Modeling
Modeling Introduction
Our modeling can be divided into four parts. Firstly, in order to enable our project to be applied in real life, we designed a device placed in soil, which can attract and kill nematodes by modified engineering bacteria inside the device. Secondly, assuming there is a farmland, we took advantage of gas diffusion model and nematodes’ movement analogue simulation to find the best position where the device should be placed. Thirdly, we established a database to enlarge the range of our application, using it and our method to kill more different pests. We would appreciate that the new synthetic biological and environment-friendly method can be shared and improved with the science researchers all over the world.
Design
Device 1.0
In order to enable our project to be applied in real environment, we designed and made an entitative device, which we called device 1.0. On one hand, the production of attracting substance produced by E.coli, which attracts nematodes is low. On the other hand, the price of attracting substance is high. It was demonstrated that carbon dioxide has a function of attracting nematodes. Therefore, we choose CO2 as a low-cost assistant attracting substance.
Our device has four areas. The first area is carbon dioxide generating area. We produce CO2 by adopting limestone and diluted hydrochloric acid method, which is widely used in industry. The second area is E.coli culturing area. It includes a medium inside the device - to culture modified engineering bacteria. The third area is light controlling area, which includes a LED light. After turning on it, red emission will activate the promoter and bacterial cells will express attracting substance; turning off it, toxalbumin. The forth area is made up of a cuboid outer shell, which can support our device.
The figure above shows our real product – Device 1.0. Meanwhile, we did an experiment to show the usage of our device in lab condition.
There are mainly nine steps to apply our device in farmland just as they are showed in the video above:
Step 1. We gathered a box of soil in our farmland.
Step 2. We added culture medium onto slide glasses. Unfortunately, because of the limitation of our wet lab condition, we didn’t apply real engineering bacteria this time.
Step 3. We gathered several small stones used as CaCO3 and put them into the test tube.
Step 4. We added HCl into the separating funnel.
Step 5. We opened the faucet of the separating funnel in order to let HCl flow into the test tube under the atmospheric pressure. Then small stones reacted with HCl and produced CO2. We also showed the usage of the red LED light in the video.
Step 6. Put safety into consideration, we did our simulation in the fume hood.
Step 7. We put the device into the soil.
Step 8. After 3 hours’ experiment, we took out the device then take down the slide glasses.
Step 9. Finally, we tested the results by using microscope. And in the video, we showed the movement of a nematode that we separated from soil in Hebei Province in China.
Device 2.0
After our device has been improved, we want to figure out that how we can put our device into practice in the farmland, especially that whether or not our device would be more sufficient and economical than the killing nematodes methods used at present (crop-dusting mostly). In order to answer those questions, we need to do an analogue simulation of the movement of nematodes to determine the most suitable place in the farmland to put our device. Our modeling process is as follows:
Firstly, we suppose that modified engineering bacteria can produce ideal concentration of attracting substance and toxic protein (the ideal concentration is in reasonable range). Then, because E.coli can only grow on the surface of the medium and considering the problem of space utilization percentage, we changed the medium’s shape to sphericity to obtain the highest space utilization percentage. Meanwhile, our device has been shaped to sphericity too, and the LED light has been moved to the center so the whole surface of medium can get the same radiation. Moreover, we choose mini LED light bulb and solar energy as the power to save cost and energy.
We also made a video to show the inner structure of device 2.0.
As you can see, device 2.0 has two shells – outer shell and inner shell. There are tiny holes on the outer shell, which allow nematodes to come into the device. And the holes are not big enough for some other animals in soil to come in. There should be a mould, which is shown neither in the schematic diagram or in the video of device 2.0, to help cover culture medium onto the inner shell. With the help of the mould, there is a thin culture medium layer covered on the outer surface of the inner shell. The red LED light can be supplied with the power from solar power pane, which will be put on the surface of farmland. And we can achieve remote control by using radio technology.
Modeling in Farmland
After our device has been improved, we want to figure out that how we can put our device into practice in the farmland, especially that whether or not our device would be more sufficient and economical than the killing nematodes methods used at present (crop-dusting mostly). In order to answer those questions, we need to do an analogue simulation of the movement of nematodes to determine the most suitable place in the farmland to put our device. Our modeling process is as follows:
Modeling assumption
- Nematodes can be attracted if the attraction concentration of limonene is higher than the lowest attractant concentration and move towards the direction of the highest odor concentration after attracted by the limonene smell.
- Supposing that engineering bacteria in our device are able to produce enough limonene as we need.
- Supposing that the creeping speed of nematode is fixed to 290μm/s.
- Supposing that nematodes move on a 2D plane. Because the movement range of nematodes is within 10cm and the distance between two devices is much higher than 10cm, we can ignore the depth.
- When the gas diffuses in space, the concentration isn’t affected by temperature, wind or other factors.
- The device emits the gas continuously and the concentration is fixed everywhere. And after the gas diffusion, the attractant concentration will tend to be stable.
Modeling approach
the longest distance between nematodes and the equipment=nematodes’ crawl speed×time nematodes need to develop into adult.
Firstly, we consider regular square farmland, to minimize the number of equipment we use, the arrangement mode of equipment is as follows.(first, we consider the situation with four equipment).
Model solution
Allowing that we are supposed to control the density of nematodes in a proper range, we hope to kill all the adult nematodes within certain period of time under the identical condition. And because different species of nematodes have different life cycles, our attraction time will also be different. We make time d be the half time of which nematodes grow from eggs to larvae. We plan to apply our “attract – and – kill” process in two rounds. We will attract nematodes into our device in time d and kill them in time d. After the two rounds, we can assume that all nematodes are in death. Additionally, it takes some time for nematodes to reach the device, so we can determine the distance between the devices we place according to the ten-day-period and the crawl speed of nematodes.
L is the longest distance between nematodes and the equipment, V is nematodes’ crawl speed, and T is time nematodes need to develop into adult.
Firstly, we considered regular square farmland d, to minimize the number of equipments we use, the arrangement mode of equipment is as follows. (firstly, we consider the situation with four equipment)
As shown in the picture, represents the device of colon bacillus, while circle represents diffusion, with the same odorousness in a circle. What’s more, squares ABCD are the simplified farmland. It’s obvious that in this farmland (do not consider points on the sides of the square ), point F is the farthest point away from the four equipment. Based on the longest distance between nematodes and the equipment which has been acquired in the 1） question, we obtain:
$$AB = {2\sqrt{2}EF} = D$$
N is the distance between the two equipment
| Running Time of Attractant(Days) | Distance between Divices |
| 0.5 | 17.7137 |
| 1 | 35.4345 |
| 1.5 | 53.1518 |
| 2 | 70.8691 |
| 2.5 | 88.5863 |
| 3 | 106.3036 |
Considering that odorousness will be reduced with the increase of distance away from the equipment, we should only considering the superposed odorousness in point F(considering four equioments now) to reach the lowest attractant concentration. Thus we obtain:
$$C_1 = C_0/4
C1 is the superposed odorousness diffused from the device, C0 is the lowest attractant concentration.
We get the 3-D gas diffusion model according to Fick Law, and then we simplify the question into 1-D situation according to isotropy.
$$\frac{\partial C_{A}}{\partial f} = D_{A}\frac{\partial ^2 C_{A}}{\partial x^2}$$
Boundary value condition is: C（t,0）==N
Then we obtain the solution
$$c(x,t) = \frac{C_{0}}{2}(1-erf\frac{x}{2\sqrt{Dt}})$$
Adding that
$$erf(x) = \frac{2}{\sqrt{\pi}}\int^{x}_{0}e^{-\lambda^{2}}d\lambda$$
Then we can obtain the arithmetic solution.