The EMBO Journal Vol.17 No.15 pp.4238–4248, 1998
Response regulator output in bacterial chemotaxis
Uri Alon1,2, Laura Camarena3,
Michael G.Surette4, Blaise Aguera y Arcas1,
Yi Liu1, Stanislas Leibler1,2 and
Jeffry B.Stock1,5,6
1Department of Molecular Biology, 2Department of Physics,
5Department of Chemistry, Princeton University, Princeton, NJ 08544,
USA, 3Department of Molecular Biology, Instituto de Investigation
Biomedicas, UNAM, Apartado Postal 70-228 04510, Mexico D.F.,
Mexico and 4Department of Microbiology and Infectious Diseases,
University of Calgary, Calgary, AB, Canada T2N 4N1
6Corresponding author
Chemotaxis responses in Escherichia coli are
mediated by the phosphorylated response-regulator
protein P-CheY. Biochemical and genetic studies have
established the mechanisms by which the various
components of the chemotaxis system, the membrane
receptors and Che proteins function to modulate levels
of CheY phosphorylation. Detailed models have been
formulated to explain chemotaxis sensing in quantitative
terms; however, the models cannot be adequately
tested without knowledge of the quantitative relationship
between P-CheY and bacterial swimming
behavior. A computerized image analysis system was
developed to collect extensive statistics on freeswimming
and individual tethered cells. P-CheY levels
were systematically varied by controlled expression of
CheY in an E.coli strain lacking the CheY phosphatase,
CheZ, and the receptor demethylating enzyme CheB.
Tumbling frequency was found to vary with P-CheY
concentration in a weakly sigmoidal fashion (apparent
Hill coefficient ~2.5). This indicates that the high
sensitivity of the chemotaxis system is not derived from
highly cooperative interactions between P-CheY and
the flagellar motor, but rather depends on nonlinear
effects within the chemotaxis signal transduction network.
The complex relationship between single flagella
rotation and free-swimming behavior was examined;
our results indicate that there is an additional level of
information processing associated with interactions
between the individual flagella. An allosteric model of
the motor switching process is proposed which gives a
good fit to the observed switching induced by P-CheY.
Thus the level of intracellular P-CheY can be estimated
from behavior determinations: ~30% of the intracellular
pool of CheY appears to be phosphorylated in
fully adapted wild-type cells.
Keywords: bacterial swimming/Escherichia coli/image
analysis/P-CheY
Introduction
Bacteria such as E.coli swim by rotating several flagella
(for a recent review of E.coli motility see Macnab, 1996).
4238 © Oxford University Press
Each flagellum is attached to the cell at a complex basal
body apparatus that functions as a bi-directional rotary
motor. Rotating flagella filaments coalesce into a bundle
that pushes the cell body in a curvilinear trajectory termed a
‘run’. Runs are interrupted when the flagella fly apart and
the cell tumbles in place, randomizing the direction of the
subsequent run. By modulating the frequency of tumbles,
the bacteria are able to perform chemotaxis, achieving a
net motion towards attractants and away from repellants
(Berg and Brown, 1972). The motion of individual motors
can be visualized by tethering a flagellum to a coverslip
and viewing the rotation of the cell body. From such
experiments it has been determined that there is a general
correlation of running behavior with counterclockwise
(CCW) motor rotation, and a correlation of tumbling
behavior with clockwise (CW) motor rotation (Larsen
et al., 1974).
Escherichia coli regulate their tumbling frequency
through the activity of the Che proteins, which form
a signal transduction network (for recent reviews see
Eisenbach, 1996; Stock and Surette, 1996; Falke et al.,
1997). This network interacts with the motor via the
response regulator protein CheY. CheY is phosphorylated
by the kinase CheA, and CheA kinase activity is regulated
by the transmembrane chemotaxis receptors. P-CheY is
dephosphorylated by the phosphatase CheZ. Genetic and
biochemical studies indicate that P-CheY binds to the
motor and promotes CW rotation. Thus, for instance,
mutant strains that are deficient in CheA or CheY tend to
run continually whereas mutants deficient in CheZ are
highly tumbly. Increases in attractant concentration inhibit
kinase activity, leading to reduced levels of P-CheY and
suppression of tumbling. Thus, when a cell runs up an
attractant gradient it tends to continue in that direction.
The chemotaxis signal transduction system has been
extensively studied under defined conditions with purified
components, and models based on these results have been
formulated to explain in quantitative terms the effects of
various mutations and stimuli on the levels of P-CheY
(Segel et al., 1986; Bray et al., 1993; Bray and Bourret,
1995; Hauri and Ross, 1995; Barkai and Leibler, 1997;
Spiro et al., 1997). The strength of this approach would be
significantly augmented if a direct quantitative relationship
between the in vivo level of P-CheY and swimming
behavior were known. In this report we have attempted
to determine this relationship.
Because of the inherent chemical instability of the
aspartyl phosphate in P-CheY, it is not feasible to measure
directly the fraction of CheY phosphorylated in the cell.
Previous studies of the effect of CheY on cell behavior
were performed using strains with undefined kinase
activity (Kuo and Koshland, 1987, 1989), so the equivalent
level of wild-type P-CheY could not be estimated. To
bypass these problems, we have constructed a mutant
Response regulator output in bacterial chemotaxis
strain that lacks both the P-CheY phosphatase, CheZ, and
the downregulator of kinase activity, CheB. Several lines
of evidence indicate that in this strain essentially all the
CheY present is phosphorylated. Variable levels of CheY
were expressed in this background from a low-copy
plasmid with a regulated lac promoter, and CheY was
quantitated by standard immunological techniques.
Tethered-cell and swimming-cell assays were employed
in parallel to establish a quantitative relation between
behavior and P-CheY levels. Computerized image analysis
(Sager et al., 1988; Khan et al., 1992; Amsler, 1996) was
used to acquire extensive statistics in both assays. Both
the tumbling frequency of swimming cells and the CW
bias of tethered motors increase with increasing P-CheY
concentration. However, the relationship between tetheredmotor
rotation and swimming behavior was not simple.
Most of the differences could be ascribed to interactions
between flagella that can be viewed as an additional
level of information processing in the chemotaxis
system. Comparing the behavior of wild-type cells with
that induced by known amounts of P-CheY indicates
that ~30% of CheY is phosphorylated in adapted wildtype
cells. The relation between P-CheY and tumbling
frequency also allowed us to compare the in vivo function
of several CheY mutants with that of wild-type P-CheY.
Our results suggest that in vivo, the constitutively active
mutant CheYD13K is quantitatively equivalent to P-CheY.
This complements a recent study in which motor rotation
was related to the intracellular concentration of a similar
activated CheY mutant (Scharf et al., 1998).
The tumbling frequency of swimming cells exhibited
only a weakly sigmoidal dependence on P-CheY (apparent
Hill coefficient ~2.5). This result has important implications
concerning our current understanding of the chemotaxis
signal transduction system. Simulations based on the
known biochemistry of the chemotaxis system indicate
that the high sensitivity that cells exhibit to attractant
stimuli (Berg and Brown, 1972; Segall et al., 1986; Khan
et al., 1993) implies a highly cooperative interaction
between P-CheY and the motor [with apparent Hill cofficients
ranging from 8 to 11 (Ninfa et al., 1991; Spiro
et al., 1997)]. The observation that this interaction is not
highly cooperative suggests that the sensitivity of the
chemotaxis system is due to some hitherto undefined
molecular interaction within the signal transduction network
that controls the level of CheY phosphorylation.
Results
Strategy for measuring behavior as a function of
P-CheY
Escherichia coli strain PS2001, a derivative of the
chemotaxis wild-type strain RP437 with a deletion from
the beginning of cheB through cheY to the end of cheZ,
was transformed with the low-copy-number plasmid
pLC576 in which cheY is under control of the lac promoter
(Table I). Production of CheY was controlled by varying
the concentration of isopropyl-β-D-thiogalactoside (IPTG).
In this strain, lack of CheB leads to full methylation of
the chemoreceptors, and thus to a high activity of the
kinase, CheA, which phosphorylates CheY. In addition,
CheZ is missing, greatly reducing the rate of CheY
dephosphorylation. Thus, in this strain virtually all of the
4239
CheY expressed is expected to be phosphorylated. This
is supported by three lines of evidence. (i) From in vitro
measurements of CheY phosphorylation by highly methylated
receptor-CheA complexes, and of P-CheY dephosphorylation
in the absence of CheZ, one would predict
that Ͼ99.9% of CheY is maintained in a phosphorylated
state in PS2001–pLC576 (Table II). From these calculations,
even if the in vivo rate of CheY phosphorylation
were 100-fold lower than the in vitro estimates, Ͼ90% of
CheY would still be phosphorylated in this strain. (ii) The
tumbling frequency of RP1616, a strain deleted for CheZ,
is the same as the tumbling frequency of PS2001–pLC576
with CheY induced to wild-type level. (iii) The tumbling
behavior of PS2001–pLC576 was not affected by addition
of repellents (50 mM L-leucine or 100 µM indole, at
various levels of CheY induction; data not shown). Thus,
repellents can not further increase the P-CheY levels in
this strain, consistent with phosphorylation of essentially
all of CheY.
Cultures of PS2001–pLC576 grown in the presence of
varying concentrations of the inducer IPTG were harvested
at mid-log phase and the rotation of single tethered cells
as well as the behavior of free-swimming cells was
analyzed. Cells from each culture were also pelleted and
frozen for subsequent quantitation of CheY by Western
blot determinations. CheY expression increased with IPTG
concentration from a basal level of ~700 CheY/cell in the
absence of IPTG to ~35 000 CheY/cell in cells grown in
50 µM IPTG (Figure 1, inset). The total protein per cell,
as well as the number of flagella per cell (6.7 Ϯ 0.5,
mean and SE for 25 cells), did not measurably vary with
CheY expression.
Tethered cells
To measure the rotation of single flagellar motors, cells
were tethered to coverslips coated with anti-flagella antiserum
and analyzed by computerized image-processing.
The analysis included all rotating cells in a field of
view according to uniform criteria, eliminating any bias
introduced by manual cell selection procedures. From the
angular velocity trace for each cell, switches between
CCW and CW motion were determined. Each cell typically
displayed approximately the same absolute angular velocity
in both CW and CCW states. The average fraction
of time spent turning CW, fCW, increased with increasing
CheY concentration with an apparent Hill coefficient of
3.5 Ϯ 1.0 (Figure 1). The switching process was further
characterized by the mean duration of CW and CCW
intervals (Figure 2). As expected, the mean CW duration
increased and the mean CCW duration decreased with
increasing P-CheY concentration. These results are similar
to those of Kuo and Koshland (1989) who measured the
effects of CheY expression in a strain that contained an
incomplete deletion from cheA to cheZ that produces a
fragment of CheA that is not subject to receptor activation.
Because of the kinase deficiency, one might assume that
relatively low levels of P-CheY were present in these
experiments. Our results indicate that, in fact, a large
fraction of the CheY must have been phosphorylated in
these cells. A kinetic analysis based on in vitro rate
estimates is consistent with this interpretation (Table II).
A recent study showed a similar dependence of motor
rotation on the level of an activated CheY mutant (Scharf
U.Alon et al.
Table I. Strains and plasmids
Comment Source
Strain
RP437 wild-type for chemotaxis, lacY–, ara– J.S.Parkinson
PS2001 ∆cheBcheYcheZ this study
PS2002 ∆cheA–cheZ, ‘gutted strain’ this study
RP1616 ∆cheZ J.S.Parkinson
Plasmid
pHSG576 low copy, CmR Takeshita et al. (1987)
pLC576 low copy, cheY under lac promoter, CmR this study
pMS164 low copy, cheYD13K under lac promoter, CmR this study
pMS168 medium copy, cheYD57A under araBAD promoter, AmpR this study
Table II. Estimates of fraction of CheY phosphorylated in various strains, based on in vitro rate constants
Strain Kinase CheA autophosphorylation Fraction of CheY phosphorylated
activity, kA (s–1)
PS2001–pLC576 20 0.9995
RP1616 (∆cheZ) 13 0.9990
Kuo and Koshland (1987, 1989) 0.1 0.5–0.9
The relevant reactions are: CheA ϩ MgATP – kA → P-CheA ϩ MgADP; P-CheA ϩ CheY ← KD → P-CheA–CheY – ktrans → CheA ϩ P-CheY;
and P-CheY – kY → CheY ϩ Pi. The fraction of CheY phosphorylated was calculated from the steady state equation: kYϫ[P-CheY] ϭ kA[CheA]
([CheY]total – [P-CheY])/([CheY]total – [P-CheY] ϩ KD). Measurements with purified components indicate that the equilibrium dissociation constant
for CheY binding to P-CheA, KD, is ~2 µM (Li et al., 1995; Shukla and Matsumura, 1995), the phosphotransfer reaction from P-CheA to CheY is
not rate-limiting (ktrans Ͼ600/s; Stewart, 1997), and the rate of P-CheY dephosphorylation in the absence of CheZ is relatively slow, kY ~0.04/s
(Hess et al., 1988; Lukat et al., 1991). Estimated rate constants for CheA autophosphorylation at saturating MgATP, kA, in PS2001–pLC576 and in
RP1616 correspond to values measured for CheA in complexes with CheW and the fully modified (all Q) or half modified (QEQE) receptor
signaling domains, respectively (Borkovich et al., 1992; Liu et al., 1997). The strain used by Kuo and Koshland (1989) expressed a CheA–CheZ
fusion that is not subject to receptor activation. The value of kA in the Kuo and Koshland experiments is thus assumed to correspond to that of pure
CheA in the absence of receptor (Tawa and Stewart, 1994; Surette and Stock, 1996). The level of CheA in E.coli has been estimated to be ~5 µM
(Wang and Matsumura, 1997). The calculated values for fraction of CheY phosphorylated are essentially constant over the range of total CheY
concentrations used in these studies (Ͻ100 µM) in the case of PS2001–pLC576 and RP1616, but with the much lower kinase activity in the strain
used by Kuo and Koshland the fraction of CheY phosphorylated is expected to vary with total CheY as indicated.
et al., 1998; Figure 1). This indicates that the mutant has
approximately the same activity as P-CheY.
Motor behavior displays significant variations from
cell to cell (Berg and Tedesco, 1975; Spudich and
Koshland, 1976; Ishihara et al., 1983; Eisenbach et al.,
1990; Levin et al., 1998). We found that in PS2001–
pLC576, at levels of CheY induction that caused
approximately wild-type motor bias, a distribution of
behaviors similar to wild-type was observed (Figure 3).
This suggests that the plasmid system used in the
present study does not introduce fluctuations between
cells larger than those found naturally.
Swimming cells
Swimming behavior of cells was determined using the same
cultures that were used to analyze the rotation of tethered
motors. Cells were placed between a glass slide and a cover
slip in a thin fluid layer of ~10 µm thickness. Their motion
was observed by dark-field microscopy and recorded on
videotape. The cells remained in the focal plane of the
microscope at all times. The videotapes were analyzed by a
computerized image analysis method developed to acquire
extensive statistics on various aspects of swimming
behavior. As expected, in the absence of CheY no tumbles
were observed and cells tumbled with increasing
frequency as P-CheY increased (Figure 4A–C). At very
high levels of induction, however, the cells actually became
4240
less tumbly (Figure 4D). At low CheY concentrations, the
tumble frequency increased in a weakly sigmoidal fashion
with an apparent Hill coefficient of 2.5 Ϯ 1 (Figure 5). The
maximal degree of tumbling, 1.8 Ϯ 0.1 tumbles/s, was
observed at CheY concentrations of ~50 µM. At higher
CheY concentrations, cells tumbled less, dropping to ~1.4
tumbles/s at 100 µM CheY. It seems probable that this
decrease in tumbling frequency at CheY concentrations
Ͼ50 µM is due to runs caused by the formation of CW
rotating rather than CCW rotating flagella bundles (Wolf
andBerg,1989).TheexistenceofsuchCWbundlesandtheir
ability to support runs has previously been demonstrated in
strains with mutations that lock the motor in a CW state
(Khan et al., 1978). The average run speed decreased
slightlywithincreasingCheYlevels(Figure6),witharather
sharp drop to ~50% of the maximal run speed at CheY
concentrations Ͼ50 µM. The initial gentle decrease in run
speed with increasing tumbling frequency is probably due
to the fact that the cell speed takes a certain amount of time
to recover from each tumble (Berg and Brown, 1972).
We also measured the duration of run and tumble
events. The mean run duration decreased with increasing
CheY concentration until a minimum was reached at a
CheY concentration of ~50 µM (Figure 7B). In contrast,
the duration of tumbling intervals remained approximately
constant at 0.20 Ϯ 0.05 s over the entire range of CheY
induction (Figure 7A).
Response regulator output in bacterial chemotaxis
Fig. 1. Fraction of time tethered cells spend turning CW (fCW). Cells
induced with various amounts of IPTG were tethered and their motion
was analyzed using video tracking. Each point is an average of data
from 15–40 different tethered cells, analyzed for 100 s each. Open
circles, strain PS2001–pLC576; solid circle, wild-type strain RP437–
pHSG576. Error bars correspond to standard error of the mean. Solid
line, fit to the allosteric model (see Discussion). The model parameters
are: N ϭ 30 binding sites for P-CheY, allosteric constant of L0 ϭ 107,
dissociation constant for P-CheY binding K ϭ 7.6 µM and ratio of
binding affinity to CW and CCW states Ψ ϭ 2.0. Dashed line,
allosteric model with K ϭ 12.5 µM and Ψ ϭ 2.3, a best fit to the data
of Scharf et al. (1998), where tethered-cell CW bias was measured as
a function of the concentration of the activated CheY mutant
CheYD13KY106W. Inset, intracellular CheY concentrations as a
function of IPTG induction of strain PS2001–pLC576. The number of
CheY molecules/cell were determined using Western blots. CheY
intracellular concentration was calculated assuming that 1000
molecules/cell correspond to 2.8 µM (Scharf et al., 1998). The line is
a smooth fit.
Fig. 2. Mean duration of CCW (A) and CW (B) intervals of tetheredcell
rotation in PS2001–pLC576, as a function of intracellular CheY
concentration.
Estimates of P-CheY levels in strains that contain
wild-type levels of CheY
In order to estimate the fraction of CheY that is phosphorylated
in wild-type cells, we employed the computerized
tethering and swimming assays on strain
RP437, the parental strain of all mutants used here, which
4241
Fig. 3. Distribution of CW bias between different individual cells.
Plotted is the fraction of time spent CW, fCW, divided by the mean of
fCW over all cells with the same CheY induction level, ϽfCWϾ. White
bars, cumulative data from PS2001–pLC576 cells induced to a level of
~10, 14 and 20 µM CheY. Shaded bars, wild-type cells RP437–
pHSG576. Error bars represent standard errors of the mean.
Fig. 4. Paths of swimming cells expressing varying amounts of
P-CheY. Each path represents the trajectory of an individual bacterium
over an average of ~2 s. (A) Strain deleted for cheB, cheY and cheZ
(PS2001), the bar is 100 µm long, (B) PS2001–pLC576 expressing
10 Ϯ 2 µM CheY, (C) PS2001–pLC576 expressing 60 Ϯ 10 µM
CheY, (D) PS2001–pLC576 expressing 100 Ϯ 20 µM CheY,
(E) RP437–pHSG576 (wild-type) and (F) RP1616–pHSG576 (∆cheZ).
is wild-type for chemotaxis. We determined the total
amount of CheY in RP437 under the present experimental
conditions to be 17 500 Ϯ 1000 molecules/
cell (average Ϯ SE of eight independent measurements),
corresponding to a cytoplasmic concentration of
~49 Ϯ 3 µM. This is close to the CheY levels in
Salmonella typhimurium (15 000–20 000 CheY/cell; Stock
et al., 1985; Zhao et al., 1996), but is ~3-fold higher than
the value previously determined for the copy number in
E.coli (Kuo and Koshland, 1987), perhaps due to the
different growth conditions used in that study. In tethering
assays, RP437 spent 0.22 Ϯ 0.05 of the time turning CW
(Figure 1). PS2001–pLC576 cells exhibited an equivalent
behavior at a CheY concentration of ~13.5 Ϯ 1 µM. Thus,
in wild-type cells under these steady-state conditions
~30% of the intracellular pool of CheY is phosphorylated.
The same conclusion was obtained from an analysis of
swimming behavior. Wild-type cells exhibited a tumbling
U.Alon et al.
Fig. 5. Tumbling frequency as a function of CheY concentration. Open
circles, PS2001–pLC576 induced with various amounts of IPTG; solid
circle, wild-type (RP437–pHSG576); solid triangle, ∆cheZ (RP1616–
pHSG576) cells. The tumbling frequency is the total number of
tumbles detected by the computerized algorithm, divided by the total
duration of all paths. The error bars represent standard errors of the
mean. Solid line, fit to a Hill equation, with Hill coefficient of 2.5 and
half maximal effect at 18.8 µM. Dashed line, guide to the eye.
Fig. 6. Run speed as a function of CheY concentration in strain
PS2001–pLC576 (open circles), wild-type (RP437–pHSG576) (solid
circle) and ∆cheZ (RP1616–pHSG576) cells (solid triangle). Run
speed is defined as the mean of the top 10% of the speeds along each
bacterial trail, averaged over all trails. Shown are means Ϯ SE of the
mean.
frequency of 0.53 Ϯ 0.05/s, and PS2001–pLC576 cells
display the same tumbling frequency when the concentration
of CheY is 13 Ϯ 1 µM. Thus, the swimming assay
also suggests that ~30% of the CheY is phosphorylated
in RP437. The tumbling behavior and level of CheY
expression in RP437 were not affected by the presence of
the plasmid pHSG576, nor by growth in the presence of
50 µM IPTG (data not shown).
The swimming speed measured for wild-type cells
(RP437) was 16.5 Ϯ 1.0 µm/s (Figure 6). This is in good
agreement with previous measurements where the cells
were tracked near a glass slide (Amsler et al., 1993; Khan
et al., 1993), though it is lower than some measurements
of the run speed by three-dimensional tracking of cells
4242
Fig. 7. Mean duration of tumbles (A) and runs (B), as a function of
CheY concentration in PS2001–pLC576 in the wild-type strain
(RP437–pHSG576) (solid circle) and ∆cheZ (RP1616–pHSG576) cells
(solid triangle).
swimming far from any surface (Lowe et al., 1987). In
the present assay, the cells swim in a thin fluid layer at a
distance of at most ~5 µm from a surface. Evidently, this
has an effect on cell motion as compared with motion in
a free solution (Ramia et al., 1993; Frymier et al., 1995;
Vigeant and Ford, 1997). This of course should not affect
the use of the present method as a read-out of the
intracellular P-CheY levels.
The swimming behavior of RP1616–pHSG576 was also
measured. This strain lacks the CheY phosphatase CheZ.
Because of the CheZ defect, P-CheY levels are expected
to be high in this strain (Table II), and in fact its tumbling
frequency, 1.7 Ϯ 0.1/s, is approximately equal to the
maximal tumbling frequency of PS2001–pLC576 corresponding
to wild-type levels of CheY (Figure 5). Thus, the
observed RP1616 tumbling rate is consistent with the
assumption that it contains a wild-type amount of CheY
protein, essentially all in the phosphorylated state.
In vivo function of cheY mutants
The relation between P-CheY and tumbling frequency
allowed us to compare quantitatively the in vivo activity
of CheY mutants with that of wild-type P-CheY. Various
amounts of the mutant proteins were expressed from
inducible promoters, protein expression was quantified
and swimming behavior was measured using the same
procedure as for wild-type CheY. Two mutants were
studied: CheYD13K, an activated mutant that causes
tumbling in the absence of phosphorylation (Bourret
et al., 1993), and CheYD57A, a mutant that cannot be
phosphorylated. The corresponding mutant genes were
cloned into expression plasmids (Table I): cheYD13K was
cloned into the low-copy vector pHSG576 under lac
control, and cheYD57A into a complementary multicopy
plasmid under an arabinose inducible promoter. The
plasmids were transformed separately and together into
the ‘gutted’ strain PS2002 that contains no Che genes
(deleted from the beginning of cheA to the end of cheZ).
Whereas the activated mutant CheYD13K caused tumbling
(Figure 8), CheYD57A induced no tumbles even at
Response regulator output in bacterial chemotaxis
Fig. 8. Tumbling frequency as a function of mutant CheY proteins
expressed in the gutted strain PS2002 which is deleted for cheA–cheZ.
Open circles, PS2002–pMS164 induced with various amounts of IPTG
expressing CheYD13K; solid circles, PS2002–pMS164–pMS168
induced with various amounts of IPTG expressing CheYD13K and
CheYD57A, the latter induced with 0 µM arabinose; open squares,
PS2002–pMS164–pMS168 induced with 100 µM arabinose and
varying amounts of IPTG (CheYD13K coexpressed with CheYD57A,
the latter at an intracellular concentration of 260 Ϯ 40 µM). The solid
and dashed lines represent the tumbling frequency induced by wildtype
CheY in strain PS2001 (from Figure 5).
intracellular concentrations Ͼ200 µM (data not shown).
Moreover, swimming behavior as a function of CheYD13K
concentration was not affected by simultaneous expression
of Ͼ200 µM CheYD57A (Figure 8). Thus, unphosphorylated
CheY does not appear to compete with active CheY
for binding to the motor, and does not appear to cause
either tumbles or runs. This result is consistent with the
in vitro studies of CheY binding to FliM where it has
been shown that CheY binding to the motor switch protein
is substantially enhanced by phosphorylation (Welch et al.,
1993, 1994).
The activated mutant, CheYD13K, had approximately
the same quantitative effect in vivo as P-CheY (Figure 8).
This finding was unexpected; previous in vitro studies
have indicated that CheYD13K binds FliM only marginally
more avidly than unphosphorylated CheY (Welch et al.,
1994), and it has also been shown that the crystal structure
of CheYD13K is similar to that of unphosphorylated
CheY (Jiang et al., 1997). Our results therefore raise the
possibility that CheYD13K behaves somewhat differently
in vivo and in vitro. The measurement of CheYD13K
activity complements a recent study relating tethered
motor rotation to the level of the activated CheY mutant
CheYD13KY106W (Scharf et al., 1998). In that study, a
dependence of CW bias on the activated CheY mutant
level was established, which is quantitatively similar to
the relation we observe between CW bias and wild-type
P-CheY (Figure 1). The similarity in behavior is consistent
with an approximately equivalent activity of CheYD13KY106W
and P-CheY.
Finally, it is worth noting that wild-type CheY expressed
in the gutted strain, PS2002, did not induce tumbling even
at levels of ~100 µM (data not shown). This indicates
that sources of CheY phosphorylation other than the
chemotaxis network are negligible in vivo under the
conditions used.
4243
Discussion
Molecular mechanism of signal transduction
The present study establishes a quantitative relationship
between measurable parameters of cell behavior (motor
rotation, tumbling frequency, speed) and the output of the
chemotaxis signal transduction network (P-CheY). This
enables determination of the P-CheY levels in wild-type
cells (~30% under steady-state conditions) and evaluation
of the activity of CheY mutants. Most importantly, this
relationship forms a basis for the quantitative evaluation
of molecular models of the chemotaxis network. For
instance, we find that swimming behavior is relatively
insensitive to changes in the level of P-CheY (apparent
Hill coefficient ~2.5). Similarly, tethered cell CW bias has
an apparent Hill coefficient of ~3.5. It has been established,
however, that E.coli is highly sensitive to small changes
in attractant concentrations (Berg and Brown, 1972; Segall
et al., 1986; Khan et al., 1993). Attempts to use the known
biochemistry to model chemotaxis have accounted for
this high sensitivity by assuming a highly cooperative
interaction between P-CheY and the motor [apparent Hill
coefficients ranging from 8 to 11 (Ninfa et al., 1991; Spiro
et al., 1997)]. From this discrepancy, we can conclude
that the high sensitivity of the chemotaxis system must
derive from some additional, hitherto undefined, biochemical
interactions in the receptor-mediated control of
CheY phosphorylation.
Relationship between tethered motor rotation and
swimming behavior
We have directly compared the behavior of tethered and
swimming cells under the same conditions. It is wellestablished
that increased CW motor rotation generally
corresponds to a higher tumble frequency. Quantitative
comparisons, however, reveal clear differences (Ishihara
et al., 1983). In tethered cells CW intervals become longer
and CCW intervals become shorter with increasing PCheY
concentration (Figure 2). If there were a direct
correlation between CW rotation and tumbling, one would
expect tumbling intervals to become longer as CW rotation
increases, and this was not observed. The average duration
of tumbles was found to be 0.20 Ϯ 0.05 s, independent
of CheY concentration (Figure 7). This extends the findings
of Berg and Brown (1972), who reported an equal mean
tumble duration (~0.14 s) in several strains, including a
wild-type strain and a tumbly mutant. In contrast, the
mean duration of runs decreased dramatically with PCheY
concentration (Figure 7), from continually running
in the absence of P-CheY down to 0.3 s runs at the
maximally tumbly P-CheY concentration (~50 µM). Thus,
it appears that during chemotaxis the bacteria mainly
modulate the duration of their runs, keeping their
tumbles brief.
It seems likely that the observed lack of correlation
between the duration of CW intervals and tumbles is
primarily due to the details of bundle reformation after a
tumble. In returning to a run state, the flagella must restore
contact with one another and re-assemble into a bundle
(Khan et al., 1978; Macnab, 1996). This may occur
gradually (Berg and Brown, 1972) where first a partial
bundle is formed that begins to propel the cell and the
ensuing fluid velocity sweeps back the other flagella to
U.Alon et al.
re-constitute a full bundle. A crude estimate of the typical
time for such hydrodynamic interactions is the bacterium
length (a few micrometers) divided by its velocity (10–
20 µm/s), yielding a tumble duration of the order of tenths
of seconds. One may view the flagella interactions as an
additional level of information processing in the chemotaxis
response. The result of this processing is that whereas
individual motors display prolonged CW intervals, swimming
cells keep their tumble duration short and independent
of P-CheY. This behavior of swimming cells is close
to the expected optimal behavior. Since it is only during
runs that the bacteria sample their environment and reach
favorable regions, each tumble should be kept as brief as is
necessary to randomize the heading of the subsequent run.
An additional difference between tethered motors and
free-swimming cells is observed at very high P-CheY
levels. Whereas CW rotation increases monotonically
(Figure 1), swimming cells become less tumbly at P-CheY
levels higher than ~50 µM (Figures 4 and 5). This is
probably caused by the runs associated with CW rotating
bundles that have previously been documented in flagella
switch mutants that lock the motor in an extreme CW
state (Khan et al., 1978; Wolfe and Berg, 1989). The
average run speed drops abruptly at high P-CheY levels
to ~50% of the wild-type run speed (Figure 6), in agreement
with the observation that speed generated by CW
bundles is about half the speed generated by CCW bundles
(Khan et al., 1978). It should be noted that CW runs only
predominate at P-CheY levels that exceed the total CheY
content of wild-type cells. At all levels of P-CheY that
could possibly be attained in wild-type cells (i.e. 0 to
~50 µM), the tumbling frequency increases with increasing
P-CheY. It is only at P-CheY levels exceeding the maximal
physiological level that the tumbling frequency begins to
decrease with increasing P-CheY. This latter behavior can
be detrimental since it leads to reverse chemotaxis where
cells move towards repellants and away from attractants
(Khan et al., 1978). Strikingly, the cell appears to have
tuned the signal transduction pathway (kinase activity and
CheY concentration) to give the highest possible maximal
tumbling response that does not carry over to the reverse
chemotaxis regime.
Molecular mechanism of response regulation
There appear to be ~30 potential binding sites for P-CheY
at each motor (Macnab, 1995; Zhao et al., 1996). From
this one might expect a high degree of cooperativity in
P-CheY-induced switching. The motor CW rotation fraction
appears, however, to have a low order dependence
on P-CheY (apparent Hill coefficient, 3.5 Ϯ 1.0; Hill
coefficient of ~4.2 in Scharf et al., 1998). The tumbling
frequency of swimming cells exhibits an even lower
order dependence on P-CheY (apparent Hill coefficient,
2.5 Ϯ 1.0). In order to reconcile the high number of
binding sites with the observed lack of strong cooperativity,
we propose an allosteric model of P-CheY-induced motor
switching. The model extends the model of Macnab (1995)
and related analyses by Block et al. (1983) and Turner
et al. (1996).
The model is based on the classical model of allosteric
enzymes (Monod et al., 1965). The entire motor, a large
multi-protein ensemble, is considered as an allosteric
switch. The motor is assumed to display equilibrium
4244
Fig. 9. Allosteric model for the motor switch. The motor is assumed
to be in one of two states, CCW or CW. It displays spontaneous
stochastic transitions between the states, with a (large) equilibrium
constant L0. The motor is assumed to have N independent, identical
binding sites (represented here by open circles) for P-CheY (stars).
Both of the rotation states can display multiple P-CheY occupancy
states, with between 0 and N sites bound by P-CheY proteins. The
probability of P-CheY binding is not the same for the two states. The
equilibrium dissociation constants for P-CheY binding are K for
binding to the CCW state and K/Ψ for binding to the CW state
(vertical arrows). Transitions between CW and CCW states with m
binding sites occupied by P-CheY occur with equilibrium constants Lm
(horizontal arrows). In the model, P-CheY binds preferentially to the
CW state (Ψ Ͼ1), and thus increasing cytoplasmic concentrations of
P-CheY shift the equilibrium towards a higher fraction of time spent
in the CW state.
stochastic concerted transitions between two discreet conformational
states, CCW and CW (Figure 9). P-CheY is
assumed to bind with greater affinity to the CW state, and
therefore high P-CheY levels shift the equilibrium towards
CW rotation. The fraction of time the motor spends turning
CW is given by the expression:
fCW ϭ [1 ϩ Ψ (P-CheY)/K ]N/[(1 ϩ Ψ [P-CheY]/K )N ϩ
L0 (1 ϩ [P-CheY]/K )N]
where N is the number of P-CheY binding sites in a
motor switch complex, L0 is the equilibrium constant for
spontaneous concerted transitions between the CCW and
CW states (Turner et al., 1996), and K and K/Ψ are
the equilibrium dissociation constants of P-CheY to the
CCW and CW states, respectively. The model can be fit
to the experimental data (Figure 1), using reasonable
values for the parameters. For example, assuming
N ϭ 30 binding sites per motor, and L0 ϭ 107 (Turner
Response regulator output in bacterial chemotaxis
et al., 1996), the best fit value of the P-CheY equilibrium
constant K is 7.6 Ϯ 2 µM, and Ψ, which corresponds to
the ratio in P-CheY binding affinity to the CW and CCW
states, is 2.0 Ϯ 0.2. One important prediction of the model
is that to obtain the observed weak cooperativity with a
large number of P-CheY binding sites implies that there
can only be a relatively small difference in P-CheY affinity
for the CW and CCW states (~2-fold, Ψ ~2). This is
similar to the prediction of a related model by Scharf
et al. (1998), in which the free energy of the CCW state
increases and that of the CW state decreases by a small
amount with each P-CheY bound.
Fitting data to a model does not, of course, constitute
a validation of the model’s assumptions. We hope, however,
that this model can serve as a simple basis for
comparison for future experiments that could shed light
on the switch mechanism. For example, the model supplies
a way of understanding the effects of mutations of Tyr106
in CheY (Zhu et al., 1996). Cells with these mutations
are deficient in chemotaxis despite the fact that these
CheY variants can be phosphorylated and show a phosphorylation-dependent
binding to FliM that is comparable
with the wild-type CheY protein. In view of the
present model, these mutations might affect the preferential
binding of the mutant CheY to the CW state (i.e. these
mutations could affect Ψ). We would predict that a
mutation that caused P-CheY to bind more strongly to the
CCW state would be a dominant suppressor of tumbling
caused by wild-type CheY. The idea that differential
binding to the two motor states is required for switching
could explain the observation that the binding of P-CheY
to the motor and the generation of tumbles appear to be
mutationally separable events (Bourret et al., 1990; Welch
et al., 1994; Ganguli et al., 1995).
Conclusions
Previous work has elucidated many of the quantitative
interactions of chemotaxis network components, as well
as many aspects of behavioral physiology. The present
work connects these two modes of description by
establishing the precise dependence of measurable cell
behavior on the response regulator output of the signal
transduction network (P-CheY). This allows the direct
experimental assessment of theoretical analyses, and
allows the identification of gaps in our understanding of
the biochemistry of chemotaxis signal transduction. For
instance, we can now say that the molecular mechanisms
responsible for the high sensitivity of the chemotaxis
system to small changes in attractant stimuli are yet to be
elucidated.
Materials and methods
Bacterial strains and plasmids
All strains were derived from an E.coli K-12 derivative, RP437, which
is wild-type for chemotaxis. RP437 and RP1616 (∆cheZ) were obtained
from Dr J.S.Parkinson. The strains PS2001 (∆cheBcheYcheZ) and PS2002
(∆cheA–cheZ) were constructed from RP437 by the overlap extension
method (Ho et al., 1989), using the gene replacement vector pK03 (gift
of Dr G.Church). Briefly, genomic DNA from RP437 was used as
template to amplify two DNA fragments that flank the chemotaxis genes
to be deleted by the polymerase chain reaction (PCR). For PS2001 the
primers cheRF1 (5Ј-CAGGGATCCGAGCGCCTGGCGCTTTCC), and
cheRR1 (5Ј-CTGGTATCGAATTCGTTAATCCTTACTTAGCGC), were
used to amplify a 814 bp cheR fragment that includes the cheR stop
4245
codon; a 1132 bp fragment from the end of cheZ to fhlB was amplified
using the primers cheZF1 (5Ј-GGATTAACGAATTCGATACCAGCAAAGCCGGTG),
and flhBR1 (5Ј-CTCGCTGCATCTGACGGATCCGCC).
For construction of PS2002, a 634 bp fragment from motB
that includes the stop codon of motB, was amplified using the primers
motBF1 (5Ј-CGTGGATCCGCAGCCGAACATCGAAGAGCTG), and
motBR1 (5Ј-GTATCGACCGAATTCTGTCACCTCGGTTCGGCTG); a
757 bp fragment from the end of cheZ to the middle of flhB was obtained
using the primers cheZF2 (5Ј-GTGACAGAATTCGGTCGATACCAGCAAAGCCGG)
and flhBR2 (5Ј-GAAGGATCCCCGTCACGCTGCCAACCAGG).
These fragments were purified and cloned into pTZ19R
(Pharmacia) which has been previously modified to eliminate the
recognition sequence of EcoRI endonuclease. A resistance marker (KanR)
was cloned into an EcoRI site present in the linker region used to
generate the deleted fragment. The complete insert was excised using
BamHI, and ligated into the BamHI site in pKO3. The resulting construct
was used to transform RP437 selecting for Kan resistance. At its nonpermissive
temperature (42°C), pKO3 cannot replicate and genomic
integrants are selected. At the permissive temperature (30°C) recombinants
are selected that have lost the plasmid. The sequence of all PCRgenerated
fragments was determined to ensure no errors were introduced
in the sequence during the amplification reaction. Confirmation of the
deletions was obtained by PCR.
CheY was expressed under control of lacOP using the low copy
plasmid pLC576 (CmR). This plasmid was engineered by cloning a
DNA fragment encoding E.coli CheY, generated by PCR, into the
polylinker region of pUC-lac1 (Surette and Stock, 1996). A fragment
carrying the lac-Iq gene as well as lacOP-cheY from the resulting
construct was cloned into the polylinker region of the low-copy-number
plasmid pHSG576 (Takeshita et al., 1987). The cheY gene in this plasmid
was sequenced to ensure no errors were introduced during amplification.
The cheYD13K and D57A mutations were generated by site-directed
mutagenesis using standard protocols and subsequently, the cheYD13K
gene was cloned into pLC576 (replacing the wild-type cheY gene) to
generate pMS164 and the cheYD57A gene was cloned into pBAD18
(Guzman et al., 1995) to generate pMS168. We note that a different
unphosphorylatable mutant, CheYD57N, was found to cause some
tumbles when expressed at high levels (data not shown).
Isolation of plasmid DNA was carried out using Qiaprep spin columns
(Qiagen). PCR was performed using Ultima enzyme (Perkin Elmer
Cetus) or Pfu polymerase (Stratagene) according to the supplier’s
instructions. DNA sequencing reactions were done by the dideoxy method
using modified T7 DNA polymerase Sequenase (UA Biochemical) or
were carried out by the Oligonucleotide Sequencing/Synthesis Facility,
Department of Molecular Biology, Princeton University, NJ.
Behavioral assays
Strains were grown overnight in Tryptone broth (1.3% Bacto tryptone
and 0.7% NaCl) at 30°C and diluted 1:50 into Tryptone broth supplemented
with selective antibiotics as appropriate. After 1.5 h of growth,
the cultures were induced with IPTG and/or arabinose. The cells were
harvested at mid-log phase (OD600 ϭ 0.50 Ϯ 0.03, corresponding to
5.3ϫ108 Ϯ 0.3ϫ108 cells/ml). A sample from each culture was
pelleted and frozen at –20°C for quantitation of CheY (see below).
Cells from 1 ml of culture were harvested by centrifugation at 800 g
for 5 min at room temperature and gently resuspended into 1 ml motility
medium [7.6 mM (NH4)2 SO4, 2 mM MgSO4, 20 µM FeSO4, 0.1 mM
EDTA, 60 mM potassium phosphate pH 6.8], centrifuged at 800 g for
5 min at room temperature and gently resuspended in a final volume of
0.5 ml motility medium.
For swimming behavior, 0.5 µl of this suspension was placed on a
glass slide (Gold Seal) in the center of a circle inscribed by a grease
pencil, and covered by a No. 2 coverslip (Corning). This created a fluid
layer of ~10 µm thickness, as estimated from the area of the fluid film.
The cells were thus confined to motion in two dimensions, and could
not move out of the focal plane of the microscope. After 5 min, the
samples were observed with a Zeiss Dialux dark field microscope
mounted with a video camera and swimming behavior was recorded for
several minutes on a JVC S-VHS video recorder. The field of view
spanned 180 µm; 30 s segments of the video were analyzed by
computerized image analysis as described below.
For tether analysis, 400 µl of the cell suspension was passed through
a 28 gauge needle 40–60 times to shear the flagella. The cells were
harvested and washed by centrifugation as described above. A 20 µl
drop of the suspension was placed under a coverslip mounted on a glass
slide and sealed with paraffin. The coverslip (No. 1.5, Corning) was
pretreated with anti-flagellin polyclonal antibodies for 20 min and then
U.Alon et al.
washed with motility media. The cells were allowed to attach to the
coverslip for 15–30 min. The tethered cells were observed with a Zeiss
Dialux dark-field microscope mounted with a video camera and behavior
was recorded for several minutes for each of several fields of view on
a JVC S-VHS video recorder. Segments of the video were analyzed as
described below.
Preliminary experiments showed that cells washed into another commonly
used chemotaxis buffer (67 mM NaCl, 0.1 mM EDTA, 10 mM
potassium phosphate pH 7.0; Scharf et al., 1998) displayed the same
tumbling frequency as cells washed into the present motility medium.
In general, however, when comparing results from chemotaxis assays
performed under different conditions, it is worth noting that there
are factors that can affect motor behavior independently of CheY
phosphorylation (Khan and Macnab, 1980; Montrone et al., 1996; Turner
et al., 1996; Barak et al., 1998).
Computerized image analysis of swimming cells
Video images at 30 frames/s, at a resolution of 640ϫ480 pixels, were
loaded into computer memory using a Silicon Graphics Indy workstation
with a Cosmo real-time video compression/decompression board. Images
were digitally thresholded, and clusters of pixels above the threshold
intensity were detected and their center of mass was recorded, each
representing one bacterium. Bacteria in successive frames were grouped
into ‘trails’, where each trail represented the trajectory of a bacterium.
Trails were terminated when a bacterium left the screen or overlapped
with another cell. This software was implemented in Cϩϩ. Tumbles
were detected by processing trail data with an algorithm implemented
in Matlab (Mathworks). The algorithm extends the computerized tumbledetector
of Amsler (1996), allowing accurate quantitation of tumbles in
a wide range of phenotypes from continually running to very tumbly.
The tumble-detection software accepted a file containing the list of
bacteria center of mass positions for each trail. Trails shorter than 1 s
were discarded. In order to reduce the noise in the data, and yet to
preserve sharp transitions in the bacteria trajectory, the trails were filtered
using a modified median filter. In this filter, a window of five time points
is considered, the five are sorted and the filtered value is given by the
average of the central three sorted points. The speed of each bacterium
as a function of time, V, is calculated, as is the rate of change of
direction (RCD; angular velocity) of the trajectory: RCD ϭ |AxVy –
VxAy|/V2, where Vx and Vy are the x and y components of the velocity,
and Ax and Ay are the x and y components of the bacteria acceleration.
RCD (Khan et al., 1992) has units of rad/s. RCD was employed for
characterizing the chemotactic response of wild-type and mutant bacteria
in recent studies (Khan et al., 1993, 1995).
Plotting the bacterial speed as a function of time reveals a signal
which can be roughly characterized by two states: periods of high speed
(Ͼ10 µm/s) are punctuated by short spans of low speed (Ͻ5 µm/s). The
angular velocity, RCD, has the inverse behavior: it tends to be low (of
the order 0.1 rad/s) when the bacterium is fast, and displays pronounced
peaks (of the order 1–10 rad/s), which represent rapid reorientation of
the bacterium’s heading, correlated with low V intervals. In the tumble
detection algorithm, the high V, low RCD regions are identified as runs,
and the low V, high RCD intervals as tumbles. The following criterion
is used. The run speed, VR, for each trail is defined as the average of
the top 10% of the speed in the trail. A tumble is detected at times when
both V Ͻ0.5ϫVR and RCD Ͼ3 rad/s. These threshold values were
selected so that the tumble detector agrees best with manually collected
data. Comparing the tumble detector with a set of 200 manually analyzed
trails of wild-type RP437 bacteria, each on average 5 s long, the
algorithm correctly identifies 96% of the tumbles, and has an additional
5% ‘false-positive’ detections where no tumble was observed by eye. In
addition, a manual estimate of the tumbling rate was performed in
parallel to the automatic analysis, for PS2001–pLC576 cells in which
P-CheY was induced to yield cells which span the entire range of
phenotypes from continually running to highly tumbly. In each recording,
the tumble frequency was manually measured by counting the number
of tumbles that occur in 20 different cells, each followed for a 5 s
interval. The discrepancy between the manual and the computerized
mean tumble frequency was Ͻ20% in all cases. The sensitivity of the
results to the tumble detection threshold values was checked on the 200
wild-type trail data set. The value of the speed threshold could be
changed between 0.4ϫVR and 0.6ϫVR yielding a Ͻ10% change in the
tumble frequency and a 15% change in the mean tumble duration. The
RCD threshold could be varied in the range 1.5–6 rad/s, with a Ͻ10%
change in tumble frequency and a Ͻ30% change in mean tumble
duration. The detection of a tumble is less sensitive to the precise
definition of a tumble than the measurement of the tumble duration.
4246
Video movies of some of the cells were analyzed at double the temporal
resolution, 60 frames/s, and the same mean tumble duration was obtained.
Cells adhering to the coverslip or slide were automatically discarded
by the software. The criterion for rejection was that the maximal
displacement of the bacterium during a trail is Ͻ5 µm. In addition, some
small percentage of the population swam in an abnormal jittery fashion,
presumably due to some defect in the cell or its flagella (Dowd and
Matsumura, 1997). These cells could contribute significant fluctuations
to the tumble frequency if not discarded. Therefore, the trails were
sorted by tumble frequency, and the top and bottom 10% were discarded.
This criterion eliminated outlier cells and improves the reproducibility
of the tumble detector.
Computerized image analysis of tethered cells
Video movies of the tethered cells were recorded on a VCR. The video
movies were analyzed by computerized image-processing, at a rate of
60 frames/s, using the same software as for the swimming cells. The
trails were not subjected to filtering with the modified median filter, in
order to increase the temporal resolution of the system, and to detect
rapidly turning cells. The RCD of all cells in the field of view was
calculated as described above. Rotating cells were selected according
to the following criterion: the position of the peak in the distribution
of angular velocities of the cell had to be greater in absolute value
than 2 Hz (RCD Ͼ4 π rad/s). This effectively rejects stuck and diffusing
cells, since their angular velocity is strongly peaked at zero. A field of
view typically contained 20–100 motionless bacteria, and one to four
rotating tethered bacteria. One hundred-second movies of each field of
view were analyzed. Some rotating cells intermittently paused or got
stuck (Eisenbach et al., 1990). These intervals were discarded from the
analysis. The statistics of the tethered-cell motion were analyzed using
specially written Matlab software. CCW intervals corresponded to a
negative RCD, and CW intervals to a positive RCD. We estimate that
the shortest interval detectable by this system is ~50 ms (three frames).
CheY quantitation
We determined the total amount of CheY in RP437–pHSG576 under
the present experimental conditions to be 17 500 Ϯ 1000 molecules/cell
(average Ϯ SE of eight independent measurements) as follows. Cell
density was determined by viable cell count on nutrient agar. A 1.0 ml
sample from each culture was pelleted, resuspended in gel loading
buffer, boiled for 10 min at 100°C, and subjected to 15% SDS–PAGE.
Standards were prepared by adding known amounts of purified CheY to
the same number of cells of the gutted strain, PS2002–pHSG576. Each
gel contained two sets of three or four standards, and duplicate sample
lanes. Proteins were transferred to nitrocellulose membranes (0.2 µm;
Millipore) and probed with affinity-purified rabbit anti-CheY antibodies.
The immunoblots were assayed using the Western Star chemiluminescence
kit (Tropix) and exposed to X-Omat film (Kodak). Band
intensities were quantitated by scanning the developed film and analyzing
the images with NIH-Image software. Levels of CheY expression in all
other strains were determined relative to those in the wild-type, RP437–
pHSG576. Samples from these strains that had been stored frozen at
–20°C were resuspended in lysis buffer (0.9% NaCl, 0.75% SDS) and
boiled for 10 min at 100°C. Total protein was determined using the
BCA assay (Pierce) with BSA standards prepared in lysis buffer. Aliquots
of 8 µg of protein from each sample were subjected to 15% SDS–PAGE.
Samples with levels of CheY greater than wild-type were first diluted
with extracts prepared from the gutted strain, PS2002–pHSG576.
Standards which bracket the samples, each containing 8 µg of protein,
were run on the same gels. These were prepared by mixing various
amounts of wild-type RP437–pHSG576 with gutted cell extract. Each
gel contained two sets of three or four standards, and duplicate sample
lanes. Proteins were transferred to nitrocellulose membrane and estimates
of CheY levels were determined as described above. The amount of
CheY per cell was then calculated using the above measurement for the
wild-type CheY level. Concentrations of mutant CheY proteins were
measured using the same procedure, against RP437 standards mixed
with appropriate amounts of PS2002–pHSG576. In all immunoblot
quantitations, the intensity of the standard bands was linear with the
CheY content of the standards, and the standards bracketed the sample
intensities. The CheY levels presented are the averages of several
independent determinations. CheY concentrations were calculated
assuming that 1000 molecules/cell correspond to a concentration of
2.8 µM (Scharf et al., 1998). Total protein per cell was not affected by
CheY expression, as determined using the BSA assay (Pierce) against
BSA standards prepared in lysis buffer.
Response regulator output in bacterial chemotaxis
Electron microscopy
The number of flagella per cell was determined for RP437 and IPTGinduced
PS2001–pLC576 cells grown as for the behavioral assays. Cells
were harvested at 800 g and resuspended gently in motility medium.
The cells were allowed to attach to a Formvar-coated grid for 2 min,
and then stained with 1% uranyl acetate. Flagella were counted as the
number of filaments that emerge from the cell body; at least 25 cells
from each growth condition were registered.
Modeling the motor switch
Here we give further details of the allosteric model of the motor switch
described in the Discussion and Figure 9. Let [CCWm] denote the
probability that the motor is in the CCW state with m P-CheY proteins
bound, and [CWm] denote the probability that the motor is in the CW
state with m P-CheY bound, with m in the range 0–N. At equilibrium,
the ratio between these probabilities is given by [CCWm]/[CWm] ϭ Lm.
P-CheY binding is described by equilibrium dissociation constants, with
[CCWm–1]ϫ[P-CheY]/[CCWm] ϭ K, and [CWm-1]ϫ[P-CheY]/[CWm] ϭ
K/Ψ, where [P-CheY] is the cytoplasmic concentration of P-CheY.
Detailed balance considerations, relating the equilibrium constants along
closed loops in the reaction diagram (Figure 9), show that Lm ϭ L0/Ψm
(Turner et al., 1996). Thus the model is determined by four parameters:
N, the number of binding sites; K, the binding constant of P-CheY to
the CCW state; Ψ, the ratio between binding to the CW and CCW
states; and L0, the ‘allosteric’ constant, which corresponds to spontaneous
switches of the motor in the absence of CheY. Taking into account the
combinatorial factor corresponding to the number of patterns of site
occupancy that apply to each state, one finds that [CWm] ϭ [CW0]ymΨm
N!/m! (N – m)!, and [CCWm] ϭ L0[CW0]ym N!/m! (N – m)!, where
y ϭ [P-CheY]/K. The fraction of time the motor spends turning clockwise
is given by equation 1 (see Discussion). This equation is identical to the
equation describing classical allosteric enzymes (Monod et al., 1965),
despite some minor differences in the model formulation. The CCW
state corresponds to the ‘R’ state and the CW state to the ‘T’ state in
the original allosteric model. The model could be used to fit the
experimental data for fCW (Figure 1). Satisfactory fits can be obtained
for a range of the values of the parameters L0 and N. In particular, any
number of binding sites greater than five and allosteric constants larger
than ~103 allow fits of similar quality to that shown in Figure 1. In
Figure 1, the values N ϭ 30 and L0 ϭ 107 were chosen based on
previous estimates (Macnab, 1995; Turner et al., 1996). Once N and L0
are chosen, the best-fit value of the other two parameters, K and Ψ, are
found to fall in a more restricted range. For N in the range 5–100 and
L0 in the range 103–109, the range of K and Ψ variation is K ϭ 2–
12 µM and Ψ ϭ 1.1–2.5. When varying the measured tethered data
within its error bars, the standard deviation of the best-fit parameters is
10–20%. The best-fit value of Ψ becomes closer to 1 with increasing
number of binding sites. The model curve in Figure 1 that corresponds
to the data of Scharf et al. (1998) is a best fit, using N ϭ 30 and L0 ϭ
107, to eqn 3 of Scharf et al. (1998), with the parameters ∆G0 ϭ 14.4
kT, Mr ϭ 23.1 kT, and KD ϭ 9.1 µM as given in that paper. Best fits
were carried out using the fmins function of Matlab 4.2 (Mathworks),
using default settings.
Acknowledgements
We thank J.S.Parkinson for bacterial strains, and R.Macnab, L.Turner,
H.C.Berg, S.Block, J.P.Dowd, M.Elowitz, P.Cluzel, C.Guet and N.Barkai
for helpful discussions. U.A. was supported by Rothchild and Markee
fellowships. L.C. was supported by a Pew fellowship. This work was
supported by PHS grant AI20980 (to J.B.S.).
References
Amsler,C.D. (1996) Use of computer-assisted motion analysis for
quantitative measurements of swimming behavior in peritrichously
flagellated bacteria. Anal. Biochem., 235, 20–25.
Amsler,C.D., Cho,M. and Matsumura,P. (1993) Multiple factors
underlying the maximal motility of Escherichia coli as cultures enter
post-exponential growth. J. Bacteriol., 175, 6238–6244.
Barak,R., Abouhamad,W.N. and Eisenbach,M. (1998) Both acetate kinase
and acetyl coenzyme A synthetase are involved in acetate-stimulated
change in the direction of flagellar rotation in Escherichia coli.
J. Bacteriol., 180, 985–988.
Barkai,N. and Leibler,S. (1997) Robustness in simple biochemical
networks. Nature, 387, 913–917.
4247
Berg,H.C. and Brown,D.A. (1972) Chemotaxis in Escherichia coli
analyzed by three-dimensional tracking. Nature, 239, 500–503.
Berg,H.C. and Tedesco,P. (1975) Transient response to chemotaxis
stimuli in Escherichia coli. Proc. Natl Acad. Sci. USA, 72, 3235–3239.
Borkovich,K.A., Alex,L.A. and Simon,M.I. (1992) Attenuation of
sensory receptor signaling by covalent modification. Proc. Natl Acad.
Sci. USA, 89, 6756–6760.
Bourret,R.B., Drake,S.K., Chervitz,S.A., Simon,M.I. and
Falke,J.J. (1993) Activation of the phosphosignaling protein CheY. 2.
Analysis of activated mutants by F19 NMR and protein engineering.
J. Biol. Chem., 268, 13089–13096.
Block,S.M., Segall,J.E. and Berg,H.C. (1983) Adaptation kinetics in
bacterial chemotaxis. J. Bacteriol., 154, 312–323.
Bray,D. and Bourret,R.B. (1995) Computer analysis of the binding
reactions leading to a transmembrane receptor-linked multiprotein
complex involved in bacterial chemotaxis. Mol. Biol. Cell, 6, 1367–
1380.
Bray,D., Bourret,R.B. and Simon,M.I. (1993) Computer simulation of
the phosphorylation cascade controlling bacterial chemotaxis. Mol.
Biol. Cell, 4, 469–482.
Dowd,J.P. and Matsumura,P. (1997) The use of flash photolysis for a
high-resolution temporal and spatial analysis of bacterial chemotactic
behaviour: CheZ is not always necessary for chemotaxis. Mol.
Microbiol., 25,295–302.
Eisenbach,M. (1996) Control of bacterial chemotaxis. Mol. Microbiol.,
20, 903–910.
Eisenbach,M., Wolf,A., Welch,M., Caplan,S.R., Lapidus,R.I.,
Macnab,R.M., Aloni,H. and Asher,O. (1990) Pausing, switching
and speed fluctuation of the bacterial flagellar motor and their relation
to motility and chemotaxis. J. Mol. Biol., 211, 551–563.
Falke,J.J., Bass,R.B., Butler,S.L., Chervitz,S.A. and Danielson,M.A.
(1997) The two-component signaling pathway of bacterial chemotaxis:
A molecular view of signal transduction by receptors, kinases and
adaptation enzymes. Annu. Rev. Cell Dev. Biol., 13, 457–512.
Frymier,P.D., Ford,R.M., Berg,H.C. and Cummings,P.T. (1995) Threedimensional
tracking of motile bacteria near a solid planar surface.
Proc. Natl Acad. Sci. USA, 92, 6195–6199.
Ganguli,S., Wang,H., Matsumura,P. and Volz,K. (1995) Uncoupling
phosphorylation and activation in bacterial chemotaxis: the
2.1 Å structure of threonine to isoleucine mutant at position 87 of
CheY. J. Biol. Chem., 270, 17386–173933.
Guzman,L.M., Belin,D., Carson,M.J. and Beckwith,J. (1995) Tight
regulation, modulation and high-level expression by vectors containing
the arabinose PBAD promoter. J. Bacteriol., 177, 4121–4130.
Hauri,D.C. and Ross,J. (1995) A model of excitation and adaptation in
bacterial chemotaxis. Biophys. J., 68, 708–722.
Hess,J.F., Oosawa,K., Kaplan,N. and Simon,M.I. (1988) Phosphorylation
of three proteins in the signaling pathway of bacterial chemotaxis.
Cell, 53, 79–87.
Ho,S.N., Hunt,H.D., Horton,R.M., Pullen,J.K. and Pease,L.R. (1989)
Site-directed mutagenesis by overlap extension using the polymerase
chain reaction. Gene, 77, 51–59.
Ishihara,A., Segall,J.S., Block,S.M. and Berg,H.C. (1983) Coordination
of flagella on filamentous cells of Escherichia coli. J. Bacteriol., 155,
228–237.
Jiang,M., Bourret,R.B., Simon,M.I. and Volz,K. (1997) Uncoupled
phosphorylation and activation in bacterial chemotaxis. The 2.3 Å
structure of an aspartate to lysine mutant at position 13 of CheY.
J. Biol. Chem., 272, 11850–11855.
Khan,S. and Macnab,R.M. (1980) The steady-state counterclockwise/
clockwise ratio of bacterial flagellar motors is regulated by
protonmotive force. J. Mol. Biol., 138, 563–597.
Khan,S., Macnab,R.M., DeFranco,A.L. and Koshland,D.E.,Jr (1978)
Inversion of a behavioral response in bacterial chemotaxis: explanation
at a molecular level. Proc. Natl Acad. Sci. USA, 75, 4150–4154.
Khan,S., Amoyaw,K., Spudich,J.L., Reid,G.P. and Trentham,D.R. (1992)
Bacterial chemoreceptor signaling probed by flash photorelease of a
caged serine. Biophys. J., 62, 67–68.
Khan,S., Castellano,F., Spudich,J.L., McCray,J.A., Goody,R.S., Reid,G.P.
and Trentham,D.R. (1993) Excitatory signaling in bacteria probed by
caged chemoeffectors. Biophys. J., 65, 2368–2382.
Khan,S., Spudich,J.L., McCray,J.A. and Trentham,D.R. (1995)
Chemotactic signal integration in bacteria. Proc. Natl Acad. Sci. USA,
92, 9757–9761.
Kuo,S.C. and Koshland,D.E.,Jr (1987) Roles of cheY and cheZ gene
products in controlling flagellar rotation in bacterial chemotaxis of
Escherichia coli. J. Bacteriol., 169, 1307–1314.
U.Alon et al.
Kuo,S.C. and Koshland,D.E.,Jr (1989) Multiple kinetic states for the
flagellar motor switch. J. Bacteriol., 171, 6279–6287.
Larsen,S.H., Reader,R.W., Kort,E.N., Tso,W. and Adler,J. (1974) Change
in direction of flagellar rotation is the basis of the chemotactic response
in Escherichia coli. Nature, 249, 74–77.
Levin,M.D., Morton-Firth,C.J., Abouhamad,W.N., Bourret,R.B. and
Bray,D. (1998) Origins of individual swimming behavior in bacteria.
Biophys. J., 74, 175–181.
Li,J., Swanson,R.V., Simon,M.I. and Weis,R.M. (1995) The response
regulators CheB and CheY exhibit competitive binding to the kinase
CheA. Biochemistry, 34, 14626–14636.
Liu,Y., Levit,M., Lurz,R., Surette,M.G. and Stock,J.B. (1997) Receptormediated
protein kinase activation and the mechanism of
transmembrane signaling in bacterial chemotaxis. EMBO J., 16,
7231–7240.
Lowe,G., Meister,M. and Berg,H.C. (1987) Rapid rotation of flagellar
bundles in swimming bacteria. Nature, 325, 637–640.
Lukat,G.S., Lee,B.H., Mottonen,J.M., Stock,A.M. and Stock,J.B. (1991)
Roles of highly conserved aspartate and lysine residues in the response
regulator of bacterial chemotaxis. J. Biol. Chem., 266, 8348–8354.
Macnab,R.M. (1995) Flagellar switch. In Hoch,J.A. and
Silhavy,T.J. (eds), Two Component Signal Transduction. American
Society for Microbiology, Washington DC, pp. 181–199.
Macnab,R.M. (1996) Flagella and motility. In Neidhardt,F.C. et al. (eds),
Escherichia coli and Salmonella, Cellular and Molecular Biology.
ASM press, Washington DC, pp. 123–145.
Monod,J., Wyman,J. and Changeux,J.P. (1965) On the nature of allosteric
transitions: a plausible model. J. Mol. Biol., 12, 88–118.
Montrone,M., Oesterhelt,D. and Marwan,W. (1996) Phosphorylationindependent
bacterial chemoresponse correlate with changes in the
cytoplasmic level of fumarate. J. Bacteriol., 178, 6882–6887.
Ninfa,E.G., Stock,A., Mowbray,S. and Stock,J. (1991) Reconstitution of
the bacterial chemotaxis signal transduction system from purified
components. J. Biol. Chem., 266, 9764–9770.
Ramia,M., Tullock,D.L. and Phan-Thien,N. (1993) The role of
hydrodynamic interaction in the locomotion of microorganisms.
Biophys. J., 65, 755–778.
Sager,B.M., Sekelsky,J.J., Matsumura,P. and Adler,J. (1988) Use of a
computer to assay motility in bacteria. Anal. Biochem., 173, 271–277.
Segel,L.A., Goldbeter,A., Devreotes,P.N. and Knox,B.E. (1986) A
mechanism for exact sensory adaptation based on receptor
modification. J. Theor. Biol., 120, 151–179.
Scharf,B.E., Fahrner,K.A., Turner,L. and Berg,H.C. (1998) Control of
direction of flagellar rotation in bacterial chemotaxis. Proc. Natl Acad.
Sci. USA, 95, 201–206.
Shukla,D. and Matsumura,P. (1995) Mutations leading to altered CheA
binding cluster on a face of CheY. J. Biol. Chem., 270, 24414–24419.
Spiro,P.A., Parkinson,J.S. and Othmer,H. (1997) A model of excitation
and adaptation in bacterial chemotaxis. Proc. Natl Acad. Sci. USA,
94, 7263–7268.
Spudich,J.L. and Koshland,D.E.,Jr (1976) Non-genetic individuality:
chance in the single cell. Nature, 262, 467–471.
Stewart,R.C. (1997) Kinetic characterization of the phosphotransfer
between CheA and CheY in the bacterial chemotaxis signal
transduction pathway. Biochemistry, 36, 2030–2040.
Stock,A., Koshland,D.E.,Jr and Stock,J.B. (1985) Homologies between
S.typhimurium CheY and proteins involved in regulation of
chemotaxis, membrane protein synthesis and sporulation. Proc. Natl
Acad. Sci. USA, 82, 7989–7993.
Stock,J.B. and Surette,M.G. (1996) Chemotaxis. In Neidhardt,F.C. et al.
(eds), Escherichia coli and Salmonella, Cellular and Molecular
Biology. ASM press, Washington, pp. 1103–1129.
Surette,M.G. and Stock,J.B. (1996) Role of α-helical coiled-coil
interactions in receptor dimerization, signaling and adaptation during
bacterial chemotaxis. J. Biol. Chem., 271, 17966–17973.
Takeshita,S., Sato,M., Toba,M., Masahashi,W. and Hashimoto-Gotoh,T.
(1987) High-copy-number and low-copy number plasmid vectors
for lacZα-complementation and chloramphenicol- or kanamycinresistance
selection. Gene, 61, 63–74.
Tawa,P. and Stewart,R.C. (1994) Kinetics of CheA autophosphorylation
and dephosphorylation reactions. Biochemistry, 33, 7917–7924.
Turner,L., Caplan,S.R. and Berg,H.C. (1996) Temperature induced
switching of the bacterial flagellar motor. Biophys. J., 71, 2227–2233.
Vigeant,M.A. and Ford,R.M. (1997) Interactions between motile
Escherichia coli and glass in media with various ionic strengths, as
observed with a three-dimensional-tracking microscope. Appl. Environ.
Microbiol., 63, 3474–3479.
4248
Wang,H. and Matsumura,P. (1997) Phosphorylating and
dephosphorylating protein complexes in bacterial chemotaxis.
J. Bacteriol., 179, 287–289.
Welch,M., Oosawa,K., Aizawa,S.I. and Eisenbach,M. (1993)
Phosphorylation dependent binding of a signal molecule to the flagellar
switch of bacteria. Proc. Natl Acad. Sci. USA, 81, 5056–5060.
Welch,M., Oosawa,K., Aizawa,S.I. and Eisenbach,M. (1994) Effects of
phosphorylation, Mg2ϩ and conformation of the chemotaxis protein
CheY on its binding to the flagellar switch protein FliM. Biochemistry,
33, 10270–10276.
Wolfe,A.J. and Berg,H.C. (1989) Migration of bacteria in semi solid
agar. Proc. Natl Acad. Sci. USA, 86, 6973–6977.
Zhao,R., Amsler,C.D., Matsumura,P. and Khan,S. (1996) FliG and FliM
distribution in the Salmonella typhimurium cell and flagellar basal
body. J. Bacteriol., 178, 258–265.
Zhu,X., Amsler,C.D., Volz,K. and Matsumura,P. (1996) Tyrosine 106 of
CheY plays an important role in chemotaxis signal transduction in
Escherichia coli. J. Bacteriol., 178, 4208–4215.
Received May 8, 1998; accepted June 4, 1998