Overcoming stochastic variations in culture variables to quantify and compare growth curve data

Abstract

The comparison of growth, whether it is between different strains or under different growth conditions, is a classic microbiological technique that can provide genetic, epigenetic, cell biological, and chemical biological information depending on how the assay is used. When employing solid growth media, this technique is limited by being largely qualitative and low throughput. Collecting data in the form of growth curves, especially automated data collection in multi-well plates, circumvents these issues. However, the growth curves themselves are subject to stochastic variation in several variables, most notably the length of the lag phase, the doubling rate, and the maximum expansion of the culture. Thus, growth curves are indicative of trends but cannot always be conveniently averaged and statistically compared. Here, we summarize a simple method to compile growth curve data into a quantitative format that is amenable to statistical comparisons and easy to graph and display.

Keywords: Saccharomyces cerevisiae; growth curve; microbe.

FIGURE 1

Spot dilution assay of S. cerevisiae DEB sensitivity. Cells of the indicated genotypes (see^[11]) were grown to saturation in rich medium (YPD), diluted to an optical density at 600 nm of 1.0, serially diluted 10-fold to 10⁻⁴, and then 5 μL of each dilution was spotted onto YPD plates and YPD plates containing DEB. The plates were incubated at 30°C for ~36 h before imaging using a flatbed scanner. The hrq1Δ-S1 and -S2 genotypes refer to random mutations that occurred in the parental hrq1Δ strain

FIGURE 2

Problems with growth curves. (A) An example of 24-h growth curve with data taken at 15-min intervals and indicating the three major variables describing the growth kinetics of microbes: λ, the length of time the cells are in lag phase; μ, the doubling rate; and A, the maximum expansion achieved by the culture. This image is adapted from^[9]. (B) An example of two independent cultures of the same S. cerevisiae strain displaying nearly identical doubling rates but variation in both λ and A. (C) An example of three replicates of growth curve data for a single S. cerevisiae strain displaying similar λ and μ but varied A. The inset shows that averaging the data and plotting the mean and standard deviation yields a curve marred by wide error bars (standard deviation) at the end of the growth period. (D) A growth curve showing a “break” in the cell density at mid-log phase, presumably due to an air bubble interfering with the OD₆₆₀ measurements

FIGURE 3

Step-by-step data analysis with our method. (A) Three growth curves (A, B, and C) each for wild-type cells grown in rich medium (black, 0) or rich medium supplemented with 1.25 mg/mL (red, 1.25) or 2.5 mg/mL (blue, 2.5) OEO2^[]. (B) The data plotted are averages of the triplicate curves shown in (A), and the error bars correspond to standard deviation. (C) To generate the values plotted in the bar graph, the OD₆₆₀ of each growth curve in (A) was averaged for the entire 24-h growth period with the equation $({\sum }_{t=0.25}^{t_{end}}t)/n$, where t is the time interval used to collect OD₆₆₀ readings, t_end is the last time point, and n is the total number of OD₆₆₀ readings. In the graphed example, t = 0.25 h, t_end = 24 h, and n = 97. Then, the mean of the three growth curve averages for each treatment was calculated. The error bars represent the standard deviation. (D) The data in (C) were normalized to growth in the absence of OEO2 with the equation (M/M₀) × 100, where M is a mean value calculated as described above in (C), and M₀ is the mean value calculated for cell growth without added OEO2. In (C and D), the data were analyzed using multiple t-tests corrected using the Holm-Sidak method for multiple comparisons in GraphPad Prism. ** P < 0.001 and *** P < 0.0001