Team:NEFU China/Modeling
Modeling introduction：
For the modeling of our project, we used mathematic method to explain the progress and optimize our experimental design. We established some equations to simulate the biological
process.
We have considered all of the factors that influence the blue pigment production, and created the mathematic model based on the biological dynamics. As for the future work, we can use Sobol' sensitivity analysis to predict the contribution rate of the model parameters to the results,and did a predictor among 3 different values, time, the mount of AI-2, and the intensity of pigment, using the MATLAB software to draw the 3D chart.
Equation constructed：
We can use mathematic models to indicate the intracellular syntheses of proteins and the AI-2 transportation and phosphorylation.
For these two parts, we designed a set of equations. They are listed as following:
The equations of intracellular synthesis of proteins：
[1]LsrACBD: 
[2]LsrR: 
[3]LsrK: 
The equations of AI-2 in the cells:
[4]Intracellular AI-2： 
[5]Phosphorylated AI-2: 
*mRNA LsrACBD： 
*mRNA LsrRK： 
In those equations:
Preditor
1.Sobol' Sensitivity analysis.
Sobol’ sensitivity analysis method can predict the contribution rate of the model parameters to the results.
(6) We can get these equations:
In those equations:
f0-----Average value of response output.
Du-----Variance of parameter K.
Dv-----The sum of the variance of the other single parameter.
The sensitivity coefficient of parameter K is：
Results analysis:
In the model, the higher the sensitivity coefficient, the more important the kinetic parameters of the AI-2 transportation and phosphorylation in cells.
2. 3D Map
We did a predictor among 3 different values, time, the concentration of AI-2, and the intensity of pigment. Using the 3D map to find out the connection among them, that can be reference for customers to use 'yogurt gaurder'.
Modeling Software
MATLAB (matrix laboratory) is a numerical computing envionment 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 of 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.
