Modeling

In this section, we applied numerical models to simulate a three-dimensional model of time, IPTG concentration, and GLBP-VP7-VP1-GFP fluorescent protein values. According to this model, we can explore the effect of time and IPTG concentration on GLBP-vp7-vp1-GFP fluorescent protein. IPTG induction time was 0h, 2h, 4h, 6h and 8h, and IPTG concentration was 0.1 mmol ; 0.25mmol ; 0.5mmol ; 1 mmol ; 5mmol and 10mmol. Table 1 shows experimental data for IPTG concentration, time and GLBP-vp7-vp1-GFP fluorescent protein.

Since the experimental data is a typical two - dimensional array, we can establish a two - dimensional spline interpolation model to predict the maximum point and its corresponding coordinate values. With the help of the two-dimensional interpolation function of Matlab, the interpolation surface, the highest point, and the contour line can be made.

The specific code is as follows:

  clear
  clc
  x=[0.1 0.25 0.5 1 5 10];
  y=[0 2 4 6 8];
  z=[528402.0667 459117.7333 391075.0667 384583.0667 292247.4 213120.4;...
      703278.7333 538158.0667 516417.7333 554815.4 501831.4 556734.0667;...
      1265326.4 1093716.4 997797.7333 989856.4 916380.0667 1003649.733;...
      1380745.067 1216916.4 1179936.067 1126737.4 1062195.067 1152024.733;...
      1479199.067 1228957.4 1121753.4 1158131.067 1084222.733 1285061.4];
  xi=0:0.25:9;
  yi=0:0.2:10;
  [x1,y1]=meshgrid(xi,yi)
  z1=interp2(x,y,z,x1,y1,'spline');
  surf(x1,y1,z1);
  [i,j]=find(z1==max(max(z1)))
  xmax=xi(j),ymax=yi(i),zmax=z1(i,j)
  hold on
  plot3(xmax,ymax,zmax,'r*','linewidth',2')
  hold off

Thus, the surface model can be observed from different angles and its variation law can be analyzed.

Model Results：

1. The three-dimensional model diagram of the time-IPTG concentration-GFP surface.

Figure 1：The three-dimensional model diagram of the time-IPTG concentration-GFP surface.

According to figure 1, when the IPTG concentration is about 10mM and the time is about 3h,the highest of GLBP-vp7-vp1-GFP protein expression was 2.510⁶-3×10⁶.

Conclusion

At the same concentration, the model showed that the fluorescent protein GFP showed an increasing trend with time. At the same time, the fluorescent protein GFP showed a decreasing trend with the increase of IPTG concentration. The model predicted that the expression protein content of GLBP-vp7-vp1-GFP was the highest after induction for 3h at IPTG concentration of 10mM.

Membrane-associated protein GLBP can bind GLBP-vp7-vp1-GFP protein to the surface of bacteria. According to the model, the GFP signal increased with time, indicating that the fusion protein was successfully bound to the surface of bacteria. Meanwhile, the model can be used to predict the relationship the expression of GLBP-vp7-vp1-GFP protein, IPTG concentration and time. It can provide effective data support for the future production of bivalent vaccine vp1-vp7 by engineering bacteria.