
+							             <caption style='caption-side:top;'><b>Table 2: Results of Analysis, where we varied one independent variable at a time, and keeping the other two constant. The effect on the dependent variable is described in the table.</caption>
                                           <thead>
                                              <tr>
@@ Line 920: / Line 1,124: @@
                                                  <td>No impact</td>
                                                  <td>Proportional Increase</td>
-                                                 <td>Slight Increase</td>
+                                                 <td>Slight Decrease</td>
                                              </tr>
                                              <tr>
                                                  <td>Radius</td>
                                                  <td>No impact</td>
-                                                 <td>Slight Decrease</td>
+                                                 <td>Very Slight Decrease</td>
-                                                 <td>No impact</td>
+                                                 <td>Very Slight Decrease</td>
                                              </tr>
                                              <tr>
@@ Line 939: / Line 1,143: @@
                                          <p>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.</p>
                                  </div>
                              </div>
+                                <br>
                              <div class="row">
-                                 <div class="col-sm-12">
+                                 <div class="col-sm-6">
                                      <h3>A Two Stage Eyedrop Approach</h3>
                                  <p>
-                                     As shown in Table ____, we cannot alter the time to reach equilibrium, or reach full prevention. As supported by ______, the time to reach equilibrium is a property of the lens that we cannot change. However, we propose a <b>two-step eyedrop approach, of two differing nanoparticle concentrations</b>, to decrease the time needed for full prevention. A full explanation is found in the collapsible.
+                                     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 <b>two-stage eyedrop approach, of two differing nanoparticle concentrations</b>, to decrease the time needed for full prevention. A full explanation is found in the collapsible.
                                  </p>
                                  </div>
+                                <figure class = "col-sm-6">
+                                         <img src="https://static.igem.org/mediawiki/2016/a/a7/T--TAS_Taipei--Fig5Highlighted.jpg">
+                                        <figcaption class='darkblue'><b>Figure 4.8: Two Stage Eyedrop Approach. </b> Two nanoparticle designs are shown above, with high and low concentration. By applying high conc. eyedrops first until [GSR] reaches Low Eq, then switching to low conc. eyedrops to maintain Low Eq, this approach reaches equilibrium faster. </figcaption>
+                                    </figure>
                              </div>
@@ Line 970: / Line 1,181: @@
                              </div>
+                                <button class="accordion"><img src ="https://static.igem.org/mediawiki/2016/d/d2/T--TAS_Taipei--clickmeorange.gif" width:"75%" height:"75%">Model 3 Details: Single/Multiple Dose, Parameter, Analysis, Extension</button>
+                                 <div class="panel">
+                                <div class="accordionmenu1" class ="col-sm-12" >
+                                    <ul class="nav nav-tabs">
+                                         <li class="active"><a data-toggle="tab" href="#nanohome">Introduction</a></li>
+                                         <li><a data-toggle="tab" href="#nanomenu1">Single Dose</a></li>
+                                         <li><a data-toggle="tab" href="#nanomenu2">Parameters</a></li>
+                                         <li><a data-toggle="tab" href="#nanomenu3">Multiple Dose</a></li>
+                                         <li><a data-toggle="tab" href="#nanomenu4">Analysis</a></li>
+                                        <li><a data-toggle="tab" href="#nanomenu5">Two Eyedrop Approach</a></li>
+                                     </ul>
+                                    <div class="tab-content">
+                                         <div id="nanohome" class="tab-pane fade in active">
+                                             <h3>Introduction</h3>
+                                             <p>We do not put GSR directly into eyedrops, because the high turnover rate of the aqueous humor results in a lot of GSR being washed away. Instead, we encapsulate GSR into chitosan nanoparticles, which results in a greater amount of GSR delivered to the lens. This model will quantify the amount of GSR delivered to the lens over time, as new eyedrops are periodically applied.</p>
+                                        </div>
+                                         <div id="nanomenu1" class="tab-pane fade">
+                                            <h3>Single Dose</h3>
+                                             <h4>Noyes-Whitney Equation</h4>
+                                            <p> The Noyes-Whitney equation models the rate of diffusion over time through a diffusion layer, which will be the nanoparticle surrounding the drug, GSR. The following is the Noyes-Whitney equation. If chambers x and y are separated by diffusion layer z, then</p>
+                                             $$\frac{dC_x}{dt}=\frac{DS}{V_y h} (C_y - C_x)$$
+                                             <p>where Cx is the concentration of the drug in chamber x, Cy  is the concentration of the drug in chamber y (assume our drug is 100% soluble), which is across the diffusion layer z from chamber x. Vx is the volume in chamber x, h is the thickness of the diffusion layer z, D is the diffusion coefficient, S is the surface area of the diffusion layer z.</p>
+                                             <p>The diffusion constant is defined as follow:</p>
+                                             $$D = \frac{k_b T}{6 \pi \mu r}$$
+                                             <p>where $k_b$ is the Boltzmann constant, T is the temperature, $\mu$ is the viscosity of the surrounding solution, and r is the radius of the nanoparticle (Fraunfelder 2008).</p>
+                                             <h4>Differential Equations</h4>
+                                             $$\frac{dC_{in}}{dt}=\frac{DS}{V_{out} h} (C_{out} - C_{in})$$
+                                             $$\frac{dC_{out}}{dt}=-\frac{DS}{V_{in} h} (C_{out} - C_{in})$$
+                                             <p>From these equations, we get the change in GSR concentration both inside and outside the nanoparticle.</p>
+                                             <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>
+                                             $$C_{oa}(t)=C_{out}\cdot e^{-k_dt}$$
+                                        </div>
+                                         <div id="nanomenu2" class="tab-pane fade">
+                                             <h3>Parameters</h3>
+                                             <p>We know all components of the diffusion constant (temperature, viscosity, natural constants) except for nanoparticle radius. In addition, we find the volume of the aqueous humor by literature data. Other parameters, such as surface area and volume, are determined by the radius.</p>
+                                             <h4>Determination of Diffusion Layer Dependence</h4>
+                                             <p>From literature research, we estimate that the diffusion layer is on the order of -11, based on details on turnover rates in the aqueous humor and lens (Toxic). After creating our initial model to guide the experiments, we then used the experimental data to revise our initial model, by altering this constant to -2.5*10^-11</p>
+                                             <p>For initial conditions, the concentration inside the nanoparticles start at an initial value, while the concentration outside the nanoparticles start at the natural concentration of GSR (see Model 2 collapsible).</p>
+                                            <h4>Parameters</h4>
+                                             <table class="table table-bordered" style='width: 70%;margin-left:15%;'>
+							             <caption style='caption-side:top;'><b>Table E: Parameters used for Differential Equations in Model 3</caption>
+                                         <thead>
+                                                    <td>Variable</td><td>Value</td>
+                                                    <td>Notes</td>
+                                                    <td>Source</td>
+                                        </thead>
+                                             <tbody>
+                                            <tr>
+                                                <td>Boltzmann Constant (kb)</td>
+                                                <td>$1.3806 \cdot 10^{23} \cdot m^2 \cdot kg \cdot s^{-2} \cdot K^{-1}$</td>
+                                                <td>Physical Constant</td>
+                                                <td></td>
+                                            </tr>
+                                            <tr>
+                                                <td>Temperature (T)</td>
+                                                <td>$273+37 K$</td>
+                                                <td>Body Temperature</td>
+                                                <td>Assumed</td>
+                                            </tr>
+                                            <tr>
+                                                <td>Viscosity (u)</td>
+                                                <td>$1.0 \cdot 10^{-4} Pa \cdot S $</td>
+                                                <td></td>
+                                                <td>Medicalopedia</td>
+                                            </tr>
+                                            <tr>
+                                                <td>Nanoparticle Radius</td>
+                                                <td>$200-400 nm$</td>
+                                                <td>Analyzed in model</td>
+                                                <td>Determined by SEM</td>
+                                            </tr>
+                                            <tr>
+                                                <td>Volume of Aqueous Humor (V1)</td>
+                                                <td>$2.5\cdot 10^{-4} L$</td>
+                                                <td>Constant</td>
+                                                <td>Medicalopedia</td>
+                                            </tr>
+                                            <tr>
+                                                <td>Volume of Nanoparticle (V2)</td>
+                                                <td>$10^{-7} L$</td>
+                                                <td></td>
+                                                <td>Estimate with Experimental Data from our experiments</td>
+                                            </tr>
+                                            <tr>
+                                                <td>Diffusion Layer</td>
+                                                <td>(1)$10^{-11} m$<br>(2)$2.5\cdot10^{-11} m$</td>
+                                                <td>Estimate, then revised upon experiments</td>
+                                                <td>(Fraunfelder 2008)</td>
+                                            </tr>
+                                            <tr>
+                                                <td>Surface Area</td>
+                                                <td>$4 \pi r^2$</td>
+                                                <td>Depends on radius</td>
+                                                <td></td>
+                                            </tr>
+                                            <tr>
+                                                <td>Degradation (kd)</td>
+                                                <td>$1.0\cdot10^{-5}$</td>
+                                                <td>Estimate, based on turnover rate of lacrimal fluids, in order of -5.</td>
+                                                <td>(Fraunfelder 2008)</td>
+                                            </tr>
+                                        </tbody>
+						          </table>
+                                        </div>
+                                         <div id="nanomenu3" class="tab-pane fade">
+                                               <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 $n\cdot p$, 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>
+                                             $$C_{total}(t)=\sum_{n=0}^\infty {C_{oa} (t-np \cdot)e^{-k_d(t-np)} \cdot u(t-np)}$$
+                                                <p>An example of the resulting $C_{total}(t)$ is shown in Figure D. </p>
+                                             <p>Our modeling equation bares a resemblence to Fourier series, but instead we use exponentials to model the concentration function. The analysis we take later is similar to how Fourier series are analyzed. </p>
+                                            <h3>Assumptions</h3>
+                                            <p>In this model, we made the following assumptions:
+                                            <ol>
+                                                <li><b>All nanoparticles are uniform.</b> All nanoparticle doses that are manufactured will be uniform.</li>
+                                                <li><b>GSR is delivered directly into the lens.</b>It is difficult to model the function of the lens or diffusion inside the eyes, so we assume almost all GSR that is delivered</li>
+                                                <li><b>There is no limit to the concentration of GSR that can be placed into a nanoparticle.</b>This would be an issue of manufacturing, although the concentrations we use are reasonably low to ensure that manufacturing is not a problem.</li>
+                                            </ol>
+                                             </p>
+                                        </div>
+                                         <div id="nanomenu4" class="tab-pane fade">
+                                             <h3>Analysis of Changing Variables</h3>
+                                             <p></p>
+                                             <p>We vary each variable, nanoparticle radius, concentration, and dose frequency, one at a time, while keeping the other two variables constant. </p>
+                                             <h4>Changing Radius</h4>
+                                             <div class="row">
+                                             </div>
+                                             <p>We find that changing the radius has little impact on the resulting graph, shown in Figure 4.D. Equilibrium is slightly decreased when radius is increased. We will ignore nanoparticle radius. We will use whatever range that is most convienient for manufacturers. For our purposes, we will use r = 200 nm.</p>
+                                             <p>Although we disregard nanoparticle radius, this simplification is only true in our desired range of 200 to 400 nm. Extremely small or large nanoparticles will show a difference in release. </p>
+                                             <div class="row">
+                                                     <figure class = "col-sm-6">
+                                                     <img src="https://static.igem.org/mediawiki/2016/3/31/T--TAS_Taipei--RadiusGSRChange.png">
+                                                    <figcaption class='darkblue'><b>Figure 4.D: Changing Radius. </b>As shown in this graph, when concentration and dose frequency are kept constant, changing nanoparticle radius results in essentially no change in the concentration graph. </figcaption>
+                                                 </figure>
+                                                 <figure class="col-sm-6">
+                                                     <img src="https://static.igem.org/mediawiki/2016/f/ff/T--TAS_Taipei--MultipleDose_ConcChange.png">
+                                                    <figcaption class='darkblue'><b>Figure 4.E: Changing Concentration. </b>When concentration is changed, its resulting equilibrium concentration increase proportionally. However, the time to reach equilibrium does not change. </figcaption>
+                                                 </figure>
+                                             </div>
+                                             <h4>Changing Concentration</h4>
+                                             <p>We find that changing the concentration impacts the equilibrium concentration. There is a direct relationship between GSR concentration inside the nanoparticles, and the equilibrium outside. Higher concentrations also make the graph more unstable, however, shown in a greater amplitude of oscillation in Figure 4.E sample graph is shown above.</p>
+                                             <h5>Changing Frequency</h5>
+                                             <div class="row">
+                                                 <figure class = "col-sm-8">
+                                                     <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>
+                                                 </figure>
+                                             </div>
+                                             <p>We find that changing the frequency does not impact equilibrium concentration, but does change the stability at equilibrium, as shown in Figure 4.F. The concentration oscillates at a greater amplitude about the equilibrium, which is undesirable, when frequency is too low. Therefore, daily doses are definitely preferred.</p>
+                                             <p>We graphed each of the three dependent variables as a function of the three independent variables, and found the quantitative relationship between them. <b>This engineering technique allows us to find an equation for the equilibrium concentration as a function of the three independent variables.</b></p>
+                                             <p>Notice that the time to reach equilibrium (related to the time constant) cannot be altered. See the two eyedrop appraoch to overcome this problem. </p>
+                                        </div>
+                                        <div id="nanomenu5" class="tab-pane fade">
+                                            <div class="row">
+                                                <div class="col-sm-6">
+                                                    <h3>Two Stage Eyedrop Approach</h3>
+                                            <h4>Explanation</h4>
+                                            <p><b>Problem: We cannot decrease the amount of time until the concentration reaches equilibrium, where full prevention is effective. </b></p>
+                                            <p><b>Solution: We propose the two stage eyedrop approach. For the first days of treatment, a higher concentration of eyedrop will be used before using a lower concentration.</b> This will speed up the time to reach equilibrium.</p>
+                                            <p>In the diagram, we wish to reach the low equilibrium (in blue) as soon as possible. Using the higher concentrated nanoparticles results in the red curve. By applying the higher concentrated nanoparticles in the first days, then switching to the lower concentrated nanoparticles afterwards, we follow the highlighted path. This allows us to reach equilibrium faster.</p>
+                                            <p>We need to figure out the concentration of GSR in naoparticles for the blue and red curves. The blue curve (eyedrop 2) requires the original results of our model (outside collapsible). The red curve (eyedrop 1) requires some calculations.</p>
+                                                </div>
+                                                <figure class = "col-sm-6">
+                                         <img src="https://static.igem.org/mediawiki/2016/a/a7/T--TAS_Taipei--Fig5Highlighted.jpg">
+                                        <figcaption class='darkblue'><b>Figure 4.8: Two Stage Eyedrop Approach. </b> Two nanoparticle designs are shown above, with high and low concentration. By applying high conc. eyedrops first until [GSR] reaches Low Eq, then switching to low conc. eyedrops to maintain Low Eq, this approach reaches equilibrium faster. </figcaption>
+                                    </figure>
+                                            </div>
+                                            <div class="row">
+                                                <div class="col-sm-12">
+                                             <h4>Finding the Concentration of Eyedrop 1</h4>
+                                            <p>We cannot change the shape of the concentration graphs, because we cannot change the amount of time to reach equilibrium. This means we can find a formula for the percent of GSR delivered. At equilibrium, the value is 1. By curve fitting an exponential to the graph, we find our "percent delivered" function. </p>
+                                            <p>The concentration depends on the desired amount of time to reach equilibriu, which we will call "time limit". By plugging the time limit into our percent function, we will know the percentage delivered at the time limit. We divide our goal concentration by this percentage, to find the equilibrium concentration of the red curve. Using the results our model, we can find the concentration of GSR in nanoparticles of eyedrop 1.</p>
+                                            <p>We built a functional calculator to find the concentrations of both eyedrops. This is an extention of the eyedrop provided at the bottom of the Model page.</p>
+                                        </div>
+                                            </div>
+                                            <div class="col-sm-12">
+                                        <h3 style="padding:0">Prevention</h3>
+                                        <script>
+                                            function round(value, decimals) {
+                                                return Number(Math.round(value+'e'+decimals)+'e-'+decimals);
+                                            }
+                                            calculateeeTwo = function(){
+                                                var XInputLOCSPTwo = document.getElementById("inputLOCSTwo").value;
+                                                var TimeLimit = document.getElementById("TimeLimit1").value;
+                                                var percentFunc =  1.001-1.027*Math.exp(-0.1717*TimeLimit);
+                                                var XCrystDamPTwo = -0.04559+0.3627*(XInputLOCSPTwo)-0.06248*Math.pow(XInputLOCSPTwo,2)+0.03313*Math.pow(XInputLOCSPTwo,3);
+                                                var XGSRPTwo = 171.9*Math.exp(-5.497*XCrystDamPTwo)+41.23*Math.exp(-0.955*XCrystDamPTwo)+27.01;
+                                                var XNPConcPTwo = (XGSRPTwo/10-1)/((0.04555-7.9*Math.pow(10,-6)*200));
+                                                var XEyedropPTwo = XNPConcPTwo/14.04;
+                                                var XResultPTwo = XEyedropPTwo*50/100;
+                                                XNPConcPid2.innerHTML = round(XNPConcPTwo,2);
+                                                XResultPid2.innerHTML = round(XResultPTwo,2);
+                                                XNPConcPid1.innerHTML = round(XNPConcPTwo/percentFunc,2)
+                                                XResultPid1.innerHTML = round(XResultPTwo/percentFunc,2);
+                                            }
+                                        </script>
+                                    <div class="row">
+                                        <div class="col-sm-6">
+                                        <span style="width:70%">LOCS Score Threshold:  </span><input id = "inputLOCSTwo" type="text" style="width:40%" value="2.5"><br>
+                                        <span style="width:70%">Time Limit (Days)  </span><input id = "TimeLimit1" type="text" style="width:40%">
+                                        <br><span style="font-size:13px">We guarentee that by applying this prevention eyedrop daily, your LOCS score will remain below your threshold for 50 years.</span>
+                                        <br><button onclick = "calculateeeTwo()">Calculate!</button><br>
+                                        <br>
+                                        </div>
+                                        <div class="col-sm-6">
+                                        <table class="table table-hover fixed" style="font:16px">
+                                            <col width="150px" />
+                                            <col width="150px" />
+                                            <col width="100px" />
+                                            <thead>
+                                                <tr>
+                                                    <th>Variable</th>
+                                                    <th>Eyedrop 1</th>
+                                                    <th>Eyedrop 2</th>
+                                                </tr>
+                                            </thead>
+                                            <tbody align="right">
+                                                <tr>
+                                                    <td>Nanoparticle Conc.</td>
+                                                    <td> <span id="XNPConcPid1">&nbsp;&nbsp;&nbsp;</span>&nbsp; uM</td>
+                                                    <td> <span id="XNPConcPid2">&nbsp;&nbsp;&nbsp;</span>&nbsp; uM</td>
+                                                </tr>
+                                                <tr>
+                                                    <td>Eyedrop Result</td>
+                                                    <td> <span id="XResultPid1">&nbsp;&nbsp;&nbsp;</span>&nbsp; mg/mL</td>
+                                                    <td> <span id="XResultPid2">&nbsp;&nbsp;&nbsp;</span>&nbsp; mg/mL</td>
+                                                </tr>
+                                            </tbody>
+                                        </table>
+                                        </div>
+                                                </div>
+                                    </div>
+                                        </div>
+                                     </div>
+                                </div>
+                                </div>
                          <h2 id="model4">Model 4: Eyedrop Prototype</h2>
                              <div class="row">
-                                 <div class="col-sm-12">
+                                 <div class="col-sm-8">
                                  <p>
                                      We have found a nanoparticle design to deliver GSR. We also need to model the function of eyedrops, to <b>determine the concentration of GSR-loaded nanoparticles to put in <u>eyedrops</u>, and analyze how sensitive the resulting system is.</b>
                                  </p>
-                                 </div>
+                                 <br><br>
-                            </div>
-                            <div class="row">
-                                <div class="col-sm-8">
                                  <h3>Bioavailability of GSR Delivery</h3>
                                  <p>
-                                     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.
+                                     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).
                                  </p>
-                                </div>
-                                </div>
-                            <div class="row">
-                                <div class="col-sm-8">
                                  <p>
-                                     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 (Schoenwald 1997). In the case of nanoparticles, which are much larger than chemical molecules, more is lost. (Clinical Ocular Toxicology)
+                                     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).
                                  </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)
+                                     <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>
                                  </div>
+                                <figure class = "col-sm-4">
+                                         <img src="https://static.igem.org/mediawiki/2016/9/91/T--TAS_Taipei--Figure6_Model.jpg">
+                                        <figcaption class='darkblue'><b>Figure 4.9: Bioavailability. </b>For every 1 g of nanoparticles in the eyedrops, only 14.04 ug of them get through the cornea and into the lens. </figcaption>
+                                </figure>
                              </div>
+                                 <br><br>
                              <div class="row">
-                                 <div class="col-sm-8">
+                                 <div class="col-sm-12">
                                      <h3>Necessary Adjustments in Eyedrops</h3>
                                  <p>
-                                     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.
+                                     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.
                                  </p>
-                                    <p>[Calculations]</p>
                                  <p>
-                                     We conclude that we need 5.48 mM of GSR in nanoparticles to maintain 43.5 uM GSR and thus 2.5 LOCS.
+                                     We conclude that we need <b>5.48 mM of GSR in nanoparticles in our final eyedrop to maintain 43.5 uM GSR and thus 2.5 LOCS.</b>
                                  </p>
                                  </div>
@@ Line 1,018: / Line 1,504: @@
                              </div>
                              <div class="row">
-                                 <div class="col-sm-8">
+                                 <div class="col-sm-12">
                                      <h3>Sensitivity Analysis: Revisiting Nanoparticles Model</h3>
                                  <p>
-                                     The mechanism for eyedrop delivery is complex, and there are variances in the bioavailability depending on the conditions of the eye. The thickness of the cornea, lens, other eye diseases, age, and even time of day may impact the bioavailability of the drug. We use a stochastic model to simulate Model 3 again, but this time, add a degree of variance.
+                                     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.
                                      </p>
                                  <p>
@@ Line 1,032: / Line 1,518: @@
                                  </div>
+                            </div>
+                            <div class="row">
+                                <figure class = "col-sm-12">
+                                         <img src="https://static.igem.org/mediawiki/2016/5/5f/T--TAS_Taipei--StochasticComp.png">
+                                        <figcaption class='darkblue'><b>Figure 4.10: Stochastic Model.</b> This model takes into account randomness and uncertainty related to the conditions of the eye. The average case (deterministic) is shown in blue, while each test trial is shown in various colors. Clearly, daily eyedrops is superior as this decreases the sensitivity of our model.</figcaption>
+                                </figure>
+                            </div>
+                                <br><br>
+                                <button class="accordion"><img src ="https://static.igem.org/mediawiki/2016/d/d2/T--TAS_Taipei--clickmeorange.gif" width:"75%" height:"75%">Model 4 Details: Basic Stochastic Analysis</button>
+                                <div class="panel">
+                                <div class="accordionmenu1" class ="col-sm-12" >
+                                         <div id="gsrhome" class="tab-pane fade in active">
+                                             <h3>Stochastic Analysis</h3>
+                                             <p>Mathematica provides a built-in process for stochastic analysis. We try to model our percent function (from Model 3), which calculates the ratio of current GSR versus final equilibrium GSR. Our percent function is:
+                                             $$P(t)=1-1.027*e^{-0.1717t}$$
+                                            where t is in days.</p>
+                                             <p>Our stochastic model is based off the following differential equation, written in differential form:
+                                                 $$dC_R=dP + \sigma \frac{dP}{dt} dw(t)$$
+                                                 where $C_R$ is the concentration ratio of current to final at equilibrium (like $P$, ranges from 0 to 1), $P$ is the percent function, $\sigma$ is the standard deviation of delivery, and $w(t)$ approximates the stochastic Wiener stochastic process.</p>
+                                             <p> The standard deviation is found from the square root of the variance divided by the equilibrium to get a number between 0 and 1, multiplied by a factor related to the frequency. The greater the frequency, the less GSR there is to every dose of eyedrop, so the standard deviation would decrease, and vice versa.</p>
+                                             <p>For full details, please see the research paper: Hanson, F.B. (2007).Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis and Computation. Chicago, IL:The Society for Industrial and Applied Mathematics. </p>
+                                        </div>
+                                </div>
+                                </div>
+                                <br><br>
+                            <div class="row">
+                                <div class="col-sm-12">
+                                    <h3>Insights into Manufacturing & Clinical Use</h3>
+                                    <p>
+                                        Using the details from Models 1-4, we offer the following suggestions for manufacturing our eyedrops, as well as prescribing them to patients.
+                                        <ol>
+                                            <li>Frequent doses of low concentration eyedrops are more stable than occasional doses of high concentration eyedrops. (Model 3)</li>
+                                            <li>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)</li>
+                                            <li>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) </li>
+                                            <li>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)</li>
+                                            <li>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)</li>
+                                        </ol>
+                                    </p>
+                                </div>
+                            </div>
+                        <h1 id="treatment">Treatment</h2>
+                            <div class="row">
+                                <div class="col-sm-12">
+                                <p>
+                                    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. </p>
+                                    <p>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.</p>
+                                    <p>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.</p>
+                                </div>
                              </div>
+                        <br><br>
@@ Line 1,157: / Line 1,714: @@
-                                         <span style="width:70%">LOCS Score Threshold:  </span><input id = "inputLOCSTget" type="text" style="width:30%">
+                                         <span style="width:70%">Your current LOCS Score:  </span><input id = "inputLOCSTget" type="text" style="width:30%">
                                          <br><span style="font-size:13px">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.</span>
@@ Line 1,224: / Line 1,781: @@
                                     </div>
                              </div>
+                             <div class="row">
+                                 <div class="col-sm-12">
+                                    <h2 id="software">Software</h2>
+                                    <p>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. </p>
+                                    <p>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.</p>
+                                    <a href="https://docs.google.com/spreadsheets/d/1kOSX_8kB_JrRxCTKfz8-xIw6D3ocg9k6pY2wdRickec/edit?usp=sharing"><button type="button" class="btn btn-primary btn-lg">Click to visit our Nanoparticle Customizer!</button></a>
+                                </div>
+                            </div>
                              <div class="row">
                                  <div class="col-sm-12">
                                      <h3>Conclusion</h3>
-                                     <br><br><br><br><br><br>
+                                     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.
+                                    <br><br><br>
                                  </div>
                              </div>
+                            <div class="row">
+                                <div class="col-sm-12">
+                                    <h3>Citation</h3>
+                                    <br>
+                                    <p>Adimora, N.J., Jones, D.P., & Kemp, M.L. (2010). A model of redox kinetics implicates the thiol proteome in cellular hydrogen peroxide responses. Antioxidants & Redox Signaling, 13(6), 731-43</p>
+<p>Ault, A. (1974). An introduction to enzyme kinetics. Journal of Chemical Education,51(6), 381, DOI: 10.1021/ed051p381</p>
+<p>Bonate, P.L., & Howard, D.R. (2005) Pharmacokinetics in Drug Development Volume 2: Regulatory and Development Paradigms. American Association of Pharmaceutical Scientists </p>
+<p>CALVO, P., ALONSO, M. J., VILA‐JATO, J. L., & ROBINSON, J. R. (1996). Improved ocular bioavailability of indomethacin by novel ocular drug carriers. Journal of Pharmacy and Pharmacology, 48(11), 1147-1152.</p>
+<p>Chylack, L.T., Wolfe, J.K., Singer, D, M., Leske, C., Bullimore, M, A., Bailey, I.L., Friend, J., McCarthy, D., & Wu, S. (1993). The Lens Opacities Classification System III. The Longitudinal Study of Cataract Study Group. American Medical Association. 111(6), 831-36.</p>
+<p>Cui, X. L., & Lou, M. F. (1993). The effect and recovery of long-term H 2 O 2 exposure on lens morphology and biochemistry. Experimental eye research, 57(2), 157-167.</p>
+<p>Dominguez-Vincent, A., Birkeldh, U., Carl-Gustaf, L., Nilson, M., Brautaset, R., & Al-Ghoul. K.J. (2016).Objective Assessment of Nuclear and Cortical Cataracts through Scheimpflug Images: Agreement with the LOCS III Scale. PLoS One.11(2), doi:  10.1371/journal.pone.0149249</p>
+<p>Fraunfelder, F.T., Fraunfelder F.W., & Chambers, W.A.(2008) Clinical Ocular Toxicology: Drug-Induced Ocular Side Effects. Saunders </p>
+<p>Gaudana, R., Ananthula, H.K., Parenky, A., Mitra, A.K. (2010). Ocular Drug Delivery. AAPS Journals, 12(3), 348-360 doi:  10.1208/s12248-010-9183-3</p>
+<p>Griffiths, W.J., Khalik, J.A., Crick, P.J., Yutuc, E.,  & Wang, Y. (2016). New methods for analysis of oxysterols and related compounds by LC–MS. Journal of Steroid Biochemistry and Molecular Biology, 162, 4-26, http://dx.doi.ordg/10.1016/j.jsbmb.2015.11.017</p>
+<p>Jones, D.P. (2008). Radical-free biology of oxidative stress. American Journal of Physiology. Cell Physiology,  295(4), 849-68</p>
+<p>Lux, A., Maier, S., Dinslage, S., Suverkrup, R., & Diestelhorst, M.(2003). A comparative bioavailability study of three conventional eye drops versus a single lyophilisate. British Journal of Ophthalmology, 87(4), 436-440.</p>
+<p>Martinovich, G.G., Cherenkevich, & S.N., Sauer. (2005). Intracellular redox state: towards quantitative description. European Biophysics Journal, 34(7), 937-42</p>
+<p>Ng, C.F., Schafer, F.Q., Buettner, G.R., & Rodger, V.G.(2007).The rate of cellular hydrogen peroxide removal shows dependency on GSH: mathematical insight into in vivo H2O2 and GPx concentrations. Free Radical Research, 41(11), 1201-11</p>
+<p>Norlin, M., Andersson, U., Bjorkhem, I., & Wikvall, Kjell. (2000). Oxysterol 7α-Hydroxylase Activity by Cholesterol 7α-Hydroxylase (CYP7A)*. The American Society for Biochemistry and Molecular Biology, J. Biol. Chem.  34046-34053. doi:10.1074/jbc.M002663200 </p>
+<p>Salvador, A., Savageau, M.A. (2005). Evolution of enzymes in a series is driven by dissimilar functional demands. National Academy of Sciences of the USA, 103(7), 2226-2231.</p>
+<p>Saravanakumar, S., Eswari, A., & Rajendran, L. (2015). Mathematical analysis of immobilized enzyme with reaction-generated pH change on the kinetics using Asymptotic methods.International Journal of Advanced Multidisciplinary Research, 2(8), 98-119</p>
+<p>Spector, A., Wang, G.M., Wang, R.R., Garner, W.H., & Moll, H. (1993). The prevention of cataract caused by oxidative stress in cultured rat lenses. I. H2O2 and photochemically induced cataract.Current Eye Research, 12(2), 163-79</p>
+<p>Pi, N. A., Yu, Y., Mougous, J. D., & Leary, J. A. (2004). Observation of a hybrid random ping‐pong mechanism of catalysis for NodST: A mass spectrometry approach. Protein science, 13(4), 903-912.</p>
+<p>Tajmir-Riahi, H.A., Nafisi, Sh., Sanyakamdhorn, S., Agudelo, D., & Chanphai, P. (2014). Applications of chitosan nanoparticles in drug delivery. Methods in Molecular Biology, 165-84,  doi: 10.1007/978-1-4939-0363-4_11</p>
+<p>Torchilin, V.P.(2006). Nanoparticles as Drug Carriers. Imperial College Press</p>
+<p>Wang, J.J., Zeng, Z.W., Xiao, R.Z., Xie, T., Zhou, G.L., Zhan, X.R., & Wang, S.L. (2011). Recent advances of chitosan nanoparticles as drug carriers. Int J Nanomedicine, 6, 765-774 doi:  10.2147/IJN.S17296</p>
+<p>Wong, M.M., Shukla, A.N., & Munir, W.M.(2012). Correlation of corneal thickness and volume with intraoperative phacoemulsification parameters using Scheimpflug imaging and optical coherence tomography. Journal of Cataract & Refractive Surgery, 40(12), 2067-75 doi: 10.1089/ars.2009.2968.</p>
+                                </div>
+                            </div>

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

Latest revision as of 03:49, 3 December 2016

C◎UNTERACTS

Model

Introduction

Guiding Questions

Focus of Models

Prevention: GSR Function

Model 1: Crystallin Damage

Measurement of Cataract Severity

LOCS to Absorbance: Literature Data

Absorbance Equivalence to Crystallin Damage: Experimental Data

Conclusion

Motivation

Quantification of Crystallin Damage

Data Documentation

LOCS to Absorbance

Absorbance to Crystallin Damage

Assumptions of Model 1

Data Analysis

Using Experimental Data for Model

Model Adjustment

Discussion

Error Analysis

Significance of Model

Model 2: GSR Pathway

Chemical Kinetics Model: Differential Equations

Blackbox Approach: Testing GSR Impact

Crystallin Damage vs. GSR Level

Conclusion

Introduction

Enzyme Kinetics

Differential Equations

Parameters & Initial Conditions

Procedure

Assumptions

Results

Confirmation of Initial Value of GSR

Prevention: Prototype Function

Model 3: Nanoparticle Protein Delivery

Single Dose: Change in GSR Concentration

Comparison with Experimental Data

Multiple Dose: Change in GSR Concentration

A Two Stage Eyedrop Approach

Generalized Nanoparticles: Customizer

Conclusion

Introduction

Single Dose

Noyes-Whitney Equation

Differential Equations

Protein Degradation

Parameters

Determination of Diffusion Layer Dependence

Parameters

Multiple Dose

Assumptions

Analysis of Changing Variables

Changing Radius

Changing Concentration

Changing Frequency

Two Stage Eyedrop Approach

Explanation

Finding the Concentration of Eyedrop 1

Prevention

Model 4: Eyedrop Prototype

Bioavailability of GSR Delivery

Necessary Adjustments in Eyedrops

Sensitivity Analysis: Revisiting Nanoparticles Model

Stochastic Analysis

Insights into Manufacturing & Clinical Use

Treatment

CALCULATOR

Prevention

Treatment

Software

Conclusion

Citation

Prevention

GSR Eyedrop

Treatment

LOCS: 0