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Applied and Environmental Microbiology, July 1999, p. 2847-2852, Vol. 65, No. 7
0099-2240/99/$04.00+0
Copyright © 1999, American Society for Microbiology. All rights reserved.
Quantification of Chemotaxis to Naphthalene by
Pseudomonas putida G7
Randall B.
Marx* and
Michael D.
Aitken
Department of Environmental Sciences and
Engineering, School of Public Health, The University of North
Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7400
Received 6 August 1998/Accepted 15 April 1999
 |
ABSTRACT |
The capillary assay was used to quantify the chemotactic response
of Pseudomonas putida G7 to naphthalene. Experiments were conducted in which the cell concentration in the assay chamber, the
naphthalene concentration in the capillary, or the incubation time was
varied. Data from these experiments were evaluated with a model that
accounted for the effect of diffusion on the distribution of substrate
and the transport of cells from the chamber through the capillary
orifice. By fitting a numerical solution of this model to the data, it
was possible to determine the chemotactic sensitivity coefficient,
0. The mean of the best-fit values for 0
from the three types of experiments was 7.2 × 10
5
cm2/s. A less computationally intensive model based on
earlier approaches that ignore cell transport in the chamber resulted
in 0 values that were approximately three times higher.
The models evaluated in the present study could simulate the results of
capillary assays only at low chamber cell concentrations, for which the
effect of consumption on the distribution of substrate was negligible. Results from this work suggest that it is possible to use the capillary
assay to quantify taxis towards environmentally relevant chemoeffectors
that have low aqueous solubility.
| |
INTRODUCTION |
The effect of bacterial motility on
the bioremediation of contaminated subsurface environments is poorly
understood. There has been speculation that motility might be required
to ensure the proper distribution of the degrader organisms relative to the target pollutant (28), yet little evidence exists to
support this hypothesis. Studies on the influence of chemotaxis
(30) or random motility (5, 23, 26, 29, 34) on
substrate utilization have focused on hydrophilic substrates not
commonly considered to be pollutants. Recently Pseudomonas
putida G7 was shown to be chemotactic to naphthalene
(16), one of the most prevalent groundwater contaminants at
sites contaminated with polycyclic aromatic hydrocarbons
(9). However, a role for chemotaxis in the biodegradation of
naphthalene or other substrates of limited aqueous solubility in
contaminated environments has not been documented.
The positive effect of either type of bacterial motion is manifested as
a bacterial flux, which serves to change the distribution of bacteria
relative to substrate. In a one-dimensional system, the flux of
bacteria due to chemotaxis and random motility can be represented as
follows (22):
|
(1)
|
where µ is the random motility sensitivity coefficient,
B is the bacterial concentration, and
vc is the one-dimensional chemotactic velocity.
The net effect of the chemotactic flux, vcB,
will be for bacteria to move closer to a chemoattractant, which should in turn permit a higher rate of chemoattractant utilization
(17). The chemotactic velocity, vc,
has been shown to be a function of bacterial species-specific
parameters, the chemoattractant concentration, and the chemoattractant
concentration gradient (7, 31):
|
(2)
|
where v is the three-dimensional cell swimming speed,
0 is the chemotactic sensitivity coefficient,
C is the substrate concentration, and
Kd is the dissociation constant for the chemoreceptor.
The influence of chemotaxis on pollutant biodegradation will depend on
the value of 0 for a given organism relative to the value of µ, in addition to the distribution of substrate and bacteria (11, 12, 24, 25). However, there is a lack of data on the
sensitivity coefficients for random motility and chemotaxis in systems
of interest in bioremediation. In the few cases wherein these
parameters have been determined, the organism was not a soil
microorganism (10), the chemoattractant was not a pollutant (32), or the chemoattractant was not metabolized
(3). Metabolism of the substrate of interest is important if
the actual chemoeffectors are intermediates of the degradation pathway
(18, 21) or central metabolism (4).
The standard capillary assay (2) has been used to quantify
coefficients for random motility (22) and chemotactic
sensitivity (13, 32). A complication in the use of the
capillary assay with substrates of low aqueous solubility, such as
naphthalene, is that chemotactic organisms may not respond to these
attractants at all under some conditions (16). The
solubility limit of poorly soluble substrates could constrain the
magnitude and extent of substrate concentration gradients, which could
in turn result in a chemotactic response that cannot be detected. In
addition, constraints on substrate concentration gradients caused by
low aqueous solubility can be exacerbated by consumption of the
substrate. One approach to estimating 0 under such
conditions is to account for the overall effect of consumption on the
distribution of substrate in the capillary system (13). As
the mathematical approximation used in this approach is difficult to
verify, an alternative approach would be to render the level of
consumption negligible by lowering the concentration of bacteria in the
chamber surrounding the capillary mouth (32). Such a
modification has been shown to increase the sensitivity of the
capillary assay in other systems in which the chemoattractant is
metabolized (2, 36).
The purpose of the work reported here was to evaluate the range of
conditions and mathematical models for which the standard capillary
assay could be used to quantify the sensitivity coefficients relevant
to the chemotaxis of P. putida G7 to naphthalene. Since existing models (13, 32) include untested assumptions about the concentration of bacteria and substrate at the capillary mouth, we
also evaluated an approach that incorporates a model of the chemoattractant concentration surrounding the capillary mouth (14) and the corresponding spatial distribution of bacteria in the chamber.
| |
MATERIALS AND METHODS |
Media.
Tryptone broth was made from 10 g of tryptone
and 5 g of NaCl per liter of distilled water. For the growth of
P. putida G7 on a single carbon source, a mineral salts
buffer was used which contained 25 mM KH2PO4,
25 mM Na2HPO4, 0.1%
(NH4)2SO4, and 1% Hutner's
mineral base (15, 19). Phosphate buffer (pH 7.0) used for
cell suspensions and the preparation of solutions used to fill the
capillaries consisted of 25 mM KH2PO4, 25 mM
K2HPO4, and 10 µM EDTA (2). CFU
were enumerated on plates containing R2A agar (Difco Laboratories,
Detroit, Mich.).
Saturated solutions of naphthalene in phosphate buffer were made by
melting about 0.1 g of naphthalene (Aldrich, Milwaukee,
Wis.) in a
16-by-125-mm test tube submerged in a boiling water
bath. After the
melted substrate recrystallized at room temperature,
5 ml of sterile
phosphate buffer was added, and the tube was shaken
on a wrist-action
shaker for at least 12
h.
Culture conditions.
P. putida G7 was obtained from
Caroline Harwood (University of Iowa). It is stored cryogenically
(
80°C) in 1.5-ml aliquots of overnight cultures grown in tryptone
broth subsequently supplemented with dimethyl sulfoxide to 10%
(vol/vol).
Tryptone broth (5 ml) was inoculated from a stab of frozen culture.
After 1 day, 1 ml of culture was centrifuged for 1 min,
the supernatant
was decanted, and the pellet was resuspended in
1 ml of mineral salts
buffer containing 5 mM sodium salicylate.
Approximately 5 µl of the
suspension was diluted in 20 ml of mineral
salts buffer containing 5 mM
sodium salicylate and then placed
on a rotary shaker (240 rpm) at
25°C and grown to an optical density
at 590 nm (OD
590) of
0.2 to 0.3 (requiring 16 to 20 h). The cells
were then centrifuged
at 2,800 ×
g for 3 min, the supernatant
was decanted,
and the pellet was resuspended in phosphate
buffer.
Cell swimming speed.
Cells were diluted to an
OD590 of 0.1 to 0.2 in phosphate buffer. A 10-µl drop of
culture was placed on an uncovered microscope slide. Images of bacteria
swimming along the plane of the slide were viewed with the 20×
objective and projected onto a computer screen that was calibrated to
convert screen distances to actual distances. The movements of several
cells were tracked and analyzed simultaneously for 1 min by using a
Hobson Tracker (Hobson Tracking Systems Ltd., Sheffield, England).
Twenty-two 1-min segments, each tracking about 12 bacteria, were
analyzed. The average speed determined for all of the runs was used for
the cell swimming speed.
Diffusivity and solubility of naphthalene.
The diffusivity
of naphthalene in aqueous solution was determined by using the
Wilke-Chang equation (35). The solubility of naphthalene in
phosphate buffer was determined by measuring the absorbance at 256 nm
for a solution of phosphate buffer saturated with naphthalene and
converting this absorbance into a concentration value with a standard curve.
Capillary assay.
Several minor modifications to the original
procedure (2) were made to optimize reproducibility,
convenience, and the plating conditions of P. putida G7.
Multiple chamber assemblies were prepared on a 25-by-50-cm glass plate.
Triplicate 1-µl capillaries for each experimental condition were
prepared by moving the flame-sealed capillaries onto a glass petri
dish. The dish was then placed on a hot stir plate for at least 15 min.
Hot capillaries were then immersed, with the open side down, into the
substrate solution. After a cooling period of 5 to 10 min, the
capillaries were placed individually in the culture chambers. The glass
plates with completed assemblies were incubated at 25°C for 60 min,
unless stated otherwise. The capillaries were then removed, rinsed with
deionized water, broken, and emptied into an aliquot of mineral salts
buffer. The suspensions were diluted, if necessary, and plated onto R2A
agar plates, which were counted after 20 to 30 h of incubation at
30°C.
Chemoreceptor constant.
The chemoreceptor half-saturation
constant, Kd, was determined by using a
capillary assay in which the concentration of naphthalene was varied in
both the capillary and the chamber but in which the ratio between the
two concentrations remained constant at 2. A sensitivity curve (6,
27) was fitted to the data from this experiment by using
nonlinear regression (ProStat; Poly Software International, Salt Lake
City, Utah), with Kd as the fitted parameter.
Random motility sensitivity coefficient.
The random motility
coefficient was determined from data on bacterial accumulations in the
capillary in the absence of chemoattractant (33):
|
(3)
|
where
NRM is the accumulation in the
capillary containing phosphate buffer only,
t is the time of
capillary incubation in
seconds,
rc is the
radius of the capillary, and
B(0,
t) is the
concentration of
bacteria at the capillary mouth. The best-fit
value of µ was
determined by performing linear regression of
NRM2 versus
4
rc4[
B(0,
t)]
2t,
where
B(0,
t) is assumed to equal
Bch,
the concentration of
bacteria in the chamber, for experiments in which
the capillary
contained phosphate buffer
only.
Modeling approach.
For assays in which capillaries contained
naphthalene, the total accumulation, N, was due to both
random motility and chemotaxis. The accumulation due to random motility
was accounted for by differentiating equation 3 and expressing the
result in finite-difference form:
|
(4)
|
An expression for the net accumulation of bacteria in the
capillary due to chemotaxis (
N NRM) is
based on the chemotactic
flux of cells (equation 1) across the entrance
to the capillary
(
13). Shown in finite difference form:
|
(5)
|
The chemotactic velocity (
vc) is a
function of the concentration and concentration gradient of
chemoattractant at the entrance
to the capillary (equation 2). To
determine the distribution of
chemoattractant, it is necessary to have
a model that incorporates
the geometry of the capillary assay system.
In our system, the
capillary lies flat on a glass surface, so diffusion
in the chamber
is predominantly hemispherical with the mouth of the
capillary
at the center and the glass plate forming the flat surface.
Futrelle
and Berg (
14) proposed a model, which was
substantiated experimentally,
to account for the distribution of
substrate near the mouth of
the capillary tube in which diffusion in
the capillary toward
the mouth is linear, while diffusion away from the
mouth is hemispherical.
The resulting concentration and gradient at the
mouth are as follows:
|
(6)
|
|
(7)
|
where
C0 =
C(
x,0),
= 2
Dt/3
rc, and
D is the diffusivity
of the substrate. The corresponding solution for chemoattractant
concentration in the chamber (
14) is:
|
(8)
|
As substrate diffuses from the capillary into the chamber,
bacteria will swim towards the capillary mouth. To determine
B(0,
t),
material balance equations for bacteria in a series
of hemispherical
shells radiating from the capillary mouth were solved
in the radial
direction for each time interval:
![&Dgr;B(r,t)=[J(r+&Dgr;r,t)·A(r+&Dgr;r,t)−J(r,t)·A(r,t)]·<FENCE><FR><NU>&Dgr;t</NU><DE>V(r+&Dgr;r)−V(r)</DE></FR></FENCE>](/content/vol65/issue7/fulltext/2847/img009.gif)
|
(9)
|
where
B(
r,
t) is the change in bacterial
concentration over the time interval,
J(
r,
t) is the flux in
the radial direction
(similar to equation 1),
A(
r,
t) is the
surface area of the hemispherical
shell, and
V(
r+
r,
t)
V(
r,
t) is the volume of the shell. The
chemotactic velocity as a
function of radial distance was determined
by incorporating the
attractant concentration (equation 8) and
the concentration gradient,
which was determined by linear interpolation
of concentration between
the nodes. By solving the sequence of
mass balance equations for
sequential time steps, it is possible
to determine the concentration of
bacteria at the mouth,
B(0,
t),
for any time
t.
This approach is similar to that used in a previous
study on the
distribution of chemotactic bacteria within a system
where the
attractant concentration varied in one dimension (
25).
Ford and Lauffenburger (
13) suggested a simpler model to
simulate the accumulation of chemotactic bacteria in a capillary
tube
that contains a chemoattractant. They assumed that
B(0,
t)
is
constant and equal to
Bch, the initial
concentration of bacteria
throughout the chamber, and that the
concentration of substrate
at the capillary mouth is constant with
respect to time:
|
(10)
|
where
n is a number between 0 and 1. The
corresponding one-dimensional substrate concentration gradient at the
mouth of the
capillary is (
8):
|
(11)
|
The value of
n in equations 10 and 11 was determined
by solving equation 6 over a 1-h period. Although the concentration
of
substrate at the mouth is not constant with time, it was found
that the
average concentration was approximately 0.03
C0.
Thus,
a value of
n equal to 0.03 was used in simulations
involving the
Ford and Lauffenburger (F/L)
model.
The model formulation that incorporated the method of Futrelle and Berg
(
14) for estimating conditions at the mouth of the
capillary
and in the chamber is referred to as the F/B model.
The F/L formulation
incorporated the assumptions of Ford and Lauffenburger
(
13)
for conditions at the capillary mouth. To run either model,
the
chemotactic velocity [
vc(0,
t)] and
the bacterial concentration
[
B(0,
t)] at the mouth were
used to determine the accumulation
due to random motility (equation 4)
and chemotaxis (equation 5)
as a function of time. Programs for both
models were written in
Visual Basic for Applications (Microsoft Corp.,
Redmond, Wash.).
For the F/B model, equations 6 and 7 were first solved
for each
time interval by using MatLab (The Mathworks, Inc., Natick,
Mass.).
The resulting values of substrate concentration and its
gradient
at the mouth of the capillary were then imported into the
Visual
Basic model. The values of the biological and system parameters
that were used in all computer simulations are shown in Table
1.
Chemotactic sensitivity coefficient, 0.
The
best-fit value of 0 was determined by running each model
with a range of assumed 0 values. For each assumed
value, the predicted and measured accumulations of cells in the
capillary containing chemoattractant were compared. The best-fit
0 was that which resulted in the minimum sum-of-square
errors between predicted and measured accumulations for all of the data
within a given experiment. In all cases, the µ value determined from a given experiment was used in the models to estimate the value of
0 for the same experiment.
The discretization error of the mathematical models solved by numerical
methods was evaluated by running the models with decreasing
time
intervals until the predicted accumulation did not change
significantly. The simulations were tested with a reasonable
0 value and it was found, with both models, that time
intervals
of 10 s or less produced accumulation results which
varied from
each other by less than 1%. Time intervals of 1 s
were used in
the reported simulations. The radial discretization for
the mass
balance of cells in the chamber was
2
rc, so that the approximation
of radial
symmetry applies to the system (
14).
| |
RESULTS |
In the capillary assay, there are several experimental variables
that can be adjusted when designing an experiment. Among the readily
controlled variables are the initial concentration of bacteria in the
chamber, Bch; the initial substrate
concentration in the capillary, C0; and the time
of the assay, t. By designing each experiment around one of
these three variables, it should be possible to discern how well the
role of each is accounted for in each model.
Experimentally measured accumulations of cells, as well as predicted
accumulations for the best-fit 0 values, are shown for the three different independent variables in Fig.
1, 2, and
3. The best-fit 0 values
for each experiment are summarized in Table 2. In all three experiments, the
0 determined from the F/L model is between two and three
times the value found according to the F/B model.
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FIG. 1.
Effect of chamber cell concentration on the accumulation
of P. putida G7 in the capillary assay. Solid circles
represent data for accumulations in the capillaries containing
phosphate buffer saturated with naphthalene, while the open circles
represent data for accumulations in the capillaries that contained
buffer only. The upper solid and dashed lines correspond to simulations
of accumulation in the naphthalene capillaries based on the F/B and F/L
models, respectively, using the best-fit values of 0 for
each model. The lower, solid line is the best fit for accumulations in
the capillaries that contain buffer only. Error bars represent the
standard deviations for triplicate measurements; error bars for the
blank capillaries are not shown for clarity.
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FIG. 2.
Effect of the initial naphthalene concentration in the
capillary on the accumulation of P. putida G7. The
concentration of bacteria in the chamber was 2.9 × 105 CFU/ml. The solid line represents the simulation with
the F/B model, while the dashed line represents the simulation with the
F/L model.
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FIG. 3.
Accumulation of P. putida G7 in the capillary
with time. The concentration of bacteria in the chamber was 3.2 × 105 CFU/ml. Symbols and lines are as described for Fig. 1.
Accumulations of cells in the capillaries containing buffer only were
all below 10 CFU.
|
|
The accumulation of cells in the capillaries containing naphthalene was
more easily distinguished from that in the blank capillaries as the
initial concentration of cells in the chamber decreased (Fig. 1). From
Bch values of about 5 × 105
CFU/ml to as low as 8 × 104 CFU/ml, the experimental
accumulation in the naphthalene capillary is parallel to the best-fit
line for the accumulation in the blank capillary, representing the
region for which N/NRM is constant. Models that
do not account for substrate consumption result in simulations wherein
the ratio, N/NRM, is not a function of
Bch (13). Therefore, experimental
conditions in which the resulting N/NRM is
constant are indicative that substrate consumption could be ignored for
modeling purposes. At concentrations of more than 5 × 105 CFU/ml, N/NRM decreases with
increasing Bch, so that the models for
chemotaxis which ignore substrate consumption cannot be applied directly. Thus, only the first three data points were used in estimating a 0 value for the experiment illustrated in
Fig. 1. Subsequent experiments used bacterial concentrations in the
chamber of less than 5 × 105 CFU/ml.
| |
DISCUSSION |
The capillary assay is a simple experimental system that can be
used to study chemotaxis and to quantify chemotaxis parameters by
fitting mathematical models to the experimental data. Previous models
(13, 32) incorporated assumptions about the bacterial and
substrate concentrations at the mouth that merit further examination. The F/L model (13) specified that the concentration of
substrate at the capillary mouth in the absence of consumption is the
average of the initial concentration of substrate in the chamber and
the concentration of substrate in the solution used to fill the
capillary tube. For instance, if the capillary tube were filled with
phosphate buffer saturated with naphthalene and the concentration of
naphthalene in the chamber were zero, the value of n in
equations 10 and 11 would be 0.5. Using this value, we obtained
0 values which were at least 1 order of magnitude
greater than previously reported values for P. putida
(2) and simulations that did not match the trend in the data
of Fig. 2 qualitatively. Several investigators have provided evidence
that the relative substrate concentration at the mouth is much lower,
on average, than 0.5. Weiss et al. (36) did a theoretical
analysis under slightly different conditions in which the average
concentration at the mouth (relative to the bulk capillary
concentration) was predicted to be 0.02 to 0.01 for 20 to 60 min into
the capillary assay. In an experimental analysis, Hazelbauer
(20) was able to explain chemotactic responses of
Escherichia coli to galactose in the capillary assay with
the assumption that the relative substrate concentration at the mouth was, on average, ca. 0.01. We found that for the conditions in the
present study, the average n over a 1-h experiment was
approximately 0.03 with the F/B model. This value was used in
simulations involving the F/L model.
Another assumption used in previous models (13, 32) is that
the concentration of cells at the capillary mouth remains constant and
is equal to the initial concentration in the chamber. While this
condition may hold if the chamber is completely mixed, the experimental
studies that accompanied these models did not incorporate mechanical
mixing. Furthermore, mixing in the chamber would influence the motility
of bacteria by creating advective currents, which are not accounted for
in any model of the capillary assay.
Adler (1) has observed that E. coli cultures
accumulate near the mouth of a capillary containing 2 mM aspartate. Our
modeling approach also predicted a net accumulation of cells near the
capillary mouth. For the experiments wherein the initial concentration
of naphthalene in the capillary was at the aqueous saturation point, the predicted bacterial concentration at the mouth according to the F/B
model ranged between two and three times the initial concentration throughout the chamber over a 1-h simulation (not shown).
The accumulation of cells at the capillary mouth predicted in the F/B
model accounted for much of the difference between it and the
F/L model. The predicted substrate concentration gradients for
each model (equations 7 and 11) were nearly identical (not shown), and
the chemotactic flux was not very sensitive to the time-dependent
changes in the substrate concentration at the mouth, so these were not
significant sources of the differences between the two models.
The two models provided similar fits to the experimental data both
qualitatively (similar lines in Fig. 1 and 3) and quantitatively (sum-of-squares errors in Table 2). The greatest difference
between the models was manifested for the dose-response experiment
(Fig. 2). Although both models involve approximations and simplifying assumptions, we believe the model based on the work by Futrelle and Berg (14) is a more rigorous method for determining
0. The F/B model calculates substrate concentrations
near the mouth of the capillary in a manner that was substantiated
experimentally and accounts for accumulation of bacteria at the
capillary mouth. However, the F/B model is also more computationally
intensive than the F/L model and a simple analytic expression for
0 derived from it (13). The F/L models may be
appropriate under conditions where it can be shown that the
concentration of bacteria at the mouth does not change significantly.
Such circumstances are predicted in the system we studied for
naphthalene concentrations that are below 10% of the aqueous
saturation point.
Significance of the 0 value for chemotaxis to
naphthalene by P. putida G7.
The average
0 value of P. putida G7 for naphthalene
determined from the three different experiments is 7.2 × 105 cm2/s. This is below the published values
of E. coli for fucose, 8 × 105
cm2/s (10); E. coli for 
-methyl
aspartate, 7.5 × 104 cm2/s
(32); and P. putida PRS 2000 for
3-chlorobenzoate, 1.9 × 104 cm2/s
(3). However, the magnitude of the chemotactic sensitivity coefficient may not be as significant as its value relative to the
random motility coefficient. Lauffenburger et al. (25)
predicted that the relative growth of chemotactic bacteria compared to
nonmotile bacteria is proportional to the ratio of chemotactic to
random motility sensitivity coefficients, 0/µ. With a
ratio greater than 1, the advantage of chemotaxis to growth is
significant under a variety of conditions. For P. putida G7, with naphthalene as the chemoattractant, the ratio
is approximately 225. The ratios for E. coli on fucose
and methyl aspartate and for P. putida on 3-chlorobenzoate
were 5 (10), 50 (32), and 7 (3) respectively.
Implications for quantifying chemotaxis to hydrophobic, metabolized
substrates.
Data and simulations shown in Fig. 1 to 3 reveal
possible strategies for detecting and studying chemotaxis to other
poorly soluble, metabolized substrates. If the concentration of
bacteria is sufficiently low so that the overall loss of substrate due to consumption is insignificant, the accumulations in the attractant capillary should parallel those in the blank capillary in a log-log plot against the concentration of cells in the chamber (Fig. 1). However, a model that accounts for substrate metabolism may be necessary to determine the 0 value in systems for which
substrate consumption cannot be neglected. While a model has been
proposed to account for the effect of metabolism on cell accumulation
in the capillary (13), this model did not describe well the
results of the capillary assays for P. putida G7 at higher
cell concentrations in the chamber than those used to estimate
0 values in this work.
The data in Fig.
2 indicate that the peak chemotactic response to
naphthalene occurs at or near its saturation concentration
in phosphate
buffer. For metabolizable chemoattractants that are
less soluble than
naphthalene, it would be more difficult to design
experiments that
preclude substantial effects of metabolism. Therefore,
with poorly
soluble chemoattractants, aqueous saturation conditions
may be the most
likely to allow quantification and detection of
chemotaxis by the
capillary
assay.
The incubation time can also be adjusted to minimize the effects of
chemoattractant metabolism (Fig.
3). Shorter experimental
times will
reduce the overall level of consumption, and such a
strategy may also
help define conditions for which the level of
substrate consumption in
the system is
insignificant.
Quantification of the chemotactic sensitivity coefficient is essential
to evaluating the potential role of chemotaxis in the
biodegradation of
pollutants in the environment. While the quantification
of chemotactic
sensitivity coefficients to hydrophobic, metabolized
substrates by
using the capillary assay may seem problematic,
this study suggests
that methods are available to achieve such
quantification.
| |
ACKNOWLEDGMENTS |
We thank Bob Bourret (University of North Carolina, Chapel Hill
[UNC-Chapel Hill]) and Alan Wolfe (Loyola University of Chicago) for their help with the development of experimental methods. Bob Bourret also provided access to the Hobson Tracker. Ann Grimm (University of Iowa) provided useful suggestions on the handling of
PpG7. Roseanne Ford (University of Virginia) and Howard C. Berg
(Harvard University) offered essential comments on the
application of the previously published mathematical models.
Markus Hilpert, Joseph Pedit, and Joseph Kanney (UNC-Chapel Hill)
assisted in the development of the F/B model. Glenn Walters and Thomas
Long (UNC-Chapel Hill) offered helpful editorial comments. We thank two
anonymous reviewers for questioning assumptions made in
earlier models, which led us to revise and, we believe,
improve the overall modeling approach.
This work was supported by the National Institute of Environmental
Health Sciences under the Superfund Basic Research Program (grant
P42ES05948) and by the National Science Foundation (grant DMS-9807666).
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Department of
Environmental Sciences and Engineering, CB #7400, Rosenau Hall, School of Public Health, The University of North Carolina, Chapel Hill, NC
27599-7400. Phone: (919) 966-3860. Fax: (919) 966-7911. E-mail: rmarx{at}emailunc.edu.
| |
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Applied and Environmental Microbiology, July 1999, p. 2847-2852, Vol. 65, No. 7
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Abstract
Introduction
