Revisiting with a Relative-Density Calibration Approach the Determination of Growth Rates of Microorganisms by Use of Optical Density Data from Liquid Cultures

To solve the problems of measuring the growth rates of microorganisms from optical density (OD)-growth time plots, we used relative-density (RD) plots. The relationship of OD and RD was built from the diluted grown cultures. This method was satisfactorily applied to study the growth of Escherichia coli and the cyanobacterium Anabaena spiroides.In spite of the popularity of the optical density (OD) method, the direct use of OD records of liquid cultures of microorganisms to study their growth kinetics may yield problematic results. For instance, for an Escherichia coli culture, the cell doubling time as derived from incremental OD rates varies from 46 to 38 min, depending on the wavelength of light used for measurement (Fig. ​(Fig.1A).1A). Here, we report an approach to obtain more reliable results (Fig. ​(Fig.1B).1B). Briefly, the OD of the liquid cell culture is recorded frequently throughout the growth period. At or near the end of cultivation, the cell density of the culture is arbitrarily defined as a relative density (RD) of 1.0, and aliquots of the culture are diluted to prepare reference samples of various RD values. For example, a reference sample of 0.3 RD is prepared by diluting 0.3 ml of grown cell culture with 0.7 ml of fresh growth medium. The ODs of the reference samples are also determined and plotted against the RD values to construct an OD-RD calibration curve using the equation OD = m × RD/(n + RD), where m and n are empirical constants (Fig. ​(Fig.1B).1B). The recorded ODs of the cell culture are converted into RD values, and the cell doubling time is determined from the RD-growth time plot (Fig. ​(Fig.1C).1C). We determined the growth rates of E. coli bacteria and Anabaena spiroides cyanobacteria (Fig. ​(Fig.2)2) using this method. We found that a common laboratory E. coli strain, BL21(DE3), doubled every 31 ± 3 min (mean ± 1 standard deviation SD]) (Fig. ​(Fig.1C),1C), irrespective of the light wavelength used for measurement, consistent with the incremental rate of the absolute density (AD; CFU/ml) of the E. coli cells (32 ± 4 min) (Fig. ​(Fig.1C).1C). Furthermore, the growth rates obtained from RD-time plots and OD-time plots were statistically different (t test P values were ≪0.05 for RDs versus ODs with wavelengths used). We also found that E. coli DH5α, another common E. coli laboratory strain, doubled every 46 ± 2 min (data not shown). For Anabaena spiroides, the cells doubled every 18.5 ± 1.5 h, agreeing with the result of 17.6 ± 0.8 h obtained from the incremental AD rate (Fig. ​(Fig.2B).2B). Again, the results were not affected by the wavelength of light used for OD measurements.Open in a separate windowFIG. 1.The use of OD readings to determine growth rates of E. coli bacteria. (A) OD-time response of an E. coli culture monitored with light of different wavelengths. The OD of an LB broth-grown E. coli BL21(DE3) culture at 37°C was monitored with light of the indicated wavelengths (e.g., OD600 for measurements with 600-nm light). The doubling times of E. coli cells in the logarithmic growth phase were estimated to be 46 ± 3 min, 43 ± 2 min, 40 ± 2 min, and 38 ± 2 min (mean ± 1 SD) for measurements with 450-nm, 500-nm, 600-nm, and 700-nm light, respectively. The differences among these values are significant (analysis of variance P value, 0.006). (B) RD-OD calibration curves of the bacterial culture whose OD results are shown in panel A. Aliquots of the grown culture were diluted with various amounts of fresh LB broth to prepare reference samples, and their ODs were recorded with light of different wavelengths. (C) RD and AD as a function of growth time of the E. coli culture whose OD results are shown in panel A. The RD data were derived from OD-RD calibration curves and plotted against the growth time. The AD of the cell culture at each indicated time was determined by plating the serially diluted bacterial cultures on LB plates and counting the colonies. An OD of 1.09 at 600 nm corresponds to (3.0 ± 0.5) × 10⁸ CFU/ml. The growth rates are expressed as cell doubling times, which were inferred from the slopes of the regression lines. The error bars represent three standard deviations of the OD600, RD600, and AD measurements (three repeats). For clarity, only the SDs of measurements with 600-nm light are shown. The SDs of measurements with light of other wavelengths were very close to those with the 600-nm light. The reported growth rates are the results of four growth experiments. KaleidaGraph (version 4.0; Synergy Software) was used for curve fitting. Note that in the experiment, we added pregrown cells into prewarmed (37°C) LB medium to avoid the initial slow growth of the cells. The details of E. coli strains and culture conditions are given in the supplemental material.Open in a separate windowFIG. 2.Determination of growth rates of the algal cyanobacterium Anabaena spiroides. (A) OD-RD calibration of an A. spiroides algal culture. The grown algal culture was diluted with fresh medium as described in the text, and light of the indicated wavelengths was used to measure the ODs of the reference samples. (B) RD and AD as functions of growth time of the algal culture shown in panel A. The algal cells were grown in an aerated plain medium for ∼100 h (see the supplemental material for details). The growth of the algal cells was monitored by measuring the OD of the culture with light of the indicated wavelengths. Absolute cell density (cells/ml) was determined by counting the observed cell number under a bright-field microscope. The error bars represent three standard deviations. For clarity, only SDs of measurements (three repeats) with the 720-nm light are shown. The SDs of the measurements with light of other wavelengths were similar to those with the 720-nm light. The growth rates are the results of three growth experiments.The problems from using OD-time plots to determine the growth rates of microorganisms are in the misuse of the Beer-Lambert law, which is only applicable to light-absorbing molecules (3, 6). However, when light hits microorganisms, the light may be scattered and/or absorbed, and the OD of a liquid culture of microorganisms is the combination of light scattering and light absorption (3, 6). Generally, light scattering will be prominent when the particle sizes are close to the wavelength of the light (e.g., the size of E. coli cells and the visible light wavelengths). Also, the intensity of light scattering is not linear with particle concentrations (3). Thus, it is not surprising that measurements with lights of different wavelengths in OD-time plots yield wavelength-dependent growth rates.We propose the use of RD-time plots to obtain the growth rates of microorganisms. In fact, the relationship among OD, RD, and AD can be expressed mathematically, and the use of RD-time plots to derive the growth rates of microorganisms can be justified (see the supplemental material). Our idea was inspired by the use of standard curves in biochemical studies. This method has two features. First, it employs serial dilutions of grown cultures. Second, it uses OD-RD calibration curves to infer RD values from OD records. There are precedents for using dilution methods to study the growth of microorganisms. For example, in the method of Baranyi and Pin (1, 2, 5), the microorganisms are serially diluted into several flasks before cell culture, and the growth rates can be inferred from the delayed time intervals for the diluted cultures to reach a given OD. By using the method of Baranyi and Pin (1, 2, 5), we obtained a similar averaged growth rate for our E. coli strain BL21(DE3)], with a larger standard deviation (34 ± 5 min) (unpublished data of T.-C. Kuo). On the other hand, Lawrence and Maier also noticed the problems of using OD to determine the actual cell density of bacteria (4). They proposed the use of the OD of the diluted grown cultures to establish OD-dry weight calibration curves for bacteria. However, they did not extend their idea to determine the growth rates of bacteria.In this study, we used bacteria with different physical characteristics to test the applicability of our method, because the OD of the microorganism culture is the result of light absorption and light scattering by the cells. For E. coli cells, which are colorless, relatively small (∼0.5 μm by 1 μm), and single celled in liquid culture, the OD is mainly the result of light scattering (3), as suggested by the observation that at a given RD, the OD decreased as the light wavelength increased (Fig. ​(Fig.1B).1B). On the other hand, the cells of the photosynthetic algal cyanobacterium Anabaena spiroides are pigment rich, large (∼3 μm by 5 μm), and filament forming. The visible light spectrum of the algal culture is similar to that of the purified phytochromes of the algae (data not shown), suggesting that light absorption is the major factor in the OD measurements of the algal culture. Moreover, in the OD-RD calibration curves of the A. spiroides algae (Fig. ​(Fig.2A),2A), at a given RD, the OD reading did not decrease as the light wavelength increased, again indicating that light scattering was not the main factor in OD measurements. For both organisms, the growth rates obtained from the RD-time plots and the AD-time plots were very close, and the results were independent of light wavelength, as predicted by the theory (see the supplemental material).Despite the promising results, we caution that our method is applicable only if the morphology (e.g., color, size, shape, etc.) of the microorganism of interest and the optical properties (e.g., color) of the culture medium both do not vary with culture time.Finally, for routine cultures of the same microorganism (i.e., E. coli DH5α) under conditions that are identical except for culture dates and growth periods, it is not necessary to prepare the OD-RD calibration curves each time. The OD records of new cultures can be converted to RD by using the RD-OD calibration curves of previous cultures, as long as the identical instrument is used for recording ODs (see the supplemental material). This eliminates the need for dilution work. The reason for this shortcut is discussed in the supplemental material.