Modeiling

In this part, we used a numerical model to simulate the effect of the concentration of positive compounds PF-04937319 and compound 13926 on glucokinase activity. Then, according to the numerical results, the concentrations of the compounds PF-04937319 and 13926 corresponding to the peak enzyme activity were predicted. The effect of the concentration of positive compound PF-04937319 and compound 13926 on glucokinase activity was compared. Table 1 presents the experimental data on the concentration of positive compound PF-04937319 and glucokinase activity. Table 2 shows the experimental data on the concentration of compound 13926 and glucokinase activity.

Table 1. Effect of the concentration of positive compound PF-04937319 on glucokinase activity2. Inoculate glycerol bacteria pQE-30

Concentration of PF-04937319（μM)	Glucokinase activity
10	1.133620825
1	1.220936
0.5	1.0094828
0.1	0.67019705
0.01	0.14211823
0.001	0.105418715
0.0005	0.031034483
0.0001	-0.031280798
0.00001	0.053078823
0.000001	0.1724138

Table 2. Effect of the concentration of compound 13926 on glucokinase activity

Compound 13926 concentration（μM)	Glucokinase activity
200	1.075
100	1.155820075
50	1.10079395
20	0.99140215
10	1.100529075
1	0.64272485
0.5	0.534744267
0.2	0.311772475
0.1	0.292063475
0.05	0.169973548
0.01	0.224603175
0.001	0.167460318
0.0005	0.026587301
0.0001	0.188492075
0.00001	0.241402105
0.000001	0.2276455

1. Input software analysis, we can find that the data conforms to the law of negative index. A differential equation (1) can be used to establish the relationship between concentration of compound and glucokinase activity. Using the data, the parameter values of the analytic solution ( 2 ) of the differential equation are fitted.

The differential equation is as follows：

The analytical solution of the equation is as follows：

d_y

d_x

= b(y-c)

Where a, b and c is the parameter. y is glucokinase activity, and x represents compound concentration.

y =

ae^bx+c

2. Using nonlinear fitting by MATLAB can give two sets of data corresponding to the value of the parameters.

Coding

y1=[1.133620825 1.220936 1.0094828 0.67019705 0.14211823 0.105418715 ... 0.031034483 0.053078823 0.1724138];
x2=[10 1 0.5 0.2 0.1 0.05 0.01 0.001 0.0005 0.0001 0.00001 0.000001];
y2=[1.100529075 0.64272485 0.534744267 0.311772475 0.292063475 0.169973548 ... 0.224603175 0.167460318 0.026587301 0.188492075 0.241402105 0.2276455];% Glucokinase=@(a,t)a(1)*exp(-t/a(2))+a(3);%Glucokinase a0=[-2 2 1];
b0=[-1 0.5 1];%
a=nlinfit(x1,y1,Glucokinase,a0)%
b=nlinfit(x2,y2,Glucokinase,b0)%
PF_04937319=0:0.01:12;
PF_13926=0:0.01:12;%
Glucose_activity_1=Glucokinase(a,PF_04937319);%
Glucose_activity_2=Glucokinase(b,PF_13926);%
plot(x1,y1,'k*',PF_04937319,Glucose_activity_1,'r','linewidth',2');
hold on
plot(x2,y2,'k+',PF_13926,Glucose_activity_2,'g','linewidth',2');
hold off

Model Results：

1. The model between PF-04937319 and glucokinase activity

Figure 1. Model diagram of positive compound PF-04937319 concentration and glucokinase activity

2. The model between compound 13926 and glucokinase activity

Figure 2. Model diagram of compound 13926 on the activity of glucokinase activity

3. The model of PF-04937319 and compound 13926 on glucokinase activity.

Figure 3. Model diagram of compound 13926 and PF-04937319 on glucokinase activity.

Conclusion

From the simulation results, our models can accurately simulate the experimental data (R-square>0.95). Based on the above numerical results, we can predict compound 13926 and PF-04937319 on glucokinase activity. As shown in Figure 1~ Figure 3, the glucokinase activity increased first, and then stabilized with the increase of compound 13926 concentration and PF-04937319. When the concentration of compound 13926 was 100μM, the glucokinase activity was the highest. But when the concentration of PF-04937319 was 10μM, the activity of glucokinase was the highest. This model can be used to analyze the effect of compound 13926 on insulin secretion and evaluate the potential of compound 13926 in the treatment of type 2 diabetes.