Modeling
In this part, a mathematical model can be established by using the relationship between the number of colonies and the length of the inserted fragment. The lengths of inserted target gene fragments are:1258bp-TIR-Kan gene,2623bp-TIR-Kan gene,3292bp-TIR-Kan gene,3360bp-TIR-Kan gene, and 3452bp-TIR-Kan gene. Table 1 shows the fragment length and colony number of the target gene.
Table 1 Fragment length and colony number of target gene
Segment size（bp） 1258 2151 3292 3452
Number of colonies 500 350 100 100
Here, we used Model (1) to simulate the fragment length and colony number of target gene.
Linear regression model：
Where:
Substitute the sample point of the experiment into the calculated value. The results are as follows：
Coding
    
      x=[1258 2151 3292 3452];
      y=[500 350 100 100];
      A=polyfit(x,y,1)
      Gene_fragment_length=[800:4000];
      Insertion_efficiency=polyval(A,Gene_fragment_length);
      plot(x,y,'b*',Gene_fragment_length,Insertion_efficiency,'r','linewidth',2');
Model Results：
Figure 1. Model diagram of gene fragment length and colony number.
Conclusion
The higher the number of colonies, the higher the efficiency of gene insertion. The results showed that the length of the target gene fragment was inversely proportional to the insertion efficiency. This model can predict the insertion efficiency of gene fragments.And the model predicted that the maximum length of the inserted gene fragment is 3913.5bp.