Modeling
Table 1 shows the experimental data of the antibacterial ability test of five different antimicrobial peptides. We tried different models to fit the data and found that the following model can accurately simulate the experimental data.
f(x)=(p1x+p2 )/(x+q1) (1)
Where p_1, p_2 and q_1 are the parameters need to be determined.
Table 1. OD600 values of the five antimicrobial peptides measured at different concentrations.
Concentration(μM) Hydramacin-1-6His Spheniscin-2 LL-37 Sparamosin 26-54 Fusion
0.1 0.9527 0.950566667 0.957533 0.9635 0.9572
1 0.812333333 0.808566667 0.900667 0.940167 0.883133
2 0.684866667 0.858166667 0.864067 0.9234 0.881878
4 0.570133333 0.840466667 0.817233 0.896633 0.851444
6 0.518966667 0.755133333 0.714233 0.8241 0.764489
8 0.433133333 0.6409 0.640467 0.807067 0.696144
10 0.4179 0.674366667 0.601267 0.7796 0.685078
15 0.2364 0.616166667 0.577733 0.672467 0.622122
20 0.112166667 0.569466667 0.533833 0.6305 0.577933
25 0.504566667 0.514433 0.630033 0.549678
50 0.362966667 0.2645 0.524167
Coding
Below is the code for our calculation of the model (1) in MATLAB:
    
      clear;clc
      AA=importdata('Table1.txt'); 
      con=AA(:,1);
      c_20=con(1:9);
      c_25=con(1:10);
      c_50=con;
      hyd=AA(:,2);hyd=hyd(1:9);
      sph=AA(:,3);
      LL=AA(:,4);
      spa=AA(:,5);
      fusion=AA(:,6);fusion=fusion(1:10);
      %
      p1=[-0.2963 0.1248 0.0656 0.3266 0.3097];
      p2=[10.62 21.04 18.24 19.88 13.6];
      q1=[11.56 23.11 19.29 20.32 14.25];
      x=0:0.05:500;
      y1=(p1(1)*x+p2(1))./(x+q1(1));
      y2=(p1(2)*x+p2(2))./(x+q1(2));
      y3=(p1(3)*x+p2(3))./(x+q1(3));
      y4=(p1(4)*x+p2(4))./(x+q1(4));
      y5=(p1(5)*x+p2(5))./(x+q1(5));
      %
      figure,plot(x,y1,'-')
      hold on, plot(c_20,hyd,'s'),xlim([0 25])
      %
      figure,plot(x,y2,'-')
      hold on, plot(c_50,sph,'d'),xlim([0 55])
      %
      figure,plot(x,y3,'-')
      hold on, plot(c_50,LL,'p'),xlim([0 55])
      %
      figure,plot(x,y4,'-')
      hold on, plot(c_50,spa,'o'),xlim([0 55])
      %
      figure,plot(x,y5,'-')
      hold on, plot(c_25,fusion,'h'),xlim([0 30])
Model Results：
1. Hydramacin-1-6His
Figure 1. Fitting results of Hydramacin-1-6His
Coefficients (with 95% confidence bounds):
    p1 = -0.2963 (-0.7429, 0.1502)
    p2 = 10.62 (2.431, 18.82)
    q1 = 11.56 (1.929, 21.2)
Goodness of fit:
    SSE: 0.01202
    R-square: 0.9788
    Adjusted R-square: 0.9717
    RMSE: 0.04476
2. Spheniscin-2
Figure 2. Fitting results of Spheniscin-2
Coefficients (with 95% confidence bounds):
    p1 = 0.1248 (-0.1875, 0.4371)
    p2 = 21.04 (2.966, 39.12)
    q1 = 23.11 (2.193, 44.03)
Goodness of fit:
    SSE: 0.0144
    R-square: 0.9522
    Adjusted R-square: 0.9402
    RMSE: 0.04243
3. LL-37
Figure 3. Fitting results of LL-37
Coefficients (with 95% confidence bounds):
    p1 = 0.0656 (-0.1894, 0.3206)
    p2 = 18.24 (6.142, 30.33)
    q1 = 19.29 (5.647, 32.93)
Goodness of fit:
    SSE: 0.01348
    R-square: 0.9678
    Adjusted R-square: 0.9597
    RMSE: 0.04104
4. Sparamosin 26-54
Figure 4. Fitting results of Sparamosin 26-54
Coefficients (with 95% confidence bounds):
    p1 = 0.3266 (0.201, 0.4523)
    p2 = 19.88 (11.11, 28.64)
    q1 = 20.32 (10.95, 29.69)
Goodness of fit:
    SSE: 0.002975
    R-square: 0.9864
    Adjusted R-square: 0.9829
    RMSE: 0.01928
5. Fusion
Figure 5. Fitting results of Fusion
Coefficients (with 95% confidence bounds):
    p1 = 0.3097 (0.1204, 0.499)
    p2 = 13.6 (4.785, 22.41)
    q1 = 14.25 (4.63, 23.87)
Goodness of fit:
    SSE: 0.003162
    R-square: 0.9826
    Adjusted R-square: 0.9776
    RMSE: 0.02125
Model Prediction
We used the model (1) to predict the OD600 values of the five antimicrobial peptides at which the concentration would reach zero.
Figure 6. OD600 values of the five antimicrobial peptides varying with concentration predicted by the model.
Conclusion
According to the above simulation results (Figure 1~5), our model (1) can accurately simulate the experimental data (R-squares of the fitting results are higher than 0.95). Therefore, we used the model (1) to predict the antibacterial effect (OD600 values) of the five antimicrobial peptides varying with concentration. As shown in Figure 6, when the concentration of Hydramacin-1-6His approached 35.8μM, the OD600 value would decrease to 0. In contrast, the OD600 values of other antimicrobial peptides can hardly be reduces to 0 even when the concentration is increased to a high level.