Molecular Microbial Ecology Group, Department of Microbiology, The Technical University of Denmark block 301,DK-2800 Lyngby, Denmark1
Department of Mathematical Modelling, The Technical University of Denmark, DK-2800 Lyngby, Denmark2
Environmental Engineering Group, Department of Civil Engineering, NorthWestern University, Evanston, Illinois, USA3
Author for correspondence: Søren Molin. Tel: +45 45 25 25 13. Fax: +45 45 93 28 09 e-mail: imsm{at}pop.dtu.dk
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ABSTRACT |
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Keywords: biofilm structure, quantification, statistical analysis, COMSTAT, reproducibility
Abbreviations: GFP, green fluorescent protein
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INTRODUCTION |
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Biofilms in nature are often difficult to investigate and experimental conditions are ill defined. Therefore a number of different laboratory-based experimental biofilm model systems have been developed (Palmer, 1999 ). These systems allow studies of biofilms under defined conditions; such model systems are necessary in order to perform well-controlled reproducible experiments.
There have been various attempts to quantify biofilm structures (see Heydorn et al., 2000 , for references). However, despite the many reports on quantification of biofilm structures, the reproducibility of biofilm experiments has not been addressed until now. In this communication we present a general method for quantitative comparison of biofilm structures and assessment of experimental reproducibility between independent biofilm experiments, by using a novel computer program, COMSTAT (Heydorn et al., 2000
).
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METHODS |
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Flow-chamber experiments.
Biofilms were grown at 30 °C in three-channel flow cells (Christensen et al., 1999 ) with individual channel dimensions of 1x4x40 mm supplied with a flow of 3 ml h-1 of modified FAB medium (Heydorn et al., 2000
) supplemented with 0·1 mM sodium citrate. The flow system was assembled and prepared as described by Christensen et al. (1999)
. The substratum consisted of a microscope glass cover slip (Knittel 24x50 mm st1; Knittel Gläser). Cultures for inoculation of the flow channels were prepared as described by Heydorn et al. (2000)
.
Image acquisition.
Three independent rounds of biofilm experiments were done. In each round, each of the two variants was grown in two separate channels. In each of the four channels nine image stacks were acquired at 146 h after inoculation. In all experiments, images were acquired from random positions in the upper part of the flow channel, at a distance of 510 mm from the inlet. Images were acquired in the middle two-thirds of the flow channel because the biofilm in the regions near the sides of the flow channel often displayed different behaviour compared to the biofilm in the centre of the channel. Images were acquired at 1·0 to 2·0 µm intervals down through the biofilm, and therefore the number of images in each stack varied according to the thickness of the biofilm. The nine image stacks covered a total area of 5·625x105 µm2. Korber et al. (1993) recommended that a minimum area of 1x105 µm2 be investigated in order to obtain representative data of P. fluorescens biofilms. All microscopic observations and image acquisitions were performed on a confocal scanning laser microscope (TCS4D; Leica Lasertechnik). Images were obtained with a 40x/0·75 air objective. Image scanning was carried out with the 488 nm laser line from an Ar/Kr laser.
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RESULTS AND DISCUSSION |
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The flow channels used in this study are three-channel flow cells (Christensen et al., 1999 ) with individual channel dimensions of 1x4x40 mm. The flow channels are machine made from a block of plexiglass. In this way biofilm structure variation caused by small differences in flow channel shape and size is minimized. Since there is a considerable amount of spatial heterogeneity in the flow channels (the biofilm near the inlet is typically thicker than the biofilm near the outlet), the images were acquired at random positions in the upper part of the flow channel at a distance of 510 mm from the inlet. This minimizes structural heterogeneities caused by spatial differences in the flow channels.
Biofilms were grown on a chemically defined medium with citrate as the only carbon source. An important factor turned out to be the concentration of the carbon source. At concentrations of 110 mM citrate, spatial heterogeneity in the flow channel was high. While some parts of the channel consisted only of a monolayer of cells, other areas contained large cell clusters. Size heterogeneity was also high. Structures in the biofilms ranged from single cells on the substratum (12 µm long) up to microcolonies 200300 µm high. Such size heterogeneity is almost impossible to monitor using a single objective. Finally, the structural variation between channels was high. This variation could in many cases be ascribed to one or more big microcolonies colonizing the inlet of the channel, exhausting the carbon source and leaving the rest of the flow channel essentially as a single layer of cells. Glucose was tried as an alternative to citrate, but no significant differences in biofilm phenotypes were observed. However, by reducing the carbon source concentration to 0·1 mM citrate, the spatial heterogeneity, the size heterogeneity and the structural variation between channels were all drastically reduced. Other important requirements for reproducibility were the following. (1) The history of the cultures used for inoculation should be identical for all strains and identical between different rounds of biofilm experiments. (2) The biofilms should all be grown at the same fixed temperature and temperature shifts should be avoided. If temperature shifts are necessary the time at e.g. 20 °C should be as short as possible. Temperature shifts should be reproduced in all rounds of the experiments. (3) Bacterial growth upstream of the flow channels (backgrowth) should be removed frequently, for example daily. Backgrowth can significantly alter the structure of the observed biofilm.
Image acquisition, quantification by COMSTAT and selection of variables
When the experimental conditions have been determined, several rounds of independent biofilm experiments are performed and images are acquired. In the present study, biofilms of P. aeruginosa PAO1 and an isogenic rpoS mutant P. aeruginosa MW20 were analysed. Three experiment rounds were performed. In each round, each of the two strains was grown in two separate channels. In each channel nine image stacks were acquired at 146 h after inoculation. Following acquisition, images were quantified by the COMSTAT program, which calculates a wide range of variables describing biofilm structures, such as mean thickness, roughness, surface-to-volume ratio and substratum coverage (for details, see Heydorn et al., 2000 ). Although it is theoretically possible to use all of the variables calculated by COMSTAT, in most cases a few suffice. The number of selected variables corresponds to the dimensionality of the variable vector used to describe the three-dimensional structure, and to make a subsequent multivariate analysis robust it is important to use a reasonably small number of variables. In most cases it makes sense to simply select the variables on the basis of their biological and physical interpretations in relation to the purpose of the experiments (for details on variable selection see Heydorn et al., 2000
). In the present study, only the mean biofilm thickness was analysed. Mean biofilm thickness provides a measure of the spatial size of the biofilm and is the most common variable used in biofilm literature, probably because of its simple interpretation.
Design of an analysis of variance model
An analysis of variance model is a natural choice when analysing data from experiments similar to the one described here. The general situation is that an experiment gives a univariate (one-dimensional variable) or multivariate (multidimensional variable) continuous response, which depends on a number of registered factors, that in turn may or may not be controlled by the person doing the experiment. The factors may be categorical or continuous, random or fixed (for details see Littell et al., 1996 ). In cases where the same experimental unit (for example mean thickness) is sampled at different time points, time can be included as an additional factor in an analysis of variance model, or the experiment can be analysed as a repeated measurements experiment (Diggle et al., 1994
). The main objective of the present statistical analysis was to verify the reproducibility of experiments, and secondly to distinguish between biofilms of the two P. aeruginosa strains after 146 h of biofilm growth. The factors of the variance model are: bacterial strain (two levels: wild-type and rpoS mutant), experimental round (three levels: 1, 2, and 3), and channel (two levels: 1 and 2). Bacterial strain is assumed to be a fixed (or deterministic) factor, whereas experiment round and channel number are assumed to be random factors. They will be denoted b, R and C, respectively. Finally, the image stacks for each combination of bacterial strain, experiment round, and channel are treated as replications. Replication is always assumed to be a random factor. The model thus becomes a variance component model:
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Furthermore, all random effects are assumed to be independent of each other, both within and between effects. If the effect of bacterial strain turns out to be significant (i.e. bi0) in the analysis of variance, pairwise t-tests can be performed in order to assess which pairs of strains differ from each other.
The analysis of variance model presented here applies to a wider range of scenarios than the simple experiment described. For example, a larger number of strains could be included, more experimental rounds could be performed and more channels per strain could be used.
Analysis of variance model assumptions
The above model assumptions imply that observations are normally distributed with the mean value µ+bi, and that they have the same variance. The assumption of equal variances is the most important and can be checked numerically, e.g. by Levenes test for homogeneity of variances (Milliken & Johnson, 1984 ), or visually, by examining a suitable plot of the data. In some cases a transformation of the data (e.g. by taking the logarithm) or a weighting scheme may help stabilize the variance. The best result is obtained if the weights are proportional to the inverse variance of the observations. However, since the true variance of the observations is rarely known, it is customary to estimate the variance from the experimental data. Figs 2(a)
and (b)
show box-and-whiskers plots (Hoaglin et al., 1991
) of the original and log-transformed data, respectively. The original data in Fig. 2(a)
clearly display overall differences in the variance of the data, and the variance seems to depend on the mean. Therefore a logarithmic transformation of the data was applied. The log-transformed data generally display a more stable variance (Fig. 2b
). Levenes test for equal variances was implemented by PROC GLM in the SAS statistical package (SAS Institute, 1997
) and showed severe differences in variance between the groups. For the original data the F-test statistic was 10·5 on (11, 96) degrees of freedom, corresponding to a P-value <0·0001, whereas for the log-transformed data the F-statistic was somewhat smaller, at 7·4 on (11, 96) degrees of freedom, however still corresponding to a P-value <0·0001. Consequently, both the original data and the log-transformed data displayed severe differences in variance between the groups. It was therefore chosen to perform a weighted analysis of variance, using the inverse estimated variance for each group of data as weights (Fig. 2c
).
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Examination of experimental reproducibility
According to ISO standard no. 3534-1 (International Organization for Standardization, 1995a ) reproducibility conditions are conditions where test results are obtained with the same method on identical test items in different laboratories with different operators using different equipment, whereas repeatability conditions are conditions where independent test results are obtained with the same method on identical test items in the same laboratory by the same operator using the same equipment within short intervals of time. From these definitions, it is not clear whether the variability between experimental rounds in the present experiments should be termed repeatability or reproducibility. We have chosen to use the term reproducibility.
The analysis of variance was performed using PROCMIXED from the SAS statistical package (SAS Institute, 1997 ). The default estimation technique in PROCMIXED, restricted maximum-likelihood, was used. Reproducibility was assessed by examining the magnitude of the variance of the effects round (
) and the interaction between bacterial strain and round (
). They were estimated at 0·23 µm2 (SE 1·24 µm2, P-value=0·85) and 0·00 µm2, respectively. Therefore, regarding the variable mean thickness we consider the experiments reproducible. This conclusion is very important in many respects. First, it shows that there are no major variance components that are not considered in the analysis of variance model. Secondly, it demonstrates that the experiments are well controlled, and that other scientists should be able to reproduce the experiments given the same set of experimental conditions. Finally, if reproducibility is expected to be a general property of the present model system, future experiments can be conducted in parallel, i.e. in less time.
The overall F-test for the effect of bacterial strain was found to be significant [P-value=0·0112 on (1, 2) degrees of freedom], showing that the mean thicknesses of the wild-type and the MW20 biofilms were significantly different. The least-square mean estimates of mean thickness were 6·31 µm (SE 0·81 µm) for the wild-type and 16·85 µm (SE 0·87 µm) for MW20. The difference in mean thickness between the two strains was estimated at 10·54 µm (SE 1·12 µm). The effect of different channels was assessed by the variance component , which was estimated at 3·40 µm2 (SE 1·81, P-value=0·060). Although this is not significant at the 5% level, it indicates that the channels differ slightly. Finally, the residual or repetition variance
2 was estimated at 0·99 µm2 (SE 0·14, P-value <0·0001). Both un-weighted and weighted analyses of variance were performed on both the original and the log-transformed data. In all four cases the results were very similar. This implies robustness of the analysis of variance.
Biofilm formation of P. aeruginosa PAO1 and MW20
The rpoS gene in P. aeruginosa is involved in the general stress response, the accumulation of certain virulence factors, and twitching motility (Jørgensen et al., 1999 ; Suh et al., 1999
). As in E. coli, the stationary-phase sigma factor, RpoS, in P. aeruginosa accumulates as cultures enter the stationary phase (Fujita et al., 1994
). Recently, it was shown that the lasIlasR quorum-sensing system is necessary for development of P. aeruginosa biofilms (Davies et al., 1998
). Moreover, the rpoS gene has been shown to be poorly expressed in a P. aeruginosa lasR mutant (Latifi et al., 1996
), and it has also been shown that RpoS represses the transcription of rhlI (Whiteley et al., 2000
). However, several questions remain to be answered about the regulatory interactions between RpoS and the quorum-sensing systems in P. aeruginosa.
We found in the present investigation that P. aeruginosa MW20 formed significantly thicker biofilms than the isogenic parent strain (6·3 and 16·9 µm, respectively). This tendency was not only significant at 146 h, but could already be observed 24 h after inoculation and throughout the experiment (312 h) (data not shown). Planktonic growth curves of P. aeruginosa PAO1 and MW20 in citrate minimal medium showed that the doubling times were virtually identical (53 min and 56 min, respectively, at 37 °C). Thus, the thicker biofilms formed by MW20 compared to the wild-type do not simply reflect differences in growth rates. Adams & McLean (1999) found that biofilm cell density of E. coli grown in a modified Robbins device was reduced by 50% in an rpoS mutant compared to the isogenic parent strain. There are several differences in the role of RpoS between E. coli and P. aeruginosa (Jørgensen et al., 1999
; Suh et al., 1999
). It is therefore not surprising that RpoS may play different roles in biofilm development in E. coli and P. aeruginosa.
Concluding comments
Despite the many attempts to quantify biofilm structures, the reproducibility of biofilm experiments has not been addressed until now. We present a general method for quantitative comparison of biofilm structures and assessment of experimental reproducibility between independent biofilm experiments. By using a novel computer program, COMSTAT, biofilm structures can be quantified and subsequently analysed statistically by an analysis of variance model. In the analysis of variance model presented here, experimental reproducibility was assessed by estimating the magnitude of the variance of the effects round () and the interaction between bacterial strain and round (
). Securing experimental reproducibility is a necessary prerequisite for conclusions concerning differences between different strains.
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ACKNOWLEDGEMENTS |
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Received 12 June 2000;
revised 14 July 2000;
accepted 21 July 2000.