Modeling

In this part, we attempted to build a model to fit the inhibitory effect of the compound 355 on gluconeogenesis and gluconeogenic key enzymes (i.e., G6Pase and PEPCK). Table 1 shows the influence of the compound 355 concentration on the inhibitory effect of the gluconeogenesis, G6Pase and PEPCK.

According to the analysis and numerical experiment, the following model was adopted to fit the experimental results:

f(x) = a∙e^bx + c∙e^dx (1)

Where a, b, c and d are the parameters need to be determined.

Coding

Below is the code for our calculation of the model (1) in MATLAB:

clear;clc;
% exp. data
con=[0 5 10 20]; % concentration
TYS=[1.7571045  1.375465667 1.125697333 0.435672333];
G6=[149.3977    107.2091    96.04601    83.69484];
PEPCK=[222.4381 60.78495    29.26984    12.59625];
% model simulation
a=[1.749 40.85 168.2];
b=[-0.04519 -0.4011 -0.3964];
c=[-1.974*10^-15 108.5 54.24];
d=[1.628 -0.01301 -0.07325];
x=0:0.1:25;
y1=a(1)*exp(b(1)*x)+c(1)*exp(d(1)*x);
y2=a(2)*exp(b(2)*x)+c(2)*exp(d(2)*x);
y3=a(3)*exp(b(3)*x)+c(3)*exp(d(3)*x);
% figures
figure, plot(con,TYS,'o')
hold on, plot(x,y1,'-')
%
figure, plot(con,G6,'s')
hold on, plot(x,y2,'-')
%
figure, plot(con,PEPCK,'s')
hold on, plot(x,y3,'-')
        

Model Results：

1. Gluconeogenesis

Figure 1. Fitting results of Gluconeogenesis

Coefficients:
        a = 1.749
        b = -0.04519
        c = -1.974e-15
        d = 1.628

Goodness of fit:
        SSE: 0.000617
        R-square: 0.9993
        Adjusted R-square: NaN
        RMSE: NaN

2. G6Pase

Figure 2. Fitting results of G6Pase

Coefficients:
        a = 40.85
        b = -0.4011
        c = 108.5
        d = -0.01301

Goodness of fit:
        SSE: 4.133e-23
        R-square: 1
        Adjusted R-square: NaN
        RMSE: NaN

3. PEPCK

Figure 3. Fitting results of PEPCK

Coefficients:
        a = 168.2
        b = -0.3964
        c = 54.24
        d = -0.07325

Goodness of fit:
        SSE: 5.807e-19
        R-square: 1
        Adjusted R-square: NaN
        RMSE: NaN

Conclusion

From the simulation results, the model (1) is accurate with R-square close to 1 for all three sets of data. We believe that this model can be used to predict the inhibitory effect of the compound 355 on the gluconeogenesis. This model is still of great significance for promoting the development of diabetes drugs and guiding drug dosage.