Team:Nanjing-China/Modeling
Modeling may seem to be a little bit alien and unfamiliar to students who major in Biology solely. However, modeling plays an increasingly vital role in the research of synthetic biology. Then, what is modeling? Modeling aims to build and use a model which provides a theoretical way to explain a phenomenon in a simpler fashion than the real situation. The procedure of modeling consists of observing a phenomenon, identifying what parameters may influence if and sorting them out so that the decisive ones remain. According to the results of modeling, you may predict what would happen under different conditions.
Modeling also takes different forms, and the following is some examples of models:
1) Mathematical equations
This model is used widely. In theory, we can build the model of almost every problem if certain parameters are sorted out.
2) Numerical simulations
It seems more accessible than mathematical equations but the building of it depends on certain software to some extent.
3) Drawings and outlines
Sometimes, a simple drawing is understandable enough to clarify biological processes, even without captions!
We use Matlab to do the modeling work.
Matlab is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis and numeric computation. Using matlab, we can solve technical computing problems much faster.
Matlab has a wide range of applications, including signal and image processing, communications, control design, test and measurement, financial modeling and analysis, and computational biology.
In our modeling, we use matlab to find out the influences imposed on protein expression by certain parameters, such as pH, ion concentration, etc.
Our project uses Bacillus subtilis as the bioreactor to deal with heavy metals: Au, Pb and U. B. subtilis is not the bacteria used the most widely in iGEM competition, so we want to acquire thorough understanding of it through modeling part.
In the modeling part, we have built three models: Growth, Transcription-Translation and Bioabsorption. In the first part, we worked out growth curves of B. subtilis‘s vegetative state and spore state, using Logistic model. In the second part, we compared the efficiency of three different promoters we use: Pveg, Ptas and Pcot and try to find which one has the highest efficiency. In the third part, we used GolB-Au as an example to shed light on the optimal concentration of metal ions and the time for binding proteins’ saturation.
Through modeling, we know B. subtilis better and find optimal experimental conditions. Besides, we can also find out whether our wet lab results conform to the modeling results.
Here comes our modeling.
Considering the fact that proliferation is unhindered when resources are sufficient and minimal when resources have run out, our model couples growth (N) with resources (R).
As f(R) is the Hill function, where
f(R)=Rα/(1+Rα)
the growth of cells is modelled as:
dN/dt=k*N*f(R)
dR/dt=-α*N*f(R)
Spore formation is usually triggered by a lack of nutrients, and usually occurs in gram-positive bacteria. In spore state, bacillus subtilis is dormant and with strong resistance to the unfavorable conditions. According to the previous research, PH and the resources play crucial roles on the growth of bacillus subtilis.[reference1] Referred to Logistic model, here are our equations.
dN/dt=k*N*(1-N/Nm)
| N | the number of cells |
| k | cell growth rate |
| Nm | the maximum of cell number |
The experiment data shows that the number growth rate increases with PH increase when PH is lower than 7.0, but decreases with PH increase (>7.0). Therefore, optimal PH for growth is 7.0.
Combining the experimental data with modelling, we found that sucrose is the best carbon resource for the high growth rate and maximum cell number.
Combining the experimental data with modelling, we found that using corn flour as the nitrogen resource contributes to a high growth rate of bacillus subtilis, while yeast cream yields to the maximum in cell number.
Assumptions:
- The functional genes of the plasmid are successfully recombined with DNA of bacillus subtilis.
- Concentration of RNA polymerase is constant.
- The concentration of the ions to be absorbed outside the cell has little influence on the transcription of the absorptive proteins.
Variables:
[mtasA-AP] [mcotC-AP] |
Concentration of mRNA of tasA and absorptive protein Concentration of mRNA of cotC and absorptive protein |
|---|---|
[tasA-AP] [cotC-AP] |
Concentration of conjugates of tasA and absorptive protein Concentration of conjugates of cotC and absorptive protein |
| Parameter | Description |
| tc1 | Transcription rate of tasA-AP in vegetative state |
| tc2 | Transcription rate of cotC-AP in spore state |
| deg1 | Degradation rate of tasA-AP mRNA in vegetative state |
| deg2 | Degradation rate of tasA-AP in nutrient state |
| deg3 | Degradation rate of cotC-AP mRNA in spore state |
| deg4 | Degradation rate of cotC-AP in spore state |
| fl1 | Folding efficiency of tasA-AP in vegetative state |
| fl2 | Folding efficiency of cotC-AP in spore state |
| tl1 | Translation rate of tasA-AP in vegetative state |
| tl2 | Translation rate of cotC-AP in spore state |
| ou1 | Extracellular transport rate of tasA-AP |
| ou2 | Extracellular transport rate of cotC-AP |
Ordinary differential equations as follows:
d[mtasA-AP]/dt=tc1-deg1*[mtasA-AP]
d[tasA-AP]/dt=tl1*[mtasA-AP]*fl1-deg2*[tasA-AP]-ou1*[tasA-AP]
d[mcotC-AP]/dt=tc2-deg3*[mcotC-AP]
d[cotC-AP]/dt=tl2*[mcotC-AP]*fl1-deg4*[cotC-AP]-ou1*[cotC-AP]
In the 16 kinds of parallel constructs we designed, our model chose one of them to show the specific modelling results. The instanced construct
Based on a set of differential equations describing the kinetics of absorptive protein absorbing specific ions, the model is designed to predict the efficiency and affinity of the binding process. Given a certain initial concentration of absorptive protein, the model calculates the time necessary for a certain proportion of absorptive protein to be occupied, simulating the efficiency of the heavy ion-capturing process.
Assuming that three types of absorptive protein are not interfered by each other and possess similar characteristics, we can simulate the gold ion-capturing process to make a basic prediction of the other two.
Since the initial concentration of gold ion injected into the system is typically very large compared to the initial concentration of GolB, we consider that the concentration of gold ion is unchanged.
In the solution,
In this equation,
[Au-GolB](0)=0；
[Au-GolB](∞)=[GolB] (0), assume that GolB binding sites can be fully saturated given enough time, as ka1[Au]>> .
With the parameters determined from the experiments, the model is then instantiated and used to predict the time period necessary for the binding sites to be saturated.
As is shown on the graph, with higher concentration of gold ion, the ion-capturing process tends to be quicker. Whereas, the final balance is supposed to be similar. Besides, around 3 hours is enough for GolB protein binding sites to be saturated. This result helps us find out the optimal concentration of Au and the time for GolB’s saturation during experiments.
The modeling results of Pb(II) and UO22+ capturing process of absorptive proteins are showed below. Similar to gold ion capturing, the main trend of the whole process is that higher ion concentration leads to a faster absorption process. Since the different types of protein possess different characteristics and interactions with corresponding ions, the time needed to build a balance varies. (PbR: about 1h; UBP: about 35min) Interestingly, with a lower concentration of UO22+, the final complex concentration seems higher, which we assume results from the decrease of competitive inhibition.
https://2014.igem.org/Team:INSA-Lyon/Modeling
http://www.mathworks.nl/products/matlab
http://www.ncbi.nlm.nih.gov/Structure/mmdb
Wei Wei, Tianze Zhu, et al, Engineering a gold-specific regulon for cell-based visual detection andrecovery of gold, Chem. Sci., 2012, 3, 1780–1784
Lu Zhou, Mike Bosscher, et al, A protein engineered to bind uranyl selectively and with femtomolar affinity, Nature Chem., 2014,3:236-241
Wei Wei, Xiangzhi Liu, et al, Simple Whole-Cell Biodetection and Bioremediation of Heavy Metals Based on an Engineered Lead-Specific Operon, Environmental Science & Technology,2014,6,3363-3371