Modeling
In order to find the optimal condition for alcohol production by our engineered yeast, we designed several control groups and collected samples respectively to detect the alcohol yield by Megazyme Ethanol Kit.
Below is the initial data and there are two factors, enzyme concentration and fermentation hours influencing the alcohol production of our engineered strains.
After analyzing the scatterplots, we chose to use two-dimensional interpolation to construct models by MATLAB and we also give the coding below:
clear;clc;
t0=[0 4 8 12 16 20 24];
x0=[0 0.3 0.6 1];
z1=[0.16566911 0.158452214 0.151526625 0.182264212 0.178289281 0.180093505 0.199272782;...
0.155877436 0.159194577 0.165697301 0.180394209 0.190777894 0.165969814 0.184500698;...
0.160923625 0.151958887 0.141687966 0.174812391 0.163376242 0.183852305 0.169841378;...
0.138944042 0.151883711 0.12808111 0.175648724 0.162624482 0.169634644 0.167388761];%1号样本
z2=[0.167116248 0.141349674 0.143915055 0.182828032 0.166223533 0.191557845 0.179604861;...
0.185017533 0.150511749 0.158405229 0.185412207 0.181286924 0.192187444 0.180976823;...
0.173384047 0.168469416 0.146555612 0.186755978 0.19386011 0.186229746 0.181521849;...
0.15533241 0.157127237 0.154646429 0.19198071 0.175056713 0.174662039 0.182987781];%2号样本
z3=[0.150154663 0.148237675 0.137271376 0.198154539 0.196528858 0.186098188 0.166693383;...
0.143229074 0.138934645 0.146471039 0.190721512 0.196735592 0.176362896 0.172453744;...
0.150276824 0.14330425 0.146818728 0.183467028 0.184472507 0.181164763 0.173346459;...
0.145709882 0.1465932 0.126145328 0.162304984 0.182095066 0.163000362 0.15570829];%3号样本
z4=[0.150878232 0.156281507 0.154308137 0.168760723 0.188231307 0.1738445 0.176898525;...
0.155407586 0.171504647 0.139084997 0.188080955 0.19630333 0.182470946 0.178928277;...
0.146048174 0.147927574 0.158771712 0.199629868 0.19113498 0.187141255 0.179961947;...
0.156027788 0.149713004 0.149534461 0.175676915 0.198041775 0.170865651 0.180807677];%4号样本
t=0:0.5:24;%每间隔0.5小时取一个时刻
x=0:0.01:1;%浓度间隔为0.01
zA=interp2(t0,x0,z1,t,x','spline');%1号样本插值
zB=interp2(t0,x0,z2,t,x','spline');%2号样本插值
zC=interp2(t0,x0,z3,t,x','spline');%3号样本插值
zD=interp2(t0,x0,z4,t,x','spline');%4号样本插值
subplot(2,2,1),surf(t,x,zA);
subplot(2,2,2),surf(t,x,zB);
subplot(2,2,3),surf(t,x,zC);
subplot(2,2,4),surf(t,x,zD);
zAmax=max(max(zA))
zBmax=max(max(zB))
zCmax=max(max(zC))
zDmax=max(max(zD))
[i1,j1]=find(zA==max(max(zA)));
t1=t(j1)
x1=x(i1)
[i2,j2]=find(zB==max(max(zB)));
t2=t(j2)
x2=x(i2)
[i3,j3]=find(zC==max(max(zC)));
t3=t(j3)
x3=x(i3)
[i4,j4]=find(zD==max(max(zD)));
t4=t(j4)
x4=x(i4)
Finally, we obtained the interpolation curved surfaces of the 4 yeast groups as showing below:
Figure 1. Alcohol production ability of 4 different engineered yeast against enzyme concentration and fermentation hours
By MATLAB, it can be calculated that the highest value of alcohol concentration (g/L) and the corresponding fermentation conditions:
- For A strain, the highest value of alcohol concentration is 0.1993 g/L when enzyme concentration is given 0 and the fermentation time is 24 hours;
- For B strain, the highest value of alcohol concentration is 0.1991 g/L when enzyme concentration is given 0.01 and the fermentation time is 22 hours;
- For C strain, the highest value of alcohol concentration is 0.2049 g/L when enzyme concentration is given 0 and the fermentation time is 13.5 hours;
- For D strain, the highest value of alcohol concentration is 0.2018 g/L when enzyme concentration is given 0.56 and the fermentation time is 13 hours.
Overall consideration, we strongly recommend yeast C for alcohol industry use which requires less fermentation hours, less additional enzyme but higher yield.