## Design of Experiments

**Achievements:**

1. Multifactorial optimisation of protein expression for enhanced phosphate sequestration.

2. Robust characterisation of PPK protein expression profile.

3. Expand the use of Design of Experiments within iGEM for more efficient, robust part characterisation.

**Introduction**

Design of Experiments (DoE) is a statistical method that allowed us to design the most efficient experiments to determine the factors that influence the expression of our PPK enzyme and the expression of our Eut (microcompartment) proteins. By using DoE, we can efficiently explore a very large experimental space in a small number of experiments, allowing us to test multiple hypotheses at once in a rapid and robust manner. Performing our measurements using the statistical tools of DoE allowed us to develop an improved understanding of the experimental factors affecting protein expression in the Phosphostore system, within the limited time frame available for an iGEM project.

**Method - PduD(1-20)_mCherry_cgPPK ( BBa_K2213005) Expression Optimization**

In order to optimise the efficiency of our engineered phosphate-accumulating organism, we wanted to find the ideal expression conditions for the PduD(1-20)_mCherry_cgPPK (**BBa_K2213005**) under a T7 promoter in BL21 (DE3) *E. coli* cells. We used JMP software by SAS to design our experiments. We decided to focus our analysis on continuous factors as more information can be extracted from a small number of experiments. With this in mind, we chose to investigate the following factors:

- OD at induction
- IPTG concentration in inducer: (0.1 - 1.0mM)
- Post induction temperature: (20ºC and 37ºC)
- post induction time: (4 and 24 hours)

**Round 1 of DoE:**

**Figure 1.**Relative mCherry fluorescence from raw liquid culture expressing the PduD(1-20)_mCherry_cgPPK (

**BBa_K2213005**) construct under different conditions.

**Round 2 of DoE**

With the results from the first round, it was clear that a higher OD at induction yielded more protein. Because of this we decided to fix the induction OD at 0.8. This removed one of the factors, allowing us to create higher resolution data with the same number of runs. With our remaining factors we used the inbuilt interaction profiler to decide on the ranges of our factors for round 2.

**Figure 2.**The interaction profile of the input factors, maximised for yield. OD600 at induction consistently correlated with higher yields. The profiler also suggests that optimal conditions for expression of PduD(1-20)_mCherry_cgPPK (

**BBa_K2213005**) are above 20°C, a post-induction growth period above 24 hours and an IPTG concentration above 1mM.

With this information we chose the following ranges for the factors listed below:

IPTG concentration (mM) | 1 – 10 |

Post induction temperature (ºC) | 16, 20, 24 |

Post induction time (hours) | 24, 48 |

These choices in ranges proved to be significantly closer to the optimum as evident from figure 3:

**Figure 3.**mCherry fluorescence measurements from round one (Purple), mCherry fluorescence measurments from round 2 (Pink). The readings from the second round have saturated the detector which is why all of the peaks are the same.

As you can see from the graph above, The results from round 2 all exceed the results of round 1. This is because we have shifted the ranges within each variable towards the optimum, thus shifting the range of our yield to a higher level.

**Conclusion**

From these 2 rounds of DoE we saw a huge increase in the yield of the protein. We found the optimal conditions to be:

Optical Density (ABS λ 600 nm) | 0.8 |

IPTG concentration (mM) | 1 |

Post induction temperature (ºC) | 24 |

Post induction time (hours) | 48 |

This is just one example where we have used DoE in our project but the scope for its application is huge as it allows the user to eliminate factors with little influence, focusing sequential rounds on the factors that matter the most. We used DoE to optimise the synthesis of EutM protein; the results of which can be seen at **BBa_K2213001**. In conclusion we found DoE to be an incredibly useful tool and would recommend it to any other teams with projects where optimisation, characterisation or enhanced statistical understanding is key.