Team:SDSZ China/Model

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Modeling
Introduction
        To investigate how we could potentially develop our model, our Team, who focuses on the project on ancient buildings restoration through microbial mineralization, decided to use biological materials to test out the most efficient method to achieve mineralization. We created a multi-variable model of mineralization activity for each biological material used in the research paper, to see how much minerals they could produce based on the mineralization. For reference, we used the math model created by 2017 SZU's math model, and modified a brand new model according to our own experiments.
The Four Factors
        The four factors being used in our Model are shown below:
Principle
         Next, for our model. We referred to 4 different sets of data about Mineralization, in particular, using the 4 corresponding E.coli bacterial strains, to show the “Mineralization Activity” intuitionistic for our research. After acquiring the mathematical equation, we then use it to predict the BL21 strain, in which we got an essential result, which shows that nitrogen source has the maximum weight, whereas pH has the minimum weight–––meaning that nitrogen source is the most essential nutrition for BL21 bacteria strain. But soon we find another problem: “the low weight of pH shows that bacteria strains are not sensitive to the change of pH in a relatively apt range ”. Thus, we conclude that pH is NOT in direct proportion to BL21 (although there is a sharp decline in activity when pH reaches 11).
Algorithm
1. Standardizing variables: transforming variables into the same scale. Here we utilize the z-score standardizing method, such that where the symbols in the formula are variable, standardized variable, sample mean, and standard deviation respectively.
2. Fitting functions of each variable with polynomial function.
3. Getting the overall relationship using linear least square method.
Code
clc
clear
close all
for i=1:4
switch i
case 1
x=[-0.98 -0.9 -0.8 -0.65 -0.4 -0.1 0.2 0.5 1.2 2];
y=[54 53 56 85 83 81 81.5 72 78 71];
case 2
x=[-0.75 -0.49 0.2 0.8 1.48];
y=[74 78 87 89 91];
case 3
x=[-1.36 -0.7 -0.3 0.3 0.8 1.35];
y=[48 64 78 87 90 81];
case 4
x=[-1.3 -0.82 -0.46 -0.1 0.39 0.7 1.62];
y=[22 32 86 92 95 83 31];
end

xx=x;
yy=y;
xl=linspace(xx(1),xx(end),100);
c=polyfit(xx,yy,2);
a=c(1);
b=c(2);
P=polyval(c,xl);
switch i
case 1
plot(x,y,'b*','LineWidth',0.7)
hold on
plot(xl,P,'-b','LineWidth',2)
case 2
plot(x,y,'g*','LineWidth',0.7)
hold on
plot(xl,P,'g-','LineWidth',2)
case 3
plot(x,y,'r*','LineWidth',0.7)
hold on
plot(xl,P,'r-','LineWidth',2)
case 4
plot(x,y,'m*','LineWidth',0.7)
hold on
plot(xl,P,'m-','LineWidth',2)
end
end
hold off
title('Comparison of Various Mineralization in Standard Score')
xlabel('Standard Score(1)')
ylabel('Mineraliztion Activity(%)')
legend('c(BL21)','c(BL21)','c(C3H5O3Na)','c(C3H5O3Na)','c(NaNO3)','c(NaNO3)','pH','pH')
set(gca,'fontsize',20);
        The fitted functions are showed as follows:
        Fitted with y linearly to get the overall regression equation which can describe the weight of four variables respectively.
Overall regression equation:
With:
Model and Result
X: About different factors’ “Standard Score”
Y: It’s totally show that Mineralization Activity are affected by different factors
        The figure indicates that Mineralization Activity is affected by different factors.
        Result: The graph above depicts the polynomial regression of 4 factors. In general, for each of those four factors, the mineralization activity shows the similar tendency of going up first and down later with the increase of each factor.
Conclusion
        For our result, since we successfully found out the proper materials being used in professional research, the model we constructed was able to help us better understand how each biological material can be impacted under different concentrations. This model can also be referenced by other teams or paper in the future if needed.
Reference:  https://2017.igem.org/Team:SZU-China