Team:NCKU Tainan/Model


Model

In one word, Laplace transform


Overview

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.

Background

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.

Our goals

  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.


Model 1: Deformation of Contact Lens

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


Contact lens

Literature research stated that the increase in patients’ IOP will result in the deformation of cornea, further leading to a structural change in contact lens[2]. We utilized this phenomenon to design a pair of contact lenses that structurally change in response to fluctuations in intraocular pressure.

Our contact lens will be fitted with a tubular semipermeable chamber that is filled with our engineered bacteria, IPTG, NO precursor - L-arginine, and DAP. The volume change of the chamber will cause water to flow out thus increasing the IPTG concentration inside the chamber. The increase in IPTG will induce the bacteria to produce more Nitric Oxide Synthase, which can then convert L-arginine into nitric oxide to lower the intraocular pressure (IOP). This structural change is then able to induce dynamic drug delivery.

IOP simulation experiment

To prove the concept of our contact lens and our device, we designed an IOP simulation experiment with porcine eye.By changing the drip bag’s height, water pressure will directly increase IOP in the porcine eye, enabling precise control of IOP for experiments[3][4].

For more details, please visit proof of concept and hardware.

Fig. 1. The structure and design of contact lens.

Gene Design

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.

Nitric Oxide Synthases (NOS)

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.

Fig. 2. Plasmid design for NOS.

Functional Test

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.

Biosafety

DAP-deficient strain

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.

Fig. 3. Design of biosafety chassis.

Functional Test

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.

Overexpression csgD and csgA

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.

Functional Test

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.

Growth switch

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.

Fig. 4. Plasmid design for grow switch

Functional Test

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 42oC, 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.


Device

IOP Detector

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.

Functional Test

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.


References

  1. Muenster S, Lieb WS, Fabry G, et al. The Ability of Nitric Oxide to Lower Intraocular Pressure Is Dependent on Guanylyl Cyclase. Investigative Opthalmology & Visual Science. 2017;58(11):4826.
  2. Lam A. The effect of an artificially elevated intraocular pressure on the central corneal curvature. Ophthalmic and Physiological Optics. 1997;17(1):18-24.
  3. Chen G-Z, Chan I-S, Leung LKK, Lam DCC. Soft wearable contact lens sensor for continuous intraocular pressure monitoring. Medical Engineering & Physics. 2014;36(9):1134-1139.
  4. Zhang J, Zhang Y, Li Y, et al. Correlation of IOP with Corneal Acoustic Impedance in Porcine Eye Model. BioMed Research International. 2017;2017:1-6.
  5. BRENDA - Information on EC 1.14.13.39 - nitric-oxide synthase (NADPH). Brenda-enzymes.org. https://www.brenda-enzymes.org/enzyme.php?ecno=1.14.13.39#pH%20OPTIMUM. Published 2020. Accessed September 9, 2020.
  6. Dante RA, Neto GC, Leite A, Yunes JA, Arruda P. Plant Molecular Biology. 1999;41(4):551-561.
  7. McLennan N, Masters M. GroE is vital for cell-wall synthesis. Nature. 1998;392(6672):139-139.