Team:IISER-Tirupati India/Model
Introduction
Natural systems are highly complicated to be studied with just experiments. Thus mathematical models are built using the existing data and information to predict and extrapolate the outcomes. This subsequently gives an insight into the working of the system with less experimental probing. Here is an attempt to examine various theoretical aspects of Ovi Cloak. It helps give pointers for future experiments and implementations.The ways in which the genetically modified bacteria of interest would be introduced to the system and its interaction with the environment will be explored. This cascade study aims to find to what extent GMC proliferates and then compute the minimum theoretical efficacy of the whole process. :
- GMO delivery
- GMO growth and colonisation
- Protease production
- Diffusion and ovum Hardening
- Kill switch for reversibility
- Kill switch for Biosafety
Delivery & Colonisation
INTRODUCTION: THE JOURNEY OF GMO BEGINS
The GMC i.e modified lactobacillus acidophilus needs to be delivered to the Ampulla of the fallopian tube where they shall colonise as long as contraception is needed. The bacteria attach to the mucous membrane and colonise with the help of nutrients available through the oviductal fluid. They constantly produce ovastacin until progesterone levels rise post ovulation, hence three days pre and post ovulation the GMC act on hardening the ovum ZP2. This module deals with the transport and growth of the bacteria in the fallopian tube.
PART A: Delivery
OVERVIEW
Delivery is an essential part of our project as it determines the range of users we reach. Multiple options were explored to deliver GMC in a user-friendly way with minimum invasion. Minimum invasion means the bacteria should not colonize the whole reproductive tract or reach the ovaries. The device should ensure bacterial colonization specifically in the ampulla region of the fallopian tube.
There were several limitations and constraints we faced such as immotility of the GMC, strictly selective region for colonisation, the estimated time taken for the whole process etc. Several ways were attempted (Direct injection of a fluid from ostia, Cell encapsulation, etc. from the data provided in[1]), which should be within the desirable limit of the constraints, however all of these efforts were fruitless. Eventually, on further discussions with an IVF specialist Dr.Sidra Khot, gynecologists Dr.Prameela Menon and Dr. Frances Grimstad, it could be concluded that hysteroscopic techniques would be the best for our purpose[4]. This method gives an advantage by delivering the bacteria directly into the ampulla region.
PROCEDURE
GMC will be delivered directly to the ampulla using a technique called Hysteroscopy [4]. It’s done with medical assistance and requires constant X-Ray monitoring to ensure the catheter is inserted without any issues. The reason is that the Ostia and the Fallopian tube are dynamic structures and that there is no chemical or significant physical difference between the ampulla and the other components of the Fallopian tube.
As advised and recommended by the IVF specialist. The diameter of the Hysteroscope is 2.9 mm and it further narrows for the part that enters the Fallopian Tube and the volume of the Hysteroscope is 2-3mL. We’ll use air as our pushing entity to inject 1-2 mL oil or a saline solution containing our GMC. Oil is USG opaque which helps in guidance for the injection of the droplet. The bacteria is sensitive to light so any transparent part of the equipment is covered or tinted. First light is used for guidance and then the bacteria is injected in the absence of light.
A solution of GMC of a specific concentration is prepared. Then the catheter is inserted under medical guidance up to the ampulla. Then an injector is projected with narrow long incisions on both sides of it, which ensures that the GMC forms a ring along the circumference of the tube. Ovum is now 360° surrounded by the GMC.
The introduced bacteria on the wall produces our desired protease-ovastacin denoted diagrammatically as the red circle in the image below. The ovum is the green circle (size is greatly exaggerated) and only an area segment is shared between the two circles. I.e, not all ovastacin produced is in contact with the ovum and not all parts of the ovum is affected by the ovastacin. Those that matter are represented by the intersecting area between the two circles.
The GMC Lactobacillus acidophilus has pili which expectantly forms hydrogen bonds at the tube circumference with mucin found in mucus. The GMC is now adhered to the walls and multiplies once it adjusts to the introduced environment (lag phase)[6,7].
FUTURE ASPECTS:
Since we aim to make our final product more accessible, the hysteroscopic technique, we speculate, is expensive (mostly in private hospitals). We also considered using hydrogels for the delivery of bacteria at a pH-specific region.
Why is this system compatible with the delivery of bacteria in the ampulla of the Fallopian tube region?
We found out that the pH in the oviductal Ampulla region is close to 8.0. That’s why we considered using hydrogels for bacterial delivery, which swells up at a pH range of 7.8 to 8.0.
Amongst the stimuli-responsive hydrogels, pH-sensitive hydrogels are the most studied hydrogels. The rate at which hydrogels respond depends upon their size, shape, cross-linking density, number of ionic groups, and composition, which can be tailored by varying these factors. The response rate increases with increasing pore size and number of ionic groups and decreasing their size and cross-linking density.
For a delivery in a basic medium, we planned to use anionic hydrogels, such as carboxymethyl chitosan, which swell at higher pH (basic medium) due to ionization of the acidic groups[3][5]. As a result, the ionized negatively charged pendant groups on the polymer chains cause repulsion leading to swelling. This property of hydrogels can be exploited for GMC delivery at pH 7.4 in the ampulla of the fallopian tube. However, this idea of cell encapsulation by hydrogels was scrapped as it provides no additional benefit as compared to the aforementioned Hysteroscopic method under USG guidance.
References
[1] Soriano-Úbeda, C., García-Vázquez, F., Romero-Aguirregomezcorta, J. et al. Improving porcine in vitro fertilization output by simulating the oviductal environment. Sci Rep 7, 43616 (2017). https://doi.org/10.1038/srep43616
[2] Human Reproduction Update, Volume 24, Issue 1, January-February 2018, Pages 15–34, https://doi.org/10.1093/humupd/dmx028
[3] Carboxymethyl Chitosan and Its Hydrophobically Modified Derivative as H-Switchable Emulsifiers Langmuir 2018 Feb 27;34(8):2800-2806. doi: 10.1021/acs.langmuir.7b03959. Epub 2018 Feb 13.
[4] Howard W. Jones, John A. Rock - Te Linde’s Operative Gynecology-LWW (2015)
[5] Hydrogels and Their Applications in Targeted Drug Delivery Radhika Narayanaswamy and Vladimir P. Torchilin Molecules. 2019 Feb; 24(3): 603. Published online 2019 Feb 8. doi: 10.3390/molecules24030603
[6] Buck, B. L., Altermann, E., Svingerud, T., & Klaenhammer, T. R. (2005). Functional analysis of putative adhesion factors in Lactobacillus acidophilus NCFM. Applied and environmental microbiology, 71(12), 8344–8351. https://doi.org/10.1128/AEM.71.12.8344-8351.2005
[7] Jugal Kishore Das, Rajani Kanta Mahapatra, Shubhransu Patro, Chandan Goswami, Mrutyunjay Suar, Lactobacillus acidophilus binds to MUC3 component of cultured intestinal epithelial cells with highest affinity, FEMS Microbiology Letters, Volume 363, Issue 8, April 2016, fnw050, https://doi.org/10.1093/femsle/fnw050
PART B: Colonization
OVERVIEW (why is it necessary to study growth and colonization)
In biosynthesis, growth kinetics is a crucial study to be conducted. The growth of a cell comprises both the size and the number. These growths are affected by external factors such as temperature, the chemical composition of the growth nutrient, etc., and by different physiological factors such as growth factor proteins[1][2]. The cells in a particular environment extract the nutrients from the growth media and produce biomolecules, which humans utilize for different purposes. This phenomenon has applications, from producing delicious Italian wine to getting antibiotics which saves millions of lives every year. We will be using this simple formula to reach the goals of our project. To have a qualitative understanding of the protein production by the Genetically Modified anism(GMO), we need to have a theoretical approach. We need to understand how we can calculate the growth of GMOs [3]. This, in turn, will help us figure out protein production. This detailed study of growth kinetics will help us calculate the initial inoculation required for the production of a protein that we need.
For a better understanding, we will be considering two cases. The first comprises the study of the growth of Bacillus Subtilis in normal petri dish conditions. This is the known environment and we can have this condition easily in computer simulation and/or lab and reconfirm our model. The second case of study is the continuous culture model where we study the growth of Lactobacillus Acidophilus in the fallopian tube, which is our target region.
GROWTH MODELS
PETRI DISH MODEL (Bacillus Subtilis, curve fitting)
CONTINUOUS CULTURE MODEL (lactobacillus acidophilus + fallopian tube environment)
INOCULUM CALCULATIONS (connection with 2nd module)
Protease production
OVERVIEW ( overall picture)
Well known for extracellular protease production[1], Bacillus subtilis is our model organism for the proof of concept experiments. Moreover, it is a gram-positive bacteria which even if not too close but is closer than e coli (gram-negative) to our proposed bacteria lactobacillus Acidophilus. This module deals with the whole mechanism of action ideally the GMO must follow for contraception to be attained. To know how this module developed to what it is, please refer to the engineering success (hyperlink).
Let's create the flow, you must know by now that we plan to produce the protease known as ovastacin, an indigenous protease[2] to the human ovum. It is known to cause Zona pellucida hardening naturally used by the ovum to prevent polyspermy[3]. To see the mechanism of zona pellucida hardening click here (goes to project overview where it is explained).
1] Total amount of ovastacin required:
[We assume one active ovastacin cleaves one ZP2 glycoprotein present in the Zona pellucida matrix. To get the number of molecules of ovastacin needed, we calculated the number of ZP2 glycoproteins present on the surface of the ovum. For this, we reached out to studies that looked at the thickness of the ovum with and without the zona pellucida layer to find its overall thickness and the radius of the ovum[4].
Constants and calculations:
| Parameter (need alternative) | Value | References |
|---|---|---|
| Zona pellucida thickness | 18.9 μm | Does zona pellucida thickness influence the fertilization rate? E. Bertrand1 , M.Van Den Bergh and Y.Englert |
| Oocyte diameter | 123.5 μm | Does zona pellucida thickness influence the fertilization rate? E. Bertrand1 , M.Van Den Bergh and Y.Englert |
| Size of ZP2 | 90–110 kDa | Characterization of human zona pellucida glycoproteins A R Bauskin 1, D R Franken, U Eberspaecher, P Donner DOI: 10.1093/molehr/5.6.534 |
| Diameter of ZP2r | 0.0092 μm | Zetasizer Nano Sensitivity Calculator (Classic) |
Assuming cuboid with all spheres of size same as ZP2 to get volume of one unit = 3.1 e-6 μm3
Volume occupied by whole ZP matrix = 12.4 e5 μm3
Calculated the number of ZP2 glycoproteins present in the ZP matrix = 3.92 x 1011 molecules
Assuming 1 ovastacin cleaves 1 ZP2
No. of ovastacin = No. of ZP2 = 12.4 e5 / 3.1 e-6 = 3.92 x 1011 molecules ]
In order to cause complete hardening __ number of molecules are required to reach the ovum. The next question that arises is how much is produced and how much of produced ovastacin will reach the ovum. So we have two major things left to look at:
2] Production and transport of ovastacin by GMO
The production of ovastacin is required for three days pre and post ovulation, please go to “Genetic Circuits” to learn details regarding the genetic circuit.
GENETIC CIRCUIT
Progesterone repressible system
JOURNEY OF OVASTACIN
From the papers, we know that the ovum is propelled by the ciliary motion away from the uterus and that means the ovum is in contact with the wall. Thesize ampulla region of the Fallopian tube (2.5 mm ≤ radius ≤ 5 mm ) is much larger than the radius of the ovum (61.7μm) A molecule under the influence of Brownian motion move according to the equation
- < r 2 >= 4Dt (for 2-D)
- < r 2 >= 6Dt (for 3-D)
- < r 2 > → mean squared (radial) distance travelled by the molecule
- kB = 1.38064852 ×1023 m2 kg-2 s-1 K [Boltzmann constant]
- η = 0.799 Pa·s [Viscosity of Oviductal Fluid]
- T = 35.5 + 273.15 = 308.65 K [Temperature of Oviduct]
- r = 22kDa = 2.43 nm [Radius of ovastacin molecule]
- a = 61.7 μm [Radius of the ovum]
- s = 5 mm [Radius of the ampulla region of the oviduct]
- N0 = 3.92 ×1011 molecules = 0.000650946529392 nanomoles [Number of ovastacin to react with all ZP2]
- t → Time elapsed
Where,
using,
For, Ovastacin D=1.1644194699 ×10-13 m2 s-1
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