Difference between revisions of "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:

Constant:

V_1,V_2-----Maximum transcription rate of lsrACBD/lsrRK

Km_{1  -----}Affinity constant between lsrR and lsrACBD

Km_{2  -----}Affinity constant between lsrR and lsrKR

Ki_{1    -----}Inhibition constant between lsrR and lsrACBD

Ki_{2    -----}LsrR inhibition constant on lsrR

h₁,h_{2 -----}Degradation of mRNA lsrACBD and lsrKR

r_{1      ------}Degradation of lsrACBD

r₂,r_{3  ------}Degradation of lsrR and lsrK

K_{1    ------}Translation rate of mRNA lsrACBD

K_{2    ------}Translation of lsrRK

l_{1 ------}Binding between LsrR and phosphorylated AI-2

l_{2 ------}Binding between LsrK and AI-2

l_{3 ------}Binding between LsrACBD and extracellular AI-2

S_{R ------}AI-2 synthesis rate

E_{R ------}Excretion constant

D_{R ------}Dimerization rate（active LsrR to inactive LsrR）

Variable:

R_1-----mRNA lsrACBDFG

R_2-----mRNA lsrKR

P_1-----LsrACBD

P_2-----LsrR

P_3-----LsrK

S_1-----Intracellular AI-2

S_2-----Extracellular AI-2

S_3-----Phosphorylated AI-2

Preditor

1.Sobol' Sensitivity analysis.

Sobol’ sensitivity analysis method can predict the contribution rate of the model parameters to the results.

We can get these equations:

In those equations:

f₀-----Average value of response output.

D_u-----Variance of parameter K.

D_v-----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.

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