In this part, we established a mathematical model of fermentation time and yeast OD600 to predict the high yeast concentration. The types of yeast were yeast YEP, yeast YEP-FAS1, and yeast YEP-FAS2. The fermentation time of yeast was 0h, 15h, 23h, 38h, 46h, and 61h. Table 1 shows the fermentation time of yeast, and yeast OD600 experimental data.
| Fermentation time（h） | YEP | YEP-FAS1 | YEP-FAS2 |
|---|---|---|---|
| 0 | 0.0625 | 0.0635 | 0.053 |
| 15 | 1.4195 | 1.2355 | 1.538 |
| 23 | 1.511 | 1.55 | 1.6035 |
| 38 | 1.6015 | 1.729 | 1.756 |
| 46 | 1.5755 | 1.7375 | 1.735 |
| 61 | 1.6035 | 1.7685 | 1.7955 |
Based on the analysis of the scatter diagram, we use the logarithmic function to fit experimental data. Model 1shows a reflection rate inversely proportional to time.
y = a ln(bx + c) (1)
clear;clc;
t0=[0 15 23 38 46 61];
y10=[0.0625 1.4195 1.511 1.6015 1.5755 1.6035];
y20=[0.0635 1.2355 1.55 1.729 1.7375 1.7685];
y30=[0.053 1.538 1.6035 1.756 1.735 1.7955];
yy=@(a,t)a(1)*log(a(2)*t+a(3));%
a0=[1 0.01 0.01];%
b0=a0;%
c0=a0;%
a=nlinfit(t0,y10,yy,a0);%
b=nlinfit(t0,y20,yy,b0);%
c=nlinfit(t0,y30,yy,c0);%
t=0:0.5:72;
y1=yy(a,t);%
y2=yy(b,t);%
y3=yy(c,t);%
figure(1)
plot(t0,y10,'b*',t,y1,'r','linewidth',2')
figure(2)
plot(t0,y20,'k*',t,y2,'b','linewidth',2')
figure(3)
plot(t0,y20,'g*',t,y3,'m','linewidth',2')
figure(4)
plot(t,y1,'r',t,y2,'b',t,y3,'m','linewidth',2')
xx1=[3 25.5 51];
yy1=[1.231 1.512 1.771];
hold on
plot(xx1,yy1,'k*','linewidth',2')
hold off
Figure 1. Modeling results of yeast OD600 and fermentation time
According to figure 1, the OD600 of yeast YEP, yeast YEP-FAS1, and yeast YEP-FAS2 were not significantly different between 1.4 and 1.6. It can be seen that the OD600 of yeast YEP, yeast YEP-FAS1, and yeast YEP-FAS2 increased first and then stabilized with the increase of time, which was consistent with the growth curve of yeast.
Through the growth curve of yeast, it can be predicted that the concentration of yeast can reach a high level after 30-50 hours of fermentation. Meanwhile, the maximum concentration of yeast YEP-FAS1 and yeast YEP-FAS2 was not significantly different from that of yeast YEP. It indicating that overexpression of the ethyl caproate gene did not affect the growth of yeast strains. This model can lay a foundation for improving the yield of ethyl caproate by overexpression of the ethyl caproate gene, further improving the quality of flavor liquor and increasing the content of aroma substances.
