# Review on Rehydrating Dry Yeasts and Viability Stains

Eureka and welcome to a new science post. I would like to discuss the results from a paper about rehydrating yeasts and viability staining. Since dry yeasts are widely used in the homebrewing scene and even on industrial scale, lots of discussions are about the effects of rehydrating the dry yeasts before use. Some rehydrate the active dry yeast (ADY) in some water and others just sprinkle the yeast in the beer. Some prefer to use warm water and others prefer colder temperatures.

During the drying process, the water flows out of the yeast cells rather rapidly and leads to a collapse of the cytoskeleton (Rodriguez-Porrata et al (2008)). During the first minutes of the rehydration process, the cell’s membrane are not functionally active yet and lead to membrane leakage. In this process, molecules from within the cell flow out of the cell. During the rehydration process, the cellular membranes get repaired and thus stop the membrane leaking. If the cells cannot stop the leakage, it is going go die.Jenkins et al studied the effects of rehydration conditions on yeast viability and came to some remarkable results. The authors studied three different yeast strains (LAL1 a lager strain, LAL2 Nottingham strain and LAL4 a Munich strain), rehydrated the cells at different temperatures and for a different amount of time. In addition, they measured the viabilities at certain time points during the rehydration process using four different techniques: Slide cultures, methylene blue, MgANS (8-anilino-1-naphthalene-sulfonic acid hemi-magnesium salt hydrate) and Oxonol staining. For the slide cultures, a small volume of yeast suspension was added to a small amount of agar on a slide and the arising microcolonies from the yeast cells within the agar were counted after 18 h. Thus a staining independent method to asses viability.

For this test, Jenkins et al used 1 g of ADY and added 10 times the weight of water (water temperatures 25°C and 30°C). Time point A was taken immediately after adding the ADY to the water. Time point B was taken after leaving the ADY rehydrate for 15 min. The yeast-water mixture was then mixed and samples were taken after additional 15 min each (time points C1 to C4).

Lets look what they found out. In case of the Lager strain, the viabilities at the different time points are shown in Fig 1. I would like to leave the different temperatures aside since its effect is strain dependent and not important for my main message here. What they could observe is a lower viability at time point A compared to the other time points. This effect seems to be independent of the water temperature (not shown). Further on to notice are the different viability values one obtained using the four techniques. For the Lager strain, measuring the viability using methylene blue lead to lower values compared to the other two staining techniques.

Fig 1: Viabilities of Lager strain at different time points at 25°C by Jenkins et al (2011)

The lower viabilities at time point A could also be observed for the Nottingham (Fig 2) and the Munich yeast (Fig 3). Again, the lower viabilities seem not to depend on the water temperature of the water used for the rehydration process (not shown).

Fig 2: Viabilities of Nottingham strain at different time points at 25°C by Jenkins et al (2011)

Fig 3: Viabilities of Munich strain at different time points at 25°C by Jenkins et al (2011)

Putting this observations together. Measuring the yeast viability using staining methods such as methylene blue within the first minutes of rehydration seems to lead to significant lower values compared to values obtained from later time points. What is the reason for this you may ask? This is where it gets interesting.

The first question one has to address is how yeast viabilities can increase in the first place (as observed in the figures from time point A to B and C1 in case of the staining). Please note that the viability measured with slide cultures in case of the Munich strain are highly similar to later time points (Fig 3). Viability, in a biological sense, can only increase by the formation of new, viable cells. One other way would be for dead yeasts to get alive again which is not very likely in my opinion (though I don’t have any proof for my statement). Due to the chosen time points, it is very unlikely for the yeasts to undergo divisions and thus increasing the viabilities again from time point A to B and C1. There has to be a different effect.

The answer to the question lies within the methods. As previously mentioned, dried yeasts don’t have active membranes. During the rehydration process, the membranes get repaired again (Rodriguez-Porrata et al). Since most of the viability stainings, such as methylene blue rely on active membranes (the dye should only be taken up by dead cells with inactive membranes), dry yeasts behave much like dead cells within the first time points and thus leading to lower viability values. With time, the membranes get active again, and the dye is probably exported from the cells and thus increasing the viability. This is a very nice example of a method’s limitations.

However, there seems to be an effect in the slide culture method as well. This might be due to osmotic pressure issues when the dry yeasts get in contact with a highly osmotic agar which enhances the leaking of the cells.

Assessing viability measurements using methylene blue on dry yeasts is a valid method but has to be done with caution. Especially if one wants to assess whether dry yeasts have a higher viability if added to water first or pitched to wort directly. Consider the right time points for such experiments.

I hope this was interesting to read and might give you a better insight into viability stains and its limitations.

# Bibliography

Jenkins DM, Powell CD, Fischborn T, Smart A (2011) Rehydration of Active Dry Brewing Yeast and its Effect on Cell Viability, J. Inst. Brew. 117(3), 377-382 (http://onlinelibrary.wiley.com/doi/10.1002/j.2050-0416.2011.tb00482.x/abstract)

Rodriguez-Porrata B, Novo M, Guillamon J, Rozès N, Mas R, Cordero Otero R (2008) Vitality enhancement of the rehydrated active dry wine yeast. International Journal of Food Microbiology. 126, 116-122
(http://www.sciencedirect.com/science/article/pii/S0168160508002560)

# Tasting: #40 Gielis Tripel

Eureka, and welcome to a new blog post of mine. This is about a batch bottled a few months ago, the Gielis Tripel brewed in September 2011. This post was sitting around for ages. And now is the time to spread the word how the beer tasted in the end.

Aroma: Very elegant smell: Phenolic, pepper notes, lavender, fruity (gooseberries) and nice hop aroma (fresh-cut grass). No alcohol detectable nor any other off-flavors.

Appearance: Golden to yellow color, clear, with a nice frothy white head, nice bubbling going on. Head disappears rather quickly (as seen in picture above).

Flavor: Sweet malt character with phenolic yeast character. Very subtle character and balanced bitterness. Really well made. No component overpowers another.

Mouthfeel: Medium body, low to average carbonation level (could be a bit more), dry finish with no alcohol warming sensation.

Overall Impression: What a treat. I see Belgian Tripels as a very hard to make beer style because the aroma and flavors are rather subtle and mainly derive from the yeast strain. This makes it especially hard to cover any off-flavors. Any off-flavor would be recognizable immediately. I would like to mention, that the beer now has some autolysis character (umami taste and smell). I would therefore drink this beer within a few months. Last to mention, this beer (brewed by my brother) won him a first place at a national homebrew competition. Nothing to add more. In my opinion, a spot on example of the Belgian Tripel style. Since we now have the base recipe, its time to play around to make this Tripel unique in its own. Thanks for reading, commenting and stay tuned!

# A glimpse into yeast flocculation

Eureka, science post! This is an entire review post about yeast flocculation. Flocculation describes the ability of yeast cells to aggregate into clumps/flocs and then drop out of suspension. This happens during the end of fermentation and the yeast cells form a sediment at the bottom of the fermenter. The flocculation treat is mainly genetically derived and thereby depends on the yeast strain. Flocculation characteristics can sometimes change and lead to early flocculation to occur or to loss of flocculation. Despite the genetics, there are a lot of ways a homebrewer can influence the yeast flocculation.

In this post I would like to cover the basic principles how flocculation functions on a genetic and biochemistry level, then speak about factors influencing the flocculation and end with some words about how a homebrewer can influence the flocculation of yeasts. Lets begin with a general overview about flocculation.

Yeast flocculation profiles can be distinguished into three groups:

• High flocculate strain (strongly sedimenting): Flocculation starts after 3-5 days (if kept at correct fermentation temperature). These strains tend to flocculate earlier during the fermentation and form a sediment at the bottom of the fermenter. Most of the English yeasts belong into this group. Such yeasts tend to lead to lower attenuation (higher terminal gravity) and sweet beers since the yeasts cells are not in suspension anymore and in contact with the sugars. In addition, a lot of fermentation byproducts stay in the beer such as diacetyl and esters for example.
• Medium flocculate strain (powdery): Flocculation starts after 6-15 days. Typical ale strains and lager strains. Such yeasts give you a clean and balanced beer. Such yeast stay in contact with the beer and can continue to ferment and metabolize fermentation byproducts such as diacetyl.
• Low flocculate strain (non-flocculate): Flocculation starts > 15 days. Most of the wild yeasts, Hefeweizen- and Belgian yeasts plus some lager strains belong into this category. Such yeasts tend to stay in suspension and lead to a cloudy, yeasty beer. In addition, such strains can make filtering of beer rather difficult.

Comparing the three different groups above, it is obvious that non-domesticated yeasts (named wild yeasts) are low flocculating. The flocculation character in domesticated yeast cells got improved by selective pressure. One easy way to do so it harvest the yeast from the bottom of the fermenter and therefore only harvest the highly flocculent yeasts. More about that later on.

# How flocculation in yeast works

As already mentioned, the flocculation is mainly genetically driven. I would like to start with the phenotypes first and then get into the genetical setup since it might be easier to understand the different genes and what they do.

## Cell biology of flocculation

One trait that influences flocculation is the charge surface charge of the yeast cell. The surface charge is mainly negatively charged but the charge depends on the strain, the phase of growth, the oxygen content in the wort, starvation of the cell and cell age. Most of these factors can be influenced by the brewer. Due to the negatively charged surface yeast cells repel each others. Such repulsions prevent yeasts from flocculating since flocculation involves yeast cells to get in contact first. Top-fermenting strains seem to have a less negatively charged cell surface than bottom-fermenting strains (Amory and Rouxhet, 1988).

The yeast cells have a cell membrane and a cell wall. The cell membrane’s function is mainly to regulate what gets in and out of the cell. The cell wall’s job is to stabilize the whole cell and is therefore responsible for the integrity of the yeast cell. One of the most important building blocks is mannan. We will come back to the cell membrane and mannan later on.

Non-flocculent yeast cells appear as smooth cells on a SEM (scanning electron microscope) micrograph and flocculent yeast cells appear to have some sort of hairs. Non-flocculent yeast strains collide but don’t form clumps. On the other hand, flocculent strains form clumps if they collide. As previously mentioned, yeast cells are in general negatively charged and therefore repel each other. What is the reason for the flocculent yeast strains to form clumps then?

## Biochemistry of flocculation

Yeast cells like mammalian cells have a lot of surface proteins on/in their cell membranes. Such proteins are necessary for the yeast strains for signalling (interacting with the environment) and get molecules into and out of the cell. One could easily write books only about surface proteins and that’s why I will not get into further details here. One possible way to explain the interaction of flocculent yeasts is the lectin hypothesis.

Fig 1: Mannose and glucose structures

This hypothesis states that controlled interactions of specific surface proteins between different yeast cells are involved in the flocculation. One such protein is called zymolectin which is produced by the yeast cell and then incorporated into the cell wall. As one can tell zymolectin belongs to the family of lectins which is a family of proteins that bind sugars. Zymolectin can bind the sugar molecule mannose (Fig 1). In addition, it can also bind to mannan, the building block of the cell wall (Fig 2), which is made from mannose molecules. A bond between zymolectin and mannan (from different yeast cells) therefore links two cells together and initiates the formation of yeast flocs.

Fig 2: Mannan structure

The critical step for the flocculation to occur is the point where zymolectin gets active and establishes the connection to another yeast cell. Not much is yet known about the zymolectin expression. Zymolectin may become active at the end of exponential growth and might be triggered by depletion of nutrients such as sugars and an increase of fermentation byproducts such as ethanol. Lets have a closer look at the zymolectin family members.

• Flo1 (Flocculin-1): (http://www.uniprot.org/uniprot/P32768) Synonyms are FLO2 and FLO4. This protein selectively binds to mannan residues in the cell wall and is inhibited by mannose but not glucose, maltose, sucrose of galactose. The protein is 1,537 amino acids (aa) long and has a sugar recognition site between position 197- 240. Interestingly, there are 18 repeated domains (flocculin repeats) in this protein each with a length of 45 aa plus a PA14 domain which is responsible for binding sugars (Fig 3)

Fig 3: FLO1 with 18 flocculin repeats (red) and a PA14 domain (blue) (Pfam)

• Flo5 (Flocculin-5): (http://www.uniprot.org/uniprot/P38894) 1,075 aa long. The protein consists of one P414 domain, 8 flocculin domains and 3 flocculin type 3 domains. Plus a sugar binding site
• Flo8 (Transcriptional activator FLO8): (http://www.uniprot.org/uniprot/P40068) 799 aa long. Putative transcription factor of FLO1, FLO9 and FLO11/MUC1
• Flo9 (Flocculin-9): (http://www.uniprot.org/uniprot/P39712) 1,322 aa long. The protein consists of one P414 domain, 13 flocculin domains and 3 flocculin type 3 domains. Plus a sugar binding site
• Flo10 (Flocculin-10): (http://www.uniprot.org/uniprot/P36170) 1,169 aa long. The protein consists of one P414 domain
• Flo11 (Flocculin-11): (http://www.uniprot.org/uniprot/P08640) 1,367 aa long. No conserved domains found. This protein is involved in filamentous growth (see next post)
• Lg-Flo1 (must be present in lager yeast)
• NewFlo: These proteins bind to mannose and glucose. Mannose, glucose, maltose and sucrose can inhibit zymolectin. There are two different proteins belonging into this group of zymolectins:Lg-Flo6p: (http://www.uniprot.org/uniprot/E9P9E1) 428 aa. Not much is known for this protein. However, there is a PA14 domain and 3 flocculin repeats presentLg-Flo10p: (http://www.uniprot.org/uniprot/E9P9E2) 492 aa. Not much is known for this protein either. However yet again, one PA14 domain and 5 flocculin domains

The longer the flocculin protein (the more flocculin repeats), the stronger the flocculation is (Vidgren et al 2011). Flo1 therefore shows a strong flocculation character. The NewFLo phenotype is very common in brewer’s yeast. Lets summarize, so far three groups of flocculation phenotype have been described:

• Flo1 type (is inhibited by mannose only). This phenotype occurs in Lager and ale yeast strains and is associated with FLO1 gene. Flocculation occurs independently on wort sugars (not suitable for brewing)
• NewFlo type (is inhibited by mannose, glucose, maltose, sucrose). Suited for brewing. Flocculation occurs if wort sugars are metabolized.
• Mannose insensitive. This phenotype occurs in ale but not in lager strains. Calcium ions are necessary. As it can be concluded from the name, this phenotype is not inhibited by mannose. Flocculation can be induced by low ethanol concentrations (Dengis et al, 1995). One possible mechanism for this phenotype might be by simply changing the cell surface charge. However, the evidence that small amounts of calcium are necessary and that FLO11 is involved points to an adhesion-mediated mechanism as well but not based on flocculin repeats.

In addition to the three groups, co-flocculation can occur as well if a non-flocculent and a flocculent strain get in contact. In this case the zymolectin from the flocculent strain binds to the mannose of the non-flocculent strain and pulls the non-flocculent strain down. Co-flocculation can occur with bacteria such as Acetobacter, Lactobacillus and Pediococcus as well (Vidgren et al 2011).

## Genetical setup of flocculation

One to three genes are present in yeast strains which are inherited dominant. Flocculation therefore can be improved by crossing yeast strains: Cross a high flocculent strain with a low flocculent strain leads to a high flocculent yeast. Although the flocculent trait is dominantly inherited, flocculation can also decrease.

• FLO1 (Flocculin-1) Located on chr01 and encodes Flo1 protein https://www.ncbi.nlm.nih.gov/nuccore/NM_001178230.1 4,614 bp. No introns. This gene seems to be Saccharomyces specific since I could not find any other organism with similar genes.FLO2 and FLO4 are alleles of FLO1 and FLO5, FLO9 is a homologue of FLO1. Any expression of FLO1, FLO2, FLO4, FLO5 or FLO9 leads to the initiation of flocculation of the Flo1 phenotype.
• Lg-FLO1 can be found in Lager yeasts and is responsible for the NewFlo phenotype

The FLO genes are relatively unstable due to mutations and the highly repetitive pattern due to flocculin repeats. Highly repetitive sequences in the genome change more rapidly than regions with less repetitive motifs (Vidgren et al, 2011). A lot of mutations happen in the FLO genes and the most commons ones lead to deletions or any other alterations leading to a decrease of flocculation. In addition, FLO genes are near telomeres (ends of chromosomes) and can get transcriptionally silenced. Nevertheless, flocculation not solely relies on the FLO genes but implies physical interactions of yeast cells (collision of yeast cells).

Putting it all together. For flocculation to occur the following factors have to be true:

• Flocculins have to be expressed by the yeast and present in the cell wall (for Flo1 and NewFlo type)
• Physical interaction between yeast cells
• Absence of inhibitory sugars (in NewFlo type)
• Small amounts of calcium ions present. Calcium is necessary for the correct conformational shape of the zymolectin molecules
• Right environmental conditions

# Environmental factors influencing flocculation

Now that we covered the biochemistry and genetics lecture part about flocculation, let’s have a look at some environmental factors affecting flocculation.

## What environmental factors influence yeast flocculation?

• Fermentation temperature
• Lower temperatures seem to initiate flocculation as well as higher temperatures above the recommended fermentation temperatures
• Wort pH. Top-fermenting yeast strains flocculate within a pH range of pH 3 – 4.5, bottom fermenting ones between pH 3.5 – 6
• Original gravity
• Poor wort aeration can result in an early flocculation. Oxygen content at pitching increases sterol and fatty acid content in cell membrane and increases the cell surface hydrophobicity
• Depletion of inhibitory sugars such as sucrose, glucose, maltose (all inhibit flocculation in NewFlo type only)
• Increase of fermentation byproducts such as ethanol can influence flocculation as well
• Factors increasing the chance that yeast cells collide
• Pitching rate (higher pitching rate gives a higher yeast cell density)
• turbulence by carbon dioxide production
• Yeast age. Older yeast cells tend to have a rougher cell surface due to the undergone budding events and are therefore prone to stick to other cells
• Factors decreasing the cell surface charge (decrease of electrostatic repulsion)
• Ethanol concentration
• pH of wort
• Changes in cell wall composition
• Expression and incorporation of flocculins into the yeast cell wall
• Premature yeast flocculation-inducing factors (PYE) from the barley husks can lead to premature flocculation. Barley produces PYE as a response to microbial growth during the steeping process. Further investigations are necessary to fully understand the PYE influence on flocculation

This list might look very frightening to homebrewers. A closer look reveals some common factors which can be broken down into:

• Adequate oxygenation of the wort. Poor oxygenation not only leads to possible off-flavors but to incomplete fermentation due to delayed flocculation and reduced sterol content in the cell membranes
• Temperature. Flocculation is temperature dependent. In general a lower temperature favors yeast flocculation. However, this is very yeast strain dependent
• Pitching rates. Higher pitching rates increase amount of older cells and therefore favors flocculation. However, I do not recommend to overpitch to improve the flocculation character of a yeast strain

## Beside oxygenation, temperature and pitching rates, how can a homebrewer lower the changes to encounter problems due to different flocculation behaviour?

• Choose the right yeast strain. If you plan on brewing a clear beer, better stick to a yeast strain with a high to very high flocculation potential. Flocculation behaviours can be looked up on the yeast suppliers webpages
• Decrease temperature to 0°C (32°F) after the fermentation reached terminal gravity. Lowering the temperature results in higher flocculation rates and leads to clearer beers. Don’t chill the beer too early
• Get yeast out of beer by filtration or centrifugation (if you can’t wait for the yeast to drop out itself)
• Add collagens (positively charged) and pull down the yeast cells. This is commonly used in real ales by adding Isinglass. By doing this, one can use the positive character a low flocculate yeast strain might contribute to a beer without having a cloudy pint of beer in the end
• Collect yeast from the bottom of the fermenter or from kräusen and thereby select for the highly flocculate yeast cells. If you collect yeast from the yeast cake, the most flocculate yeasts will be in the middle part of the yeast sediment. The non-flocculate or poorly flocculate yeasts will be in the top layer and older cells, dead cells in the bottom layer
• Yeast storage. Use a method without excessive stressing the yeast cells such as low/high osmolarity of the storage media. Storing yeast at lower temperatures (4°C) can result in reduced flocculation. However, these effects are strain dependent
• Keep acid washing steps at a minimum. Washing cells with acid can change the surface protein composition and therefore might have an impact on the surface charge and surface hydrophobicity
• Avoid excessive re-pitching of the same yeast over and over again. Don’t re-pitch your yeast for more than 5 – 10 times.

## What to do if your yeast does not flocculate as before?

• A change of flocculation behaviour can have several causes such as mutations, mixed cultures (infections), different environmental factors. Finding the cause for the different flocculation behaviour might be hard. Therefore:
• Don’t use the same strain for another batch of beer. Start with a fresh yeast
• If a high flocculent strain is used, get the yeast back into suspension by either swirling or venting some carbon dioxide into the fermenter

# To keep in mind:

• Flocculation character of a yeast directly impacts the flavor and fermentation performance of a beer. Therefore choosing the right flocculate yeast strain is very important in the first place
• Keep as much of the fermentation factors as consistent as possible. This includes fermentation temperatures, pitching rates, oxygenation etc.
• Keep record to be able to observe changes in flocculation
• Flocculation itself depends on yeast strain and its FLO genes, environmental factors and the physical interaction between yeast cells

Flocculation seems to be Saccharomyces yeast specific and a lot of research is still done to further understand how flocculation works. I hope I could give you a small glimpse into the topic and got you an idea what flocculation is all about. Including some advice what influences flocculation and what a (home)brewer can do about it to keep flocculation behaviours as constant as possible. The next post concerning flocculation will cover the biological function of FLO genes and therefore the biological function of flocculation for the yeasts cells and further insights into other flocculins and their biological role in Saccharomyces. Cheers!

# References:

• Amory DE, Rouxhet PG (1998) Surface properties of Saccharomyces cerevisiae and Saccharomyces carlsbergensis: chemical composition, electrostatic charge and hydrophobicity. Biochim. Biophys. Acta, 938: 61 – 70
• Dengis PB, Nélissen LR, Rouxhet PG (1995) Mechanism of Yeast Flocculation: Comparison of Top- and Bottom-Fermenting Strains. Appl Environ Microbiol, 61(2): 718 – 728
• Fix G (1999) Principles of brewing science: a study of serious brewing issues. Brewers Publication, 2nd edition
• Narziss L (2005) Abriss der Bierbrauerei. WILEY-VCH, Weinheim, 7th edition
• Verstrepen K, Industrial Microbiology Part II – Fermentation, Katholieke Universiteit Leuven, http://www.biw.kuleuven.be/dtp/cmpg/G%26G1/assets/internal/IM-class2-Fermentation-v4.pdf
• Verstrepen KJ, Derdelinckx G, Verachtert H, Delvaux FR (2003) Yeast flocculation: what brewers should know. Appl. Microbiol. Biotechnol, 61: 197 – 205
• Vidgren V, Londesborough J (2011) 125th Anniversary Review: Yeast FLocculation and Sedimentation in Brewing. J. Inst. Brew. 117(4): 475 -487
• White C (2012) Flocculation Basics. www.whitelabs.com/beer/Flocculation_help.pdf
• White C, Zainasheff J (2010) Yeast: The Practical Guide to Beer Fermentation. Brewers Publication, 1st edition
• Wikipedia (2012) Flocculation, http://en.wikipedia.org/wiki/Flocculation
• Wyeast (2012) Flocculation/Clarification http://www.wyeastlab.com/hb_clarification.cfm

# About the morphology of colonies

Eureka, today’s post covers some general information about the morphology of bacteria, yeasts and other microorganism on agar plates and why it is important to know at least a bit about it to get the most information out of your agar platings.

Q: What do you mean by morphology of colonies?

The morphology of a colony describes how microorganisms appear on agar media such as Sabouraud, malt agar etc. Morphology just describes the colonies. If you streak some microorganisms on agar plates, they grown (if the media is appropriate for this particular organism) and form visible colonies. The colonies appear as spots like shown in Fig 1. It is important to remember that a colony are thousands to millions of microorganisms together, not a single microorganism cell. Ideally all the cells within a colony originated from one single cell at the beginning (clonal expansion). If single cells are closer together on the agar, the individual colonies overlap and no single colonies are visible (left-upper part in Fig 1). In this case, the concentration of the yeasts is just too high to observe individual colonies.

Fig 1: Brettanomyces bruxellensis on Sabouraud agar plate after 11 days

Fig 1 shows what you get if you streak some Brettanomyces yeast on Sabouraud agar. The roundish spots are the colonies (as you can see on the right side in Fig 1).

Q: How do you get single colonies?

To get an accurate description of a colony, single colonies are necessary. But how do you get single colonies in the first place? As mentioned above, if the individual cells after streaking are to close to each other, the colonies might overlap. To get single colonies one simply has to ensure a low concentration to prevent such colony-overlays. One example to do so is to dilute the cells directly on the plate itself by using a special streak technique called dilution streak or Z-streak (Fig 2). How this is done is shown in a video (YouTube) as well.

Fig 2: Dilution streak done with three streaks

Begin with a cell suspension. You might even use a yeast slurry in the first place. A first streak is done to get some cells on the plate (Fig 2, streak 1). One expects a lot of cells visible on the trajectory of the first streak and the individual colonies overlay each others. After the first streak, you sterilize your inoculation loop, let it cool down and collect some cells by passing the inoculation loop through the first streak for a second one. This time the concentration of cells is already lower because you only pick a subset of yeast cells. This process can be done for a second time to get three streaks in the end (Fig 2). The plate after a dilution streak might look like shown in Fig 1. Unfortunately, there are no colonies visible in the third streak anymore. Anyway, I hope you get the idea.

Single colonies are not only useful to describe their morphology but also to differentiate between different microorganisms. For instance, if you are interested in separating the Saccharomyces yeasts (brewer’s yeast) from Brettanomyces yeasts you can use the dilution streak and hopefully some colonies arise from single Saccharomyces colonies and others from Brettanomyces cells.

Q: Why is the morphology important?

Lets assume the morphology of a colony, representing one kind of microorganism (remember the concept of the single cell at the beginning), is unique for every microorganism there exists. The morphological description could therefore be used to identify the kind of microorganism on your agar plate. This is just an assumption because there are a lot of microorganisms which have similar morphologies. To summarize, the morphology of the colonies can be useful to identify the kind of microorganism you have on your plate. Lets go through some examples. Have a look at Fig 3.

Fig 3: Girardin bugs on Sabouraud agar plate

I assume it is obvious that there are different kinds of colonies and hence morphologies. There are differences in shapes, size and colors. To conclude, different morphologies originate from different microorganisms. I can give you even further information here. The white colonies (big ones and wavy) are yeast cells, the flat beige ones bacteria. The very small white colonies are another kind of bacteria. You see, the morphology can even be used to differ between yeasts and bacteria. That’s why agar media are very common in microbiology labs to identify different kinds of yeast/bacteria. One application here could be to test a beer for spoilage organisms such as Lactobacillus (beer turned sour). Plate some of the sour beer on a plate where Lactobacillus can grow and if colonies arise with a typical Lactobacillus morphology, you can be certain to have a Lactobacillus contamination in your beer. I will not get into further detail about the different media and strategies used to do these tricks. Just to give you an idea what the whole agar media method is capable of.

Fig 4: Water kefir on Sabouraud agar plate

Maybe an example to show that the colonies are not always circular. Some microorganisms tend to form large flat colonies as it can be seen in Fig 4. In this case, I plated some of my kefir culture on a Sabouraud agar plate. You can even observe some yellowish colonies. Colonies are not always white or beige either. Not only can you choose different kind of agar media but also add some dyes for further characterization. One such example is shown in Fig 5. In this case bromocresol green is added to differentiate between microorganisms that can grow as white colonies and such as green ones. The color differences suggest that there are at least two different kinds of microorganisms on the plate shown in Fig 5.

Fig 5: Jolly Pumpkin’s Madrugada Obscura dregs on bromocresol green Sabouraud agar

Q: How do you determine the morphology of a colony?

First you need a pure culture of the microorganism. This is important because the morphology can differ if other microorganisms are in the same colony. The morphology can even be different on other agar media. Lets assume you want to describe the morphology of a pure brewers yeast (Saccharomyces cerevisiae). The first thing to do is streaking the yeast on a suitable agar media with a dilution streak and incubate the plate until colonies arise like shown in Fig 6. Sabouraud is a typical agar media for Saccharomyces and other yeasts. Malt agar media works as well.

Fig 6: Wyeast’s 2112 California Lager on Sabouraud Agar plate

In case of Fig 6, I streaked some of Wyeast’s 2112 California Lager yeast on a plate to check the purity. Now what about the morphology? Lets take a single colony and describe the following characteristics: form, margin, elevation (shape of the colony from the side), size, texture, appearance, pigmentation, opacity. The following descriptions are just an example.

Fig 7: from: http://commons.wikimedia.org/wiki/File:Bacterial_colony_morphology.png#filelinks; (Adapted and redrawn from Seeley, HW & Vandemark, PJ (1962) Microbes In Action: A laboratory manual of microbiology. WH Freeman (San Francisco, London) by user Ewen)

One might describe the colonies shown in Fig 6 as following:

Margins: Entire
Form: Circular
Elevation: Convex
Surface: Smooth
Opacity: Not transparent, shiny
Color: Off-white

That is what you can expect when you streak a yeast colony on a Sabouraud plate. The morphology of Saccharomyces is very similar on malt agar. Maybe some of you observed that there are yet some other different colonies on the plate in Fig 6. There were some impurities in this yeast sample as expected in the first place.

Q: Is the morphology of a given microorganism always the same?

Unfortunately not. The morphology of colonies can depend on the type of agar media used, if oxygen is present, nutrients, vitality, pH-levels, incubation time, other microorganisms present… Just keep in mind that a morphology description is not universal. If you encounter a morphology description of a specific microorganism, always check the type of agar media used and the conditions how the plates were incubated.

Q: Is it possible to differentiate between Saccharomyces and Brettanomyces based on morphology?

One of the most simple tricks to differentiate between the two yeasts is the incubation time. Saccharomyces colonies arise relatively quickly (within few days). Brettanomyces grow much slower (days to weeks). The second trick is to use a microscope and have a look at the different colonies. A third one might be (haven’t tried that one yet) to inhibit the growth of Saccharomyces by adding some growth inhibiting substances. Differentiating those two yeasts based on morphology is not that easy in my opinion.

Q: Is it possible to differentiate between top and bottom fermenting yeasts or even yeast strains based on colony morphologies?

As far as I know and from my experiences, differentiating between bottom and top fermenting yeasts base on colony morphologies is not possible. And it is not possible as well to differentiate between different yeast strains as well. Although I encountered some different morphologies for wheat strains at one point. However, I would not do any strain differentiation based on morphologies.

I hope there were some useful information in this post to give you a better understanding of agar media cultivation. Agar media are a very powerful tool in microbiology and is also widely used in breweries to check for impurities in beer or water. Understanding the concept of colony morphologies is therefore very important to get the most information out of agar media cultivation. And know about some limitations of the method as well.

# A glimpse into Brettanomyces growth kinetics

Eureka, second yeast kinetic post. I further discuss Monod growth kinetic models with the inclusion of some inhibition parameters. I would advice you to first read the yeast kinetic introduction post if you haven’t done so already. One inhibition phenomena has been studied on Brettanomyces by looking at growth behaviour under aerobic and anaerobic conditions and the influence of initial acetic acid. All the values of the coefficients are taken from a publication written by Yahara et al (2007). The goal of this publication was to investigate the glucose utilization rate of Brettanomyces bruxellensis at different acetic acid levels under aerobic and anaerobic conditions. The authors first conducted experiments and then proposed an extended Monod model to simulate the growth kinetics under different conditions.

I would like to start by discussing the basic equations used for the extended Monod model used by Yahara et al (2007). The basic Monod equations have been discussed in my introductory post.

$\mu = \mu_{max} \frac{S}{K_S + S + K_i^q \cdot S \cdot X^q}$

$\frac{dX}{dt} = \mu \cdot X$

$\frac{dS}{dt} = - \frac{\mu \cdot X}{Y_{X/S}}$

$\frac{dP}{dt} = \mu \cdot X \cdot Y_{P/X}$

• µ specific growth rate [h-1]
• µmax maximum of the specific growth rate [h-1]
• X is the biomass concentration [g L-1]
• S is the substrate concentration [g L-1]
• KS is the substrate saturation constant [g L-1]
• Ki is the reciprocal of the inhibitor constant [L g-1]
• q is the exponent for the inhibitor constant and biomass [ - ]
• YX/S Biomass on substrate yield coefficient [gX gS-1]
• YP/X Product on biomass yield coefficient [gP gX-1]
• dX is the change of the biomass concentration [g L-1]
• dS is the change of the substrate concentration [g L-1]
• dP is the change of the product concentration [g L-1]
• dt is the change of time when dX and dS happen [h]

The first differential equation for the specific growth rate µ is now slightly modified to include an inhibition factor Ki and an exponent q. The authors cultivated Brettanomyces bruxellensis under aerobic and anaerobic conditions with varying initial acetic acid concentrations (1, 2, 3 and 4 g L-1). The substrate (glucose) and inoculation rate were the same throughout the whole experiments. Two products were included into the model, ethanol (P1) and acetic acid (P2). The only difference in the Monod model here are two different yield factors (YP/X) and one equation for ethanol (dP1/dt) and one for acetic acid (dP2/dt). µmax was obtained the same way as I showed in the introduction post. All the remaining coefficients were obtained by iterative approaches.

I would like to show some of the growth curves published by Yahara et al (2007) which I obtained by using their coefficient values running the model using Berkeley Madonna.

# Aerobic growth and acetic acid concentrations

Aerobic growth and different initial acetic acid concentrations. All the graphs show the substrate concentration (glucose) in red, the biomass concentration in black, the ethanol concentration in green and the acetic acid concentration in blue. In addition, I included the values of the coefficients in the individual graphs.

Fig 1: Aerobic growth with initial 1 g L-1 acetic acid. Glucose (red) g L-1, yeast biomass (black) g L-1, ethanol (green) g L-1, acetic acid (blue) g L-1

The first graph shows the growth one can observe under aerobic conditions and an initial acetic concentration of roughly 1 g L-1 (Fig 1). The glucose is fully metabolized by the yeasts within 100 h of cultivation. It can also be observed that Brettanomyces produce ethanol and some acetic acid.

Fig 2: Aerobic growth with initial 4 g L-1 acetic acid. Glucose (red) g L-1, yeast biomass (black) g L-1, ethanol (green) g L-1, acetic acid (blue) g L-1

The next graph shows the growth under aerobic conditions and an initial acetic concentration of roughly 4 g L-1 (Fig 2). In this case the glucose is not fully metabolized after 100 h as previously shown (Fig 1). The Brettanomyces still grow but at a slower rate. Still some ethanol is produced and a minor amount of acetic acid.

From these two graphs one can already conclude, that the amount of initial acetic acid in the media seems to significantly impair the growth of Brettanomyces. At higher acetic acid levels the Brettanomyces seem to grow substantially slower.

# Anaerobic growth and acetic acid concentrations

The next graphs show the growth curves in absence of oxygen again with different initial amounts of acetic acid.

Fig 3: Anaerobic growth with initial 1 g L-1 acetic acid. Glucose (red) g L-1, yeast biomass (black) g L-1, ethanol (green)

The graph shows the growth one can observe under anaerobic conditions and an initial acetic concentration of about 1 g L-1 (Fig 3). Yet again the glucose is fully metabolized within 140 h of cultivation as previously observed under aerobic conditions and low initial acetic acid concentration (Fig 1). Although the Brettanomyces under anaerobic conditions seem to metabolize glucose at a slower rate than under aerobic conditions. The Brettanomyces produce again ethanol. But no measurable amount of acetic acid. Under anaerobic conditions, Brettanomyces produces much more ethanol. In comparison to aerobic condition, the Brettanomyces grow faster in presence of oxygen.

Fig 4: Anaerobic growth with initial 6 g L-1 acetic acid. Glucose (red) g L-1, yeast biomass (black) g L-1, ethanol (green) g L-1

At higher initial acetic acid concentrations and anaerobic conditions, Brettanomyces still grow but again at a slower rate (Fig 4). A lot of the glucose is not metabolized after 140 h of cultivation. The yeasts still produce some ethanol but the growth curve of the biomass stays roughly the same. Indicating a very slow growth rate.

Because the authors could not measure any acetic acid production under anaerobic conditions, one can conclude that the yeasts do not produce measurable amounts of acetic acid under anaerobic conditions. In addition, higher levels of acetic acid inhibit the growth of the yeasts.

Summary

• B. bruxellensis grows faster in presence of oxygen
• B. bruxellensis produces ethanol under aerobic and anaerobic conditions
• More ethanol is formed under anaerobic conditions
• In presence of oxygen and low amounts of initial acetic acid, B. bruxellensis can produce up to 4 g L-1 of acetic acid
• Acetic acid can inhibit the growth of B. bruxellensis
• No measurable amount of acetic acid is produced under anaerobic conditions
• The proposed model based on a Monod model can describe the dynamic growth curves of B. bruxellensis

Uscanga et al (2003) already showed that B. bruxellensis grows faster in aerobic conditions, produces acetic acid in presence of oxygen, and higher initial amounts of acetic acid inhibits the growth of B. bruxellensis. In addition, Uscanga et al (2003) further showed that higher oxygen amounts lead to a decrease in glucose metabolization, the amount of ethanol produced decreases and the acetic acid level increases. This might be an indicator that high levels of oxygen inhibit the metabolism of B. bruxellensis as well like high initial acetic acid levels.

For the brewers: Brettanomyces slow grower under anaerobic conditions, form more ethanol but no acetic acid. Acetic acid is only produced if oxygen is present.

One has to keep in mind that this model can’t describe everything. For example, if one runs the model using a high substrate concentration, the Brettanomyces will continue to grow even in presence of very high ethanol concentrations. In reality, Brettanomyces have an alcohol tolerance as well where they stop growing. However, this can easily be included in the model. This example was just to show that one has to be careful with models.

I hope this post was interesting to read and gave you an idea how models can be used to describe growth behaviours under inhibitory conditions.

The next post about yeast kinetic models will be concerning yeast calculators.

# Bibliography

• Kurtzman CP, Fell JW, Boekhout T (2011) The Yeasts, a Taxonomic Study. Volume 1. Fifth edition. Elsevier (Link to sciencedirect)
• Uscanga MG, Délia ML, Strehaiano P (2003) Brettanomyces bruxellensis effect of oxygen on growth and acetic acid production. Appl Microbiol Biotechnol. 60: 157- 162; DOI: 10.1007/s00253-002-1197-z
• Yahara GA, Javier MA, Tulio MJM , Javier GR, Guadalupe AUM (2007) Modeling of yeast Brettanomyces bruxellensis growth at different acetic acid concentrations under aerobic and anaerobic conditions. Bioprocess Biosyst Eng. 30: 389 – 395; DOI: 10.1007/s00449-007-0135-y

# A glimpse into yeast growth kinetic models

Eureka, science post! Some math, model building and biology: I would like to start talking about yeast growth kinetic models today. In general, growth kinetics describes how different conditions (substrate, oxygen amount, metabolism products, inoculation rate, growth inhibitors etc) influence the growth of a microorganism in a time dependent manner. At the end one can construct mathematical models to describe the growth behaviour. In most cases one begins with experiments with fixed conditions and the growth of the organism is observed over time. A next experiment can be conducted with the change of one condition and the growth over time is observed once again. And so forth.

All these kinetic models can be very powerful tools. Not only can one improve for example the efficiency of yeast propagation but also investigate the effect of different parameters such as the inoculation rate of yeast, the substrate concentration, oxygen- or ethanol concentration on yeast growth. One application for growth kinetics could be to calculate yeast propagation like done in other yeast growth calculators for homebrewers.

This post is a general introduction about yeast kinetics and I would like to show you how one can get from experimental data to a simple growth kinetic model. Future posts will go into more detail and I would like to give a general introduction first.

# Exponential growth of microorganism

One of the most basic models in mathematical biology is the exponential growth equation for microorganisms. This equation can be used to calculate the amount of microorganisms or biomass (X) after a certain amount of time (t). Biomass can be the physical mass of the microorganisms, the cell concentration or any other measurement related to specify how many microorganisms there are (like optical density). I will stick to the physical mass of microorganisms as biomass in this post. In the exponential growth equation model no inhibition or substrate limitation is included. Substrate by the way is a term for any food source for the microorganisms such as glucose, maltose etc.

$X_t = X_{t0} \cdot e^{\mu_{max} \cdot t - t_0}$

• Xt is the biomass concentration at the time point t [g L-1]
• X0 is the biomass concentration at the time point zero [g L-1]
• µmax is the maximum specific growth rate [h-1]
• t Time [h]
• t0 Time where the experiment begins. Normally zero [h]

Lets make an example. Lets say you have a 1 L yeast starter (with indefinite amount of substrate) and add 10 g of yeast (X0) at the beginning (t0). You might ask yourself how many yeast cells you have after waiting for 90 min. The only thing you might not know is the specific growth rate (µmax). These coefficients can be looked up and for yeast µmax is somewhere around 0.5 h-1. My solution for this question would be 21.2 g L-1. So roughly double the amount.

You can even calculate the doubling time (tD) after changing the previous equation (doubling time specifies the time needed to double the initial amount of microorganisms):

$ln(\frac{X_t}{X_{t0}}) = \mu_{max} \cdot t$

By the way, the equation above will be important later on to get µmax. Moving on, at the time of doubling (tD), Xt equals 2 times Xt0:

$ln(\frac{2 X_{t0}}{X_{t0}}) = \mu_{max} \cdot t_D$

$ln(2) = \mu_{max} \cdot t_D$

$t_D = \frac{ln(2)}{\mu_{max}}$

Common doubling times for Saccharomyces cerevisiae are around 90 min [1]. This gives you a µmax of roughly 0.5 h-1.

In the exponential growth equation model substrate limitations are not included and therefore makes it not that useful to fully describe the growth behaviour if you want to investigate the effect of the substrate concentration itself. Let go to the next model.

# Monod equation for biomass

A very widely used model to describe the growth of microorganisms is the Monod model. The whole model is based on the Michaelis-Menten equation widely used in enzyme kinetics. I don’t want to go into further details here how one came up with these equations. In the end, the Monod model is again a simplified version of reality (like every model is). The first equation for the Monod model is:

$\mu = \mu_{max} \frac{S}{K_S + S}$

• µ is known as the specific growth rate [h-1]
• µmax is the maximum specific growth rate [h-1]
• S is the substrate concentration [g L-1]
• KS is the substrate saturation constant [g L-1]

We already know µmax, S is just the substrate concentration. For example the amount of dry malt extract you use for your yeast starter. Or glucose or whatever you are interested in. Just keep in mind that µmax depends on the used substrate. The definition of µ is:

$\mu = \frac{dX}{dt} \cdot \frac{1}{X}$

• µ is known as the specific growth rate [h-1]
• X is the biomass concentration [g L-1]
• dX is the change of the biomass concentration [g L-1]
• dt is the change of time when dX happens [h]

and depends on the change of biomass within an indefinite amount of time (dt). You could therefore write the Monod equation like:

$\frac{dX}{dt}= \mu_{max} \frac{S}{K_S + S} \cdot X$

and you already have your first differential equation for your model to describe the change of biomass in a time dependent manner.

This leaves KS. This is similar to the Michaelis constant Km in the Michaelis-Menten equation. In the case of the Michaelis-Menten equation, Km describes the substrate concentration at which the enzyme reaction is equal to half of the maximum speed. In the case of Monod, KS describes the substrate concentration (therefore S as index) where you have half of µmax. This is all so far for the first part of Monod.

# Monod equation for substrate

In the previous section, I introduced the basic Monod equation which can be used to describe the change of biomass over time. Next we like to include the change of substrate. In case of yeast one might be interested to investigate the behaviour of dry malt extract. For that we have to introduce another coefficient:

$Y_{X/S} = \frac{\frac{dX}{dt}} {\frac{dS}{dt}}$

• YX/S Biomass on substrate yield coefficient [gX gS-1]
• dX is the change of the biomass concentration [g L-1]
• dS is the change of the substrate concentration [g L-1]
• dt is the change of time when dX and dS happen [h]

YX/S simply defines how much biomass you can get from substrate (thus the index X and S). For example how much biomass you get from one gram of substrate. Looking at the previous equations, you can already see how to get a differential equation for the substrate:

$\frac{dS}{dt} = - \frac{\mu_{max} \frac{S}{K_S + S} \cdot X}{Y_{X/S}}$

Per definition, the equation is multiplied by minus one because the slope of dS over dt is negative (substrate is metabolized and therefore only decreases).

This leaves us to look at product kinetics. In case of yeast, one might be interested to describe the production of ethanol as a product. This is very similar to the substrate shown above. In this case you need another yield factor:

$Y_{P/X} = \frac{\frac{dP}{dt}}{\frac{dX}{dt}}$

• YP/X Product on biomass yield coefficient [gP gX-1]
• dP is the change of the product concentration [g L-1]
• dX is the change of the biomass concentration [g L-1]
• dt is the change of time when dX and dP happen [h]

In this case the product depends on the biomass and not on the substrate. Once again one can write down the differential equation for the product formation:

$\frac{dP}{dt} = \mu_{max}\frac{S}{K_S + S} \cdot X \cdot Y_{P/X}$

Are you still reading? Yes? You must either be very interested and/or be a math geek like me… I would like to stop with the introduction here and discuss other things such as inhibition etc in a future post. I now would like to share some information how you could/can get the coefficients for the equations above from empirical data.

# Coefficient determination from experimental data

All the data below is from a S. cerevisiae batch cultivation I cultivated during my undergraduate studies. I don’t want to get much into detail here but some information to understand the values you get afterwards. The batch cultivation was done in a 16 L reactor (4.2 gal) under sterile conditions and glucose as the only carbon source (substrate). All the values below therefore are for glucose only.

During the cultivation (8 h), every 30 min the optical density (OD) and glucose concentration was measured and every 60 min the dry mass was determined. The optical density is another measurement method to get an idea about the yeast concentration. The glucose was measured enzymatically and the dry mass was determined by filtration, drying of the filter paper and finally determining the mass of yeast on the filter paper.

# µmax determination based on dry mass

As previously mentioned, the following equation can be used to get the µmax value by plotting the logarithmic ratio of the biomass against the time (t). This should give you a linear function with the slope µmax as shown in Fig 1:

$ln(\frac{X_t}{X_{t0}}) = \mu_{max} \cdot t$

Fig 1: Log dry mass ratio against time. µmax determined from slope of linear fit function

One can easily see that the amount of yeast grew steadily up to the time point of six hours where the yeast concentration stayed the same (Fig 1). After six-hour the whole glucose was already metabolized (not shown) and no further yeast growth could be observed (Fig 1). The linear fit function therefore only makes sense between time point zero and six hours. The slope of the linear fit function was 0.43 h-1. Please remember, this µmax value is for the dry mass and is close to known values [2].

Lets quickly calculate the doubling time for this µmax. This give you a doubling time of roughly 97 min. Not that far away from the 90 min stated in source [1].

# µmax determination based on optical density (OD)

The same can be done for the OD (Fig 2).

Fig 2: Log OD ratio against time. µmax determined from slope of linear fit function

Once again after five to six hours, the yeast growth came to a stop (Fig 2). This time the slope of the linear fit function was 0.53 h-1. A nice example that not every µmax is the same. One has to be very careful how the specific µmax was determined. Either based on the optical density, dry mass weight or even the cell count.

# Biomass on substrate yield coefficient (YX/S)

To determine the yield coefficient, one can plot the measured yeast dry mass or OD against the measured glucose values and use the linear slope to determine the yield factors (Fig 3).

Fig 3: Determine the biomass to glucose yield factor

The yield factor based on the dry mass was -0.5 g g-1, and -0.1 g g-1 for the OD. Known yield factors for yeast based on glucose and dry mass are between -0.3 and – 0.5 g g-1 [3].

# Building growth models

Now its time to put all the equations and values into a model. The only coefficient not known so far is KS. This value is hard to determine and the easiest way to get this value is by iterative approaches. You simply use the model to get KS. I use Berkley Madonna for this purpose. What you have to do is input all the different differential equations, the measured values and run an iterative algorithm to let the model function approximate the measured values. If you do this the right way you might get graphs like below (Fig 4).

Fig 4: Yeast kinetic model 1, explanation in text below

In this case the substrate concentration (S) and the yeast concentration (X) are plotted against time. In addition, the black dots correspond to the measured glucose concentrations. I included the values I used for the different coefficients in the graph as well. Unfortunately, one cannot fit the measured glucose concentration curve with the numerical values of the determined coefficients. I therefore had to use slightly different values for the yield coefficient (in this case 0.3 g g-1) and 0.51 h-1 for µmax. The differences between the numerical values of the parameters might be due to measuring inaccuracies for the glucose concentration and/or yeast concentration. In the end, one can determine KS to be around 0.031 g L-1.

You now can use the model to investigate how the different conditions affect the growth of the yeast. For instance different substrate conditions or inoculation rates. All this can be useful to understand the behaviour of yeast growth under different conditions. However, one has to keep in mind that all this is based on a simplified model and it does not have to represent reality. Model building is sometimes hard work because iteration processes might get stuck and lead to wrong results (such as negative substrate concentrations).

# Summary

Growth kinetics models can be used to describe the growth of microorganisms. Because biological systems can hardly be approximated by simple fit functions, more sophisticated methods need to be applied. Such as the models described in this post.

# Outlook

This was just a basic introduction about growth kinetics and models. Future posts will go into more details covering additions to the basic Monod model. The next post concerning growth kinetics will be about Brettanomyces growth and is a nice organism to introduce inhibition effects.

I would like to do some small-scale experiments with yeast propagation and determine the individual model-parameters in the future. The resulting models therefore might be useful to approximate yeast starters under different conditions. Just be patient, I am currently really busy with my real scientific work. Thanks for reading and comment if you like. Cheers!

# Bibliography

[1] : http://dbb.urmc.rochester.edu/labs/sherman_f/yeast/4.html, “An Introduction to the Genetics and Molecular Biology of the Yeast Saccharomyces cerevisiae” (2012)
[2] : http://www.atcc.org (2012)
[3] : B. Sonnleitner, Lecture slides Bioprozesstechnik 1, ZHAW Wädenswil, 2010