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Previous Article | Next Article 
Applied and Environmental Microbiology, August 2001, p. 3350-3357, Vol. 67, No. 8
0099-2240/01/$04.00+0 DOI: 10.1128/AEM.67.8.3350-3357.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
Quantitative Analysis of Bacterial Gene Expression
by Using the gusA Reporter Gene System
Jun
Sun,1
Ilse
Smets,2
Kristel
Bernaerts,2
Jan
Van
Impe,2
Jos
Vanderleyden,1,* and
Kathleen
Marchal3
Centre of Microbial and Plant
Genetics,1 BioTeC-Bioprocess Technology
and Control,2 and SISTA, Department
of Electrical Engineering,3 Katholieke
Universiteit Leuven, B-3001 Heverlee, Belgium
Received 21 December 2000/Accepted 2 May 2001
 |
ABSTRACT |
An Azospirillum brasilense Sp7 strain containing a
plasmid-borne translational cytN-gusA fusion was grown in a
continuous culture to quantitatively evaluate the influence of
extracellular signals (such as O2) on expression of the
cytNOQP operon. The dissolved oxygen concentration was
shifted at regular time intervals before the steady state was reached.
The measured 
-glucuronidase activity was used to monitor
cytN gene expression. However, as the -glucuronidase
activity in the experimental setup not only depended on altered
transcription of the hybrid gene when the signal was varied but was
also influenced by cellular accumulation, degradation, and dilution of
the hybrid fusion protein, a mathematical method was developed to
describe the intrinsic properties of the dynamic bioprocess. After
identification and validation of the mathematical model, the apparent
specific rate of expression of the fusion, which was independent of the
experimental setup, could be deduced from the model and used to
quantify gene expression regulated by extracellular environmental
signals. In principle, this approach can be generalized to assess the
effects of external signals on bacterial gene expression.
| |
INTRODUCTION |
Gene fusions containing reporter
genes are widely used to monitor and quantify the effects of external
signals on bacterial gene expression (11, 14). However,
complications may arise if the external signals, such as the levels of
O2 and other substrates utilized by the bacteria, cannot be
kept constant during the test (7). Since O2
level is a very important external signal regulating expression of
certain genes, a reliable method is needed to study the influence of
O2 on bacterial gene expression.
The use of a continuous culture in an O2-stat to test the
influence of O2 on expression of a gene represents a major
improvement in such studies (5, 12, 23, 24). In a
continuous culture the O2 concentration can be adjusted
easily; thus, the effects of fluctuating cell densities and respiratory
rates on O2 concentrations can be compensated for. When the
effects of constitutive O2 shifts on gene expression are
studied, measurements in a continuous fermentation are usually taken
after establishment of a steady state (5, 12). Such
experiments require extended fermentation times and therefore might
involve a high risk of biological instability problems.
An experimental setup in which measurements could be taken after the
O2 shift occurs and before a steady state is reached would
significantly enhance analysis. It should be noted that in such a setup
the absolute expression level not only is dependent on altered
transcription of the hybrid gene when the signal is varied but also is
influenced by the cellular accumulation, degradation, and dilution rate
of the hybrid fusion protein. (It should also be noted that even in a
steady state, the absolute value for fusion protein activity depends on
the implemented dilution rate and therefore is not completely
independent of the experimental setup.) Therefore, a reliable method
which is independent of the experimental parameters to describe the
influence of O2 on expression of genes can facilitate
interpretation of the experimental data.
In this study, a method was developed to determine the mere influence
of O2 on expression of target genes. A general dynamic model was used to describe cell growth and fusion protein expression in
a continuous culture in which the dissolved oxygen (DO2)
concentration was shifted at regular time intervals before the steady
state was reached. The apparent specific rate of expression of the gene fusion, which was intrinsically independent of the experimental parameters, was defined and deduced from a validated mathematical model. The model was used to study induction of cytN gene
expression by O2 in Azospirillum brasilense Sp7
based on the activities of a cytN-gusA fusion. The A. brasilense cytNOQP operon, encoding a cytochrome
cbb3 terminal oxidase, has been shown to be
involved in microaerobic growth and respiration (16).
Model-based data analysis indicated that the optimal DO2
level for expression of the cytNOQP genes is in the
microaerobic range, which is consistent with a previous study
(16).
| |
MATERIALS AND METHODS |
Plasmids, bacterial strains, and growth conditions.
The
strains and plasmids used in this study are listed in Table
1. Luria-Bertani medium was used for
Escherichia coli, while MMAB medium (29) was
used for Azospirillum strains. When required, ampicillin
(100 µg/ml) or tetracycline (10 µg/ml) was added to the medium.
To construct the translational cytN-gusA fusion used in this
study, a 517-bp upstream region of the cytN gene was PCR
amplified and inserted into the PstI-XbaI sites
of plasmid pFAJ1171 (25) to generate plasmid pFAJ870.
After verification by DNA sequence analysis, a 2.6-kb
PstI-EcoRI fragment from pFAJ870, containing the
cytN upstream region fused to the promoterless
gusA reporter gene, was cloned into the corresponding sites
of plasmid pLAFR3 (21), yielding pFAJ873, which contained
427 bp of the cytN upstream region and the sequences
encoding the first 29 amino acids of CytN fused to the GusA coding
sequence. This plasmid was mobilized from E. coli DH5
to
A. brasilense Sp7 by triparental conjugation.
Continuous fermentation was performed in a 2-liter O2-stat
fermentor as previously described (16) by using MMAB
medium (29). The concentration of DO2 was
controlled by varying the air flow into the fermentor on the basis of
the measured DO2 value. Gaseous nitrogen was sparged into
the fermentor at a flow rate of 1.27 liters/min at low DO2
levels (0 to 15% DO2).
Analytical procedures.
Quantitative -glucuronidase
activity was measured as previously described (26); this
activity was expressed in Miller units (17) but was
calculated per hour instead of per minute. Cell growth was monitored by
measuring the optical density at 578 nm (OD578) with a
Perkin-Elmer Lambda 2 UV spectrum spectrophotometer. The
L-malate concentration in the culture broth was determined with a test kit from Boehringer (Mannheim, Germany). All data in this
paper are averages based on at least two replicates.
Fermentation strategy.
The bacteria were first cultivated in
a batch fermentation. At the end of the exponential growth phase,
continuous fermentation started. Consecutive small DO2
concentration shifts were made before a new steady state was reached.
The profiles of DO2 concentrations during fermentation are
shown in Fig. 1A,
2A, and 3A.
Samples were taken about each 1.5 h (just before a DO2
concentration shift) and used to determine the -glucuronidase
activity and cell density. To monitor strain stability and purity,
samples were collected at the end of the fermentation period and spread
on indicator plates containing bromo-4-chloro-3-indolyl--glucuronide
(X-Gluc) (11). During the continuous fermentation, the
carbon source (malate) was designed to be the limiting factor.
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FIG. 1.
Identification of the mathematical model. (A) Profile of
on-line-measured values for DO2 concentration
(DO2) (solid line) and dilution rate (D) (dashed and dotted
dot line). (B to D)  , experimental data; solid line, simulation
results obtained with the full model; dashed line, simulation results
obtained with the simplified model. EFT, elapsed fermentation time;
GUS, -glucuronidase.
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|
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FIG. 2.
Validation of the mathematical model. The symbols and
abbreviations are the same as those described in the legend to Fig.
1.
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FIG. 3.
Further validation of the mathematical model with a
different DO2 profile. The symbols and abbreviations are
the same as those described in the legend to Fig. 1.
|
|
Analysis of the fermentation data.
Changes in the
-glucuronidase activity of a hybrid gene reporter in the presence of
a changing external signal indicate that the external signal is the
transcriptional activation signal. However, in the experimental setup
described above, not only alterations in transcriptional activation of
the plasmid encoding the cytN-gusA fusion induced by the
DO2 concentration shifts but also accumulation and turnover
of the fusion protein can account for the -glucuronidase activity
measured. Therefore, only the specific rate of expression of the fusion
protein, which is independent of the experimental design, can reflect
the influence of O2 on expression of the target gene. In
order to derive the specific rate of expression of the fusion protein
from the -glucuronidase activity measured, the following general
dynamic mathematical model based on mass balances was applied
(28):
|
(1)
|
|
(2)
|
|
(3)
|
where X is the concentration of biomass (grams
of cells per liter), S is the concentration of the carbon
source (grams of malate per liter), Sin is the
concentration of the carbon source in the feed flow (grams of malate
per liter), P is the concentration of the fusion protein
(grams of protein per liter), D is the dilution rate (per
hour), µ is the specific growth rate of cells (per hour), 
is the
specific rate of consumption of the carbon source (grams of malate per
gram of cells per hour), 
is the specific rate of expression of the
fusion protein (grams of protein per gram of cells per hour), and
k is the in vivo rate of degradation of the fusion protein
(per hour).
According to the definition of -glucuronidase activity
(17), the -glucuronidase activity value is assumed to
be proportional to the amount of fusion protein per cell:
|
(4)
|
where U is the -glucuronidase activity (Miller
units [enzyme activity per gram of cells per hour]) and is a
proportionality constant (grams of protein per gram of cells per Miller unit).
By combining equation 4 with equations 1 and 3, the following equation
can be deduced:
|
(5)
|
where is / (Miller units per hour), the apparent
specific rate of expression of the fusion protein, and reflects the direct influence of the external signal on transcriptional activation of the hybrid gene fusion.
The three specific reaction rates can be correlated with
equation 6:
|
(6)
|
where YXS (grams of cells per gram of
malate) and YUS (Miller units per gram of cells)
are two positive constant yield coefficients.
To complete the model, the following kinetic expressions are
proposed. A double Haldane model is used to describe the specific growth rate of cells as a function of two substrates, malate and O2 (1). The apparent specific rate of
expression of the fusion protein is described as a function of the
carbon substrate (malate) concentration with a Monod model
(18) and as a function of DO2 concentration
with a Haldane-like model in which background expression of the fusion
protein is introduced since constitutive background expression of the
fusion protein has been observed under anaerobic conditions (data not
shown). Although it is generally known that E. coli
-glucuronidase is a very stable enzyme in cell extracts and in cells
(10, 11), no value for in vivo decay of any
-glucuronidase protein in A. brasilense has been
described so far. However, the dependence of degradation of the fusion
protein on DO2 concentration has also been observed in
experiments carried out in test tubes (data not shown). The rate of
degradation of the fusion protein can be expressed as a function of
DO2 concentration in the frame of the Monod model
(18). Therefore, the following equations are proposed:
|
(7)
|
|
(8)
|
|
(9)
|
where DO2 is the concentration of
dissolved oxygen (percent); KMXS and
KIXS are the saturation constant and inhibition
constant of malate for cell growth (grams of malate per liter),
respectively; KMXG and
KIXG are the saturation constant and inhibition
constant of DO2 for cell growth (percent), respectively;
KMPS is the saturation constant of malate for
fusion protein expression (grams of malate per liter);
KMPG and KIPG are the
saturation constant and inhibition constant of DO2 for
fusion protein expression (percent), respectively; KBPG is the constant for background expression
of the fusion protein (percent); Kk is the
saturation constant of DO2 for decay of the fusion protein
(percent); µmax is the maximal growth rate of cells (per
hour); max is the maximal apparent rate of expression of the fusion protein (Miller units per hour); and
kmax is the maximal rate of degradation of the
fusion protein (per hour).
In order to assess the influence of DO2 on the
specific level of expression of the cytN-gusA fusion, the
measured experimental values were fed into the model to identify the
appropriate parameters. Once the values are identified, the complete
model (parameters and model structure) can be used to predict the
behavior of the hybrid fusion protein as a function of the external variables.
Simulation and parameter identification for the model described above
were performed by using Matlab 5.3 (The MathWorks, Inc., Natick, Mass.)
on a Linux platform.
| |
RESULTS |
Parameter identification.
A. brasilense Sp7
containing plasmid pFAJ873 was cultivated in a fermentor for 13 h.
Subsequently, continuous fermentation was started by maintaining the
dilution rate at 0.15 h
1. The DO2
concentrations were shifted before a steady state was reached at
regular intervals (about 1.5 h). The profile of DO2 concentration is shown in Fig. 1A. The parameters in the mathematical model were identified by minimizing the following cost function (J):
|
(10)
|
where i is the sampling time; j is the
components X, S, and U; n
(n = 3 in this case) and m are the number of
components and the sampling time, respectively;
Ys,ij is the data set for the simulation
results; Ye,ij is the data set for the
experimental results; 
e,j is the
average value for the components; and sj is the standard deviation of the experimental data. In order to diminish the effects of the different physical quantities of the measurements, the relative errors, (Ys,ij 
Ye,ij)/e,j,
are taken into account in cost function J.
The identification results are shown in Figure 1B to D, while the
values for the identified parameters are summarized in Table 2. The estimated initial (zero-time)
values were as follows: S = 5.2087 g of malate per
liter; X = 0.0554 OD578 unit; and
U = 41.9123 Miller units. The carbon source
concentration in the feed flow (Sin) was 5.0075 g of malate per liter. Because cell density rather than dry weight of
cells was used to monitor cell growth, the yield coefficient
YXS as defined in equation 6 was expressed in
OD578 units per gram of malate instead of grams of cells
per gram of malate. The agreement between the simulation results and
the experimental data is remarkable.
Validation of the mathematical model.
To validate the model
structure and parameters, an experimental test set was generated by
performing a continuous fermentation similar to the one used for
parameter identification but with a slightly different DO2
profile (Fig. 2A) and different initial values. The continuous
fermentation started at 10 h with a dilution rate of 0.1125 h1. The following initial values for validation were
chosen from the first experimental measurements: S = 4.8388 g of malate per liter; X = 0.097
OD578 unit; and U = 25.5267 Miller units.
For the carbon source concentrations in the feed flow, the following experimentally measured value was used: Sin = 4.989 g of malate per liter. Both the simulation results, as
obtained by applying the model and parameters identified above, and the
experimental data are shown in Fig. 2. The good agreement between the
simulated and experimental results indicates the applicability of the
model when comparable experimental conditions (such as DO2
profile) are used.
In order to further validate the applicable range of the model, a
continuous fermentation with a totally different DO2
profile (Fig. 3A) was performed. The DO2 concentration was
kept at 10% during the batch fermentation, and it was subsequently
shifted from low to high values during the continuous fermentation. The continuous fermentation started at 12 h with a dilution rate of 0.1193 h1. The following initial values used for
validation were based on the first experimental measurements:
S = 5.3812 g of malate per liter; X = 0.038 OD578 unit; and U = 126.84
Miller units. For the carbon source concentration in the feed flow, the
following measured value was used: Sin = 5.308 g of malate per liter. The simulation results and the
experimental data are shown in Fig. 3. The agreement between the
simulated and experimental results corroborates the generality of the model.
Influence of O2 on the rate of expression of the target
genes.
As indicated in Fig. 4A and
B, the rate of expression of the
cytN-gusA fusion is very dependent on the DO2
concentration, and the maximal values occur under microaerobic
conditions (a DO2 concentration of 2.23% results in
maximal expression).
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FIG. 4.
(A) Apparent specific rate of expression of fusion
protein as a function of the concentrations of the substrates malate
and DO2. (B) Cross section of panel A at a constant malate
concentration of 1 g/liter. (C) Specific rate of degradation of fusion
protein as a function of DO2 concentration.
|
|
As shown by the values for KMXG and
KIXG in Table 2, the model predicts that
O2 is not a limiting factor for cell growth under the
conditions tested. In view of the highly efficient microaerobic metabolism of Azospirillum (30), such behavior
is not unexpected. The minor effect of carbon substrate concentration
on the apparent specific rate of expression is also predicted by the
model, implying that the cytNOQP operon is not subject to
catabolic repression by malate. Furthermore, the specific rate of
degradation of the fusion protein as a function of the DO2
concentration is shown in Fig. 4C. The maximal specific rate of
degradation of the fusion protein is 0.1270 h1,
corresponding to a half-life of 5.46 h. The native CytN protein is
a transmembrane protein (16), but its GusA fusion
counterpart lacks any potential transmembrane region and should
therefore be cytoplasmically located. The cytoplasmic GusA fusion
appears to be a stable protein in A. brasilense.
Towards a simplified model.
When the general model structure
represented by equations 1, 2, 5, and 6 to 9 is examined and the large
range of orders of magnitude for the 14 parameters summarized in Table
2 is considered, a legitimate question is whether a similar
high-quality fit of the experimental data can be obtained with a
simplified model that includes fewer parameters. In order to
mathematically investigate this possibility, a thorough sensitivity
analysis was performed.
The dilution rate and the DO2 concentration were defined as
system inputs u1 and u2,
respectively, and the biomass concentration, the malate concentration,
and the -glucuronidase activity were defined as system outputs
y1, y2, and
y3, respectively. The parameters were denoted
pj with j ranging from 1 to 14.
A 3 × 14 sensitivity matrix containing the sensitivity functions
(
yi/pj)(t) was then computed.
These sensitivity functions represent the sensitivity of each output
(yi) to (small) variations in each model
parameter (pj). More details on sensitivity
function-related procedures have been described by Bernaerts et al.
(3).
Based on the sensitivity functions and the experimental data, the
kinetic expressions (equations 7 to 9) of the general model described
above could be substantially simplified as follows:
|
(11)
|
|
(12)
|
|
(13)
|
Meanwhile, the correlation among the three specific reaction rates
can be simplified as equation 14:
|
(14)
|
The number of model parameters has been reduced to six. The
parameters and constants in the simplified kinetic expressions (equations 11 to 13) are summarized in Table
3.
As Table 3 and equations 11 to 14 show, most of the saturation
constants are replaced by 
1 or 2. The
former is the same order of magnitude as the residual substrate
concentration (i.e., 102) and results in a 50% reduction
in the specific growth rate when the malate concentration is low. The
latter is a very small number (e.g., 106) and results in
a switch from the maximum specific rate when substrate or
DO2 is present to a rate of zero when both substrates are
absent. Furthermore, the inhibition constants (i.e.,
KIXS and KIXG) that have
been omitted can be considered replaced by an infinitely large
(positive) number corresponding to a noninhibition situation. Note,
however, that from a mechanistic point of view, it cannot be claimed
that growth of A. brasilense is not inhibited by high
substrate or DO2 concentrations. We merely concluded that an inhibition effect cannot be inferred from the available experimental data. Also, the yield coefficient YUS is assumed
to be infinitely large to reflect the negligible contribution of
product formation to the substrate consumption rate.
Figure 1 (identification) and Fig. 2 and 3 (validation) illustrate that
the descriptive quality of this simplified model is as good as the
descriptive quality of the original 14-parameter model. Note that there
was apparently no need to reoptimize the six parameters in the
simplified model (Tables 2 and 3).
Detailed exploration of the significance of model parameters in the
general model, as well as in the simplified model, is the subject of
ongoing research. Thus, optimal experiments (complemented with
parameter uncertainty analysis) will be designed to check whether the
model features present in the general model but omitted in the
simplified model (e.g., inhibition of the specific growth rate at high
substrate or DO2 concentrations, the presence of background
gene expression in the absence of DO2) are truly needed.
| |
DISCUSSION |
Use of a dynamic mathematical model allows reliable quantitative
interpretation of gene expression measurements as a function of varying
environmental conditions without a requirement for a steady state. The
parameters of the model are determined by using experimental data. When
validated, the model can be used to predict in silico the effects of
external signals on expression of the gene studied under
nonexperimentally tested conditions. The use of mathematical models
based on differential equations to describe and predict the behavior of
cellular processes is becoming widespread (4, 6, 8, 9, 13, 20,
27). According to previous studies with E. coli, a
steady state can be achieved within 5 reactor residence times
(12, 23, 24), which equals 33 h at a dilution rate of
0.15 h1. A total fermentation time of 297 h (12 days) would be needed to test nine different DO2 levels.
The overall experimental time can be decreased to only 15 h when
the DO2 level is varied each 1.5 h and a mathematical
model is used to analyze the results; this yields more detailed
information about the effects of external signals on expression of the genes.
In this study, a mathematical model was used to predict the specific
pattern of expression of an A. brasilense cytN-gusA fusion as a function of DO2 concentration. The role of the
cytNOQP-encoded oxidase during microaerobic respiration and
the presence of an FNR-binding consensus sequence in the upstream
region of the A. brasilense cytN gene (16)
point towards microaerobic regulation of the operon by an FNR-like
protein. The simulated behavior of the A. brasilense hybrid
cytN-gusA fusion, showing clear upregulation under
microaerobic conditions, was therefore in good agreement with results
obtained previously for the A. brasilense cytochrome cbb3 oxidase. Moreover, it is noteworthy that
the DO2 concentration that resulted in maximal specific
expression of the cytN-gusA fusion was approximately the
same as the DO2 concentration reported by Zhulin et al.
(30) and coincided with generation of a maximal proton
motive force. Furthermore, an expression pattern similar to the one
obtained in this study has been reported for the CytN-like protein of
Rhodobacter sphaeroides (19).
The model assumes that the shift in expression of the target gene
occurs as soon as the DO2 shift occurs. However, we cannot exclude the possibility that there may be a lag between signal transduction and fusion protein synthesis (for example, the delay between maximal mRNA synthesis and maximal protein synthesis). Usually,
such a delay in prokaryotes is minimal (15). If a longer response time is expected (2), it is advisable to adapt
the time intervals for measurements accordingly. Thus, the effects caused by the transition are similar for different DO2
levels, and the results are comparable.
On the basis of a careful sensitivity analysis, a simplified model
(with fewer parameters) was deduced in this case study, and this model
had predictive values similar to those of the full model. The key
feature of both the full model and the simplified model is mathematical
description of fusion protein biosynthesis and degradation during
bacterial growth. Given the high predictive value of these models, it
is sensible to assume that they can form a basis for evaluating the
effects of other external environmental signals, such as nitrogen
source or other substrates which can be utilized by bacteria, on
expression of target genes by using suitable fusions with the
appropriate reporter genes. In view of fermentation technology, when
optimization of heterologous gene expression is desired, such studies
might allow workers to determine the environmental conditions that
result in maximal gene expression.
| |
ACKNOWLEDGMENTS |
J.S. is a recipient of a predoctoral fellowship from the Research
Council, Katholieke Universiteit Leuven. I.S. is a research assistant
with the Fund for Scientific Research Flanders. K.B. is a research
assistant with the Institute for the Promotion of Innovation by Science
and Technology in Flanders, Belgium.
This work was supported in part by grants (to J.V.) from the Flemish
Government (GOA) and the Fund of Scientific Research-Flanders, project
OT/99/24 of the Research Council of Katholieke Universiteit Leuven and
the Belgian Program on Interuniversity Poles of Attraction, initiated
by the Belgian State Prime Minister's Office for Science, Technology
and Culture.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Centre of
Microbial and Plant Genetics, K. U. Leuven, Kasteelpark Arenberg
20, B-3001 Heverlee, Belgium. Phone: 0032-16-321631. Fax:
0032-16-321966. E-mail:
jozef.vanderleyden{at}agr.kuleuven.ac.be.
| |
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Applied and Environmental Microbiology, August 2001, p. 3350-3357, Vol. 67, No. 8
0099-2240/01/$04.00+0 DOI: 10.1128/AEM.67.8.3350-3357.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.
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Abstract
Introduction
