Get the growth parameters λ, µ, and Κ

Knowledge of generation time, lag-phase duration, and carrying capacity is key to designing rational seed-train processes. This section outlines how to determine these parameters.

Introduction

As detailed in the encyclopedia section Exponential growth model most stages of batch culture dynamics can be modeled by an exponential equation with initial lag phase. Later - as the culture is deprived of nutrients - it will typically transition to the stationary stage where other mathematical models are more suited.

Three growth parameters are particularly useful for optimizing bioprocesses:

• λ : Lag phase duration. Typically expressed in hours.

• µ : Growth rate. Typically expressed per hour

• Κ : Carrying capacity of the medium. Typically expressed as cells/mL

General recommendations

• To ensure accurate data interpretation, test the culture medium for objects that may be classified as bacteria: You do this by measuring a 1:100 dilution of the uninoculated medium using BactoBox®.

  • If the results shows >30,000 cells/mL, then it may be beneficial to eliminate this background by filtering the medium through 0.2 µm syringe/vacuum filter prior to autoclaving.

  • If the results shows <30,000 cells/mL, then there is no need to filter the medium prior to autoclaving.

• Use BacTotal_v2024-10 for measurements. This ruleset is applicable to most bacteria but does not distinguish between live and dead cells.

• For optimal oxygen transfer, the maximum fill volume for a shake flask is 20%. For a 250 mL shake flask, the maximum fill volume is 50 mL.

• The following protocol is suitable for most bacteria with a generation time of 1 hour or less. Adjustments - like less frequent sampling - may be necessary for slow-growing bacteria.

• Use sterile pipette tips for sample handling to prevent contamination.

• Ensure the sample is handled efficiently to quickly resume orbital shaking and temperature control.

Day 1: Prepare starter culture

1

Prepare flasks and media

Two flasks with media are required: one for the starter culture and another for the growth experiment.

1. Prepare the culture medium according to the manufacturer's instructions.

2. Use a magnetic stirrer to completely dissolve the powder before moving on to the next step.

3. Optionally, use 0.2 µm filters to remove particulates from the culture medium if needed. Refer to the recommendations above for further details.

4. Transfer 50 mL of culture medium into each of the two Erlenmeyer baffled flasks with vented caps. Follow the autoclaving instructions from the medium manufacturer: typically 121 °C at ~15 psi for 15 minutes.

5. Let the flasks cool to room temperature before moving on to the next steps.

2

Prepare a high-quality overnight starter culture

1. Inoculate an overnight starter culture from a cryo stock using the optimal inoculation ratio determined in the overseeding experiment. For more information, see the section Get high-quality overnight cultures from cryo stocks. Ensure to use exactly the same parameters for high-quality culture as in the overseeding experiment, including fixed inoculation ratio, incubation time, vessel type, and culture medium.

2. Place the starter culture flask under the specified incubation conditions. Similarly, place the non-inoculated flask for the growth curve experiment in the incubator to preheat the medium to the required incubation temperature.

Day 2: Track bacterial growth curve

1

Determine the bacterial concentration in the starter culture

1. As aseptically as possible, use a serological pipette to transfer 5 mL of the starter culture into a sterile tube.

2. Disaggregate cells by vortexing. Usually, 30 seconds of vortexing at maximum speed is sufficient, but some bacteria require more aggressive sample preparation. See the section Sample preparation for more details.

3. Dilute 1:100 by transferring 101 µL of the sample to 10 mL of diluent. Vortex for 10 seconds at maximum speed.

4. Dilute 1:10,000 by transferring 101 µL of the 1:100 sample into the 10 mL diluent. Vortex for 10 seconds at max speed.

5. If the result is within 30,000 - 5,000,000 note down the value. If outside this range, see the section Hit the right concentration for how to get a value within the accepted range. Note that the measurements are generally more precise when the result is within 0.5 to 5 million total/mL.

6. Calculate the bacterial concentration in the overnight starter culture, C_starter, by multiplying the cells/mL result by the dilution factor.

2

Inoculate flask for growth curve assessment

1. To determine the volume of disaggregated starter culture required to hit a target seeding concentration of 1 x 10⁷ cells/mL in a 50 mL culture medium, apply the following formula. Adjust accordingly if using a different volume of culture medium. An online subcultivation calculator is available for this purpose.

   1. $V_{\text{starter}} = \dfrac{C_{\text{final}}}{C_{\text{starter}}} \cdot V_{\text{final}} = \dfrac{1 \cdot 10^7}{C_\text{starter}} \cdot 50 \; \text{mL}$

2. Transfer the calculated volume of starter culture to the growth curve flask and incubate at designated growth conditions. Note down the inoculation time.

3. Vigorously swirl for 30 seconds to evenly distribute the inoculum in the fresh medium. This flask is now referred to as the growth curve culture.

3

Determine initial concentration, N₀

1. Use a serological pipette to aseptically sample 1 mL of the growth curve culture. Transfer sample to an empty tube, and note down the sampling time. Immediately return the flask to the incubator and resume shaking.

2. Vortex sample for 30 seconds at maximum speed.

3. Dilute 1:100 in by transferring 101 µL sample to 10 mL diluent. Vortex at maximum speed for 10 seconds.

4. Use BactoBox® to measure. The result should be ~100,000 cells/mL.

4

Analyze growth over time

The goal is to get a measurement for approx. every one to two generations. Very fast-growing bacteria like E. coli necessitate frequent sampling for e.g. ½ hour sampling frequency, while it may be sufficient to sample e.g. every second hour for slower-growing bacteria.

1. Select your preferred sampling frequency, and follow the guidance from the previous step on how to sample and disaggregate.

2. Perform a BactoBox® measurement to determine bacterial concentration. As shown in the below illustration it will be necessary to adjust the dilution factor as the bacterial concentration increases. See the section Hit the right concentration for more information.

3. End the experiment when growth has stabilized. This is indicated by "similar" results over three consecutive sampling intervals. "Similar" means differences are typically within ±25%.

4. Note that it may be relevant to do BactoBox® measurements during senescence. Frequent sampling is not necessary. It is sufficient to leave the flask in the incubator and analyze a sample after 1 and 2 additional days.

Once the experiment concludes, it's time to calculate λ, µ, and Κ. These metrics will soon be available directly through SBT Access. Meanwhile, we are happy to assist with the calculations. You can submit a bundle to us for this service, free of charge: Create support case.

Preferably, use SBT Access measurement group to add metadata on dilution factors and sampling time (see Track growth curves in SBT Access). If the metadata has not been added in Access, then please include a detailed table in your bundle with the following essential information:

• Measurement IDs

• Sampling times and inoculation time

• Dilution factors