# Carrying capacity, Κ **Carrying capacity, Κ,** refers to the **maximum concentration of bacterial cells that a culture system can sustain under given conditions**. The composition of the growth medium is one of the most important determinants for reaching high carrying capacities, especially in small shake flask cultures. Other factors include temperature, pH, and oxygen availability. It is crucial to hit high carrying capacities for producing bacterial vaccines, probiotics, soil bio-stimulants, and live biotherapeutics. If the cell concentrations are insufficient, the product might not be economically feasible. Direct total cell counts by BactoBox® or fluorescence flow cytometry is one of the most reliable approach to determine Κ. In this section, we will explain why. The [Screen growth media](/mpd/workflows/best-medium.md) is a simple workflow for how to determine Κ. ## Mathematical determination of carrying capacity For batch cultures the K is obtained at stationary phase. By definition, stationary phase occurs after deceleration phase when the specific growth rate is zero (see [Growth phases](/mpd/cell-growth/growth-phases.md) for more information). There are two overall approaches two mathematically determine K: Curve-fitting and heuristic (rule-of-thumb). ### Curve-fitting In the curve-fitting approach, a mathematical model is fitted to the data. Logistic, Gompertz and Baranyi are some of the typical models used for curve-fitting as reviewed by [López *et al.* 2004](https://www.researchgate.net/profile/Mewa-Dhanoa/post/Which_is_a_better_statistic_to_use_comparison_of_means_ANOVA_or_Effect_size_statistics_in_a_feeding_trial_aquatic_animals/attachment/5b6daff1cfe4a7f7ca59bdba/AS%3A658101871067138%401533915121796/download/Lopez%2Bet%2Bal%2Bgrowth%2Bfunctions%2Bfor%2Bmicrobial.pdf). In practical terms, K is the upper asymptote, that is the flat plateau that cell concentration approaches (dashed green line in illustration 4 below).

Curve-fitting approach to determine carrying capacity, K.

### Heuristic (rule of thumb) A simple rule-of-thumb is that the culture is entering stationary phase if the relative change over a fixed time interval is below a certain threshold. A typical threshold is a relative increase by less than 5% over 1-2 doubling times. This approach works well for most cultures, like *E. coli* in LB medium where the concentrations in stationary phase are very constant (relative increase is within 5% relatively to 1-2 doubling times).

Onset of stationary phase for a simple growth curve. E. coli cultivated in LB medium as an example of a culture with a normal onset of stationary phase. BactoBox® cells/mL (lavender) and plate counts (yellow) were determined in single replicates with frequent sampling.

## Pitfalls in determining carrying capacity Unexpected phenomena such as [diauxic growth](https://en.wikipedia.org/wiki/Diauxic_growth) can complicate the determination of K. After depleting the first substrate, bacteria undergo an adaptation period before switching to a secondary substrate. It may seem as if the culture has hit stationary phase (dashed cyan line), but after a while growth resumes. This is exemplified by *P. fluorescens* grown in TSB medium, where a transient pseudo-stationary phase is observed at approximately 13 hours. Three hours later, however, the cell concentration increases to nearly twice the level (dashed green line) observed during the pseudo-stationary phase. For the more complex situations like the *P. fluorescens* example, it is recommended to extend the normal measurement window, thereby ensuring that the plateau for the true stationary phase has been met. The above curve-fitting approaches are not suited for capturing the second growth phase, but more complex models like double-logistic or bi-Gompertz may be applicable. These models are more challenging to implement and in many cases it is simpler and sufficient to use the heuristic principles.

Onset of stationary phase for a complex diauxic growth curve. P. fluorescens in TSB medium as an example of a culture that hits a transient pseudo-stationary phase (dashed cyan line) and then starts to regrow. BactoBox® cells/mL (lavender) and plate counts (yellow) were done in triplicate repeats

## Summary Carrying capacity is the maximum concentration of bacterial cells that a culture system can sustain. In the coming sections we will review existing methods for determination of K. Click the links below to jump straight to the section. * [Overview of methods for Κ](/mpd/cell-growth/carrying-capacity-k/overview-of-methods-for-k.md) * [BactoBox® for Κ](/mpd/cell-growth/carrying-capacity-k/overview-of-methods-for-k/bactobox-r-for-k.md) * [Fluorescence Flow Cytometry (FFC) for K](/mpd/cell-growth/carrying-capacity-k/overview-of-methods-for-k/fluorescence-flow-cytometry-ffc-for-k.md) * [Microscopy for K](/mpd/cell-growth/carrying-capacity-k/overview-of-methods-for-k/microscopy-for-k.md) * [Optical methods for Κ](/mpd/cell-growth/carrying-capacity-k/overview-of-methods-for-k/optical-methods-for-k.md) * [Plate counts for Κ](/mpd/cell-growth/carrying-capacity-k/overview-of-methods-for-k/plate-counts-for-k.md) * [Dry cell weight for Κ](/mpd/cell-growth/carrying-capacity-k/overview-of-methods-for-k/dry-cell-weight-for-k.md) --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://help.sbtinstruments.com/mpd/cell-growth/carrying-capacity-k.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.