Theoretical background
The rod - shaped bacteria Escherichia coli divide very precisely at the midpoint of the
long axis of the cell to produce two daughters of nearly equal length. The asymmetry
coefficient has been found to be as low as 4%. One of the key questions in bacterial cell
biology is how the correct division plane is identified.
Models for E.coli division site placement
Several different models have been proposed to explain the location of the division site
at midcell. The most popular of them are the nucleoid occlusion model and the model of
the pole-to-pole oscillations of Min proteins.
Nucleoid occlusion [1] postulates that the nucleoid inhibits FtsZ formation at the
regions it occupies. (The role of FtsZ is to form a ring, the Z- ring, that marks the division
plane.) Hence, this model is incomplete because it does not account for the high
precision of the division site. Besides, Z-rings are often present near the middle of
anucleate cells [2].
Another model for division site selection is the model of the pole-to-pole oscillations of
Min proteins [3], [4]. According to this model, the Z-ring placement is regulated by the
Min system that consists of three proteins: MinC, MinD and MinE. MinC is an inhibitor
of FtsZ assembly, whereas MinD enhances the activity of MinC by recruiting MinC to
the membrane and driving an oscillation of the two proteins from one cell pole to the
other. MinE, on the other hand, localized as a ring near midcell independently of FtsZ,
although its localization is not as precise as that of FtsZ. The MinE ring is proposed to
counteract MinCD inhibition in its vicinity, allowing the Z-ring to assemble safely
nearby. Because the low precision of the MinE ring position, it is not likely that the Min
proteins alone may guide the FtsZ to such an accurate position along the bacteria.
Therefore, it was proposed [5] that there are two main topological regulators of Z-ring
assembly in E. coli: the nucleoid and the Min system. This integrated model postulates
that the nucleoid allows the septation in nucleoid – free regions, which includes the
region between newly segregated nucleoids and the cell poles and the Min system
prevents FtsZ formation at the poles. Accordingly, the constriction is initiated between
segregated nucleoids and occurs after the termination of DNA replication.
One of the possible ways to test the last model is by determining the times of the
morphological events during the cell cycle.
Such research was performed by Blaauwen et al [6]. In their work, the timing of the
appearance of the FtsZ ring as a function of cell age and with respect to other cell cycle
parameters has been investigated in two E.coli strains that were grown at a range of
generation times. Timing of morphological data was obtained by classifying fixed cells
according to length and by establishing a relationship between length and age of the cells.
It was shown that the FtsZ ring appears approximately simultaneously with the
termination of DNA replication and occurs well before the cells show a visible
constriction and separated nucleoids (Fig.1).
1
Fig. 1. Schematic representation of the cell cycles of E. coli B/rA and K-12
growing with a generation time of 85 min [6] . The C period shows the duration
of the DNA replication cycle. The D period is the time required between the
termination of DNA replication and the separation into two daughter cells. The
Z period shows the duration of the period in which FtsZ can be detected at
midcell. The P period shows the period of septal peptidoglycan synthesis,
and the T period is the duration of the constriction.
Based on these results it was concluded that termination of DNA replication could
provide a signal for the initiation of cell division as suggested in the nucleoid occlusion
model.
The experimental techniques
In most studies a description of the cell cycle in morphological terms has been based
on phase contrast and fluorescent microscopy techniques [2], [4] - [7].
Phase contrast microscopy is a contrast enhancing optical technique that can be utilized
to produce high-contrast images of transparent specimens, such as cells. This technique
employs an optical mechanism to translate minute variations in phase into corresponding
changes in amplitude, which can be visualized as differences in image contrast. One of
the major advantages of phase contrast microscopy is that living cells can be examined in
their natural state without previously being killed, fixed and stained.
The disadvantage of phase contrast is a “halo” around objects. Another disadvantage is
not specific to phase contrast and common to all light microscopy techniques is the
diffraction-limited resolution of the images.
When light from the various points of a specimen passes through the objective and is
reconstituted as the image, the various points of the specimen appear in the image as
small disks (not points) known as Airy disks (Fig. 2). This phenomenon is caused by
diffraction or scattering of light as it passes through the specimen and the circular back of
2
the objective. The smaller the Airy disks projected by the objective in forming the image,
the finer the detail of the specimen discernible because the disks are less likely to overlap
one another. The limit of resolution of a microscope objective refers to its ability to
distinguish between two closely spaced Airy disks in the diffraction pattern (Fig. 2).
The image of a point source is known as the point spread function (PSF), and is
illustrated in the lower portion of Figure 2. The PSF can be expressed as
PSF (r )  (
2 J 1 ( )

)2
where J1 is a Bessel function of the first order,  
2
r
N . A.
,  is the wavelength of the
M

light, r  x  y is a coordinate in the image plane of the microscope, M is the
objective magnification, and N.A. – the numerical aperture of the objective.
2
2
Fig. 2. Airy disks and resolution. (a-c) Airy disk size and the corresponding intensity
profile (point spread function) for different numerical apertures of the objective. (d) Airy
disks at the limit of resolution. (e) Two Airy disks so close together that their central
spots overlap.
3
A basic principle of optical imaging is represented as a convolution process. Each point
in the image has an intensity given by the function g1 ( x, y) . If the system were ideal, then
the perfect image would be just a suitably magnified version of g1 ( x, y) , g1 ( M x , M y ) .
However the system has a finite point spread function (PSF(x,y)) and therefore any object
viewed with this system will have a slightly blurred image. The blurred image is the
convolution of g1 ( M x , M y ) and PSF(x,y).
Another method of studying biological specimens is fluorescence microscopy. It is a
tool for studying materials that can be made to fluoresce, either in its natural form
(primary or autofluorescence) or when stained with chemicals capable of fluorescing
(secondary fluorescence). Fluorescence microscopy is based on the property of some
substances to absorb light in a certain wavelength range, the energy of which is
subsequently partly emitted in the form of light. The wavelength of the emitted light is
longer than that of the absorbed light .This difference allows to separate the emitted light
from the exciting light using an appropriate combination of filters.
To visualize structure and location of the proteins within living cells, the fusion of
green fluorescent protein (GFP) to different proteins has become a valuable tool.
Research proposal
We propose to investigate the timing of morphological events during the cell cycle of
individual living E.coli cells. The advantage of studying individual living cells is that
basic cell cycle events such as nucleoid segregation, initiation and termination of the
constriction can be observed in real time and with better precision than by statistical
methods. In our study the description of the cell cycle of E.coli is based on light
microscope observations. The properties of the bacteria are obtained by analysis of phase
contrast and fluorescent images. Because of the limited resolution of the light microscope
there are many difficulties in analyzing such images. For example, from the plot of
intensity (I) profile of the bacterial edge (Fig. 3) one can see that there is no sharp
boundary between the bacterium and it’s surrounding.
From this picture it is impossible to decide at which intensity level to set the threshold
that separates the bacterium from the background. Therefore, it is necessary to develop
accurate and objective methods for quantitative image analysis. These methods must
include the estimation of an appropriate threshold level that corresponds to the edge of
the bacterium, determination of the phase contrast intensity between newborn bacteria,
detection of the appearance of the constriction and nucleoid segregation.
4
1.6
I
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
0
-0.4
2
4
6
8
10
Pixels
b
a
Fig.3. (a) Phase contrast image of an E.coli bacterium.
(b) Intensity profile plot on the bacterium edge. Setting the
mean background intensity to be 1 and the mean intensity inside
the bacterium to be 0 normalizes the intensity in this plot.
(The green line represents the profile line along which the profile
is measured.)
Experimental procedures and setup
Bacterial strain and growth conditions
Our experiments are performed with E.coli mutants WM162 [7] in which GFP is fused
to HU protein. HU is a “histone-like” protein, which is required for DNA packing. As
was shown [7] DAPI and HU-GFP co-localize on the E.coli nucleoid and therefore HU is
a natural tracer for DNA in bacterial cells.
The E.coli cells are grown in Luria-Bertani (LB) medium at 37 0 C to an optical density
of 0.2 at 600 nm. For induction of HU-GFP synthesis, 0.2% L-arabinose is added. For
microscope observation, 10µl of cell solution are pipetted on top of 100µl LB+1.1% agar
slides.
Microscopy and data acquisition
Our experimental system includes the inverted microscope (IX 70, Olympus) (Fig. 4).
The specimen is placed on the stage with its surface of interest facing downward. The
objectives are mounted under the stage with their front lenses facing upward towards the
specimen and focusing is accomplished by moving the objective up and down. Digital
images of the bacterial cells are acquired using a cooled CCD camera (MicroMAX).
5
12
Temperature control during the experiments is achieved using a heating band and
temperature sensor both mounted on the objective ( 100 oil immersion phase contrast
objective, NA=1.3).
Using this system we perform time-lapse experiments in living cells over the entire cell
division cycle. The cells are monitored in phase contrast mode with the time interval of
10 seconds between frames; from time to time we also take fluorescence images.
Fig.4. The scheme of our microscope.
6
Preliminary results
To quantify the evolution of the cells morphology, we first need to obtain the cell
contours.
For this, the bacterial membrane was stained with cytoplasmic membrane (CM)
FM 4-64 dye (Molecular Probes). It has a bright red fluorescence and binds to the outer
membrane.
To determine the cell borders in phase contrast images, formaldehyde fixed and
FM 4-64 stained bacteria were examined by both phase contrast and fluorescence
microscopy (Fig. 5). The contour of each bacterium was obtained by connecting the local
maxima in the fluorescence image. The mean intensity of phase contrast image at
fluorescence contour sites was taken to be the threshold intensity separating the
bacterium from the background.
In order to further use this threshold intensity for the analysis of images with varying
illumination, we normalized it by taking the mean value of background to be 1 and the
mean intensity in the narrow region inside the bacterium to be 0. The value of the
normalized threshold was found to be 0.35  0.02 .
Fig. 5. Phase-contrast (left) and fluorescence (right) images of
E.coli bacteria, stained with FM 4-64.
The next step in data extraction by image processing was to find the intensity between
two dividing bacteria that corresponds to the end of division in the phase contrast image.
For this we examined the cells with deep constriction that were stained with FM 4-64 dye
and measured the fluorescent and phase contrast intensities in the middle of the
constriction. Plotting the ratio between fluorescent intensity in the middle of the
7
constriction and the mean fluorescent intensity at the cell’s poles ( I / I 0 ) versus the mid cell phase contrast normalized intensity ( I p ) it is possible to see that all points may be
separated into two groups (blue and red points in Fig. 6 ). In the first group of points the
I / I 0 ratio is increasing with the increasing of ( I p ) (the blue points in Fig. 6). On the
other hand, I / I 0 is decreasing with the increasing of ( I p ) in the second group of points
(the red points in Fig. 6).
2.2
I / I0
1.8
1.4
1
0
0.3
0.2
0.1
Ip
Fig. 6. Plot of the relative fluorescent intensity as a function of normalized phasecontrast intensity in the middle of the constriction
Our explanation for this behavior is based on the fact that due to the limited
microscope resolution it is unable to distinguish between the image of two barely
separated bacteria and that of a bacterium in the last stage of division (with a deep
constriction). Therefore, the blue points correspond to the not yet divided cells at
different stages of division and the red points correspond to the two daughter bacteria at
different small distances between their caps (Fig.7). The value of the phase-contrast
intensity at the point of contact between two newborn bacteria can be obtained from the
intersection of the two lines. At the intersection point the relative fluorescence intensity
with respect to fluorescence intensity of cell poles is 1.60  0.07 and the normalized
phase-contrast intensity is equal to 0.18  0.02 .
8
To independently determine the relative fluorescence intensity between two cells that
have just separated, we numerically convoluted the PSF with a double bacterial contour.
The double contour was obtained by reflection of a young bacterium contour with respect
to the axis that is perpendicular to bacterial orientation and passes through its pole. PSF
was found using fluorescent beads with diameter that is smaller than the optical
resolution (0.1m). The ratio of fluorescence intensity between the center of
symmetry and the region of the poles that was obtained by this method is 1.67  0.03.
This result is in agreement with our previous finding.
I /I0
Ip
Fig.7. Schematic representation of the midcell fluorescent intensity as a function
of phase contrast intensity with respect to different bacterium stages.
The method described above allows us to estimate the birth time and division time of
individual living cells from time-lapse microscopy images. In Fig. 8 we show the
normalized phase contrast intensity at the central point versus time during the whole
cycle of a single bacterium. As can be seen from this plot, the phase intensity of the
young bacterium is almost constant. The range where the phase contrast intensity
increases corresponds to the late division stage, which is characterized by a clearly visible
constriction.
Plotting the linear range (Fig.9) and using a linear fit, the behaivor of the normalized
phase contrast intensity as a function of time was obtained. Using the previously found
phase contrast intensity between two newborn bacteria, it is possible to estimate the
division time.
We calculated the generation time τ for 12 bacteria (Table 1). The mean value of τ is
  (27.9  2.3) min and its coefficient of variation (CV) is 28%. According to [8] the
coefficient of variation in generation time is 20% (this result is explained on the basis of
the observed 10% coefficient of variation of the size at division), but Powell and
9
Errington [9] suggested that “the coefficient of variation of generation times is greater,
the greater the chemical complexity of the growth medium”.
Ip
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05 0
-0.1
-0.15
200
400
600
800
1000
1200
1400
1600
1800
t, sec
0.4
0.35Plot of the normalized phase contrast intensity versus time during the entire cell
Fig. 8.
cycle of0.3a single bacterium.
0.25
0.2
0.15
0.1
0.05
0
p
-0.05 0
-0.1
-0.15
I
0.35
0.3
0.25
200
y = 0.0008x - 0.6827
400R2 = 0.9586
600
800
1000
1200
1400
1600
1800
0.2
0.15
0.1
0.05
0
800
900
1000
1100
1200
1300
1400
t, sec
Fig. 9. Plot of the normalized phase contrast intensity versus time for the linear range of
Fig 8 (circles). The straight line represents the corresponding linear fit.
10
Table 1. The generation times of 12 different bacteria.
(   ) min
43.3  0.5
17.5  0.6
20.0  0.7
30.7  1.1
24.7  0.6
21.5  0.4
24.8  0.7
28.3  0.7
38.8  0.6
33.7  0.8
32.6  1.2
19.4  0.7
Another event of the cell cycle that we want to time is the start of the septal
constriction. The optical resolution does not allow to image the beginning of the
constriction process. To solve this problem we propose a model that describes the
dynamics of the constriction width. This model rests on two assumptions: 1.the bacterial
caps are hemispheres; 2.the rate of membrane growth during the process of constriction is
constant. These assumptions lead to the equation:
(
t
W 2
1
)  (
t  c )2 1
D
  tc   tc
where W is the constriction width, D is the bacterial diameter,  is the generation time,
t c is the constriction initiation time and t is time. From the phase contrast images we can
W
measure the constriction width as a function of time. Parabolic fit of ( ) 2 as a function
D
of time allows to estimate t c . An example of such a fit is shown on Fig. 10. For this
bacterium, the t c  (1.5  0.1) min , whereas one can visually observe the presence of the
constriction only 8.5 min after birth.
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t (sec)
W
D
Fig.10. The time dependence of ( ) 2 (circles) and the corresponding parabolic fit
(line).
Research plan
Timing of appearance FtsZ and FtsA proteins at a division site
An alternative approach for verifying the model that describes the dynamics of the
constriction width will be obtaining t c for the FtsZ-gfp and FtsA-gfp mutants [10], [11]
and comparing t c with the time of the appearance of FtsZ (FtsA) proteins in the division
plane.
Calculation of nucleoid segregation time
The next challenge of this research will be to calculate the cell age at which separation
of nucleoids occurs. The closeness of nucleoids leads to overlapping of their images due
to the broadening induced by the PSF. This fact makes it difficult to decide whether the
nucleoids in the microscopic image are connected by a narrow bridge or just separated.
Therefore we will need to formulate an objective criterion for distinguishing between
images of separated and unseparated nucleoids.
Cell size dependence of initiation FtsZ assembly
Blaauwen et al. [6] have reported that initiation of the assembly of the FtsZ ring occurs
at a time that is very close to the termination of replication. From this, it was suggested
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that the termination of replication might provide a signal for the initiation of cell division.
However, FtsZ rings have also been shown to form in the absence of a chromosome [2].
Therefore, one of the important questions is how cells “know” at what time they must
assemble FtsZ proteins at the division site. We propose to investigate the possibility that
FtsZ rings form in cells when they reach a certain length. From analyzing the time of
appearance of the FtsZ assembly with respect to cell size we will examine a version of
the length- dependent FtsZ triggering.
Dynamic behavior of FtsZ during the cell cycle
FtsZ proteins are generally distributed throughout cytoplasm in nondividing cells and
move to accumulate in a ring-like structure at the prospective division site early in the
division cycle. However, the fraction of FtsZ incorporated into the ring is ~ 30% [12].
Using time-lapse microscopy it is possible to investigate dynamic behavior of FtsZ-gfp
proteins. We plan to measure the ratio of fluorescence intensity in the Z-ring with respect
to fluorescence intensity in cytoplasm as a function of time and calculate the assembling
rate of FtsZ.
Dependence on cell shape of timing of morphological events
Another question for the future is what would happen if cells were to lose their
characteristic rod shape and take some other form. Would cells, for instance, of spherical
shape still retain the same timing of morphological events during cell cycle as rod shape
cells. Cylindrical cells are transformed to spheroids by addition of mecilinam [13] and
therefore it is possible to compare the timing in the strains that we study for two shapes,
namely, rods versus spheres.
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References
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4751–4756.
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division site in the absence of the chromosome. Mol. Microbiol. 29, 491-504.
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Current biology. 10, R249-R252.
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13. Zaritsky, A., Woldringh, C., L., Fishov, I., Vischer N., O., E., and Einav, M. (1999)
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