# Team:NCTU Formosa/modeling

### From 2013.igem.org

Modeling was our first step forward. When validated with our experimental data, modeling is also a verification of the accuracy of our experiments.

## Contents |

### MATLAB Introduction

MATLAB (matrix laboratory) is a numerical computing environment and fourth-generation programming language. It is developed by MathWorks, a company in United States. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran. Although MATLAB is intended primarily for numerical computing, **an optional toolbox** uses the MuPAD symbolic engine, allowing access to symbolic computing capabilities. An additional package, Simulink, adds **graphical multi-domain simulation** and** Model-Based Design** for dynamic and embedded systems.

### ANFIS Introduction

Adaptive-Network-Based Fuzzy Inference System, in short ANFIS, is a power tool for constructing a set of fuzzy if-then rules to generate stipulated output and input pairs. Unlike system modeling using mathematical rules that lacks the ability to deal with ill-defined and uncertain system, **ANFIS can transform human knowledge into rule base, and therefore, ANFIS can effectively tune membership functions, minimizing the output error.**

### Single Unit

#### Red Promoter

As shown in Figure 2, the red promoter is consisted of P_{ompc} and P_{lac}. By multiplying the experimental data of P_{ompc} + RBS + mGFP and P_{lac} + RBS + mGFP, we would be able to build a model for the red promoter. This model, however, wouldn't be so accurate. To solve this problem, **we used this model to train the actual experimental data of the red promoter by using ANFIS.** Figure 2 is the result of such a training. We obtained **a curve between our model and the actual experimental data.** This curve is the representation of the new model that has been trained and supported by the actually experimental data of P_{red}. This new model definitely contains a high degree of accuracy.

#### Lux Promoter

We did the following modeling based on the data obtained from Imperial 2007 iGEM team.
The data notes the strength of P_{lux} under **different concentrations of AHL** and **different time frames**.

Using ANFIS to train 76 sets of data and to test 20 sets of data, we ontained Figure 4. It shows that **our training data exhibits a similar trend as the testing data**, even though **the computer has no based knowledge of the trend**. This simply means that our modeling has successfully simulated the actually data.

Figure 5 is the resultant graph from input 1 (time) and input 2 (AHL concentration). According to this graph, we can observe the output (fluorescence) has two peaks about AHL concentration(at concentration of 4 nM and 40 nM).
That means **we could achieve our regulation goal with little AHL.** Also, pleas note that there is more output as time passes.

#### 37 °C RBS

We used Figure 6 biobrick to model our 37^{o}C RBS's function at different
temperatures.

First, we did a experiment that test the fluroscence at different temperature and different time.
Choosing 100 sets of data to do machine learning, then we tested 20 sets of data. **As Figure 7 shown, the curve can classify 4 groups fit in 27 ^{o}C,32^{o}C,37^{o}C and 42^{o}C.**

To test the accuracy of our model, we randomly chose 20 pairs of data which is not include in our training data to do the independent test, and the test result is shown in Figure 8. The blue dot in the figure represents the real experimental data that we randomly choose from our whole dataset, and the red star represents simulated result of our model. **It is obviously showed that our model can accurately predict the biobrick function in any condition by using ANFIS.**

From Figure 9, the maximum output is obtained at 37 ^{o}C. Under the same time frame, the output (the normalized expression of the reporter gene) is maximized at 37 ^{o}C while minimized at 25 ^{o}C. There is a dramatic decrease in the output below 30 ^{o}C and the outputs around 37^{o}C are much higher. **This modeling demonstrates that using 37 ^{o}C RBS is a plausible approach for achieving gene expression through temperature.**

###### Reference

- iGEM 2007 Imperial http://2007.igem.org/Imperial

### E.colightuner Simulation

We have all the modeling of each single unit . Now, we want to combine each unit to make a stimulation to the E.colightuner.

Figure 10 shows the essential constituent of our E. colightuner. To save our efforts experimenting with this essential engine of E. colightuner, we built **a model beforehand to help us evaluate its practicability.** Our model is consisted of four components A, B, C, and D

Figure 11 is the overall picture of our component A. Notice that component A is built from similar biobricks as our E.colightuner. The only difference between the two is the promoters used. **Both P _{red} of E.colightuner are substituted with P_{cons} in component A.** With that said, by taking the difference in the strength between P

_{red}and P

_{cons}, into calculations, we would be able to model out E. colightuner with component A. Before that, however, we would have to first build a model for component A.

To build a model for component A, we combined component B and C. As you can see in component B shown in Figure 12, it does not include P_{lux} and luxR like component A. By assuming that when luxR is expressed, P_{lux} would immediately reach its full strength, however, we can consider luxR and P_{lux} pair as simply a Pcons,that is constitutively activated. From this perspective, component A and B are the same, except that component A is also effected by the translation efficiency of 37^{o}C RBS. Component C is the model for 37^{o}C RBS which was shown in the Single Unit part above. So **by multiplying component C and component B, we would be able to obtain a model for component A.**

In order to increase the accuracy of our component A model,** we used ANFIS to fit our modeling result with the actual experimental data of our component A.** By doing this, we obtained a new modeling curve for component that is more precise and accurate, shown in Figure 13.

As mentioned above, we needed to take the effect of P_{red} into account before we could a model of E.colightuner based on component A. Component D has the model of P_{red} built in a similar way as component A model which was shown before, too. We first built a model for P_{red} and fitted it into the actual experimental data.

Having both precise model for component A and component D, we simply had to multiple them to obtain the final model for our E.Colightuner in Figure 14.

Using the single unit to predict the project we simplify like Figure 10, we got Figure 15. The predictive curve is under red light and at 37^{o}C. Due to the sRNA repression, the expression rate of mGFP is really low. This phenomenon is reasonable and interpretable. Thus, **this modeling method can accurately predict the expression trend of a new biobrick.** Applying this modeling system maturely, we can use computers to control our E.colightuner in the future.