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Direct optical density determination of bacterial cultures in microplates for high-throughput screening applications
Enzyme and Microbial Technology 118 (2018) 1–5
Contents lists available at ScienceDirect
Enzyme and Microbial Technology journal homepage: www.elsevier.com/locate/enzmictec
Direct optical density determination of bacterial cultures in microplates for high-throughput screening applications Annika Meyers, Christoph Furtmann, Joachim Jose
T
⁎
Institute of Pharmaceutical and Medicinal Chemistry, PharmaCampus, Westfälische Wilhelms-Universität Münster, Corrensstraße 48, 48149 Münster, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Optical density Bacteria Microplate reader Conversion formula Without dilution
A convenient and most abundantly applied method to determine the growth state of a bacterial cell culture is to determine the optical density (OD) spectrophotometrically. Dilution of the samples, which is necessary to measure within the linear range of the spectrophotometer, is time-consuming and not compatible with highthroughput applications. Here we present a direct approach to estimate the OD at 578 nm (OD578) of bacterial cultures in microplates without the need for sample dilution. This could be advantageous for high-throughput analysis of bacterial cells in microplates for example when optimizing growth conditions, screening for new substrates of a bacterial strain or monitoring enzymatic activity after enzyme evolution. Pseudomonas putida cells were grown in shake flasks. The OD578 was determined in parallel in a microplate directly without dilution and in a spectrophotometer cuvette after dilution. The resulting data set was used to identify a conversion formula, which enables direct and reliable transformation of OD measurements of undiluted samples into the corrected OD values as would have been obtained for diluted samples measured in a standard spectrophotometer. Subsequently we could show that just a few OD calibration points are required to adjust this conversion formula and make it suitable for other suspensions or cultures of bacterial strains different than P. putida. The OD calibration points can be obtained by any combination of microplate reader and cuvette spectrophotometer. For this purpose, conversion formulas for a formazine standard suspension and a suspension of Escherichia coli BL21(DE3) cells were successfully generated. The OD values calculated by both conversion formulas turned out to be identical with the values as obtained by the control measurements in the spectrophotometer. This indicates the general applicability of the conversion formula as described.
1. Introduction While investigating different promoters for the biosynthesis of the green fluorescent protein (GFP) in Pseudomonas putida KT2440, we were confronted with the - trivial but bothersome - problem to monitor both, the optical density at 578 nm (OD578) and the fluorescence intensity (FI) at 510 nm of bacterial cell cultures grown in shake flasks. Although the Beer-Lambert law allows the spectrophotometric quantification of substances, if the absorbance of the substance is proportional to the concentration of the absorbing species, it is strictly valid only in homogenous solutions but not in suspensions. In suspensions, for example bacterial cultures, the light with a wavelength in the range of the particle’s size (i. e., a bacterium) is scattered (Mie scattering) [1]. When the light is scattered by a single particle in a suspension with many particles, the attenuation of light and hence the measured extinction is proportional to the number of particles [2]. At
higher particle concentrations, the incident beam of light is scattered by more than one particle (‘multiple scattering’). This phenomenon results in an apparently lower optical density (OD), because multiple scattered light could reach the detector of a spectrophotometric device [3]. Therefore, monitoring the OD of a bacterial culture directly in a microtiter plate, for example during cell growth or as a control in advance of enzymatic assays, is inaccurate. To avoid ‘multiple scattering’ in OD measurements, suspensions of bacterial cells usually have to be diluted. In diluted suspensions, ‘multiple scattering’ plays a minor role and the extinction, which is defined as the sum of scattering and absorbance in this case [2], and which is measured by the spectrophotometer, can be correlated in a linear way with the number of cells in the culture. Due to the non-linearity of the OD at higher cell densities, we were forced to use two different devices, a standard spectrophotometer (SP) device for determining the OD578 as well as a microplate reader (MPR)
Abbreviations: OD, optical density; OD578, optical density at 578 nm; GFP, green fluorescent protein; FI, fluorescence intensity; FAU, formazine attenuation units; SP, spectrophotometer; MPR, microplate reader ⁎ Corresponding author. E-mail address: [email protected] (J. Jose). https://doi.org/10.1016/j.enzmictec.2018.06.016 Received 19 April 2018; Received in revised form 29 June 2018; Accepted 30 June 2018 Available online 03 July 2018 0141-0229/ © 2018 Elsevier Inc. All rights reserved.
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2.3. OD578 determination
for measuring the FI. This resulted in a time-consuming process, in which the bacterial cultures first had to be diluted to an OD578 within the linear range of the spectrophotometer, and additionally pipetted into a 96-well plate to be analyzed in a microplate reader for FI. Such a procedure is - besides being prone to errors - not compatible with highthroughput applications. A computational conversion of undiluted OD values measured in a microplate into OD values as would have been obtained for diluted samples measured with the spectrophotometer would allow a considerable simplification of cell growth monitoring, but was not available so far. Wind and Szymanski introduced a correction factor to the Beer-Lambert law, which allows transmittance measurements in aerosol media [4]. The authors restrict this solely on single forward scattering because the effects of multiple scattering are much more complicated to consider. This limitation to single scattering does not reflect the reality of a bacterial cell culture and therefore the correction factor, which was introduced into the Beer-Lambert law by Wind and Szymanski, could not be used to correct for the non-linearity of OD measurements at higher cell densities. Warringer and Blomberg did find a third-order polynomial correlation between SP and MPR measurements [5], but it was developed for yeast species and the applicability to bacterial species was not shown. Dalgaard et al. described an approach to correct for the non-linearity of the OD at higher cell densities. Herein, OD values measured with a spectrophotometer without dilution were converted into OD values measured with the same device after dilution [6]. Compared to our work, the approach by Dalgaard et al. is restricted in two respects: Firstly, the conversion formula did not deal at all with the utilization of a combination of two spectroscopic devices and therefore did not enable the transformation of OD values from undiluted microplate culture to those expected from dilution and subsequent spectrophotometry. Secondly, the authors did not show the general applicability of their OD-correction approach by a standardized suspension.
The OD578 of the bacterial culture was measured every two hours for 34 h. To determine the OD578 within the linear range of the spectrophotometer, the bacterial culture sample was diluted. The microplate reader was used to measure the OD578 of the same sample, but without dilution. For that, 200 μL of the non-diluted bacterial cell culture were pipetted into a well of a 96-well plate. The OD578 of the culture medium was measured both in the microplate reader and the spectrophotometer as well and was in both cases subtracted from the measured OD578 values of bacterial samples. 2.4. Data analysis By measuring the OD578 of the bacterial cell culture both with the spectrophotometer and the microplate reader, a dataset of 343 OD578 values of the same sample – one measured after dilution within the linear range of the spectrophotometer and the other one measured without dilution in the microplate – was generated. The data was analyzed by the use of the data analysis and graphing program Origin 9 (OriginLab, 2013). The non-linear parameter estimation was performed with the algorithm BoxLucas1 [7] and the Levenberg-Marquardt iteration algorithm with a confidence interval of 95%. 2.5. Formazine standard For the verification of the exponential fitting approach, a suspension of a defined turbidity was generated. The suspension, a formazine standard of 4000 FAU (formazine attenuation units), is usually used to determine the turbidity of water during water quality analysis. It was prepared according to the DIN EN ISO 7027:1999 [8]. The formazine standard suspension was used to prepare samples of various concentrations.
2. Material and methods
2.6. Conversion formula for E. coli BL21(DE3)
2.1. Spectroscopic devices
The supplemented Origin-worksheet (Supplementary material 1) was used to generate a conversion formula for OD578 estimation of E. coli BL21(DE3) cells. The cells were diluted serially and the OD578 values of the prepared 23 dilutions were determined as triplicates in parallel with the microplate reader without dilution and with the spectrophotometer after sample dilution. The resulting data set was inserted into the Origin-worksheet (Supplementary material 1), which gave a conversion formula with adapted parameters a and b for the OD578 values measured with the microplate reader.
In this study, a GENESYS™ 10S UV–vis spectrophotometer (Thermo Scientific, Waltham, MA, USA) and semi-micro cuvettes (SD10 PS, volume 1.5–3.0 mL, window 4.5 x 23 mm, GML-alfaplast GmbH, Munich, Germany) were used for OD578 measurements. To determine the FI of the P. putida KT2440 cells, which are synthesizing GFP, an Infinite® M200 PRO (Tecan, Männedorf, Switzerland) microplate reader was used. The samples were measured without dilution in a 96-well plate (Microplate, PS, F-Bottom, clear, Greiner Bio-One, Frickenhausen, Germany). A serial dilution of bromophenol blue in 20% (v/v) ethanol and NaOH (0.02 M) ranging from 0.5 μM to 125 μM was used to determine the linear ranges of both devices. Both spectroscopic devices were used to measure the absorbance at 578 nm and the resulting OD578 values were compared with each other.
3. Results and discussion 3.1. Comparability of spectroscopic devices and correction for differing layer thicknesses To guarantee comparability of two spectroscopic devices, both devices require identical linear ranges. If the linear ranges of two spectroscopic devices are identical, the measured absorbance will be independent of the used spectroscopic device. A solution of bromophenol blue was used to determine the linear ranges of spectrophotometer (SP) and microplate reader (MPR) used in this study. By measuring the absorbance at 578 nm, it could be shown that Infinite® M200 PRO and GENESYS™ have identical linear ranges between extinction values of 0.1 and 4.0 (data not shown). This finding guarantees comparability of both spectroscopic devices used in the following. Furthermore, we anticipate the procedure presented hereafter can be used effectively with various MPR-SP device pairings having identical linear ranges. To determine a correlation between OD578 values measured by spectrophotometer (OD578SP) and microplate reader (OD578MPR), cultures of P. putida KT2440, containing plasmids with gfp regulated by
2.2. Bacterial cell culture P. putida KT2440 cells were grown in Luria-Bertani (LB) medium, being composed of 10 g/L tryptone (Carl Roth, Karlsruhe, Germany), 5 g/L yeast extract (Carl Roth, Karlsruhe, Germany) and 10 g/L NaCl (Sigma-Aldrich, Munich, Germany) and adjusted to pH 7.0. For precultures 20 mL LB medium were inoculated with one bacterial clone. The cultures were incubated in shaking flasks for 16–18 hours at 30 °C and 200 rpm. A preculture of P. putida KT2440 was used to inoculate 200 mL of LB in a shake flask. Escherichia coli BL21(DE3) cells were cultivated similarly, but incubated at 37 °C and 200 rpm. In case of plasmid containing strains, kanamycin (50 μg/mL) (Life Technologies, Darmstadt, Germany) was added. 2
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of the microplate. The resulting quotient was multiplied by the OD578 values of the microplate reader. This resulted in the layer-corrected OD578. The correction of the layer thickness led to the transformation of undiluted OD578MPR values into the anticipated spectrophotometer values, but only in an OD578 range from 0.0 to 0.4. The non-linear progress of the curve was not affected above an OD578 value of 0.4 (Fig. 1, open circles). Not unexpectedly, the correction of the layer thickness could not solve the problem of ‘multiple scattering’. 3.2. Development of an OD578 conversion formula for P. putida KT2440 The non-linearity of the curves show in Fig. 1 – with and without correction of the layer thickness – is exactly described by A = a∙(1-exp(-b∙x))
(1)
with parameters a and b possessing positive values. To generate an OD578 conversion formula, Eq. (1) was used and fitted with Origin 9. Therefore, the dataset shown in Fig. 1 was used, but in contrast to Fig. 1, the OD578MPR values were put on the X-axis and the OD578SP were put on the Y-axis, as shown in Fig. 2 A, because the conversion formula was supposed to calculate OD578SP values from OD578MPR values as measured. This resulted in a calibration formula with parameters a = -1.6716 and b = 1.04802 (Table 1). Hence, Eq. (1) can be used to describe the course of the curve in Fig. 2 A, but now with parameters a and b being negative, because X- and Y-axis values were reversed. As shown in Fig. 2 B, transformation of the OD578MPR values with the conversion formula resulting in the OD578coverted values as given on the Y-axis, showed a linear relationship with the OD578SP values as measured in the spectrophotometer with diluted samples (Fig. 2 B, Xaxis) and hence indicated the applicability of the formula. Below 0.4 and beyond values of 6.0 such linear relationship is not given, but an OD578 range from 0.4 to 6.0 should be sufficient for most microplate applications. For OD578 values below 0.4 the conversion formula can be used as well, but the correction of the OD578MPR values by the layer thickness is a more accurate procedure. It is important to mention, that the defined parameters a = -1.6716 and b = -1.04802 are only valid to estimate the OD578MPR values of P. putida KT2440 cells. Curves of OD578MPR and OD578SP values of different strains, like E. coli, plotted as function of each other would appear slightly different, because of different morphological properties of the bacterial species. In the case other bacterial strains are investigated, or other spectroscopic devices are used, parameters a and b have to be adjusted by Levenberg-Marquardt iteration algorithm (BoxLucas1, Origin 9) to the current instance. This could be realized with little effort, as is shown below.
Fig. 1. OD578 values determined by the microplate reader plotted as functions of OD578 determined by standard spectrophotometer. To determine the OD578 values of the P. putida KT2440 culture, the Infinite® M200 PRO microplate reader was used. The values were plotted as function of OD578 values of the same sample, which were measured after dilution with the GENESYS™ spectrophotometer (filled circles). OD578 values of microplate reader after adjustment of layer thickness plotted as function of OD578 values of spectrophotometer (open circles). Ideal Beer-Lambert like behavior of the OD578 (black line).
various promoters, were grown in shake flasks and the OD578 was determined every two hours with both devices. The resulting 343 OD578SP values measured after dilution and the corresponding OD578MPR values of the same, but undiluted sample were plotted as function of each other. As expected, the curve increased in a linear fashion in an OD578 range from 0.0 to 0.4. At OD578 values above 0.4, the curve showed non-linear behavior (Fig. 1, filled circles). Not unexpectedly, it did not show a linear correlation between the two datasets and no ideal Beer-Lambert like behavior (Fig. 1, black line), as expected to occur without ‘multiple scattering’ of the incident light. Because both optical devices have different layer thicknesses, a correction of the layer thickness was performed. The layer thicknesses are 1 cm in the case of the semi-micro cuvette and 5.8 mm in the case of the microplate. The layer thickness of the microplate refers to a volume of 200 μL within one well. It was calculated based on the manufacturer’s information on the dimensions of a single well. The layer thickness of the semi-micro cuvette was divided by the layer thickness
Fig. 2. Development of a conversion formula for P. putida KT2440. A: Data points plotted as function of OD578MPR (open circles) and fitting function BoxLucas1 algorithm (black line). B: Converted OD578 values plotted as a function of the OD578 values of diluted samples. OD578 values measured with the microplate reader without dilution were converted with Eq. (1) with parameters a and b as indicated in Table 1 for P. putida KT2440 into spectrophotometer values, as would have been obtained after dilution (open triangles). The resulting curve showed perfect accordance with ideal BeerLambert like behavior (black line).
3
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spectrophotometer values (Fig. 3, closed squares). Both curves showed high accordance up to an upper OD578 limit of 6.0. The utilization of a standardized suspension to successfully develop a conversion formula proves the general applicability of Eq. (1) and therefore shows that the exponential formula is suitable for the development of a reliable conversion formula for OD578 value determination of suspensions, in particular those of bacterial cells. Furthermore, it was shown that just a few OD calibration data points are required to generate such conversion formula for suspensions. Beyond that, the exponential fitting approach was also used to generate a conversion formula for E. coli BL21(DE3) cells by using few OD calibration points. Again, an adaption of the parameters a and b (Eq. (1)) was necessary, because E. coli and P. putida possess different morphological properties. A serial dilution of 23 suspensions of E. coli BL21(DE3) cells was generated and the samples were measured both with the microplate reader without dilution and with the spectrophotometer after dilution. An Origin-worksheet, which is provided as Supplementary material 1, was generated and used in order to generate a conversion formula out of the dataset just described (Fig. 4 A). The resulting conversion formula with adapted parameters a and b (Table 1) was used to convert the OD578MPR values of 15 samples of E. coli BL21(DE3) cells which were measured without dilution and did not contribute in order to generate the conversion formula before. Above OD578 values of around 0.3, the non-corrected OD578 values plotted as function of the OD578SP determined after dilution - show the non-linear progress described previously (Fig. 4 B, open triangles). The converted OD578 values were plotted as function of the OD578SP, determined after dilution, as well (Fig. 4 B, closed triangles). The resulting curve shows good accordance with ideal linear correlation (black line), indicating that it is possible to generate a conversion formula for the OD578 of bacterial cells at higher cell densities, especially when using the supplied Origin-worksheet. Just a small number of OD calibration data points was sufficient to successfully develop an OD conversion formula for E. coli BL21(DE3). This finding will facilitate the generation of conversion formulas for OD correction of further bacterial strains in other laboratories. Every user could generate a suitable fitting function for the spectroscopic devices used in the laboratory, so far as the linear ranges of the used spectroscopic devices are identical. The user should prepare a small number of samples with different ODs, measure them with and without dilution and insert the resulting OD values into the provided Origin-worksheet (Supplementary material 1, Supplementary material 2). The software will then generate a conversion formula especially suitable for the operator’s spectroscopic devices and used strains.
Table 1 Parameters a and b of Eq. (1) as obtained for OD conversion formulas of different suspensions. suspension
a
b
P. putida KT2440 formazine standard E. coli BL21(DE3)
−1.6716 −1.94768 −1.87142
−1.04802 −0.76479 −0.94956
3.3. Experimental validation of the MPR-SP conversion formula To verify the applicability of the exponential formula (Eq. (1)) for the conversion of the OD578 values, the development of a conversion formula was performed with a suspension of defined turbidity, a formazine standard of 4000 FAU, which is usually used in water quality measurements [8]. Because of the different morphological properties of formazine and bacterial cells, generation of a modified conversion formula for formazine with adapted values for parameters a and b (Eq. (1)) was necessary. For that, a small number of just 18 formazine suspensions with defined concentrations were measured both with the spectrophotometer and with the microplate reader. The generated dataset was then used as described above to generate a conversion formula with adjusted parameters a and b by the use of Origin 9 (Table 1). Subsequently, 24 dilutions with various concentrations of the formazine standard were generated. The spectrophotometer was used to measure the OD578 values of these samples (Fig. 3, open squares). Afterwards the microplate reader was used to measure the OD578 values of the same samples and the conversion formula was applied to convert the microplate reader-measured OD578 values into the corresponding
3.4. Estimating the OD578 of P. putida KT2440 cells expressing mCherry by the conversion formula The conversion formula (Eq. (1)) with parameters a and b as indicated in Table 1 was used to estimate the OD578 of P. putida KT2440 cells synthesizing the fluorescent protein mCherry. Therefore, P. putida KT2440 cells, which contained a plasmid for the expression of mCherry on the cell surface [9,10], were grown in shake flasks. The microplate reader was used to measure the OD578 and the FI of small aliquots taken approximately every two hours. The conversion formula was used to convert the measured OD578MPR values (Fig. 5, open circles) into the expected spectrophotometer values for diluted samples. The growth curve resulting from the conversion (Fig. 5, closed circles) was visually typical of the output expected from the traditional dilution and spectrophotometry approach, with distinct stationary and exponential phase traces seen. This experiment showed, that the conversion formula developed in this work is suitable to estimate the OD578 of P. putida cell cultures with the spectroscopic devices used.
Fig. 3. Verification of the exponential fit with a formazine standard suspension. OD578 values of a formazine suspension were plotted as function of turbidity thereof. The formazine suspension of a defined turbidity was prepared according to the DIN EN ISO 7027:1999 []. The standard suspension has a turbidity of 4000 FAU and was diluted randomly. To determine the OD578 values of diluted samples, the microplate reader and the spectrophotometer were used. The microplate reader-measured values without dilution were converted into spectrophotometer values as would have been expected after dilution by the use of a BoxLucas1 exponential fit (Origin 9). OD578 values measured spectrophotometrically (open squares) and corresponding calculated values (closed squares) are consistent within the relevant OD578 range. The high accordance of both curves shows that an exponential approach is suitable for the development of a conversion formula. 4
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Fig. 4. Development of a conversion formula for E. coli BL21(DE3). A: Data points plotted as function of OD578MPR (open circles) and fitting function BoxLucas1 algorithm (black line). The fit was carried out with the supplied Originworksheet (Supplementary material 1). B: Converted (closed triangles) and non-converted (open triangles) OD578 values plotted as a function of the OD578 values of diluted samples. OD578 values measured with the microplate reader without dilution were converted with Eq. (1) with parameters a and b as indicated in Table 1 for E. coli BL21(DE3) into anticipated spectrophotometer values (closed triangles). The resulting curve showed good accordance with ideal Beer-Lambert like behavior (black line).
Above all, we could show the general applicability of the fitting approach presented. On the one hand, the use of the formazine standard suspensions proves the general applicability of an exponential conversion formula. On the other hand, the provided Origin-worksheet (Supplementary material 1) was successfully used to generate a conversion formula for E. coli BL21(DE3) cell cultures by the use of just a few OD calibration data points. Therefore, our approach could be used in other laboratories to generate similar conversion formulas for bacterial strains with other spectroscopic devices as well, if they have identical linear ranges, and by that could facilitate automated cell density determination. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.enzmictec.2018.06.016.
Fig. 5. Growth curve of P. putida KT2440 cells synthesizing mCherry. P. putida KT2440 containing a plasmid for the synthesis of mCherry on the bacterial surface [9,10], were grown in shake flasks. OD578 values were measured approximately every two hours with the microplate reader and were converted with Eq. (1) with parameters a and b as indicated in Table 1 for P. putida KT2440 into values anticipated for diluted samples. The converted growth curve (closed circles) shows the typical progress of a bacterial growth curve with exponential phase and stationary phase while the microplate reader measured curve (open circles) shows the flattened progress resulting of the nonlinearity of the OD578 at higher cell densities.
References [1] G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Annalen der Physik 330 (3) (1908) 377–445. [2] H.C. van de Hulst, Light Scattering by Small Particles, Dover Publications, Inc, Mineola, NY, 1981. [3] A.L. Koch, Turbidity measurements of bacterial cultures in some available commercial instruments, Anal. Biochem. 38 (1970) 252–259. [4] L. Wind, W.W. Szymanski, Quantification of scattering corrections to the BeerLambert law for transmittance measurements in turbid media, Meas. Sci. Technol. 13 (2002) 270–275. [5] J. Warringer, A. Blomberg, Automated screening in environmental arrays allows analysis of quantitative phenotypic profiles in Saccharomyces cerevisiae, Yeast 20 (1) (2003) 53–67. [6] P. Dalgaard, T. Ross, L. Kamperman, K. Neumeyer, T.A. McMeekin, Estimation of bacterial growth rates from turbidimetric and viable count data, Int. J. Food Microbiol. 23 (1994) 391–404. [7] http://www.originlab.de/doc/Origin-Help/BoxLucas1-FitFunc (accessed 22th of June 2018). [8] Standard according to European Committee for Standardization (CEN): European Standard EN ISO 7027:1999, Water Quality - Determination of Turbidity, CEN, (1999), https://standards.cen.eu. [9] I.E.P. Tozakidis,, S. Sichwart, M.G. Teese, J. Jose, Autotransporter mediated esterase display on Zymomonas mobilis and Zymobacter palmae, J. Biotechnol. 191 (2014) 228–235. [10] S. Sichwart, I.E.P. Tozakidis, M. Teese, J. Jose, Maximized autotransporter-mediated expression (MATE) for surface display and secretion of recombinant proteins in Escherichia coli, Food Technol. Biotechnol. 53 (3) (2015) 251–260.
4. Conclusions In summary, we applied a conversion formula that transforms OD578 values of undiluted P. putida KT2440 cell suspensions determined directly in microtiter plates by a microplate reader into OD578 values as has been determined after dilution in a standard spectrophotometer. This allows the use of the microplate reader for the simultaneous detection of the OD578 and FI and, most importantly, without the need to dilute the samples beforehand. This procedure is less time-consuming and, due to less pipetting steps, less prone to errors than the usual procedure. In addition, it allows the automation of OD measurements, because the loss of reaction volume and dilution steps are avoided. It is therefore particularly valuable when monitoring large numbers of bacterial cultures and when measuring multiple parameters simultaneously, for example OD and FI. The generated OD conversion formula is applicable up to an upper limit of OD578 = 6.0. 5
Contents lists available at ScienceDirect
Enzyme and Microbial Technology journal homepage: www.elsevier.com/locate/enzmictec
Direct optical density determination of bacterial cultures in microplates for high-throughput screening applications Annika Meyers, Christoph Furtmann, Joachim Jose
T
⁎
Institute of Pharmaceutical and Medicinal Chemistry, PharmaCampus, Westfälische Wilhelms-Universität Münster, Corrensstraße 48, 48149 Münster, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Optical density Bacteria Microplate reader Conversion formula Without dilution
A convenient and most abundantly applied method to determine the growth state of a bacterial cell culture is to determine the optical density (OD) spectrophotometrically. Dilution of the samples, which is necessary to measure within the linear range of the spectrophotometer, is time-consuming and not compatible with highthroughput applications. Here we present a direct approach to estimate the OD at 578 nm (OD578) of bacterial cultures in microplates without the need for sample dilution. This could be advantageous for high-throughput analysis of bacterial cells in microplates for example when optimizing growth conditions, screening for new substrates of a bacterial strain or monitoring enzymatic activity after enzyme evolution. Pseudomonas putida cells were grown in shake flasks. The OD578 was determined in parallel in a microplate directly without dilution and in a spectrophotometer cuvette after dilution. The resulting data set was used to identify a conversion formula, which enables direct and reliable transformation of OD measurements of undiluted samples into the corrected OD values as would have been obtained for diluted samples measured in a standard spectrophotometer. Subsequently we could show that just a few OD calibration points are required to adjust this conversion formula and make it suitable for other suspensions or cultures of bacterial strains different than P. putida. The OD calibration points can be obtained by any combination of microplate reader and cuvette spectrophotometer. For this purpose, conversion formulas for a formazine standard suspension and a suspension of Escherichia coli BL21(DE3) cells were successfully generated. The OD values calculated by both conversion formulas turned out to be identical with the values as obtained by the control measurements in the spectrophotometer. This indicates the general applicability of the conversion formula as described.
1. Introduction While investigating different promoters for the biosynthesis of the green fluorescent protein (GFP) in Pseudomonas putida KT2440, we were confronted with the - trivial but bothersome - problem to monitor both, the optical density at 578 nm (OD578) and the fluorescence intensity (FI) at 510 nm of bacterial cell cultures grown in shake flasks. Although the Beer-Lambert law allows the spectrophotometric quantification of substances, if the absorbance of the substance is proportional to the concentration of the absorbing species, it is strictly valid only in homogenous solutions but not in suspensions. In suspensions, for example bacterial cultures, the light with a wavelength in the range of the particle’s size (i. e., a bacterium) is scattered (Mie scattering) [1]. When the light is scattered by a single particle in a suspension with many particles, the attenuation of light and hence the measured extinction is proportional to the number of particles [2]. At
higher particle concentrations, the incident beam of light is scattered by more than one particle (‘multiple scattering’). This phenomenon results in an apparently lower optical density (OD), because multiple scattered light could reach the detector of a spectrophotometric device [3]. Therefore, monitoring the OD of a bacterial culture directly in a microtiter plate, for example during cell growth or as a control in advance of enzymatic assays, is inaccurate. To avoid ‘multiple scattering’ in OD measurements, suspensions of bacterial cells usually have to be diluted. In diluted suspensions, ‘multiple scattering’ plays a minor role and the extinction, which is defined as the sum of scattering and absorbance in this case [2], and which is measured by the spectrophotometer, can be correlated in a linear way with the number of cells in the culture. Due to the non-linearity of the OD at higher cell densities, we were forced to use two different devices, a standard spectrophotometer (SP) device for determining the OD578 as well as a microplate reader (MPR)
Abbreviations: OD, optical density; OD578, optical density at 578 nm; GFP, green fluorescent protein; FI, fluorescence intensity; FAU, formazine attenuation units; SP, spectrophotometer; MPR, microplate reader ⁎ Corresponding author. E-mail address: [email protected] (J. Jose). https://doi.org/10.1016/j.enzmictec.2018.06.016 Received 19 April 2018; Received in revised form 29 June 2018; Accepted 30 June 2018 Available online 03 July 2018 0141-0229/ © 2018 Elsevier Inc. All rights reserved.
Enzyme and Microbial Technology 118 (2018) 1–5
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2.3. OD578 determination
for measuring the FI. This resulted in a time-consuming process, in which the bacterial cultures first had to be diluted to an OD578 within the linear range of the spectrophotometer, and additionally pipetted into a 96-well plate to be analyzed in a microplate reader for FI. Such a procedure is - besides being prone to errors - not compatible with highthroughput applications. A computational conversion of undiluted OD values measured in a microplate into OD values as would have been obtained for diluted samples measured with the spectrophotometer would allow a considerable simplification of cell growth monitoring, but was not available so far. Wind and Szymanski introduced a correction factor to the Beer-Lambert law, which allows transmittance measurements in aerosol media [4]. The authors restrict this solely on single forward scattering because the effects of multiple scattering are much more complicated to consider. This limitation to single scattering does not reflect the reality of a bacterial cell culture and therefore the correction factor, which was introduced into the Beer-Lambert law by Wind and Szymanski, could not be used to correct for the non-linearity of OD measurements at higher cell densities. Warringer and Blomberg did find a third-order polynomial correlation between SP and MPR measurements [5], but it was developed for yeast species and the applicability to bacterial species was not shown. Dalgaard et al. described an approach to correct for the non-linearity of the OD at higher cell densities. Herein, OD values measured with a spectrophotometer without dilution were converted into OD values measured with the same device after dilution [6]. Compared to our work, the approach by Dalgaard et al. is restricted in two respects: Firstly, the conversion formula did not deal at all with the utilization of a combination of two spectroscopic devices and therefore did not enable the transformation of OD values from undiluted microplate culture to those expected from dilution and subsequent spectrophotometry. Secondly, the authors did not show the general applicability of their OD-correction approach by a standardized suspension.
The OD578 of the bacterial culture was measured every two hours for 34 h. To determine the OD578 within the linear range of the spectrophotometer, the bacterial culture sample was diluted. The microplate reader was used to measure the OD578 of the same sample, but without dilution. For that, 200 μL of the non-diluted bacterial cell culture were pipetted into a well of a 96-well plate. The OD578 of the culture medium was measured both in the microplate reader and the spectrophotometer as well and was in both cases subtracted from the measured OD578 values of bacterial samples. 2.4. Data analysis By measuring the OD578 of the bacterial cell culture both with the spectrophotometer and the microplate reader, a dataset of 343 OD578 values of the same sample – one measured after dilution within the linear range of the spectrophotometer and the other one measured without dilution in the microplate – was generated. The data was analyzed by the use of the data analysis and graphing program Origin 9 (OriginLab, 2013). The non-linear parameter estimation was performed with the algorithm BoxLucas1 [7] and the Levenberg-Marquardt iteration algorithm with a confidence interval of 95%. 2.5. Formazine standard For the verification of the exponential fitting approach, a suspension of a defined turbidity was generated. The suspension, a formazine standard of 4000 FAU (formazine attenuation units), is usually used to determine the turbidity of water during water quality analysis. It was prepared according to the DIN EN ISO 7027:1999 [8]. The formazine standard suspension was used to prepare samples of various concentrations.
2. Material and methods
2.6. Conversion formula for E. coli BL21(DE3)
2.1. Spectroscopic devices
The supplemented Origin-worksheet (Supplementary material 1) was used to generate a conversion formula for OD578 estimation of E. coli BL21(DE3) cells. The cells were diluted serially and the OD578 values of the prepared 23 dilutions were determined as triplicates in parallel with the microplate reader without dilution and with the spectrophotometer after sample dilution. The resulting data set was inserted into the Origin-worksheet (Supplementary material 1), which gave a conversion formula with adapted parameters a and b for the OD578 values measured with the microplate reader.
In this study, a GENESYS™ 10S UV–vis spectrophotometer (Thermo Scientific, Waltham, MA, USA) and semi-micro cuvettes (SD10 PS, volume 1.5–3.0 mL, window 4.5 x 23 mm, GML-alfaplast GmbH, Munich, Germany) were used for OD578 measurements. To determine the FI of the P. putida KT2440 cells, which are synthesizing GFP, an Infinite® M200 PRO (Tecan, Männedorf, Switzerland) microplate reader was used. The samples were measured without dilution in a 96-well plate (Microplate, PS, F-Bottom, clear, Greiner Bio-One, Frickenhausen, Germany). A serial dilution of bromophenol blue in 20% (v/v) ethanol and NaOH (0.02 M) ranging from 0.5 μM to 125 μM was used to determine the linear ranges of both devices. Both spectroscopic devices were used to measure the absorbance at 578 nm and the resulting OD578 values were compared with each other.
3. Results and discussion 3.1. Comparability of spectroscopic devices and correction for differing layer thicknesses To guarantee comparability of two spectroscopic devices, both devices require identical linear ranges. If the linear ranges of two spectroscopic devices are identical, the measured absorbance will be independent of the used spectroscopic device. A solution of bromophenol blue was used to determine the linear ranges of spectrophotometer (SP) and microplate reader (MPR) used in this study. By measuring the absorbance at 578 nm, it could be shown that Infinite® M200 PRO and GENESYS™ have identical linear ranges between extinction values of 0.1 and 4.0 (data not shown). This finding guarantees comparability of both spectroscopic devices used in the following. Furthermore, we anticipate the procedure presented hereafter can be used effectively with various MPR-SP device pairings having identical linear ranges. To determine a correlation between OD578 values measured by spectrophotometer (OD578SP) and microplate reader (OD578MPR), cultures of P. putida KT2440, containing plasmids with gfp regulated by
2.2. Bacterial cell culture P. putida KT2440 cells were grown in Luria-Bertani (LB) medium, being composed of 10 g/L tryptone (Carl Roth, Karlsruhe, Germany), 5 g/L yeast extract (Carl Roth, Karlsruhe, Germany) and 10 g/L NaCl (Sigma-Aldrich, Munich, Germany) and adjusted to pH 7.0. For precultures 20 mL LB medium were inoculated with one bacterial clone. The cultures were incubated in shaking flasks for 16–18 hours at 30 °C and 200 rpm. A preculture of P. putida KT2440 was used to inoculate 200 mL of LB in a shake flask. Escherichia coli BL21(DE3) cells were cultivated similarly, but incubated at 37 °C and 200 rpm. In case of plasmid containing strains, kanamycin (50 μg/mL) (Life Technologies, Darmstadt, Germany) was added. 2
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of the microplate. The resulting quotient was multiplied by the OD578 values of the microplate reader. This resulted in the layer-corrected OD578. The correction of the layer thickness led to the transformation of undiluted OD578MPR values into the anticipated spectrophotometer values, but only in an OD578 range from 0.0 to 0.4. The non-linear progress of the curve was not affected above an OD578 value of 0.4 (Fig. 1, open circles). Not unexpectedly, the correction of the layer thickness could not solve the problem of ‘multiple scattering’. 3.2. Development of an OD578 conversion formula for P. putida KT2440 The non-linearity of the curves show in Fig. 1 – with and without correction of the layer thickness – is exactly described by A = a∙(1-exp(-b∙x))
(1)
with parameters a and b possessing positive values. To generate an OD578 conversion formula, Eq. (1) was used and fitted with Origin 9. Therefore, the dataset shown in Fig. 1 was used, but in contrast to Fig. 1, the OD578MPR values were put on the X-axis and the OD578SP were put on the Y-axis, as shown in Fig. 2 A, because the conversion formula was supposed to calculate OD578SP values from OD578MPR values as measured. This resulted in a calibration formula with parameters a = -1.6716 and b = 1.04802 (Table 1). Hence, Eq. (1) can be used to describe the course of the curve in Fig. 2 A, but now with parameters a and b being negative, because X- and Y-axis values were reversed. As shown in Fig. 2 B, transformation of the OD578MPR values with the conversion formula resulting in the OD578coverted values as given on the Y-axis, showed a linear relationship with the OD578SP values as measured in the spectrophotometer with diluted samples (Fig. 2 B, Xaxis) and hence indicated the applicability of the formula. Below 0.4 and beyond values of 6.0 such linear relationship is not given, but an OD578 range from 0.4 to 6.0 should be sufficient for most microplate applications. For OD578 values below 0.4 the conversion formula can be used as well, but the correction of the OD578MPR values by the layer thickness is a more accurate procedure. It is important to mention, that the defined parameters a = -1.6716 and b = -1.04802 are only valid to estimate the OD578MPR values of P. putida KT2440 cells. Curves of OD578MPR and OD578SP values of different strains, like E. coli, plotted as function of each other would appear slightly different, because of different morphological properties of the bacterial species. In the case other bacterial strains are investigated, or other spectroscopic devices are used, parameters a and b have to be adjusted by Levenberg-Marquardt iteration algorithm (BoxLucas1, Origin 9) to the current instance. This could be realized with little effort, as is shown below.
Fig. 1. OD578 values determined by the microplate reader plotted as functions of OD578 determined by standard spectrophotometer. To determine the OD578 values of the P. putida KT2440 culture, the Infinite® M200 PRO microplate reader was used. The values were plotted as function of OD578 values of the same sample, which were measured after dilution with the GENESYS™ spectrophotometer (filled circles). OD578 values of microplate reader after adjustment of layer thickness plotted as function of OD578 values of spectrophotometer (open circles). Ideal Beer-Lambert like behavior of the OD578 (black line).
various promoters, were grown in shake flasks and the OD578 was determined every two hours with both devices. The resulting 343 OD578SP values measured after dilution and the corresponding OD578MPR values of the same, but undiluted sample were plotted as function of each other. As expected, the curve increased in a linear fashion in an OD578 range from 0.0 to 0.4. At OD578 values above 0.4, the curve showed non-linear behavior (Fig. 1, filled circles). Not unexpectedly, it did not show a linear correlation between the two datasets and no ideal Beer-Lambert like behavior (Fig. 1, black line), as expected to occur without ‘multiple scattering’ of the incident light. Because both optical devices have different layer thicknesses, a correction of the layer thickness was performed. The layer thicknesses are 1 cm in the case of the semi-micro cuvette and 5.8 mm in the case of the microplate. The layer thickness of the microplate refers to a volume of 200 μL within one well. It was calculated based on the manufacturer’s information on the dimensions of a single well. The layer thickness of the semi-micro cuvette was divided by the layer thickness
Fig. 2. Development of a conversion formula for P. putida KT2440. A: Data points plotted as function of OD578MPR (open circles) and fitting function BoxLucas1 algorithm (black line). B: Converted OD578 values plotted as a function of the OD578 values of diluted samples. OD578 values measured with the microplate reader without dilution were converted with Eq. (1) with parameters a and b as indicated in Table 1 for P. putida KT2440 into spectrophotometer values, as would have been obtained after dilution (open triangles). The resulting curve showed perfect accordance with ideal BeerLambert like behavior (black line).
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spectrophotometer values (Fig. 3, closed squares). Both curves showed high accordance up to an upper OD578 limit of 6.0. The utilization of a standardized suspension to successfully develop a conversion formula proves the general applicability of Eq. (1) and therefore shows that the exponential formula is suitable for the development of a reliable conversion formula for OD578 value determination of suspensions, in particular those of bacterial cells. Furthermore, it was shown that just a few OD calibration data points are required to generate such conversion formula for suspensions. Beyond that, the exponential fitting approach was also used to generate a conversion formula for E. coli BL21(DE3) cells by using few OD calibration points. Again, an adaption of the parameters a and b (Eq. (1)) was necessary, because E. coli and P. putida possess different morphological properties. A serial dilution of 23 suspensions of E. coli BL21(DE3) cells was generated and the samples were measured both with the microplate reader without dilution and with the spectrophotometer after dilution. An Origin-worksheet, which is provided as Supplementary material 1, was generated and used in order to generate a conversion formula out of the dataset just described (Fig. 4 A). The resulting conversion formula with adapted parameters a and b (Table 1) was used to convert the OD578MPR values of 15 samples of E. coli BL21(DE3) cells which were measured without dilution and did not contribute in order to generate the conversion formula before. Above OD578 values of around 0.3, the non-corrected OD578 values plotted as function of the OD578SP determined after dilution - show the non-linear progress described previously (Fig. 4 B, open triangles). The converted OD578 values were plotted as function of the OD578SP, determined after dilution, as well (Fig. 4 B, closed triangles). The resulting curve shows good accordance with ideal linear correlation (black line), indicating that it is possible to generate a conversion formula for the OD578 of bacterial cells at higher cell densities, especially when using the supplied Origin-worksheet. Just a small number of OD calibration data points was sufficient to successfully develop an OD conversion formula for E. coli BL21(DE3). This finding will facilitate the generation of conversion formulas for OD correction of further bacterial strains in other laboratories. Every user could generate a suitable fitting function for the spectroscopic devices used in the laboratory, so far as the linear ranges of the used spectroscopic devices are identical. The user should prepare a small number of samples with different ODs, measure them with and without dilution and insert the resulting OD values into the provided Origin-worksheet (Supplementary material 1, Supplementary material 2). The software will then generate a conversion formula especially suitable for the operator’s spectroscopic devices and used strains.
Table 1 Parameters a and b of Eq. (1) as obtained for OD conversion formulas of different suspensions. suspension
a
b
P. putida KT2440 formazine standard E. coli BL21(DE3)
−1.6716 −1.94768 −1.87142
−1.04802 −0.76479 −0.94956
3.3. Experimental validation of the MPR-SP conversion formula To verify the applicability of the exponential formula (Eq. (1)) for the conversion of the OD578 values, the development of a conversion formula was performed with a suspension of defined turbidity, a formazine standard of 4000 FAU, which is usually used in water quality measurements [8]. Because of the different morphological properties of formazine and bacterial cells, generation of a modified conversion formula for formazine with adapted values for parameters a and b (Eq. (1)) was necessary. For that, a small number of just 18 formazine suspensions with defined concentrations were measured both with the spectrophotometer and with the microplate reader. The generated dataset was then used as described above to generate a conversion formula with adjusted parameters a and b by the use of Origin 9 (Table 1). Subsequently, 24 dilutions with various concentrations of the formazine standard were generated. The spectrophotometer was used to measure the OD578 values of these samples (Fig. 3, open squares). Afterwards the microplate reader was used to measure the OD578 values of the same samples and the conversion formula was applied to convert the microplate reader-measured OD578 values into the corresponding
3.4. Estimating the OD578 of P. putida KT2440 cells expressing mCherry by the conversion formula The conversion formula (Eq. (1)) with parameters a and b as indicated in Table 1 was used to estimate the OD578 of P. putida KT2440 cells synthesizing the fluorescent protein mCherry. Therefore, P. putida KT2440 cells, which contained a plasmid for the expression of mCherry on the cell surface [9,10], were grown in shake flasks. The microplate reader was used to measure the OD578 and the FI of small aliquots taken approximately every two hours. The conversion formula was used to convert the measured OD578MPR values (Fig. 5, open circles) into the expected spectrophotometer values for diluted samples. The growth curve resulting from the conversion (Fig. 5, closed circles) was visually typical of the output expected from the traditional dilution and spectrophotometry approach, with distinct stationary and exponential phase traces seen. This experiment showed, that the conversion formula developed in this work is suitable to estimate the OD578 of P. putida cell cultures with the spectroscopic devices used.
Fig. 3. Verification of the exponential fit with a formazine standard suspension. OD578 values of a formazine suspension were plotted as function of turbidity thereof. The formazine suspension of a defined turbidity was prepared according to the DIN EN ISO 7027:1999 []. The standard suspension has a turbidity of 4000 FAU and was diluted randomly. To determine the OD578 values of diluted samples, the microplate reader and the spectrophotometer were used. The microplate reader-measured values without dilution were converted into spectrophotometer values as would have been expected after dilution by the use of a BoxLucas1 exponential fit (Origin 9). OD578 values measured spectrophotometrically (open squares) and corresponding calculated values (closed squares) are consistent within the relevant OD578 range. The high accordance of both curves shows that an exponential approach is suitable for the development of a conversion formula. 4
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Fig. 4. Development of a conversion formula for E. coli BL21(DE3). A: Data points plotted as function of OD578MPR (open circles) and fitting function BoxLucas1 algorithm (black line). The fit was carried out with the supplied Originworksheet (Supplementary material 1). B: Converted (closed triangles) and non-converted (open triangles) OD578 values plotted as a function of the OD578 values of diluted samples. OD578 values measured with the microplate reader without dilution were converted with Eq. (1) with parameters a and b as indicated in Table 1 for E. coli BL21(DE3) into anticipated spectrophotometer values (closed triangles). The resulting curve showed good accordance with ideal Beer-Lambert like behavior (black line).
Above all, we could show the general applicability of the fitting approach presented. On the one hand, the use of the formazine standard suspensions proves the general applicability of an exponential conversion formula. On the other hand, the provided Origin-worksheet (Supplementary material 1) was successfully used to generate a conversion formula for E. coli BL21(DE3) cell cultures by the use of just a few OD calibration data points. Therefore, our approach could be used in other laboratories to generate similar conversion formulas for bacterial strains with other spectroscopic devices as well, if they have identical linear ranges, and by that could facilitate automated cell density determination. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.enzmictec.2018.06.016.
Fig. 5. Growth curve of P. putida KT2440 cells synthesizing mCherry. P. putida KT2440 containing a plasmid for the synthesis of mCherry on the bacterial surface [9,10], were grown in shake flasks. OD578 values were measured approximately every two hours with the microplate reader and were converted with Eq. (1) with parameters a and b as indicated in Table 1 for P. putida KT2440 into values anticipated for diluted samples. The converted growth curve (closed circles) shows the typical progress of a bacterial growth curve with exponential phase and stationary phase while the microplate reader measured curve (open circles) shows the flattened progress resulting of the nonlinearity of the OD578 at higher cell densities.
References [1] G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Annalen der Physik 330 (3) (1908) 377–445. [2] H.C. van de Hulst, Light Scattering by Small Particles, Dover Publications, Inc, Mineola, NY, 1981. [3] A.L. Koch, Turbidity measurements of bacterial cultures in some available commercial instruments, Anal. Biochem. 38 (1970) 252–259. [4] L. Wind, W.W. Szymanski, Quantification of scattering corrections to the BeerLambert law for transmittance measurements in turbid media, Meas. Sci. Technol. 13 (2002) 270–275. [5] J. Warringer, A. Blomberg, Automated screening in environmental arrays allows analysis of quantitative phenotypic profiles in Saccharomyces cerevisiae, Yeast 20 (1) (2003) 53–67. [6] P. Dalgaard, T. Ross, L. Kamperman, K. Neumeyer, T.A. McMeekin, Estimation of bacterial growth rates from turbidimetric and viable count data, Int. J. Food Microbiol. 23 (1994) 391–404. [7] http://www.originlab.de/doc/Origin-Help/BoxLucas1-FitFunc (accessed 22th of June 2018). [8] Standard according to European Committee for Standardization (CEN): European Standard EN ISO 7027:1999, Water Quality - Determination of Turbidity, CEN, (1999), https://standards.cen.eu. [9] I.E.P. Tozakidis,, S. Sichwart, M.G. Teese, J. Jose, Autotransporter mediated esterase display on Zymomonas mobilis and Zymobacter palmae, J. Biotechnol. 191 (2014) 228–235. [10] S. Sichwart, I.E.P. Tozakidis, M. Teese, J. Jose, Maximized autotransporter-mediated expression (MATE) for surface display and secretion of recombinant proteins in Escherichia coli, Food Technol. Biotechnol. 53 (3) (2015) 251–260.
4. Conclusions In summary, we applied a conversion formula that transforms OD578 values of undiluted P. putida KT2440 cell suspensions determined directly in microtiter plates by a microplate reader into OD578 values as has been determined after dilution in a standard spectrophotometer. This allows the use of the microplate reader for the simultaneous detection of the OD578 and FI and, most importantly, without the need to dilute the samples beforehand. This procedure is less time-consuming and, due to less pipetting steps, less prone to errors than the usual procedure. In addition, it allows the automation of OD measurements, because the loss of reaction volume and dilution steps are avoided. It is therefore particularly valuable when monitoring large numbers of bacterial cultures and when measuring multiple parameters simultaneously, for example OD and FI. The generated OD conversion formula is applicable up to an upper limit of OD578 = 6.0. 5