Abstract
Using statistical design of experiments, an optimisation experiment for V. natriegens growth media was performed. The final media recipe was \(30g/L\) yeast, \(40g/L\) tryptone, \(17g/L\) \(\ce{MgSO4}\) and \(13g/L\) \(\ce{NaCl}\), resulting in a doubling time of \(15.6\) minutes.
We used a definitive screening design of \(25\) experimental units to screen \(9\) ingredients at \(3\) levels. For the main optimization we used an I-optimal custom design of \(18\) experimental units made using JMP design software to find optimal levels of the \(4\) beneficial ingredients found in the screening experiment.
Introduction
Each of the \(9\) ingredients included at the start of this media optimisation process were found in existing V. natriegens media recipes. The levels in the screening experiment {None, Base and High} were selected with ‘Base’ being a rough average of what was found in existing media recipes. ‘High’ was selected to be twice as high as ‘Base’. Ingredient levels for the main experiment were decided on with direct reference to the analysis and conclusions of the screening experiment.
The first problem we ran into was that \(\ce{MgCl2}\) and \(\ce{Na2HPO4}\) were reacting to make insoluble \(\ce{Mg3(PO4)2}\). We discovered this while making some of the media for the screening experiment, where we observed precipitate forming. This would have been a problem because a culture growing in a media with precipitate would not be able to access the nutrients that had solidified. To isolate the ingredients causing precipitation, we added them together in pairs, one at a time in different beakers and recorded which formed a precipitate.
To make sure we were only growing V. natriegens in our media optimisation experiments, we autoclaved our media at \(121\) Celsius and \(15\) psi pressure for \(15\) minutes. This process also led to a series of chemical reactions that again produced insoluble precipitate for some media. To avoid these autoclave-induced reactions, we filter sterilised these media instead of autoclaving them. Filter sterilising fulfils the same role as autoclaving, but without the high temperature and pressure. We chose not to filter sterilise all of our media, however, since it takes longer and generates more lab waste.
For each different media, \(OD_{600}\) readings of a culture of V. natriegens were taken in 20 minute intervals. From this time series, growth rate was inferred with the regression equation \(\log OD=\beta_{0} + \mu t\), where \(\mu\) is the growth rate. Then another regression was done with growth rate as the response variable across all the different media ingredients. This provided estimates of the linear and quadratic effects of each ingredient on growth rate. From these estimates, a media with optimal levels of each ingredient can be made. We were only able to accurately measure \(OD_{600}\) up to about \(0.6\), so when cultures got close to this number, we diluted them (in the cuvette) to a tenth of the concentration.
Screening Experiment
Figure 1 shows the design matrix for the screening experiment. It is a definitive screening design with \(25\) observations. Each of the ingredients are tested at \(3\) levels (details of this are found in Figure 2) to allow estimation of quadratic effects.
| Ingredient | Low (-1) | Base (0) | High (+1) |
|---|---|---|---|
| Yeast | \(0\) | \(15g/L\) | \(30g/L\) |
| Tryptone | \(0\) | \(20g/L\) | \(40g/L\) |
| \(\ce{NaCl}\) | \(0\) | \(15g/L\) | \(30g/L\) |
| \(\ce{MgSO4}\) | \(0\) | \(17g/L\) | \(34g/L\) |
| Glucose | \(0\) | \(0.5\% w/v\) | \(1\% w/v\) |
| \(\ce{KH2PO4}\) | \(0\) | \(15g/L\) | \(30g/L\) |
| \(\ce{CaCl2}\) | \(0\) | \(0.5 mg/60 ml\) | \(1 mg/60 ml\) |
| \(\ce{NH4Cl}\) | \(0\) | \(5g/L\) | \(10g/L\) |
| Glycerol | \(0\) | \(4g/L\) | \(8g/L\) |
Figure 3 shows how well the linear model predicts actual growth rate. Here we can see \(4\) out of \(25\) points outside of the \(95\%\) region. This means \(0.16\) of points are as extreme as we would expect \(0.05\) of points, so our data appears to come from a distribution that has higher kurtosis than a normal distribution (which would result in more extreme values centred around the same mean).
Figure 4 shows parameter estimates of the most significant main and quadratic effects. From this we found yeast, tryptone, magnesium sulfate and sodium chloride to be significantly beneficial at non-zero levels, and that \(\ce{KH2PO4}\) had a significant and large negative effect on growth rate. Sodium chloride also had a significant quadratic effect, suggesting the optimal level is near \(15 g/L\).
Pre-Main Scoping Experiment
The screening experiment showed that we should use more yeast, tryptone and magnesium sulfate - but how much more? Before the main experiment, we want to quickly scope out where the media becomes oversaturated and insoluble at excessively high levels of ingredients. To do this we tested the best media predicted by the screening experiment (S), a high concentration media (H), and a very high concentration media (VH). The recipes, in {Yeast, Tryptone, \(\ce{MgSO4}\), \(\ce{NaCl}\)}, were S: {\(30,40,34,15\)}, H: {\(90,120,51,15\)}, and VH: {\(120,160,68,15\)}
This test showed that after autoclaving, VH media had dry ingredients baked to the bottom of the duran bottle, but H media was fine. The conclusion of this was that we used H as our most concentrated media.
Main Experiment
For the main experiment, we used a JMP I-optimal custom design, as suggested by our contacts at JMP. We tested \(4\) ingredients at \(3\) levels (with an extra level for yeast) with \(16\) observations. The design matrix is shown in Figure 5, and specific ingredient levels can be found in Figure 6. We have two extra points S: {\(-1,-1,-1,-1\)} and H: {\(1,1,1,1\)} from the pre-main experiment giving us \(18\) observations in total for the main experiment.
| Ingredient | Low (-1) | Base (0) | High (+1) |
|---|---|---|---|
| Yeast | \(30g/L\) | \(60g/L\) | \(90g/L\) |
| Tryptone | \(40g/L\) | \(80g/L\) | \(120g/L\) |
| \(\ce{MgSO4}\) | \(17g/L\) | \(34g/L\) | \(51g/L\) |
| \(\ce{NaCl}\) | \(12g/L\) | \(15g/L\) | \(18g/L\) |
Figure 7 shows that the data from the main experiment is closer to being normally distributed with just \(1\) out of \(18\) points (\(0.056\)) outside of the \(95\%\) region. This, combined with an R-squared score of \(0.9\) and a model p-value of \(0.004\), shows that our model describes the system well.
Figure 8 shows parameter estimates again for main and quadratic effects. These estimates suggest the best media has \(30 g/L\) yeast, \(40 g/L\) tryptone, \(17 g/L\) \(\ce{MgSO4}\), and \(13 g/L\) \(\ce{NaCl}\), with a predicted growth rate of \(0.065 (0.053, 0.077)\). We then tested this recipe to verify, and measured \(0.0643\) — astonishingly close to the rate predicted!
To see in detail how we calculated our final growth rates (and to get a fuller picture of our growth data, its quality, and the variance between replicates), check out our exported Pluto.jl notebook walking through the calculation step-by-step:
Conclusion
Our best media was optimal within the design space we chose and gave a doubling time of \(15.6\) minutes. However, e\(2YT\) media gave a lower doubling time of \(13.5\) minutes, as it had an ingredient (\(\ce{Na2HPO4}\)) that we removed for precipitation reasons. To further optimise our media, we can test more ingredients, while using optimised levels of yeast, tryptone, magnesium sulfate and salt, or we could remove magnesium sulfate as a component and add \(\ce{Na2HPO4}\) back before repeating our optimization step.