Team:HUST-China/Model
「Model」
Overview
We build an ecosystem level model, in order to see how the Reebot diffuse, sense and enrich the lanthanide ions, and be recycled on Si-board. Then we can determine how should we release Reebot, how to recycle the Reebot and how much Reebot do we need for the best result. The ecosystem could derive the best strategy to make full use of Reebot.
Assumptions
The variability of temperature has no effect on our Reebot or it could be ignored.
Liquid in the container is stationary.
There is nothing else in the container which can influence Reebot.
Constant & Parameter
The description of constant, their values and the references involved in this model are listed in this table.
| Constant | Description |
|---|---|
| f1 | concentration of Initially Bacteria |
| f2 | concentration of Lanthanide ion |
| f3 | concentration of Sensed Bacteria |
| f4 | concentration of Recycled Bacteria |
| f5 | concentration of recycled sensed bacteria |
| f6 | concentration of enriched recycled bacteria |
The description of parameter, their values and the references involved in this model are listed in the second table.
| Parameter | Description |
|---|---|
| dif | the diffuse ability of bacteria |
| difl | the diffuse ability of lanthanide ion |
| deadp | dead/birth per minute of bacteria |
| vlcx | velocity of movement on x label |
| vlcy | velocity of movement on z label |
| vlcz | concentration of enriched recycle bacteria |
| krec | speed of bacteria recycled on Si-board |
| kabcs | speed of bacteria recycled on Si-board |
| rmax | the amount of bacteria recyclyed on each area of Si-board |
| csen | the lowest concentration lanthanide ion that can be sensed |
| ksen | speed of bacteria sensing the lanthanide ion |
| kcap | speed of sensed bacteria capturing the lanthanide ion |
| ccap | the lowest concentration lanthanide ion that can be enriched |
| LBlever | The amount of lanthanide ion enriched by one bacteria |
Basical Diffusion
Rome was not built in a day. At the beginning, we built a basical diffusion model, just setting the diffusion function in our model.
The function is:
We release some Reebot to the top of our hypothetical container as initial value of f1, and use ‘ode’ tool in MATLAB to run this function. Here is the result:
Recycle
Then we let our model become more complex and more powerful. We decided using Si-board to recycle the Reebot, since Reebot have Sitag, a protein tag that can combine with Si, once it was sensed. We insert recycle function in our model.
Firstly, we should change the diffusion function:
(In the end of all function, the ∂f/∂t will be delta.)
And we set the area of Si-board, if it is in Si-board area:
Bacteria that combined with Si-board maybe abscess. So taking the abscission into consideration, we should add this function:
Finally:
Set a 5×5 Si-board on the top and then run the model, the result is:
Sense and Enrichment
This is the biggest part of our model. We should take lanthanide ion, sensing and enrichment into consideration. So, our data doesn’t just contain concentration of bacteria anymore. It now contains four: concentration of initially bacteria (haven’t sensed the lanthanide ion) as f1, concentration of lanthanide ion as f2, concentration of sensed bacteria（sensed the lanthanide ion but haven’t recycled）as f3 and concentration of recycled bacteria (have enriched enough lanthanide ion) as f4.
And the sensed bacteria will enrich the lanthanide ion around it, to simplify the function, we just consider it at two status: no enriched and full enriched. The function is:
We should also modify the enrichment function. It will only use to sensed bacteria and enriched bacteria.
Finally, the model is over. Running the model, the result is:
For more intuitive, we draw a figure :
Click on the picture and you can see a clearer picture.Then click on the return key of the browser and you can return.
Put these curve into one figure:
Click on the picture and you can see a clearer picture.Then click on the return key of the browser and you can return.
It’s clearly that there are three stages during the whole simulation. The first stage is sensing, second stage is capturing and third is recycle.
Result
a. High Concentration Simulation
Firstly, we run a model which is: there are enough concentration of lanthanide ion in the consider, and we put some Reebot on the top.And we will set the Si-board later. Here is the video:
From the video, we can see that once we put Reebot into the container, the Reebot quickly diffuse. At the same time, Reebot sense the lanthanide ion around them, and express more LBT (lanthanide binding tag), sitag on their surface. Then, the LBT start to enrich the lanthanide ion in the environment. As time goes by, Reebot have enriched more and more lanthanide. At the beginning, the concentration of lanthanide ion is approximately 0.03 unit，and now, it is about 0.003.
When t = 50, we set a 6*8 Si-board on the top. The sensed bacteria and enriched bacteria are recycle to the Si-board. You can see it clearly that the edge of Si-board enriched more Reebot. In the end, many bacteria are recycled to the Si-board, but there are still many Reebot in the environment. The reason is concentration gradient caused by Si-board isn’t large enough so that the diffusion isn’t effective. So, in experiment we change the way Si-Board set, like this way.
But it's quite difficult to simulate this model, so we still use the old container model
In order to show you more details, we sum each areas’ concentration and put them into on figure:
Click on the picture and you can see a clearer picture.Then click on the return key of the browser and you can return.
From the figure, we can see lot of things. In the first 50 units of time, most Reebot quickly enriched enough lanthanide ions, the concentration of initial bacteria and sensed bacteria are very low. Then, the Si-board set, Reebot begin to recycle. At first, in the figure, Reebot enrich at about a same speed. Then enrichm speed is slower and slower.
This model simulate the ordinary use of Reebot. the result can show us the detail of process, we can determine how much Reebot to release and recycle for how long upon that.
b. Low Concentration Simulation
According to the paper, the concentration of lanthanide ion is much lower than expected. So in this simulation, we set concentration of lanthanide ion as 0.001 unit. Other parameters are same as before. Here is the result:
In this situation, Reebot enriched most of lanthanide ion. But actually, some Reebot are wasted. these Reebot sensed lanthanide ion and expressed LBT and Sitag on their surface. But sensed bacteria is so much that only part of them can enrich enough lanthanide ion. Others only enriched a little and be recycled to Si-board.
c. Intelligent Simulation
Then, we run an other simulation to show the intelligence of Reebot. In this simulation, there was no lanthanide ion at the beginning, we put lanthanide ion at some certain time.
The video and figure is here.
At the beginning, we release Reebot on the top. While there is no lanthanide ion in environment, so Reebot keep the initial status, and diffuse in the container. When passing through 20 units of time, there are some lanthanide ion release at the bottom of container. From the video, Reebot take a quick reaction, capturing the lanthanide ion and recycle. When it passes 100 units of time, other lanthanide ion release at another position in bottom. Reebot successfully enrich them too. Unfortunately, Reebot also meet waste problem in this situation. So we come to an idea that we can change the recombined protien, to let Reebot catch REE faster. So we repeat LBT sequence. And during modeling analysis, we find the three time LBT is the best.
It’s also our project’s future plan. Once we achieve it, we can release Reebot in factory’s pool. If there is no lanthanide ion, Reebot just live as a normal escherichia coli. And once lanthanide ion emerge, Reebot can sense and enrich it, then Reebot combine with Si-board.
