Following a Fermentation Kinetics by Counting Bubbles

During my PhD thesis I was working with yeasts Saccharomyces cerevisiae ("Baker's yeasts") and at some point I had to find a way to follow the growth kinetics during a fermentation reaction to be able to compare the results obtained from the technology we were working on with some kind of reference method that would be accepted by most. This is how I ended up counting bubbles escaping from a batch fermentation reaction.

During fermentation, yeast transforms a substrate S (typically glucose or sucrose) into carbon dioxide CO₂, ethanol EtOH and more yeast X (also called biomass):

with r the speed of the reaction. Because yeasts are complex biological systems, there are no absolute easy law to describe the reaction kinetics but a Monod law often works relatively well:

The following values are well accepted in the literature:

With the sensor discussed here, I will measure the amount of CO₂ produced over a small amount of time by a fermentation batch which should be a good measurement of the reaction kinetics if the time period is sufficiently small:

Measuring the ∆CO₂ term is not that trivial because the gaseous flow rate will be relatively small for common batches (unless you are working with industrial quantities!) and deriving an analog signal is never a good idea as it tends to increase the noise. So instead of relying on analog data I will use a [»] discrete sensor based on Laplace pressure which counts the number of bubbles of CO₂ produces over 1 minute (1 minute is quite small compared to the fermentation dynamics). Assuming that all bubbles have the same volume we can transform the number of bubbles per minutes to a mass of CO₂ by using the perfect gas law with the room temperature:

The number of bubbles recorded per minute should follow a Poisson distribution so the uncertainty should be around 1.96*(#bubbles)^½. For example, with a 1000 bubbles per minute, the uncertainty should be around ±62 bubbles (6% uncertainty). You shouldn't worry too much about uncertainty unless you are making academic level theories. On the other hand, you should pay attention to the temperature and local pressure used as they have a more important impact on the kinetics data. With good measurements, you should have values within 1% accuracy. To measure the volume of one bubble I have used a precision syringe to slowly inject 5 ml of air and counted the number of bubbles for that volume. If you don't have a precision syringe, simply use a long syringe and try to calibrate it with water and a lab scale. With good calibration you should be able to reach an overall 5% accuracy with no problem. But again, don't worry because if you are not making academic research the limited accuracy will only change the scale of the kinetics graph, not the noise of the data! Even the number of bubbles against time is already meaningful for quantitative research :)

Figure 1 illustrates the bubble-count graph for a sample fermentation. It shows a very clean kinetics data with two bursts. The first one, located at the beginning of the reaction, is due to air in the batch reactor which offers yeast different metabolic reactions and faster kinetics (but no ethanol production); the one at the end is due to an unknown phenomenon... I was away when it occurred but it seems to have happened when my colleague left the room and closed (slammed) the door. Anyway, the noise level is quite low and the quality is great knowing the sensor used.

By using the equivalence law it is possible to transform the number of bubbles into a mass flow which may also give the instantaneous production of ethanol or substrate consumption. By integrating these graphs, it is possible to estimate the overall ethanol produced or the overall substrate consumed. This later gives us the opportunity to check the accuracy of our sensor because the substrate level should reach zero at the end of the reaction.

The results are given on Figure 2. With an initial 16 grams of glucose, the sensor predicts a glucose level of 0.38 grams at the end of the reaction which is quite near to zero. This represents an accuracy of 2.3%. The error is probably due to the respiration at the beginning of the reaction which changes the overall stoichiometric ratios.

Finally, you may also plot the estimated growth rate of the reaction by dividing the biomass production rate by the integrated amount of biomass such as represented on Figure 3. The experiment lead to a mean growth rate of about 0.053 /h which is quite small compared to the theoretical 0.175 /h expected. This is probably due to the low temperature of the room (~20°C) which is not optimal for yeast cultures.