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Applied and Environmental Microbiology, September 1999, p. 4108-4117, Vol. 65, No. 9
Department of Microbiology, The Technical
University of Denmark, DK-2800 Lyngby, Denmark
Received 3 March 1999/Accepted 23 June 1999
In microbial communities such as those found in biofilms,
individual organisms most often display heterogeneous behavior with respect to their metabolic activity, growth status, gene expression pattern, etc. In that context, a novel reporter system for monitoring of cellular growth activity has been designed. It comprises a transposon cassette carrying fusions between the growth rate-regulated Escherichia coli rrnBP1 promoter and different variant
gfp genes. It is shown that the P1 promoter is regulated in
the same way in E. coli and Pseudomonas putida,
making it useful for monitoring of growth activity in organisms outside
the group of enteric bacteria. Construction of fusions to genes
encoding unstable Gfp proteins opened up the possibility of the
monitoring of rates of rRNA synthesis and, in this way, allowing
on-line determination of the distribution of growth activity in a
complex community. With the use of these reporter tools, it is
demonstrated that individual cells of a toluene-degrading P. putida strain growing in a benzyl alcohol-supplemented biofilm
have different levels of growth activity which develop as the biofilm
gets older. Cells that eventually grow very slowly or not at all may be
stimulated to restart growth if provided with a more easily
metabolizable carbon source. Thus, the dynamics of biofilm growth
activity has been tracked to the level of individual cells, cell
clusters, and microcolonies.
Biofilms play an important role in
almost all aspects of microbiology and may appear as either beneficial
or potentially harmful populations of microorganisms. The bacteria
constituting the biofilms in our intestines, sewage treatment plants,
bioremediation plants, etc., are mostly beneficial. Harmful biofilms
are also abundant, ranging from relatively harmless dental plaque to
Pseudomonas aeruginosa biofilms in the alveoli of cystic
fibrosis patients, but biofouling of ships and offshore material is
also a serious problem in the oil and shipping industries.
In order to improve the performance of some beneficial biofilms and to
avoid or remove harmful biofilms, it is important to understand the
mechanisms of biofilm formation, growth, and maintenance. Microbial
biofilms consisting of either single or multiple species are
structurally organized in patterns, which depend on several factors
such as nutrient supply, flow rate, pH, temperature, etc. In such
dynamic systems, the individual cells experience conditions determined
by the outer environment, the already existing structures, and the
local microbial activities. Furthermore, subpopulations may form
locally which are completely different from the majority of the
community. Microbial biofilms have been investigated either by visual
inspection of biofilms cultivated in flow cells (6, 28, 37)
or as disrupted samples withdrawn from either natural systems such as
drinking water pipes (26, 32) or artificial model systems
such as the Robbins device system (25).
In either case, the results of such analyses are primarily descriptive,
yielding limited information about parameters like growth states of
individual cells. Several methods of assessing different types of
single-cell activity have been described, such as the use of (i)
5-cyano-2,3-ditolyl tetrazolium chloride staining (33) to
identify actively respiring cells, (ii) ribosomal probing to monitor
the number of ribosomes as a measure of growth rate (13,
30), or (iii) classical visual markers such as lacZ to monitor the expression of several genes in situ (31). Energy charge has also been used to measure cell activity by cryosectioning of
biofilms (23). More recently, the green fluorescent protein Gfp (7, 10) has been used for in situ investigation of
living biofilms (8, 9, 15, 28, 29, 35). While some of these methods are useful for actively growing cells, they may not prove effective for investigation of starving cells or cells exposed to
changing environments. The intracellular marker compounds may accumulate and thus reflect the history of the cells rather than the
present growth physiological state of the organisms.
We have recently developed new derivatives of the green fluorescent
protein which, unlike the native protein, have short half-lives (3). The Gfp protein has been modified by the addition of a few amino acid residues to its C-terminal end, rendering it a target
for indigenous tail-specific proteases. Through the construction of an
expression cassette consisting of this novel gfp gene
expressed from an Escherichia coli rRNA promoter, a reporter
system was obtained which generates green fluorescence in fast-growing
cells of both E. coli and Pseudomonas putida. By
use of these monitor strains, we have been able to discriminate between
fast- and slow-growing cells in structured surface communities of
microbial biofilms and to determine the spatial and temporal
distribution of growth activity.
Strains, plasmids, and growth conditions.
The bacterial
strains and plasmids used in this study and their relevant
characteristics are listed in Table 1.
Strains were grown in FAB medium [containing 1 mM MgCl2,
0.1 mM CaCl2, 0.01 mM Fe-EDTA (Sigma E6760; Sigma, St.
Louis, Mo.), 0.15 mM (NH4)SO4, 0.33 mM
Na2HPO4, 0.2 mM KH2PO4,
and 0.5 mM NaCl], and unless otherwise mentioned, 10 mM Na-citrate was
added as a carbon source. When required, antibiotics were added at
final concentrations of 50 µg/ml for nalidixic acid and 25 µg/ml
for kanamycin.
0099-2240/99/$04.00+0
Copyright © 1999, American Society for Microbiology. All rights reserved.
Distribution of Bacterial Growth Activity in
Flow-Chamber Biofilms
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ABSTRACT
Top
Abstract
Introduction
Materials and Methods
Results
Discussion
References
![]()
INTRODUCTION
Top
Abstract
Introduction
Materials and Methods
Results
Discussion
References
![]()
MATERIALS AND METHODS
Top
Abstract
Introduction
Materials and Methods
Results
Discussion
References
TABLE 1.
Strains and plasmids used in this study
Constructions.
A linker fragment of 72 nucleotides,
containing the E. coli rrnBP1 promoter region, corresponding
to nucleotides 1156 to 1228 in the published GenBank sequence
(accession no. J01695), was synthesized with a DNA synthesizer (Applied
Biosystems 373A). The linker was designed with SacI- and
XbaI-compatible protruding ends. The promoter fragment
contains nucleotides
70 to +3 relative to the transcription
initiation site (4). Due to the high level of expression
from the rrnBP1 promoter, the linker could not be inserted
into our general high-copy-number gfp cloning vectors (pUC18
derivatives [3]). Therefore, a NotI
fragment carrying the synthetic ribosomal binding site (RBSII), the
gfpmut3b* gene, and the transcriptional terminators
T0 and T1 was moved from pJBA25 (3)
into the NotI site of the low-copy-number plasmid pLOW2 (18). The pLOW2 derivative carrying the
RBSII-gfpmut3b*-T0-T1 cassette
was subsequently digested with SacI and XbaI, and
the 72-base rrnBP1 promoter fragment was inserted to produce
plasmid pSM1690 (see Fig. 1 for details). Plasmid pSM1690 was digested with NotI, and the fragment carrying
rrnBP1-RBSII-gfpmut3b*-T0-T1 was inserted into the unique NotI site of pUT-mini
Tn5-Km, resulting in transposon delivery vector pSM1695.
pir(pSM1695),
HB101(RK600), and P. putida R1 (strain JB156), the
rrnBP1-RBSII-gfpmut3b*-T0-T1 cassette was inserted at random positions on the chromosome of P. putida R1 (JB156). One normally growing transconjugant colony was
picked and designated SM1699. For construction of a P. putida R1 derivative carrying the
rrnBP1-RBSII-gfp(AAV)-T0-T1
cassette, we used a procedure similar to the one described above,
resulting in SM1639.
The chosen transposant clones showed no sign of phenotypic changes
relative to the parent strain when tested in both liquid medium and
flow chamber biofilms. The orientation of the gfp reporter cassette within the mini Tn5 transposon was such that no
transcription from flanking chromosomal sequences could interfere with
gfp expression.
Runout experiment. Exponential growth was allowed for at least 10 generations at 30°C before the cultures were diluted (to an optical density at 450 nm [OD450] of 0.05) into prewarmed FAB medium containing 8 mM sodium citrate. After entering the stationary phase at an OD450 of ~2.0, the cultures were monitored for more than 5 h. During the entire experiment, samples were taken for measurements of OD450 and green fluorescence emitted by the cells. To avoid autofluorescence excreted by the cells into the medium, 2-ml cell suspensions were harvested by centrifugation and resuspended in 0.9% NaCl. Both resuspended cells and the supernatants were measured in a fluorometer (RF-1501; Shimadzu, Kyoto, Japan). To determine the relative fluorescence activities of the cells, the OD450 values of the resuspended cells were also determined.
Chemostat experiments. To determine specific activities of the different rrnBP1-gfp gene fusions at different growth rates, cells were grown in chemostats. A chemostat was made from a 50-ml tube (syringe) with a rubber stopper containing a glass tube for intake of air, which passed through a 0.2-µm-pore-size filter before entering the chemostat, and another tube for outlet of the effluent culture. Furthermore, we introduced a thin hypodermic needle for injection of medium and another for withdrawal of samples from the chemostat.
Five parallel chemostats were run at the same time. Tubings with different bore diameters were used in the same peristaltic pump (Watson Marlow 205S; Watson-Marlow Inc., Wilmington, Mass.) to obtain different dilution rates (resulting in different growth rates). The chemostats were each inoculated with approximately 15 ml of an overnight culture, and then medium flow was started. The volume of each operating chemostat varied between 40 and 45 ml. For each chemostat, the exact flow rate and chemostat volume were determined. The growth rates were calculated by dividing the flow rate by the chemostat volume. The chemostat cultures were run for at least 60 h before the first sample was taken from each chemostat. This corresponds to approximately 5 or 6 generations for the slowest-growing cultures and approximately 50 generations for the chemostat cultures with the highest growth rates. Samples were taken at least three times from each chemostat with intervals of approximately 12 h. All samples were harvested as described above, and OD450 and fluorescence were determined from the resuspended cells, as well as from the supernatant.Flow chamber experiments. Biofilms were cultivated in four-channel flow cells (37) with individual channel dimensions of 1 by 4 by 40 mm supplied with a flow of FAB medium supplemented with benzyl alcohol (Merck KGaA, Darmstadt, Germany) as a carbon source to a final concentration of 0.5 mM.
The flow system was assembled and prepared as described by Christensen et al. (9). The substratum consisted of a microscope glass coverslip (Knittel 24x50 st1; Knittel Gläser, Braunschweig, Germany). Flow cells were inoculated with an overnight culture of P. putida JB156, SM1639, or SM1699 diluted to an OD450 of 0.1 in 0.9% NaCl. After inoculation, the medium flow was arrested for 1 h. Medium flow was then started, and the substrate was pumped through the flow cells at a constant rate of 0.2 mm/s using a Watson Marlow 205S peristaltic pump.Embedding and 16S rRNA hybridization of hydrated biofilm samples. For 16S rRNA hybridization, probe PP986 (specific for P. putida subgroup A [16]) labeled with the indocarbocyanine fluorescent dye CY3 was used. In situ detection of biofilm cells expressing Gfp in combination with 16S rRNA hybridization was performed by fixing and embedding of the biofilm, followed by hybridization as previously described (9).
Microscopy and image analysis. All microscopic observation and image acquisition were performed on a scanning confocal laser microscope (SCLM) (TCS4D; Leica Lasertechnik, GmbH, Heidelberg, Germany) equipped with detectors and filter sets for simultaneous monitoring of fluorescein isothiocyanate/Gfp and CY3.
Simulated fluorescence projections (shadow projections) and vertical cross sections through the biofilms were generated by using the IMARIS software package (Bitplane AG, Zürich, Switzerland) running on a Silicon Graphics Indigo2 workstation (Silicon Graphics, Mountain View, Calif.). Images were further processed for display by using Photoshop software (Adobe, Mountain View, Calif.).| |
RESULTS |
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Construction of monitor strains. In order to monitor the growth activity of bacteria in a complex environment, it is important that the monitoring system respond rapidly to local environmental changes and, at the same time, be suitable for detection at the level of single cells.
We therefore employed the growth rate-regulated E. coli ribosomal P1 promoter (4, 17) to drive expression of the marker genes. An oligonucleotide linker containing the growth rate-regulated 72-bp rrnBP1 promoter sequence (4) was synthesized and inserted upstream of the various monitor genes to enable monitoring of ribosomal synthesis, i.e., bacterial growth activity. The gene encoding the green fluorescent protein is an excellent marker gene, since no external substrates or inducers are needed for its expression and detection. However, Gfp is a very stable protein (3, 36) which is only lost from cells by dilution during cell growth. Recently, we described new variant Gfp proteins (3) which have considerably shorter half-lives than wild-type Gfp. We chose one of these, Gfp(AAV), as a rapidly degradable marker protein. The rrnBP1::gfp monitor cassettes were introduced into the pUT-mini Tn5 transposon delivery system (14, 20) and subsequently inserted into the chromosome of our model biofilm organism, P. putida R1. Materials and Methods and Fig. 1 contain the details of the various constructions and the mating procedure. The resulting Pseudomonas transconjugants (monitor strains) were tested prior to biofilm growth to determine their behavior in nutrient-limited chemostats and in energy exhaustion batch experiments to verify that growth rate control of the E. coli P1 promoter took place in P. putida R1 as well.
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Gfp expression in liquid cultures. In chemostats, cells growing with fixed rates determined by the substrate dilution rate expressed fluorescence signals which could be determined as a function of the growth rate. Each strain was grown in five parallel chemostats with different dilution rates. After initial stabilization of the chemostats (60 h or more), samples were taken for determination of the fluorescence signal emitted by the culture. As the wild-type strain, even in the absence of the gfp gene, exhibits considerable fluorescence, we also did a chemostat analysis of wild-type P. putida R1 (Nalr) (JBA156). For determination of a maximum reference activity, we included measurements of bacteria grown exponentially in batch cultures in minimal medium supplemented with surplus (10 mM) citrate.
The fluorescence data for P. putida JB156 (wild type, Nalr), SM1699, and SM1639, harboring the rrnBP1-gfpmut3b* or rrnBP1-gfp(AAV) cassette, are plotted in Fig. 2A. The strains expressing stable gfpmut3b* fused to the rrnBP1 promoter showed reduced signal intensity as the growth rate was reduced. However, even at the slowest growth rates (in the present experiment, approximately 0.1 h
1), the signal intensity was more than three times
stronger than the background autofluorescence signal emitted by
wild-type strain JB156 itself. In contrast, the strain carrying the
rrnBP1-gfp(AAV) cassette showed a detectable
fluorescence signal only at growth rates above 0.4 h
1.
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Assessment of single-cell activity in biofilms. For determinations of bacterial activity at the single-cell level in complex biofilms, bacteria containing rrnBP1 fused to either the wild-type or the unstable variant gfp gene were introduced into flow chambers. To ensure that the signal emitted was caused by the Gfp protein and not by autofluorescence, we included the wild-type strain JB156 as a control. The autofluorescence of the wild-type strain was barely detectable in flow chamber experiments (Fig. 4A and B).
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Time course analysis of microbial activity during microcolony development. Using the monitor system described above, the time course of a developing biofilm was monitored. With a confocal microscope equipped with a programmable XY specimen holder, we monitored several randomly selected positions in the biofilms. One such spot is shown in Fig. 6. During the early phases, single cells and small colonies consisting of only a few cells are seen. Virtually all of the bacteria in these phases are brightly green fluorescent as an indication of relatively high growth rates. After approximately 20 h (Fig. 6C), the colonies have become larger and the fluorescence from the central parts of these colonies is reduced, probably due to a lowered rate of Gfp synthesis. At the surface of the colonies, most cells are still fluorescent, indicating locally higher activity closer to the void space. The smaller microcolonies, however, are still fluorescent throughout and remain so for some time. Eventually (Fig. 6D), all of the cells in the microcolonies turn pale and only a few bright green cells are left. At this stage, most of the cells seem to have reduced their growth activity to a low level. This condition will persist if the conditions otherwise are kept constant.
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DISCUSSION |
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The in situ rRNA hybridization technique has created a revolution in the field of microbial ecology with respect to identification of individual bacteria in the most complex environments. The ribosome target for this method has turned out to be nearly ideal, since the cellular content of this organelle most often is sufficiently high to allow unambiguous identification at the single-cell level (1, 2). It was also realized very early in the development of the technology that in addition to species identification, quantitative rRNA hybridization might provide information about the growth state of the cells due to the direct correlation between ribosome concentration and cellular growth rate, such as it was known for several bacteria (27, 30).
The ribosome counting method should, however, be used and interpreted with caution. First, when using it in the context of new or even unknown organisms, it is essential to document that the correlation between growth rate and ribosome number is valid. This requires isolation of pure cultures and tests in chemostats or other types of conditions creating different cellular growth rates. Second, the stability of ribosomes under a variety of conditions may be different in different bacteria, and consequently, single determinations of cellular ribosome concentrations are not directly comparable. In fact, it is only in cells growing under steady-state conditions that the concentration of ribosomes truly reflects the growth state of the cells (27, 34). Third, the correlation between growth rate and ribosome concentration may be relevant only for bacteria able to grow fast under optimal conditions (carrying several copies of the rRNA operon). Thus, environmental monitoring of growth activity using this approach may, at best, only give indications of overall tendencies for fast-growing bacteria and only under conditions in which bacteria have a significant nutrient supply.
In order to expand the use of the well-known stringent control of ribosome synthesis, a method allowing determinations of rates of rRNA synthesis rather than the accumulated concentration was developed to better monitor the actual growth state of the cells, in particular if the conditions are heterogeneous with respect to nutrient status or if the outer environmental conditions change over time.
In our design of such a system for monitoring of bacterial growth activity, an rRNA promoter system, the rrnB operon from E. coli, was chosen because it is very well characterized and the promoter sequences are easily manipulated. The rrnB ribosomal genes are expressed from the rrnBP2P1 promoters. The ribosomal promoters are among the strongest described in E. coli, and the background expression is rather low when the cells are in late stationary phase. However, only the P1 promoter is growth rate regulated (17), for which reason we used it for expression of the reporter gene, gfp. This growth rate control on transcription from the E. coli P1 promoter is also exerted in P. putida, as demonstrated in our chemostat experiments, which also showed that the fluorescent signal emitted by strain SM1699 seemed to decrease more with decreasing growth rate than the corresponding ribosome number estimated from data obtained from the rRNA hybridizations. The cause of this difference could be that whereas general ribosome synthesis is normally controlled by tandem promoters like P1 and P2, the Gfpmut3b expression in our test system with SM1699 is under the control of only the rrnBP1 promoter. In this way, a steeper gradient of fluorescence signal intensity between slow- and fast-growing cells was obtained.
In test tube cultures of bacteria, rates of rRNA synthesis can be determined in hybridization experiments in which the growing RNA chains are labelled over a short period with radioactive precursors. The higher the frequency of transcription of rRNA, the more radioactivity is incorporated. This scheme, however, is not relevant in a complex and heterogeneous microbial community. Instead, we employed an unstable monitor system which, on one hand, reflects the rate of synthesis and, on the other, will indicate cessation of rRNA synthesis through disappearance of the signal. The monitor system was based on the Gfpmut3b protein. In its natural form, the protein is very stable, and consequently, when it was expressed from the stringently regulated P1 promoter, the energy exhaustion experiments showed that no significant decrease in fluorescence intensity occurred after entry into the stationary phase. However, by fusing the ribosomal promoter to the gfp(AAV) gene, encoding an unstable variant of Gfp, entry into stationary phase resulted in an immediate reduction in the fluorescence signal intensity.
In chemostats, the cells are continuously growing and the amount of the stable Gfp in the cells will be determined by the rate of transcription from the P1 rRNA promoter relative to the growth rate. In cells carrying a fusion to the unstable variant Gfp, the overall amount of fluorescing Gfp was lower under similar conditions, reflecting the fact that in these cells the Gfp level is determined by the rate of synthesis as well as the rate of degradation. Cells harboring fusions between the ribosomal promoter and the stable gfpmut3b* gene are good candidates as tools for estimating bacterial growth rates when the culture is in exponential growth, as in chemostats. In nature, however, bacteria rarely experience such well-defined and stable environments, and in such scenarios, the unstable Gfp reporter system has several advantages.
Microbial surface communities exhibit, in many ways, different
physiological traits compared to suspended cultures (11), and it is therefore of interest to investigate the cellular response patterns to changing environmental conditions. If the key regulatory pathways in surface-bound cells differ from those known to control macromolecular synthesis in planktonic cells, there is a possibility of
misinterpreting measurements of specific macromolecular synthesis rates. Recently, we documented, however, that the general correlations between cellular growth and parameters such as cell volume, ribosome concentration, division frequency, and DNA content seem to be unaltered
in cells of P. putida when they are transferred from liquid-
to solid-phase growth (27). It is therefore assumed here
that the connection between rRNA synthesis rates
monitored by our gene
fusions
and cellular growth activity in biofilms does indeed mimic
what was demonstrated in the chemostats.
Thus, with the Gfp(AAV) physiological probing system, the cellular growth activity levels in biofilm samples were monitored on a temporal basis. One notable observation in biofilm microcolonies at stages later than the initial colonization phase was the appearance of dark centers in the colonies. In order to rule out the possibility that these nonfluorescent centers were caused by low oxygen concentrations (the maturation of Gfp has been reported to be dependent on molecular oxygen [19]), we measured the oxygen levels needed for Gfp maturation. Even at concentrations lower than 1% of the atmospheric oxygen tension, the maturation of Gfp was not inhibited (data not shown). DeBeer et al. (12) and others have measured the oxygen concentrations at various depths of biofilms, and within the distances which apply to our biofilms (i.e., less than 100 µm), the oxygen levels have been reported to drop less than 30-fold. Taken together, it seems unlikely that oxygen limitation inhibits Gfp maturation, even in the central parts of the microcolonies. We therefore suggest that the dark centers resulted from cells with reduced growth rates and, consequently, lower de novo Gfp synthesis. Strains tagged with stable Gfp versions were quite unaffected for the stage of colony development, and fluorescence persisted for several days in such microcolonies, in analogy with the persistence of high concentrations of ribosomes as monitored by in situ rRNA hybridization.
The down-regulation of microbial activity in the biofilm cells seemed to occur in at least two steps. First, the cells in the centers of the largest microcolonies reduced their growth activity whereas cells in smaller colonies remained highly active. Second, after a while, the cells in the smaller colonies also showed reduced growth activity. Some of the microcolonies in Fig. 6D (24.5 h after inoculation) were smaller than many of the colonies observed 7.5 h before (Fig. 6B), but nevertheless, their activity was also down-regulated. This indicates that it was not just the size of each individual microcolony that determined the reduced growth activity. It is possible that the major cause was a general exhaustion of the nutrient supply as a consequence of the overall higher density of bacteria. Thus, even in a rather thin biofilm, such as those analyzed in the present study, the microcolonies cannot be considered independent units since the activity of the single organisms inside one microcolony was dependent on factors caused by the surrounding microcolonies, e.g., depletion of nutrients.
In many studies of bacterial growth physiology, shifts or perturbations of the growth conditions have proven very informative with respect to clarification of the cellular response repertoire. A shift-up condition obtained by addition of an easily metabolizable carbon source to a slow-growing or stationary culture may thus document the level of responsiveness and the effects on different parts of the macromolecular synthesis. In bacteria with stringent control of ribosome synthesis, it is expected that ribosome synthesis is rapidly increased after a nutritional shift up. In addition to such cellular responses, the distribution of reactions to a shift up in a heterogeneous surface community may contribute to the understanding of how local environments differ with respect to penetration and diffusion of nutrients. Finally, growth inhibition of cells in structured communities could be determined by signals different from the nutrients. If the structure or size of the microcolonies determines the biological activity of the cells, a shift-up response to increased nutrient availability would not be expected.
The shift to a better carbon source in the present experiments clearly activated the cells in the microcolonies, as indicated by the significant increase in fluorescence. Moreover, the activation appeared to penetrate all the way through the microcolonies, showing that even the cells in the centers, which were the first to reduce their growth activity, were ready to respond to the improved nutrient supply. Overall, these results indicate that all of the cells in developing biofilm microcolonies are ready to respond to renewed supplies of nutrients. In addition, these findings support our conclusion that the oxygen levels in the microcolonies are sufficient for Gfp maturation.
The experiments performed in the present study have revealed a modulated growth activity of bacteria involved in the establishment of a new biofilm. In the initial phases, all cells were highly active, with ribosomal promoter activity corresponding to that of rapidly growing cells. After primary colonization and formation of small microcolonies, activity gradually decreased, first in the central parts of the microcolonies and eventually also at the surface. By choosing other variants of the Gfp protein, it is possible to construct reporter proteins with longer half-lives than those of the proteins employed here (3, 21). When fused with the rRNA promoter, such reporter systems may display alternative levels of cellular activity, which may be useful in monitoring the fine-tuning of microcolony development.
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ACKNOWLEDGMENTS |
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This work was supported by grants from the Danish Biotechnology Program.
We thank Anne Nielsen for technical assistance.
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FOOTNOTES |
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* Corresponding author. Mailing address: Department of Microbiology, Building 301, The Technical University of Denmark, DK-2800 Lyngby, Denmark. Phone: 45 45 25 25 13. Fax: 45 45 88 73 28. E-mail: imsm{at}pop.dtu.dk.
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