Modeling

Modeling of strain fermentation growth curves：

A mathematical model was applied to study the relationship between OD₆₀₀ and the growth time of SF-1 and WT. The maximum OD₆₀₀ of the engineered strain was then predicted based on the model results.

Considering the changing trend of the experimental data, we choose the following model for numerical simulation:

f(x) = a / (b + exp(-c ∙ x)) (1)

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

Below is the experimental data of the OD₆₀₀ value of SF-1 and WT changed with time.

Matlab Code:

clear;clc;
% exp. data
Data=importdata('data41.txt');
time=Data(:,1);
SF1=Data(:,2);
WT=Data(:,3);
% model simulation
aa=[0.001907 0.01861];
bb=[0.0007284 0.01497];
cc=[0.4245 0.2651];
x=0:0.5:35;x=x';
y1=aa(1)./(bb(1)+exp(-cc(1)*x));
y2=aa(2)./(bb(2)+exp(-cc(2)*x));
% figures
figure, plot(time,SF1,'o')
hold on, plot(x,y1,'-')
%
figure, plot(time,WT,'s')
hold on, plot(x,y2,'-')
        

Model Results：

1. SF-1

Figure 1. Fitting model of SF-1

General model:
        f(x) = a/(b+exp(-c*x))

Coefficients (with 95% confidence bounds):
        a = 0.001907 (-0.01341, 0.01722)
        b = 0.0007284 (-0.00505, 0.006507)
        c = 0.4245 (-0.07615, 0.9252)

Goodness of fit:
        SSE: 0.04365
        R-square: 0.9939
        Adjusted R-square: 0.9898
        RMSE: 0.1206

2. WT

Figure 2. Fitting model of WT

General model:
        f(x) = a/(b+exp(-c*x))

Coefficients (with 95% confidence bounds):
        a = 0.01861 (0.01006, 0.02716)
        b = 0.01497 (0.008301, 0.02163)
        c = 0.2651 (0.2348, 0.2953)

Goodness of fit:
        SSE: 0.0004011
        R-square: 0.9997
        Adjusted R-square: 0.9996
        RMSE: 0.01156

Conclusion

The modeling results showed that the OD₆₀₀ of SF-1 and WT showed a trend of increasing at first and then tending to be stable with the increase of time. In addition, the OD₆₀₀ of SF-1 was higher than that of WT, indicating that genetic engineering did not affect the growth of yeast strain SF-1.

According to the expression of model (1), f(x) tends to a/b as x approaches infinity. It is calculated that the OD₆₀₀ value of SF-1 will gradually approach 2.6181(0.001907/0.0007284) with time. When the time was 29.5h, the OD₆₀₀ value of SF-1 is 2.605 (99.5%×2.6181), indicating that the engineering strain was nearly stopped. The OD₆₀₀ value of WT will gradually approach 1.2432 (0.01861/0.01497) with time. When the time was 35.6h, the OD₆₀₀ value of WT is 1.2370 (99.5%×1.2432), and the engineering strain had nearly stopped growing.