Introduction

Our mice experiment has primarily proven the validity of our project. However, just like most scientific immune experiments on animals, the aim of our mice experiment was verification instead of exploring the optimal conditions for the production of our vaccine. In fact, fewer optimization experiments have been done by pure scientific researches, as most scientists care about facts and theories only, whereas exploring the optimal conditions is often viewed as the task of pharmaceutical factories. Yet since igem itself frequently involves industrial fields, which make igem seems like more an engineering competition than a science competition sometimes.
We investigated the methodology of Design of Experiment (DOE) in our project, and realized although most papers claim the wide application of DOE, the popularity of DOE is much lower in scientific fields compared with that in engineered fields. Perhaps the disparity of ideology between science and engineering determines this puzzling phenomenon. Consider the dual qualities of igem, we decided to explore on DOE further and design further experiments for pharmaceutical factories. We have also utilized DOE on our optimization of Bacillus subtilis medium experiment. Various designs have been made, and the overall runs of them all are too large for our laboratory.
But generally factories have adequate time and equipment to fulfill our designs, and different designs meet the requirement of different situations.

Sweeping factors

The final effects of the vaccine hinge on various factors, in fact perhaps over ten factors. Yet the more factors, the more runs. In our laboratory, an experiment involving over five factors is hard to design, whatever the method. Fortunately we were designing experiments for pharmaceutical factories, which enabled us to take more factors into account without sacrificing accuracy too much. The first step of any method in DOE is to make a list of controllable factors, and the second step is to find out levels of each factors. In our design, we finally selected eight factor as follows:
The rate of four engineered bacteria, which produce antigen, LTB, KNFα and reporter respectively;(We selected the concentration of antigen as our standard, fixed at 1, and the rates of other three bacteria to engineered bacteria produced antigen provides three independent factor);

• The area of the sticky vaccine;
• The concentration of bacteria per unit area;
• The body temperature of the vaccinees;
• The time consumed for culturing the bacteria;
• The molecule weight of the antigen;

The ranges of these factor is given as follows:

Factor	Level Values
LTB	-1 0 1
KNFα	-1 0 1
Reporter	-4 -3
Temperature/℃	35.5 36 36.5 37 37.5
Time/h	4 5 6 7
Area/	1 3 7 10
Concentration(the number of engineered bacteria per square centimeter )	7 8 9
Molecule Weight(K D)	10 20 40 80

Note:

The ranges of rates and concentration of engineered bacteria were too large, and thus we used the common logarithms instead of the original values. For example, the low level of LTB was -1, meaning the lowest rate of LTB to antigen was 0.1.

Abstract of DOE methods

The classification standards of DOE methods are not unified, and according to one classification the DOE methods can be classifies into three plots:
Factorial Designs: Factorial Design is the most traditional method of DOE, and theoretically all other plots origin from it. Factorial Design is recommended when the ranges of factors is too large.
Response Surface Designs: Response Surface utilizes response surface and excels in data analysis.
Taguchi Designs: Taguchi Designs utilizes orthogonal table to decrease runs, and emphasizes the stability of qualities. Some mathematicians doubt the accuracy of this method, yet its wide success has proven its power.
We have tried them all in our project.

Factorial Designs

To some extent, all DOE methods are branches of Factorial Designs. The easiest subplot of Factorial Designs is Full Factorial Designs, meaning making a list of all combinations of all levels, which in fact does nothing to minimizing the runs. Surly the overall runs of Full Factorial Designs is larger than any other method, yet it does provide the most detailed information, so it is recommended when the factory does not care about money and time.
Generally Full Factorial Design has nothing mathematically sophisticated, all required is to list the specific values of all factors without any limitation on levels, which grants us more flexibility and freedom. Here is our table of levels of factors:

Factor	Level Values
LTB	-1 0 1
KNFα	-1 0 1
Reporter	-4 -3
Temperature/℃	35.5 36 36.5 37 37.5
Time/h	4 5 6 7
Area/	1 3 7 10
Concentration(the number of engineered bacteria per square centimeter )	7 8 9
Molecule Weight(K D)	10 20 40 80

And we got our first design, whose number of overall runs is 17820!
Full Factorial Designs 17280 runs
In reality we did not deem this level values table was detailed enough, but the number of runs was already enormous. Perhaps only the biggest pharmaceutical factory can afford this design.
Next we turned to traditional Factional Factorial Designs. To minimize the runs, the levels of all factors were fixed at 2. A general 2-level-8-factor Full Factorial design contains 2^8=256 treatments, but we can further decrease the runs by defining alias. That is to say, define some specific factors as logical operation results of other factor.
Here we got a half and a quater Factional Factorial Designs, and the numbers of runs of them are 128 and 64.
Factorial Designs 64runs
Factorial Designs 128 runs
Any effort trying to decrease runs will inevitably lower the cogency of the experiments, and this influence is irreversible. Factories are supposed to strike a balance between the accuracy of experiments and the costs they can afford when designing experiments.

Plackett-Burman Design

As an important subplot of Factorial Designs, Plackett-Burman Design is excellent in dealing with mass factors. Generally it was applied in the primary experiments to select the key factors for further experiments. The number of runs can be controlled at very low values, yet it is hard to get the best treatment from Plackett-Burman Design.
Naturally the levels of all factors were two. On most occasions it is combined with other DOE methods, like RSM. In our project, we made three Plackett-Burman Designs of 12 runs, 20 runs and 48 runs. The more runs, the more reliable results will be get, but even the last design still requires further designs.
Plackett-Burman 20 runs
Plackett-Burman 12 runs
Plackett-Burman 48 runs

Response Surface Design

Utilized response surface and gradient, Response Surface Design excels in analysis of data, which makes it more mathematically gracefully than Taguchi Designs, and this accounts for why we selected it for our experiments on the optimization of medium The most widespread subplots of Response Surface Design is Central Composite Design and Box-Behnken Designs, both of which were considered when we designed our experiments on medium. The number of factors of Box-Behnken Designs is fixed on some given values, which does not include eight, therefore we had to turn to Central Composite Design (CCD). CCD itself contains three subplots, namely Central Composite Circumscribed Design (CCC), Central Composite Inscribed Design (CCI) and Central Composite Face-centered Design (CCF). Only CCC is rotatable, and thus CCC is mathematically preferred. We designed the experiments on CCC and CCF. The numbers of runs in half CCC and CCF designs were 154, whereas in quarter designs 90.
CCC 90runs
CCC 154runs
CCF 90runs
CCF 154runs
In spite of the mathematical advantages of CCC, the alpha value, which means the distance from axial point to the center point, is larger than one, some absurd treatment might be yielded. In our half CCC design the alpha value was 3.364, while in quarter CCC design 2.828. In both designs, some treatments are irrational, for their area or concentration were negative, which contradicts the common sense. However, factories can still adopt these CCC designs by giving up the irrational treatments.

Taguchi Design

Taguchi Designs use orthogonal table to decrease the runs. Created by Doctor Taguchi, it has obtained wide success all over the world, especially in Asia. Different from Response Surface Design, it does not aim to calculate a fitting surface or function but just find out the best level value of each factor. Generally the number of runs is smaller compared with RSM, yet the range of factors in Taguchi Design is relatively smaller.
We tried to make Taguchi Designs but our tool software minitab is unable to make the design with eight factor. Additionally, our ranges of factors were too large for Taguchi Design, therefore we gave up this method in our design.
If our vaccine is fortunate enough to be produced at mass scale, we hope our designs could help these pharmaceutical factories.