Experiment alone is not enough to prove the effectiveness of Eye kNOw. By building mathematical models with scientific theories, we’re able to understand how contact lens deformation induces bNOS production and further delivers nitric oxide into the eye.

As aforementioned, we aim to provide a new treatment that can release ocular hypotensive agents (nitric oxide) according to patients’ IOP in a contact lens system—Eye kNOw. Eye kNOw contains a designed chamber filled with L-arginine, IPTG, and our engineered bacteria. Here are the three main principles we used to design our contact lens:

1. bNOS produced by our engineered bacteria turns L-arginine into NO.

2. Different concentrations of IPTG induces different production rates of bNOS.

3. The proportional relationship between IOP and cornea’s radius of curvature.

Below are the steps showing how it works:

1. IOP elevates, causing the cornea's radius of curvature to change.

2. Chamber’s volume decreased due to the deformation of the cornea.

3. The semipermeable chamber only allows water and gas to pass. Therefore, the concentration of IPTG inside the chamber elevates.

4. Elevated IPTG leads to higher production rate of NOS by engineered bacteria.

5. The more NOS produced, the more L-arginine turned into NO.

6. Finally, more NO is released into the patients’ eyes.

We will need to set up two models: cornea deformation model and NO ocular delivery model. WIth the two models above, we can calculate the efficiency of Eye kNOw.

1. To set up a correct model that can mimic nitric oxide ocular delivery system.

2. To set up a correct model that can calculate the deformation of contact lens.

3. TTo calculate the efficiency of Eye kNOw, and prove that Eye kNOw will work effectively.

This model is used to predict the deformation of our contact lens under varying intraocular pressure (IOP), and research suggested that the radius of curvature of cornea increases linearly with respect to the increment of IOP, and there are no known compound to serve as a suitable biomarker that is able to be detected without invasion into the eyeball when the IOP varies, we took advantage of it and designed Eye kNOw. (See Description page)

Despite research showing how the cornea deflects when IOP changes, the pressure exerted on the contact lens while being worn is not fully studied, not to mention the volume difference of contact lens with respect to different IOP. Therefore, we assumed the contact lens to fit on the cornea perfectly, the deformation of contact lens sticks with the cornea, and the contact lens remained in the shape of sphere during the whole process of deformation, and, lastly, a static model during IOP elevation.

Considering the force equilibrium equation between the pressure of fluid and the membrane (cornea) in the section, as you can see in the figure below, we would be able to obtain equation (1)

According to Hooke’s Law, we have (2)

Under proportional limit, the radius difference - ΔR, is given by (3)

From (1), (2), (3), we obtain (4)

For a thick membrane, which means the thickness of the membrane is too large to be neglected in comparison to the radius. Thus, we have a constant term that is related to the poisson ratio, ν, in the equation (5). [1] [2]

E: Elastic modulus of the membrane (cornea of porcine in this case).

t: Thickness of the membrane (cornea of porcine ).

Notice that the p in (4) and (5) represents the pressure difference with respect to the initial pressure (IOP difference) instead of the pressure itself. We adopted the initial IOP to be 10 mmHg.

By equation (5), we predict the relation between IOP and the radius difference, or the strain, is linear.(See Proof of concept: step 1)

The volume of the ring-like compartment in Eye kNOw is calculated by the same method of the volume of revolution in calculus. Volume of compartment equals 4.4 cubic millimeters.

The volume difference is given by the elongation of the part above the compartment in meridional direction, which is given by the formula list below:

while

and

By doing so, the ratio of volume difference is approximated to be 1% when the IOP has an increment of 1 mmHg.

Eye is a complicated organ with various tissues. In other ocular delivery models, they consider the whole eye as one compartment since their drugs are stable and large enough that the difference of tissues can be ignored. However, we use NO as our drug, which is small and unstable. Thus, we need to set up a new model to simulate NO ocular delivery system.

Eye structure can be divided into three main compartments: cornea, anterior chamber, and posterior chamber. Target site of NO is trabecular meshwork, which is located at the posterior angle of anterior chamber. We simplify the eye structures into one dimension as below:

Since the tissue characteristics of the three compartments varies a lot, we need to calculate them separately by different partial differentiation equations (PDEs).

First, we calculated the initial state of NO distribution in the eye before the production of NO by Eye kNOw. After ensuring the initial state, we can calculate the NO distribution after the production of NO by Eye kNOw, which is a formula of position and time. Before all these things, we should set up the PDEs that can describe the distribution of NO. Refer table below for abbreviations and variables:

1. Setting up PDEs:

PDEs are used to describe the factors that will affect the concentration of NO. Factors are listed below:

(1) Degradation

The two main factors that will cause degradation of nitric oxide are Hemoglobin and oxygen. Hemoglobin doesn’t exist in the eye system, thus we only need to consider oxygen to calculate the amount of nitric oxide degradation.

According to papers, the formula can be written as below:

(2) Diffusion

By Fick's second law, the diffusion formula can be written as below:

(3) Endogenous production

Since aqueous humor has an initial concentration of NO around 53.4uM, there should exist endogenous NO production. There are three different types of NOS in human eyes: e-NOS, n-NOS, and i-NOS.

e-NOS and n-NOS work constantly, which are expressed on iris, cornea, vascular endothelium, etc. i-NOS only works when inflammation happens, which is not a common symptom for glaucoma, thus we can ignore it. We assume that these NOS produce NO in a constant rate, so the formula can be written as below:

(4) Convection

There’s a flow of aqueous humor in the anterior chamber, which is 2.4 uL/min. Convection will affect the distribution of nitric oxide, which can be written as below:

Combining the factors listed above, the PDE for describing the distribution of NO can be written as below:

To make the calculation easier, we need to simplify Equation 1 into homogeneous form.

First, since the concentration of oxygen can be maintained by oxygen in the air( oxygen in the air can dissolve and penetrate into our eyes), we can set k[Oxygen] as a constant.

Second, we want to simplify C^2 into C. In order to prevent over-estimation of nitric oxide concentration, we change C^2 into C(max)*C, where C(max) is the max concentration of nitric oxide in the compartment. Since C(max)*C is always larger than (or same as) C^2, we can make sure that we won’t over-estimate the concentration of nitric oxide. Since C(max) is a constant, we can set constant B = k[Oxygen]C(max).

So, the modified form of PDE will be:

2. Parameters:

Parameters used are listed below. We collected them from different papers.

We're still lacking some of the parameters. We can estimate them by solving the steady state of NO distribution.

3. Calculating steady state:

We start from the contact lens compartment. When in steady state, concentration of NO won't change by time. Thus, Equation 2.6 can be written as below:

Where subscript 1 stands for the parameters and variables of the contact lens compartment. By solving this equation, we can get the solution of C1 in steady state:

We use the approximation:

Thus turning equation 2.8 into linear form:

Since C1(0)=0 (one of the boundary conditions), the final form of C1 in steady state can be written as below:

By the same method, we can simplify the concentration of NO in cornea and aqueous humor compartments as a linear formula of position. To simplify the formulas, we set the outer surface of every compartment as the starting position of that compartment. For example, for cornea compartment, the interface of cornea and contact lens is considered the starting position, namely x=0.

As for the boundary conditions, the interfaces should have only one concentration. For example, the formula of C1 at x=0.02 should have the same value as C2 at x=0. Combining these conditions, we can get the function of C2 and C3:

Now we need to solve the slope of NO concentration, namely a1, a2, a3. Here, we use Fick’s first law as boundary conditions, that is at the interfaces, input of NO from one compartment should be the same as output of another compartment. For example, at the interface of cornea and contact lens, input of NO to contact lens should be the same as output of NO from cornea.

The input of NO to contact lens can be written as below, according to Fick’s first law:

The output of NO from cornea can be written as below:

Applying the solution we’d found before, we can get the relationship of slopes of each compartment:

Therefore, we can draw the graph of NO concentration in steady state:

Red line represents the NO concentration in contact lens, blue one represents cornea compartment, and green one represents aqueous humor compartment.

Now, there are just B and Pro not determined yet. Recall that B = k[Oxygen]C(max), we can calculator them. As for Pro, we can calculate each compartment’s total input and output, they should be the same since we’re dealing with steady state. After some calculations, the table can be filled completely:

4. Calculating NO concentration after production of NO by Eye kNOw (non-steady state):

After confirming all the parameters, we went on to calculate the NO concentration of each compartment when Eye kNOw senses the change of IOP. We assume that the production rate of Eye kNOw raised j% compared with steady state.

Start from the contact lens compartment. Below are the PDE, initial conditions, and boundary conditions:

After taking Laplace transform and inverse Laplace transform, we obtained the solutions for each compartment:

In order for our bacteria to reduce intraocular pressure, we planned to engineer our bacteria to have the ability to produce Nitric Oxide Synthase (NOS)^[5], an enzyme that can convert L-arginine into NO.

For biosafety, we engineered our bacteria to overexpress csgD and csgA for securing bacteria onto the contact lens by increasing binding affinity between bacteria and lens.

During literature research, we found out that Bacillus subtilis carries Nitric Oxide Synthases(NOS) and has the ability to produce NO, which is responsive to oxidative stress. So we cloned this gene from Bacillus subtilis' genome and designed a new biobrick which we then incorporated into our chassis, WM3064, allowing it to produce NO.

In order to dynamically express NOS as patients’ IOP fluctuate, we put NOS under the control of T7 promoter and a lacO binding site, which can be controlled by IPTG-inducible T7 RNA polymerase provided by another plasmid PDT7 (Plasmid Drive T7 RNA polymerase). As previously mentioned, the IPTG concentration inside the ring-like compartment will fluctuate according to the patients’ IOP, leading to dynamic expression of NOS.

We tested the kinetics of the enzyme using a NOS assay kit, which utilizes Griess reagents to react with NO and generate colorimetric readouts by measuring O.D.540 value. For the purpose of controlling the production of NOS, we induced bacteria with different concentrations of IPTG and cultured them for different period times.

We chose E. coli WM3064 as our chassis, which lacks the essential gene dapA. This gene encodes for 4-hydroxy-tetrahydrodipicolinate synthase that is critical to the production of lysine through the DAP pathway^[6]. Lysine is an essential amino acid in animals, including humans, but can be synthesised de novo in bacteria, lower eukaryotes and plants for utilisation in protein and peptidoglycan cell wall synthesis^[7]. Without this gene, the bacteria will have to depend on exogenous diaminopimelate (DAP) to survive.

To test whether the bacteria will survive without exogenous DAP, we made plates with and without DAP. After streaking our engineered bacteria onto these plates, we can demonstrate the result by checking its phenotype. Furthermore, we ran a SDS-PAGE to confirm the function of the T7 expression system in our engineered WM3064.

Bacteria biofilm has been shown to exhibit extraordinary ability to help bacteria bind to biotic and abiotic surfaces[measurement reference]. We exploited this property to design one of the biosafety measures.

We engineered our bacteria to overexpress CsgD, a master transcription regulator of biofilm formation, and CsgA, the major subunit of curli fibers. Overexpression of these two proteins have been reported to increase biofilm formation[measurement reference], which we anticipated to help the bacteria bind to the contact lenses more securely, thus preventing the leakage of bacteria if the contact lens encounters any damage.

We first characterized the biofilm formation using conventional congo red staining, then we developed a simple method to assess the binding ability of our engineered bacteria. For more information, please visit our measurement page.

There are several things that need to be considered before selling Eye kNOw as a product. Since Eye kNOw won’t be used by the patient immediately after being manufactured, we designed a growth switch in order to control bacteria growth in different stages of our product lifetime. We were inspired by the work of iGEM NUS 2019 who used a toxin-antitoxin system, hicA-hicB, to control the growth of bacteria. By manipulating the toxin-antitoxin ratio in a bacteria, we can determine when the bacteria should hibernate or grow.

In our design, the hicB antitoxin is constitutively expressed at a basal level, while the hicA toxin is controlled by arabinose inducible promoter. The entire hicA cassette is flanked with FRT sites, which can later be deleted by the FLP recombinase. We also added a heat-activated FRT-FLP recombinase system from pCP20 as an inducible switch. This design enables us to control the bacteria growth in three stages - production, storage and medication.

The production stage is when we are culturing our bacteria, so we need the bacteria to be able to grow normally. After the production process, the bacteria needs to be stored in the contact lens until it can be used. During the storage stage, hicA will be induced to hibernate the bacteria. The last stage is the medication stage, during which the contact lens will be used. When the contact lens is placed on the patient’s eye, the body temperature will activate the recombinase system and delete the hicA cassette, which will cause the bacteria to resuscitate and start producing the therapeutic agent.

To verify the function of the FLP-FRT system, we will culture the bacteria with three plasmids, containing hicA, hicB, and CI857 and FLP genes respectively. As the temperature rises to 42^oC, CI857 gene will be degraded, activating the FLP gene and deleting the hicA gene. If the hicA gene is present, the O.D.600 value will not increase since HicA protein represses the growth of bacteria. Hence, we can verify the function of the growth switch by measuring O.D. 600 value.

Since there are no early symptoms of glaucoma, the public is left unaware of its presence. Therefore, early detection is needed, so we developed a brand-new IOP detector - Eye Screen. By transmitting ultrasonic waves to the patient’s cornea and analyzing the reflected signal, we can get IOP readings immediately. With Eye Screen, we can quickly find people at high risk of glaucoma, without direct contact with the eyes.

To validate the function of Eye Screen, we adopted a gravity model to control the IOP of porcine eyeballs using the trocar system via microincision vitrectomy surgery. By adjusting the height of the saline bag connected to the eyeball, we can measure the IOP by calculating the difference in height of the saline and the eyeball. We then tested whether the amplitude of reflected signals can be proportional to the IOP according to the change in IOP.