Modeling Beijing Normal University
1. Modeling Introduction
Our modeling can be divided into four parts. Firstly, in order to enable our project to be applied in life, we design a device placed in soil, which can attract and kill nematodes by modified engineering bacteria inside. Secondly, assuming there is a farmland, we take advantage of nematodes’ movement analogue simulation to find the best position where the device should be placed and the best concentration of attracting substance. Thirdly, according to this concentration, we obtain the best size of the device by calculating. At last, we establish a database to enlarge applied range of our method to kill other pests. We would appreciate that new synthetic biological and environment-friendly methods can be shared and improved with the science researchers all over the world.
2. Device
2.1 Device 1.0
In order to enable our project to be applied in actual environment, we design a device and make an entitative product. Considering the production of attracting substance is low which attracts nematodes produced by E.coli. It was demonstrated that carbon dioxide (CO2) has a function to attract nematodes [1-3]. Therefore, we choose CO2 as a low-cost and assistant attracting substance.
Our device has four sections. The first one is CO2 generator adopting calcium carbonate (CaCO3) and diluted hydrochloric acid which is widely used in industry. The second section is a medium inside to culture modified engineering bacteria. Thirdly, there is a LED light; after turning on it, red emission will activate the promoter and bacterial cells will expression the toxic proteins.
In the meantime, we designed a simple experiment to check the feasibility of our device in lab condition.
2.2 Device 2.0
After device 1.0 being designed and made, our teammates discussed together about it and found out device 1.0 exists lots of shortages. For instance, the raw materials (diluted hydrochloric acid and CaCO3) this device can hold is limited restricted by its size. Therefore, if we want persistent CO2 as assist to attract nematodes, we have to change raw materials frequently, and in this way the cost of device would increase largely. Secondly, the design that put the culture medium on the glass slide result in a low usage of space, which means the amount of attractant and toxic proteins would be relatively small. The third shortage is that the LED light tube is too large and needs power to charge, so it’s not so suitable for agricultural use. Also, the utilization of light is expected to improve. However, we make changes against the three insufficient mentioned above in the device 2.0, and we are looking forward to push our device more and more efficient in the edition 3.0 and 4.0.
We have come up with an improving blue print against the shortages mentioned above, yet we haven’t make out the physical device 2.0 restricted by time and the experimental condition now available. Also, the blue print we raised is just under the identical condition. Firstly, we suppose that the E.coli transformed as engineering bacteria can produce identical concentrated attractant and toxic proteins which is in a reasonable range (we estimated preliminarily by literature review and the concrete quantitative value will be work out by the third part of modeling). Secondly, we change the place covered by cultural medium to sphere to achieve the biggest usage of surface area and meanwhile the whole device will be changed to sphere as well. Furthermore, for the sake of a better usage of LED light, we put the LED light tube at the center of the sphere medium so that its whole surface can be exposed to the light of the same intensity. This kind of design can allow us to choose smaller LED light tube at the same time, together with the change that we use the solar power instead of battery, the device 2.0 can reduce cost and save energy, which means it would be more economical and environmental friendly.
3. Modeling in Farmland
After our device has been designed, we are willing to figure out that how can we 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 for now (crop-dusting mostly). In order to answer those questions, we need to do analogue simulation of the movement of nematodes to determine the best place in the farmland to put our device. Our modeling in farmland in based on the following assumptions:
- Nematodes do sine shaped movement towards the direction of the highest odor concentration after attracted by the limonene and linalool smell [4].
- The creeping speed of nematode is fixed to 500μm/ s. (According to the literature An imaging system for standardized quantitative analysis of C.elegans behavior)
- 8.5d-10.5d[5]supposing that the effective attractive period of our device is 10d, the Meloidogyne needs 8.5d-10.5d to develop into second instar larvae from monoplast egg according to an exiting literature[5].
- Only if the attraction concentration of limonene is higher than the lowest attractant concentration (or 50% of the higher attractant concentration), it will attract the nematode.
- When the gas diffuses in space, the concentration isn’t affected by temperature, wind or other factors.
- The device emit the gas continuously and the concentration is fixed everywhere.
Allowing that we are supposed to control the density of nematodes under a relatively low range, we hope to kill all the adult nematodes in certain period of timeunder the identical condition. And as nematodes need 3 days to develop into adults, we are supposed to kill them within 3 days. Adding that it takes some time for nematodes to reach the device, we can determine the distance between the devices we place according this 3 days period and the crawl speed of nematodes.
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)
As shown in the picture,represents the equipment of colon bacillus, while circle represents diffusion, with the same odorousness in a circle. What’s more, square ABCD is the simplified farmland. It’s obvious that in this farmland(don’t 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 is accumulated in the 1） question, we obtain:
EF = the longest distance between nematodes and the equipment =
$$AB = {2\sqrt{2}EF} = D$$
We obtain that there should be N/2 between two equipment.
Considering that odorousness will be reduced with longer distance away from the equipment, we should only considering the superposed odorousness in point F(considering four equioment now) to reach the lowest attractant concentration. Thus we obtain:
the superposed odorousness in point F diffused from device E= the lowest attractant concentration÷4
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.