Modeling

In this section, numerical model was applied to investigate the rapamycin production ability of two types of Streptomyces rapamycin, including wild-type and double-knockout Streptomyces rapamycin. Table 1 presents the experimental data of the rapamycin producing ability of these two Streptomyces rapamycin species over time.

Considering the changing trend of the experimental data and the fact that the simulation results must be positive in the definition domain (0<time≤11), we choose the following model for simulation:

f (x) = p₁ ∙ x⁴ + p₂ ∙x³ + p₃ ∙ x² + p₄ ∙ x + p₅ (1)

Where p₁, p₂, p₃, p₄ and p₅ are the parameters need to be fitted.

Coding

The Matlab program code is shown below:

clear;clc;
% exp. data
Data=importdata('data.txt')
time=Data(:,1);
NRRL=Data(:,2);
M=Data(:,3);
% model simulation
p1=[-0.01129 -0.0346];
p2=[0.1287 0.3082];
p3=[-0.9952 0.16];
p4=[12.29 12.34];
p5=[3.035e-14 2.083e-14];
x=0:0.1:12;x=x';
y1=p1(1)*x.^4 + p2(1)*x.^3 + p3(1)*x.^2 + p4(1)*x+ p5(1);
y2=p1(2)*x.^4 + p2(2)*x.^3 + p3(2)*x.^2 + p4(2)*x+ p5(2);
% figures
figure, plot(time,NRRL,'o')
hold on, plot(x,y1,'-')
%
figure, plot(time,M,'s')
hold on, plot(x,y2,'-')
        

Model Results:

1. NRRL 5491

Figure 1. Comparison between simulation results and experimental data of wild-type Streptomyces rapamycin.

Coefficients:

p1 = -0.01129
p2 = 0.1287
p3 = -0.9952
p4 = 12.29
p5 = 3.035e-14

Goodness of fit:

SSE: 2.89e-27
R-square: 1
Adjusted R-square: NaN
RMSE: NaN

2. M271_14685/M271_14690

Figure 2. Comparison between simulation results and experimental data of double-knockout Streptomyces rapamycin.

Coefficients:

p1 = -0.0346
p2 = 0.3082
p3 = 0.16
p4 = 12.34
p5 = 2.083e-14

Goodness of fit:

SSE: 4.725e-27
R-square: 1
Adjusted R-square: NaN
RMSE: NaN

Conclusion

The model (1) can accurately simulate the variation of the experimental data with high R-square. According to the model simulation results, we predicted the maximum value and corresponding time of rapamycin production ability by these two Streptomyces. As shown in Figure 1 and 2, the wild-type Streptomyces rapamycin will reach peak on yield rapamycin of 7.5 day; In contrast, the double-knockout Streptomyces rapamycin will reach peak on yield rapamycin of 8.3 day.