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

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

Relation to Experiments

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

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

Relation to Overall Project

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

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

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

1. Lens Optical Cataract Scale (LOCS): Physicians use this scale, from 0 – 6, to grade the severity of cataracts.
2. Absorbance at 397.5 nm: This is the experimental method, used by our team in the lab (c.d.)
3. Crystallin Damage: This is a chemical definition. We quantify cataract severity as a function of how much oxidizing agents there are, as well as how long crystalline is exposed to oxidizing agents.

Measurement of Cataract Severity

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

Absorbance Equivalence to Crystallin Damage: Experimental Data

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

Conclusion

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

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

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

Blackbox Approach: Testing GSR Impact

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

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

Crystallin Damage vs. GSR Level

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

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

Conclusion

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

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. To maximize delivery efficiency to the lens, we encapsulate GSR in chitosan nanoparticles. We create a model of how GSR concentration changes in the lens over time after GSR-loaded are delivered into the lens. From this model, we can 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.

Nanoparticles are diffused to the lens through the cornea. Nanoparticle Diffusion can be modelled with the Noyes-Whitney equation, which takes into account the volume, surface area, and radius of nanoparticles, the temperature and viscosity of the medium, and the thickness of the diffusion layer (which is related to the type of nanoparticle). Most parameters are found through literature, while some are estimated (see collapsible).

Using these parameters, we build a differential equation model for the impact of a single dose of nanoparticles over time. We get two curves, concentration of GSR in the nanoparticles, and GSR release from nanoparticles, over time.

In addition, all protein degrade over time, so we apply an degradation factor to the amount of GSR diffused out of the nanoparticle into the aqueous humor before it enters the lens. using knowledge of turnover rates in the aqueous humor. After applying the degradation factor, the results of the single dose model are shown in Figure 1.

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.

Single Dose: Change in GSR Concentration

We alter the concentration of GSR inside the nanoparticle, to understand the resulting change in GSR concentration in the aqueous humor over time. As shown in Figure 2, for the first few days, GSR diffusion is fast due to the high concentration gradient between the inside and outside of the nanoparticle. Then, as diffusion slows, degradation causes the concentration to be restored back to the initial. The concentration inside the nanoparticle only impacts the maximum increase in the aqueous humor, but does not alter the rate equilibrium is restored.

Multiple Dose: Change in GSR Concentration

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:

• GSR equilibrium concentration equal to amount we desire (i.e. 43.5 uM from Model 2)
• Stability of concentration at equilibrium (Model 4 goes into deeper depth regarding sensitivity)
• Time to reach equilibrium (time for full prevention to come into effect)

To do so, we can alter different variables: GSR concentration in nanoparticles, nanoparticle radius, and dose frequency. For a full analysis of how each variable impacts the concentration function, see the collapsible. Below is a summary of the results:

We find the optimal combination of parameters is: _____________.

A Two Stage Eyedrop Approach

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 two-step eyedrop approach, of two differing concentrations, to decrease the time needed for full prevention. A full explanation is found in the collapsible.

Generalized Nanoparticles: Customizer

Although the model we created was made for drug delivery into the eye, by changing relevant parameters, the model can be generalized for any type of drug delivery. With the analysis performed in the single and multiple nanoparticle dose models, we build the following calculators:

Conclusion

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