The determination of growth rates of micro organisms by using the optical density data of liquid

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1 AEM Accepts, published online ahead of print on 1 January 0 Appl. Environ. Microbiol. doi:./aem.00-0 Copyright 0, American Society for Microbiology and/or the Listed Authors/Institutions. All Rights Reserved. 1 The determination of growth rates of micro organisms by using the optical density data of liquid cultures a revisit with the relative density calibration approach Hsiu-Li Lin, 1 Chien-Chung Lin, Yi-Jen Lin, Hsiu-Chen Lin, Chwen-Ming Shih, Chi-Rong Chen, Rong-Nan Huang, and Tai-Chih Kuo * Department of Neurology, General Cathay Hospital, Sijhih, Taiwan 1 ; Department of Orthopedic Surgery, Taipei City Hospital, Taipei, Taiwan ; Department of Biochemistry, Taipei Medical University, Taipei, Taiwan ; Department of Laboratory Medicine, Taipei Medical University Hospital, Taipei Medical University, Taipei, Taiwan ; Department of Biochemistry, Taipei Medical University, 0 Wu-Hsing St., Taipei, Taiwan ; and Department of Entomology, National Taiwan University, Taipei, Taiwan Corresponding author. Mailing address: Biochemistry Department, Taipei Medical University, 0 Wu-Hsing Street, Taipei, Taiwan. Phone: 0----#1. Fax: Downloaded from on October 1, 01 by guest 1 tckuo@tmu.edu.tw. 1 1

2 Abstract To solve the problems of measuring the growth rates of micro organisms from optical density (OD)-growth time plots, we use relative density (RD) plots. The relation of OD and RD is built from the diluted grown cultures. This method is satisfactorily applied to study the growth of Escherichia coli and cyanobacteria Anabaena spiroides. Downloaded from on October 1, 01 by guest

3 Main Text In spite for its popularity, the direct use of optical density (OD) records of liquid cultures of micro organisms to study their growth kinetics may yield problematic results. For instance, for a same culture of Escherichia coli (E. coli), the cell doubling time derived from the rates of OD increments varies from to min, depending on the wavelengths of measurement light (Figure 1A). Here we report an approach to obtain reliable results (Figure 1B). Briefly, the OD of the liquid cell culture is frequently recorded throughout the growth period. At or close to the end of cultivation, the cell density of the culture is arbitrarily defined as 1.0 relative density (RD), and aliquots of the culture are diluted to prepare reference samples of various RD values. For example, a reference sample of 0. RD is prepared by diluting 0. ml grown cell culture with 0. ml fresh growth media. The ODs of reference samples are also determined and plotted against the RD values to construct an OD-RD calibration curve by using the equation of OD = m RD/(n+RD), where m and n are empirical constants (Figure 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 (Figure 1C). With this method, we have determined the growth rates of bacteria E. coli and cyanobacteria Anabaena spiroides (Figure ). We found that a common laboratory E. coli, the E. coli BL1(DE) doubled every 1± min (Figure 1C), irrespective Downloaded from on October 1, 01 by guest 1 of light wavelengths, consistent with the rates of the increment of absolute densities (AD, cfu/ml) of the 1 E. coli cells (± min, Figure 1C). Furthermore, the growth rates obtained from RD-time plots and 1 OD-time plots were statistically different (t-test P values << 0.0 for RD vs. OD of used wavelengths).

4 We also found that E. coli DHα, another common laboratory E. coli, doubled every ± min (data not shown). For Anabaena spiroides, the cells doubled every 1.±1. hr, agreeing with 1.±0. hr obtained from the increment rate of absolute cell density (Figure B). Again, the results were not affected by the wavelengths of light used for OD measurements. The problems of using the OD-time plots to determine the growth rates of micro organisms are in the misuse of the Beer-Lambert law, which is only applicable to light absorbing molecules(, ). However, when light hits micro organisms, the light may be scattered and/or absorbed, and the OD of a liquid culture of micro organisms is the combination of light scattering and absorption(, ). Generally, the light scattering will be prominent when the particle sizes are close to the wavelength of the light (e.g., the size of E. coli and the visible lights). Also, the intensity of light scattering is not linear with particle concentrations(). Thus, it s no wonder that the measurements with lights of different wavelengths in the OD-time plots yields wavelength-dependent growth rates. We propose the use RD-time plots to obtain the growth rates of micro organisms. 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 micro organisms can be justified (see the supplement). Our idea was inspired by the use of standard curves in biochemical studies. This method has two features. Firstly, it employs Downloaded from on October 1, 01 by guest 1 serial dilutions of grown cultures. Secondly, it uses OD-RD calibration curves to infer RD values from 1 OD records. It turns out that there were precedents of using dilution methods to study the growth of 1 micro organisms. For example, in the methods of Baranyi and Pin(1,, ), the micro organisms are

5 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 methods of Baranyi and Pin(1,, ), we obtained the similar averaged growth rate for our E. coli (BL1(DE)) with larger standard deviations (± min) (TCK unpublished data). On the other hand, Lawrence and Maier also noticed the problems of using OD to determine the actual cell density of bacteria(). They proposed the use of OD of the diluted grown cultures to establish OD-dry weight calibration curves of bacteria. However, their idea was not extended to determine the growth rates of bacteria. In this study, we used bacteria of different physical characteristics to test the applicability of our method, because the OD of the micro organism cultures is the results of light absorption and scattering of the cells. For the E. coli cells, which are colorless, relative small (0.~1 µm) and single-celled in liquid cultures, the OD of E. coli culture mainly is caused by light scattering(), as suggested by the observation that at a given RD, the OD decreased as the light wavelength increased (Figure 1B). On the other hand, the cells of photosynthetic cyanobacteria Anabaena spiroides algae are pigment-rich, large (~ µm ~ µm), and filament-forming. The visible-light spectrum of the algae culture is similar to that of the purified phytochromes of the algae (data not shown), suggesting that the light absorption is the major cause for the OD activity of the algae culture. Moreover, in the OD-RD calibration curves of the Downloaded from on October 1, 01 by guest 1 A. spiroides algae (Figure A), at a given RD, the OD reading did not decrease as the light wavelength 1 increased, again indicating that light scattering was not the main cause of OD activity. For both 1 organisms, the growth rates obtained from the RD-time plots and the AD-time plots were very close,

6 and the results were independent of light wavelengths, as predicted by the theory (see the supplement). Despite the promising results, we caution that our method is applicable only if the morphology (e.g., color, size, shapes etc.) of the interested micro organisms and the optical properties (e.g., color) 1 of the culture media both do not vary with the culture time. Finally, for routine cultures of a same micro organism (e.g., the E. coli DHα) under identical conditions, except the culture dates and the 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 OD recording (see the supplement). This would eliminate the needs of dilution work. The reason for this short-cut is discussed in the supplement. Downloaded from on October 1, 01 by guest

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9 Legends of Figures. Figure 1. The use of OD reading to determine growth rates of bacteria E. coli. (A) The OD-time response of an E. coli culture monitored with light of different wavelength. The OD of an LB-grown E. coli BL1(DE) culture at C was monitored with light of the indicated light wavelength (e.g., OD 00 for measurements with 00-nm light). The doubling time of E. coli in the logarithmic growth phase was estimated to be ± min, ± min 0± min, and ± min (mean and one standard deviation, SD) for measurements with 0-nm ( ), 00-nm ( ), 00-nm ( ), and 00-nm ( ) light, respectively. The differences among these values were significant (ANOVA P vale 0.00). (B) The RD-OD calibration curves of the bacteria culture shown in the panel A. Aliquots of the grown culture were diluted with various amount of fresh LB to prepare reference samples, and their ODs were recorded with light of different wavelength. (C) The RD and AD as a function of growth time of the E. coli culture 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 of the indicated time was determined by plating the serially diluted bacteria cultures on LB plates and counting the colonies. 1.0 OD 00nm corresponds to.0±0. cfu/ml. The growth rates were expressed as cell doubling time, which were inferred from the slope of the regression lines. The Downloaded from on October 1, 01 by guest 1 horizontal bars represent three standard deviations ( SD) of the OD 00, RD 00, and AD 1 measurements (three repeats). For figure clarity, only the SD of measurements with the 00-nm 1 light are shown. The SD of the measurements with light of other wavelengths are very close to 1

10 those with the 00-nm light. The reported growth rates were obtained from the results of four growth experiments. KaleidaGraph (v.0, Synergy Software) was used for curve fitting. Note that in the experiment, we added pre-grown cells into a C pre-warmed LB media to avoid the initial slow growth of the cells. The details of E. coli strains and culture conditions are given in the supplementary material. Downloaded from on October 1, 01 by guest

11 Figure. The determination of the growth rates of the cyanobacteria algae Anabaena spiroides. (A) The OD-RD calibration of an A. spiroides algae culture. The grown algae culture was diluted with fresh media as described, and light of the indicated wavelength was used to measure the ODs 1 of the reference samples. (B) The RD and AD as a function of growth time of the algae culture shown in panel A. The algae cells were grown in an aerated plain media for ~0 hr (see the supplement for detail). The growth of the algae cells was monitored by measuring the OD of the culture with light of the indicated wavelength. The absolute cell density (cells/ml) was determined by counting the observed cell number under a bright field microscopy. For clarity, only the SD of measurements (three repeats) with the 0-nm light are shown by the horizontal bars. The SD of the measurements with light of other wavelengths are similar to those with the 0-nm light. The reported growth rates were resulted from three growth experiments. Downloaded from on October 1, 01 by guest

12 References 1. Baranyi, J., and C. Pin. 1. Estimating bacterial growth parameters by means of detection times. Appl Environ Microbiol : Dalgaard, P., and K. Koutsoumanis Comparison of maximum specific growth rates and lag times estimated from absorbance and viable count data by different mathematical models. J Microbiol Methods :1-.. Eisenberg, D., and D. Crothers. 1. Physical chemistry with applications to the life sciences, vol. Benjamin/Cummings, Menlo Park, CA 0.. Lawrence, J. V., and S. Maier. 1. Correction for the inherent error in optical density readings. Applied and Environmental Microbiology :.. Lindqvist, R. 00. Estimation of Staphylococcus aureus growth parameters from turbidity data: characterization of strain variation and comparison of methods. Appl Environ Microbiol :-0.. Tinoco, I. J., K. Sauer, and J. C. Wang. 1. Physical Chemistry - Principles and applications in biological sciences, vol. Prentice Hall, Upper Saddle River, NJ 0. Downloaded from on October 1, 01 by guest 1 1 1