# Model

Cataract prevention occurs over 50 years, so we cannot perform experiments directly on the long-term impact of adding GSR or CH25H. Computational biology allows us to predict cataract development in the long-term. **These models allow our team to: (1) understand the impact of adding GSR-loaded nanoparticles into the lens over a 50 year period and (2) design a full treatment plan on how to prevent and treat cataracts with our project. Therefore, the results of our model are essential in developing a functional prototype. **

For clarity, we will discuss each model in detail with respect to prevention (using GSR) only. At the end, we extend these results to treatment. In addition, we include collapsibles for interested readers and judges, in order to fully document our modeling work (eg. assumptions, mathematics, and full analysis) while keeping the main page clear with basic points only.

If you are interested in the programming/source codes of these computational models, please contact **Avery Wang**, at averyw17113532@tas.tw or averyw09521@gmail.com.

## Introduction

### Guiding Questions

How much GSR to maintain in the lens? (GSR Function)

How to maintain that amount of GSR using nanoparticles and eyedrops? (Delivery Prototype)

### Focus of Models

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

# Prevention: GSR Function

## Model 1: Crystallin Damage

The amount of damage to crystallin by H_{2}O_{2} 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)

**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.**

LOCS | Absorbance (@397.5 nm abs units) |
Crystallin Damage (M-h) |
---|---|---|

0.0 | 0.0000 | 0.0000 |

0.5 | 0.0143 | 0.1243 |

1.0 | 0.0299 | 0.2878 |

1.5 | 0.0497 | 0.4697 |

2.0 | 0.0751 | 0.6949 |

2.5 | 0.1076 | 0.9883 |

3.0 | 0.1492 | 1.3747 |

4.0 | 0.2706 | 2.5259 |

5.0 | 0.4691 | 4.3472 |

### Conclusion

To guarantee that surgery is not needed for 50 years, we need to **limit crystallin damage to 0.9883 units.** If crystallin damage goes above this threshold, then surgery is needed. This is the crystallin damage threshold for a LOCS 2.5 cataract.

## Model 2: GSR Pathway

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

### Chemical Kinetics Model: Differential Equations

By various enzyme kinetics laws, fully documented in the collapsible, we build a system of 10 differential equations based on 6 chemical reactions (Ault 1974, Pi 2004). All parameters, constants (Table B), and initial conditions (Table C) are based off literature data (Ng 2007, Melissa 2012, Saravanakumar 2015, Salvador 2005, Adimora 2010, Jones 2008, Martinovich 2005). Estimates made are also shown with assumptions and reasoning. The details are shown in the collapsible for interested readers.

### Blackbox Approach: Testing GSR Impact

Our modeling approach is seen in Figure 4.2, where vary the input, Initial GSR concentration, holding all other variables constant, and numerically solve for the amount of hydrogen peroxide over time. We can find the amount of crystallin damage accumulated over 50 years if different levels of GSR is maintained, which we graph in Figure 4.3.

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

### Crystallin Damage vs. GSR Level

According to literature data and our model, the naturally occurring GSR concentration is 10 uM (Fraunfelder 2008). All curves show crystallin damage decreasing as GSR levels are increased, which supports both research and experimental data, and suggests that this prototype is effective in preventing crystallin damage. **However, GSR levels need to be raised significantly, up to 40+ uM from the natural 10 uM of GSR in order to show long-term protection. **

Figure 4.3 shows the amount of GSR we need to maintain for 50 years in order to prevent a LOCS cataract of a certain severity. The row of interest is LOCS 2.5, the threshold for surgery. Notice that we say *“maintain”* the level of GSR. This level needs to be constant at all times for 50 years for full prevention. The delivery of GSR to maintain this level is discussed in Model 3.

### Conclusion

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

# Prevention: Prototype Function

## Model 3: Nanoparticle Protein Delivery

To maximize delivery efficiency to the lens, we encapsulate GSR in chitosan nanoparticles (Wang 2011, Tajmir-Riahi 2014). From Models 1-2, we have found the necessary concentration of GSR that needs to be maintained in the lens. Now we design nanoparticles that will maintain those amounts. **We build a model find how nanoparticles release GSR at appropriate rates to control the amount of GSR in the lens, and find the best engineered design for nanoparticles.**

### Single Dose: Change in GSR Concentration

In finding the best engineered design, we take into account variables such as nanoparticle radius and concentration. We build a differential equation model for the impact of a single dose of nanoparticles over time. To generalize the model, instead of using absolute concentrations, we use relative concentration, with respect to the natural amount, or initial amount of GSR in the lens. The full mathematics and details can be found in the collapsible.

We get two curves, the concentration of GSR outside nanoparticles subjected to degradation (Figure 4.4), and the release of GSR from nanoparticles (Figure 4.5), over time. **This allows us to predict nanoparticle delivery rates before we perform the actual experiments (Link)**

### Comparison with Experimental Data

Yet in our model, we do not know the thickness of the nanoparticle diffusion layer. **After performing experiments, we can use measurements of our prototype device to find this thickness, and refine our model.** A direct comparison of our model with our experiment data is shown in Figure 4.5.

### Multiple Dose: Change in GSR Concentration

Each dose of nanoparticles, represented in the Single Dose model, can be repeated to create the Multiple Dose model. Below is a graph of GSR concentration over time when multiple doses of nanoparticles are added.

In Figure 4.6, all curves approach equilibrium, after which the concentration oscillates about equilibrium. We have three goals, in order of importance for best nanoparticle design:

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

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

Independent Variable | Time to Reach Equilibrium | Equilibrium Concentration | Stability |
---|---|---|---|

Concentration | No impact | Proportional Increase | Slight Decrease |

Radius | No impact | Very Slight Decrease | Very Slight Decrease |

Dose Frequency | No impact | No impact | Increase |

We find the optimal combination of parameters is **daily doses** (high frequency) of **200 nm** nanoparticles (small), with a concentration of **76.88 uM of GSR** in the nanoparticles (concentration).

The calculator at the end of the page can be altered, so if the LOCS threshold is not 2.5, a new concentration can be calculated.

### A Two Stage Eyedrop Approach

As shown in Table 2, we cannot alter the time to reach equilibrium, or reach full prevention. As supported by literature research, the time to reach equilibrium is a property of the lens that we cannot change (Fraunfelder 2008). However, we propose a **two-stage eyedrop approach, of two differing nanoparticle concentrations**, to decrease the time needed for full prevention. A full explanation is found in the collapsible.

### Generalized Nanoparticles: Customizer

We built a full nanoparticle customizer, which generalizes the model to beyond delivery into the eye, found at the end of the page (Software). **We hope that other iGEM teams who are interested in nanoparticle drug delivery can utilize this customizer to help them develop their own prototype.**

### Conclusion

We find the optimal combination of parameters is **daily doses** (high frequency) of **200 nm** nanoparticles (small), with a concentration of **76.88 uM of GSR** in the nanoparticles (concentration).

## Model 4: Eyedrop Prototype

We have found a nanoparticle design to deliver GSR. We also need to model the function of eyedrops, to **determine the concentration of GSR-loaded nanoparticles to put in eyedrops, and analyze how sensitive the resulting system is.**

### Bioavailability of GSR Delivery

The eye is well protected from foreign material attempting to enter the eye. The corneal epithelium is the most essential barrier against topical drugs in eyedrops, and as a result, much of drugs in eyedrops are lost in tear drainage (Lux 2003).

Bioavailability describes the proportion of the drug that reaches the site of action, regardless of the route of administration. For example, it is estimated that only 1-5% of an active drug with small solutes in an eyedrop penetrates the cornea (Bonate 2005). In the case of nanoparticles, which are much larger than chemical molecules, more is lost (Fraunfelder 2008).

**The results show that the bioavailability of nanoparticles is about 1.404 x 10 ^{-3}%,** which means that for every gram of GSR (or any drug) we place into nanoparticles, approximately 14.04 ug of the drug reach the aqueous humor.

**The variance is 2.34 ug/g.**(Calvo 1996)

### Necessary Adjustments in Eyedrops

To ensure that sufficient concentrations of GSR are delivered, we must place an excess of GSR. To determine how much, we simply divide the concentration of GSR in nanoparticles we found in Model 3 by the fraction of GSR that reaches the aqueous humor. This result is programmed in our calculator below.

We conclude that we need **5.48 mM of GSR in nanoparticles in our final eyedrop to maintain 43.5 uM GSR and thus 2.5 LOCS.**

### Sensitivity Analysis: Revisiting Nanoparticles Model

The mechanism for eyedrop delivery is complex, and there are variances in the bioavailability depending on the conditions of the eye (Fraunfelder 2008). The thickness of the cornea, lens, other eye diseases, age, and even time of day may impact the bioavailability of the drug (Gaudana 2010). We use a stochastic model to simulate Model 3 again, but this time, add a degree of variance. The result is shown in Figure 4.10.

The variance is impacted by the frequency of eyedrops. By giving eyedrops more frequently with less amounts given each time, the variance is decreased.

Ideally, we wish to deliver 100% of the GSR concentration of the amount found in Model 2 (43.5 uM). Because of variance, the actual amount maintained in the lens is different, shown in Figure 5. The full details and mathematics of the stochastic model can be found in the collapsible.

### Insights into Manufacturing & Clinical Use

Using the details from Models 1-4, we offer the following suggestions for manufacturing our eyedrops, as well as prescribing them to patients.

- Frequent doses of low concentration eyedrops are more stable than occasional doses of high concentration eyedrops. (Model 3)
- Cataract severity is extremely sensitive to the amount of GSR concentration maintained. If this value falls below 43.5 uM even by a little, as shown in Model 2, cataracts may develop. (Model 2)
- When manufacturing, there should be a necessary upward adjustment, because even with daily eyedrops, some simulated trials resulted in less than 90% of GSR delivered. (Model 4)
- Cataract prevention is only fully effective after around 28 days of using the prevention eyedrop. (Model 3) During that time, further cataract damage may take place. The suggested order of treatment should be: start with GSR eyedrops until full prevention is in effect, the use 25HC eyedrops to reverse any existing cataract. Finally, stop 25HC eyedrop use, while continuing GSR eyedrops. (Model 1)
- To speed up the time for full prevention to take place, a two eyedrop approach to quickly deliver sufficient GSR should be used. (Model 4)

# Treatment

We use the results from our previous models, and apply them to treatment. The process is almost the exact same as that of Prevention. The only difference is that our treatment protein, CH25H, reverses cataract damage (Griffiths 2016). We find the exact concentration of CH25H to reverse a cataract of a given LOCS score. The delivery models are unchanged, with the exception that the concentration of protein delivery will be different.

We use the results of Model 1 to calculate the LOCS equivalent crystallin damage we need to reverse (“negative crystallin damage”). Then we use experimental results to calculate the concentration of CH25H needed to reverse the cataract. We do not use Model 3, as this is a one-time treatment. After applying the results of Model 4, we can find the final concentration needed in CH25H eyedrops.

We propose eyedrops with 0.8 mg/mL CH25H. The number of drops needed for treatment depends on a patient's current LOCS score, and is calculated in the software tool below.

## CALCULATOR

### Prevention

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

Prevention Results

Variable | Value | Source |
---|---|---|

Allowable LOCS | ||

Crystallin Damage | c.d. | Model 1 |

GSR Maintained | uM | Model 2 |

Nanoparticle Conc. | uM | Model 3 |

Eyedrop Conc. | mM | Model 4 |

Eyedrop Result | mg/mL |

### Treatment

Your current LOCS Score:By applying the following treatment, leaving an hour before each dose of eyedrops, we guarentee that it will lower your LOCS score to essentially 0.

Treatment Results

Variable | Value | Source |
---|---|---|

Allowable LOCS | ||

Crystallin Damage | c.d. | Model 2 |

Absorbance | a.u. | Model 1 |

CH25H | uM | Model 5 |

Eyedrop Conc. | uM | Model 4 |

Eyedrop Result | mg/mL | Model 4 |

# of Eyedrops | drops | (of 0.8 mg/mL eyedrop) |

## Software

We built a nanoparticle customizer, which allows you to track the concentration and rates of drug delivery to any part of the body using nanoparticles. You can customize your own design of nanoparticles, and analyze its function inside the body.

This computational software can be used by future iGEM teams who are interested in using nanoparticles to efficiently deliver their synthesized proteins. The calculational tool is programmed on a Google Spreadsheet. Click the button below to visit the spreadsheet. Please make a copy of the spreadsheet to freely use it.

### Conclusion

The models allowed us to extrapolate short-term experimental data to the long-term, to over 50 years, the duration for cataracts to form. In Models 1-2, with the Cataract Lens Experiments on our synthesized protein GSR (and CH25H), we found the amount of synthesized protein needed in the lens over 50 years. In Models 3-4, with the experimental results of a single dose of nanoparticle release, we simulate multiple doses to see the overall change in GSR concentration in the lens over 50 years. We calculate the exact concentrations of our eyedrop prototype, to prevent a LOCS 2.5 cataract from developing so surgery is not needed. With our predictions and simulations of cataract treatment, we offered insights into how the product should be manufactured and used in clinics. We also programmed a nanoparticle customizer to allow the results of these models to be generalized to all drug delivery iGEM projects.### Citation

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