# Measuring the effects of a nutrient mix on yeast growth

A few months ago, Escarpment Labs released their brewer-focused nutrient formula, Yeast Lightning. I was very excited: the ability to get nutrient rich formula without going through the typical route of a laboratory supplier () was welcome! Previously I was using homemade hydrolyzed bakers yeast, which was a pain to make and not very shelf-stable. I was also hoping that it sufficient for my yeast cultures, but I had no idea what key nutrients may have been missing or lacking.

My goal was to compare two yeast cultures in Pioreactors: one with generous amounts of Yeast Lightning (labelled the YL culture), and one with no added Yeast Lightning (No-YL culture). The media was 2% dextrose, with moderate amounts of DAP and hydrolyzed soy as nitrogen sources.

### Extending the typical growth curve

By pairing the Pioreactor with our dosing pumps, we are able to track yeast growth rates beyond the simple lag-log-stationary rates observed in batch cultures. Using the built-in dosing algorithms, the yeast are in an environment forever rich in nutrients, allowing them to reach their maximum biological growth rates. This is accomplished by add fresh media periodically (and removing the same amount from the bioreactor, to keep a constant volume). We accomplish this by turning on the Pioreactor's PID Turbidostat algorithm, with a low threshold and frequency dosing events.

### Results

We ran this experiment until we ran out of prepared media, which took about 4 days. Below are the growth rates produced by the Pioreactor:

We are interested in comparing the yeast growth rates between the two cultures. One very important less to understand is that growth rates are never constant. The are influenced by temperature, metabolism, evolution, and other factors. Hence we have time series of growth rates we need to compare. Below I'll compare two metrics that I suggest to do this:

1. Maximum observed growth rate. This represents what is possible for the yeast to achieve under perfect conditions. In the YL group, this was about 0.135 h⁻¹, and for the No-YL group this was about 0.075 h⁻¹. That's a very significant difference!

2. The maximum observed growth rate is not sustainable though. It also doesn't summarize the entire time series well. In this case, another metric I like is the cumulative growth rate, defined as the sum of the growth rate over the time horizon, scaled by the observation window duration (by default, that's [seconds per sample] / 3600). It can be shown this is equal to the area under the growth rate curve. For the No-YL culture, it's 4.44, and for the YL group it's 9.16 - more than twice as much!

There is also a biological interpretation of this metric. By exponentiating the cumulative growth rate, you get the (theoretical) ratio between the start population and the end population, also known as the biomass yield. For our YL culture, that ratio is exp(9.16) = 9600 - so if we started with a single yeast at time 0, at the end we would have 9600 yeasts. I say theoretically, because we aren't actually observing that population - we are pulling out yeast via the dosing algorithm into an environment that isn't favourable. Exponentiating also amplifies the difference between the two cultures: the ratio of the No-YL group is only 85. This means we saw more than a (theoretical) 110x difference in the end yeast population between these two cultures!

### Conclusion

It should be clear that using a nutrient has enormous effects on the yeast culture's potential for growth. Growth rates themselves have a non-linear effect on population sizes, hence the massive difference observed in the previous section. Above, we used a simple set up in the Pioreactor to discover and quantify new insights about our yeast cultures.

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