ARTICLE IN PRESS
Quantification of cell size distribution as applied to
the growth of Corynebacterium glutamicum
Kalyan Gayena, K.V. Venkatesha,b,
a
Department of Chemical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
School of BioSciences and Bioengineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
b
KEYWORDS
Cell size
distribution;
Image analysis;
Cumulative
distribution
function;
Growth
characteristic;
Corynebacterium
glutamicum
Summary
It is known that the cell size is related to the physiological state of a cell. Therefore, cell
size distribution directly reflects the average physiological properties of the cell
culture. Cell size distribution can be enumerated by image analysis, flow cytometry and
coulter counter. In this study, image analysis was used to characterize the cell size
distribution during the growth of Corynebacterium glutamicum and was further
analyzed by a distribution function. The parameters of the distribution function indicate
the mean value and spread of the distribution. Analysis demonstrated that the
maximum specific growth rate was higher (0.67 h1) for the growth obtained through
serial dilution of seed as compared to growth from a normal seed culture (0.53 h1).
This was due to a greater percentage of the cell population being in the state of division
for the growth through serial dilution in the mid-log phase. The measurement of the cell
size distribution demonstrated that the average cell size decreased during the course of
growth. The distribution function was also used to enumerate the average specific
growth rate of both the conditions of the culture. The demonstrated methodology can
be used to predict an average growth property of a cell culture.
Introduction
Performance of a biotechnological process depends on the physiological state of the growing
biomass. The physiological state, which may be
affected by the media composition, can be directly
related to the cell population. Most studies
typically look at average measurements of cell
property and very little information is available on
the distribution of cell population (Porrot and
Friedrich, 1995). Therefore, study of cell size
distribution is essential to gather precise knowledge about the state of the organism. Several
methods, such as coulter counter, flow cytometry
and image analysis, have been reported for cell size
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587
measurement (Boyea and Olesenb, 1991; Neagu
et al., 1994; Porrot and Friedrich, 1995; Porrot
et al., 1997).
Among these, image analysis is a very promising
and powerful tool to quantify cell distribution
based on size. The method offers advantage to
directly observe individual cells, cell aggregates or
differentiated cell masses (Ibaraki and Kenji,
2001). Image analysis has been applied to evaluate
microorganisms in various environments including
pure and mixed cultures (Pons and Vivier, 2000),
marine (Pernthaler et al., 2003), petrochemicals
(Williamson and Palframan, 1989), geological
(Tobin et al., 1999) and foods (Hood and Zottola,
1997). Image analysis has also been used to study
bacterial motility (Gualtieri et al., 1988), physiological processes in bacteria (Goldstein et al.,
1988), colony counting (Corkidi et al., 1998),
adhesion (Sjollema et al., 1990; Reinhard et al.,
2000; Mahony et al., 2005) and bacterial rock
weathering (Puente et al., 2006). Renata et al.
(1999) have reported spore crops of Bacillus subtilis
and Bacillus cereus with the help of electron
microscopy and image analysis.
Image analysis can be, therefore, used to quantify
cell size distribution (Elfwing et al., 2004). The size
distribution has been shown to be changing during the
growth of microorganisms. Erlebach et al. (2000)
have demonstrated that the cell distribution shifts
towards lower cell diameter during the course of
fermentation. Although reports for cell size distribution exist, further analysis to quantify the measured
cell size distribution is scarce.
Therefore, the main objective of the current
work was to quantify cell size distribution during
the growth of a given culture. We report the cell
size distribution of Corynebacterium glutamicum
(CECT 79), a Gram-positive organism. We have
studied the growth dynamics and size distribution
for two conditions, (i) growth obtained from normal
seed culture and (ii) growth obtained through serial
dilution of seed culture. We develop a method to
quantify cell size distribution using a cumulative
distribution function. Further, the distribution
function is used to predict an average growth
property of the cell culture, which was verified
experimentally.
Materials and methods
Microorganism and chemicals
The organism, C. glutamicum (CECT 79), obtained from Coleccion Espanola De Cultivos Tipo
(CECT, Valencia, Spain), was used for all the
experimental work. The working culture of this
organism was maintained on slant (LBG5 medium
containing 5 g l1 glucose, 5 g l1 yeast extract,
10 g l1 tryptone, 5 g l1 NaCl with 2% agar) at 4 1C.
The culture was revived once every month. Yeast
extract and tryptone, biotin, streptomycin, amino
acids were obtained from Hi-media, Mumbai, India.
Bacterial growth conditions
Seed culture
The culture was grown firstly on LBG5 media
composition described by Vallino and Stephanopolous (1993). One loop full of culture was inoculated
from the slant, into the 50 ml LBG5 seed medium in
a 250 ml Erlenmeyer flask. The seed culture was
grown at 30 1C at 230 rpm for 10 h.
Growth from normal seed culture
A total of 10% (v/v) of the seed was transferred
to the 100 ml preculturing medium (PMB) as media
composition described by Vallino and Stephanopolous (1993), in a 500 ml Erlenmeyer flask and the
growth conditions were maintained as described by
seed culture. OD was measured at different time
and samples were taken for image analysis at
various time points.
Growth from serial dilution of seed culture
In this case, the growth experiments were
performed with a fewer numbers of cells obtained
through serial dilution of the seed culture as
described by Pelczar et al. (1993). C. glutamicum
was inoculated into the seed media. At early log
phase (6 h), after serial dilution (of about 1010 fold)
50 ml of the sample was transferred into the next
seed media. Exponentially growing cells (at a cell
OD of about 1.5–2) were diluted and further,
transferred into fresh media. The same was
repeated thrice and finally, 10 ml of the seed
culture of OD 1.5 was transferred to the PMB. OD
was measured and samples were taken for image
analysis at various time points.
Cell separation protocol
Cells of C. glutamicum generally exist as a colony
of two or more cells sticking together. Therefore,
cell separation was essential before the measurement of size distribution. The method used for cell
separation was a modified procedure developed by
Noda and Kanemasa (1986). After growing the
organism on the PMB, 10 ml of the sample (fermentation broth) was separated from the preculturing
broth by centrifuging at 5000 rpm for 5 min. The
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588
Image analysis
Image analysis was performed for cell size
distribution of C. glutamicum after performing
the above protocol to separate the cells. The cell
size area was measured using an Olympus compound microscope (BX51), which was attached with
Evaluation MP Cybernetics camera. Samples were
taken at different fermentation time points, which
were followed by the cell separation protocol.
During slide preparation, special care was taken to
ensure that only a monolayer of the organisms was
present between slide and the cover slip by
appropriate dilution of the sample (about OD of
3–3.5). Snaps of images were taken through the
differential interference contrast (DIC) mode. At
each time point, snaps 15 images were taken so
that at least thousand cells were countable. The
area in terms of mm2 of the individual cell was
measured with the help of image analysis software
(Image Pro Plus version 4.5). Image Pro Plus was
able to automatically recognize clusters of brighter
pixels as cells and to calculate the area of every
cell and designate every cell with x and y
coordinates. The data was later documented as
normalized cumulative cell distribution.
maximum OD at 13 h, while the normal growth
obtained the same OD at about 17 h. The growth
through serial dilution demonstrated a steeper rise
in the exponential growth phase as compared to
the normal growth. This corresponds to a higher
maximum specific growth rate for the growth
through serial dilution (0.67 h1) as compared to
the growth rate for the normal growth (0.53 h1). It
was interesting to note that the growth rates
observed for both the growth conditions were
different although the medium was the same. It is
pertinent to raise the question regarding the
influence of the cell size distribution on the growth
rate for the two different states of the culture.
To address this issue, we analyzed two states of
the culture by image analysis and obtained the
cumulative cell size distribution with respect to the
two-dimensional incident surface areas of the cells.
The frame of the image of cells captures various
orientations of the cells giving an average cell
distribution with respect to surface area. To
eliminate a bias obtained through cell orientation,
15 such images were considered for each time point
and an average cell distribution was reported. It
can be noted that about 90% of the cells in the
image shown in Fig. 2a are oriented in the axial
direction and this minimizes the associated error
(optimal orientation of the cell is indicated by
‘arrow’, while ‘cross’ indicates an orientation
which contributes to higher error). The distribution
was measured at various time points and was
16
14
12
OD of biomass
sample was later washed once with physiological
saline solution by vortexing and centrifuging at
5000 rpm for 5 min. The cells were resuspended in
10 ml of 0.02 M phosphate buffer (with pH 7.8).
From this sample, 5 ml was transferred into a test
tube and sonicated in a bath type sonicator
(32 MHz) for 5 min. Then, 2 ml of streptomycin
(0.01 g ml1) was added to the sample to arrest the
cell size. After 10 minutes, 5 ml of 1000 ppm
nonionic surfactant (Tween 20) was added and
vortexed thoroughly and kept for 10 min. Finally,
the cells were vortexed and further sonicated for
8 min. The whole procedure was performed in a 4 1C
environment. Microscopic examination of the cells
indicated that cells were not lysed. This protocol
ensured complete separation of cells.
10
8
6
4
2
Results and discussion
0
0
2
4
6
8
10
12
14
16
18
20
Time (h)
Two different seed culturing protocols were used
to grow C. glutamicum on a growth media as
described in the methods. Figure 1 shows the
biomass concentration as OD measurement obtained at various time points for these two
protocols. It can be noted that the maximum OD
of 15.5 was observed in both the states of culture.
However, growth through serial dilution achieved
Figure 1. Growth profiles of C. glutamicum for growth
obtained through normal seed culture and growth
obtained through serial dilution of seed culture. Symbols
‘K’ and ‘m’ represents OD of biomass measured at
600 nm for normal growth and growth obtained through
serial dilution. The maximum specific growth rate of cells
in normal growth was 0.53 h1 while that for growth
obtained through serial dilution was 0.67 h1.
ARTICLE IN PRESS
589
normalized by the total cells in the frame of image.
Such a cumulative normalized cell data for the
growth of cells obtained through serial dilution at
12 h is shown in Fig. 2b. The cell distribution profile
demonstrates a classic S-type curve. Therefore, the
normalized cumulative cell distribution (N) was
represented by the following equation:
N¼
xa
,
k þ xa
(1)
a
where ‘x’ is the incident surface area (in mm2) of
the cell, ‘k’ the half saturation constant which
indicates the area attained by half of the population and ‘a’ an exponent parameter indicating the
(a)
Normalized cumulative cell distribution
1
(b)
0.9
0.8
0.7
spread of the distribution. The experimental cell
distribution obtained from image analysis was
fitted with Eq. (1) to estimate the value of ‘a’
and ‘k’ using fminsearch function in MATLAB (The
Math works Inc., USA). The fit for the growth
through serial dilution at 12 h resulted in a ¼ 7.6
and k ¼ 1.12 mm2. This indicates that 50% of the
cells were with an incident surface area of less than
1.12 mm2 at t ¼ 12 h.
Figure 3a shows the normalized cumulative cell
distribution at various time points during normal
growth of cells. Figure 3b shows the resulting ‘a’
and ‘k’ values obtained by fitting the data to Eq.
(1). It is clear from the figure that the value of ‘a’,
the exponent of Eq. (1), increases in time from 4.3
to 7, indicating that the distribution becomes
steeper in time, where as the value of ‘k’, the half
saturation constant decreases in time from 1.3 to
0.95 mm2. This implies that distribution profile
shifts to the left and also the cell size of the
population becomes more uniform during the
course of fermentation. Therefore, the percentage
of cells having lower incident surface area increases along the fermentation time.
Additionally, the equation obtained to represent
the cumulative distribution of cells based on their
surface area (N) can be used to evaluate the
normalized cell distribution (n) by differentiating
Eq. (1). Such a normalized cell distribution yields
the frequency for a particular cell size as a
continuous function. Thus, ‘n’, the normalized cell
distribution can be represented as
n¼
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
Area (µ2 )
Figure 2. (a) Frame of the image of C. glutamicum used
to determine the cell size distribution. It can be noted
that most of the cells are separated by the protocol
described in the methodology section to break the
aggregation. The ‘arrow’ shows a cell having optimal
orientation for image analysis, while ‘cross’ shows a cell
having orientation yielding higher errors in image analysis
(b) Normalized cell distribution as obtained from the
image analysis for the cells obtained through serial
dilution at t ¼ 12 h. The solid line represents the fit
obtained from Eq. (1) and dotted line represents the
experimental data points.
dN
.
dt
(2)
The estimated normalized cell distribution ‘n’ at
various time points are shown in Fig. 3c. It can be
observed that the distribution was slightly skewed
around the value of ‘k’, the half saturation
constant, towards the higher surface area. The
area under the curve equals unity since the
cumulative distribution was normalized. Also, the
number of cells with a cell size equal to the value
of ‘k’ was maximum. The value of maximum
frequency thus obtained at ‘k’ increases with
increase in time. This indicates that the distribution was steeper at higher time points (reflected by
higher value of ‘a’).
Image analysis was also performed for the growth
obtained through serial dilution, which was grown
on the same media as used for the normal growth,
but precultured in a very different manner (see
methods). The normalized cumulative cell distribution based on incident surface area is shown in
Fig. 4a for growth obtained through serial dilution.
In this case, the value of ‘a’ was almost constant in
ARTICLE IN PRESS
fermentation (see Fig. 4b). This is consistent with
the fact that the culture had the cells, which were
in a similar state of division. Such a behavior is also
termed as self-similar growth, wherein the cumulative distribution of cells only shifts in time but has
the same steepness (indicated by the constant ‘a’
value) (Ramkrishna and Schell, 1999).
The growth of the cells obtained through serial
dilution was found to be different from normal
growth (Fig. 1). This difference can be attributed
to the variation in cell distribution as the growth
medium used had the same composition. One can
predict the growth rate based on the cell division to
verify this hypothesis. It was assumed that cells
1
(a)
0.9
15
18
0.8
0.7
12
0.6
9
0.5
6
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
Area ( µ2 )
1.4
8
(b)
7
1.2
6
0.8
k
a
1
1
5
4
0.6
3
0.4
2
1
0.2
0
0
2.5
5
7.5
10
12.5
15
17.5
20
Time (h)
0.02
(c)
0.018
(a)
0.9
12
10.5
0.8
7.5
0.5
0.4
0.3
0.2
15
0.1
12
0
0
0.5
1
1.5
0.012
0.06
(b)
0.016
0.04
0.02
0
0.5
1
2.5
3
3.5
2.5
3
3.5
0.018
6
0
2
Area (µ2 )
9
0.08
6
0.6
0.014
0.01
9
0.7
0.016
1.5
2
2.5
3
Area (µ2 )
Figure 3. (a) The cumulative cell size distribution for
normal growth as measured by incident surface area
(mm2) at different time points (h) of fermentation. The
distribution is shown for time points t ¼ 6, 9, 12, 15, 18.
It can be noted that the profile shifts to the left in time.
(b) Value of a and k obtained from fitting the distribution
profile shown in Fig. 3a at various time points. Symbols
indicate: a, ’; k, n. (c) The normalized cell distribution
(as area in mm2) as estimated from Eq. (2) for the data
shown in Fig. 3a. The estimated profiles have a peak
value at incident area equal to the value of ‘k’.
the range of 7–7.6, while the value of ‘k’ lowered
in time as in the case of normal growth. This
indicates that the cell distribution was steeper at
all times but shifts to the left during the course of
Normalized cell distribution
Normalized cell distribution
18
Normalized cumulative cell distribution
Normalized cumulative cell distribution
590
12
10.5
0.014
9
0.012
7.5
0.01
6
0.008
0.006
0.004
0.002
0
0
0.5
1
1.5
2
Area (µ2 )
Figure 4. (a) The cumulative cell size distribution for
cells obtained through serial dilution as measured by
incident surface area (mm2) at different time points (h) of
fermentation. The distribution is shown for time points
t ¼ 6, 7.5, 9, 10.5 and 12 h. It can be noted that the
profile shifts to the left in time. (b) The normalized cell
distribution (as area in mm2) as estimated from Eq. (2) for
the data is shown in Fig. 4a. The estimated profiles have
a peak value at incident area equal to the value of ‘k’.
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591
having surface area greater than 1.6 mm2 grow at a
maximum rate of 0.67 h1, which was estimated
from the maximum specific growth rate of cells
growth obtained through serial dilution. Firstly, the
normalized cell distribution was used to obtain the
fraction of cells having surface area greater than
1.6 mm2 for culture in both the states. Figure 5a
shows the histogram of the cells having greater
than 1.6 mm2 for the normal growth at various time
points during fermentation. At t ¼ 6 h, 36% of the
cells have a surface area greater than 1.6 mm2 and
are assumed to be dividing maximally. And 64% of
the cells, having surface area less than 1.6 mm2, are
all assumed to be nondividing. It is clear from the
Fig. 5a, that the fraction of cells, which are greater
than 1.6 mm2, goes on decreasing in time. The
fraction of such cells decreases from 36% at t ¼ 6 h
to 1% at t ¼ 18 h.
Fraction of cells
1
(a)
0.8
0.6
0.4
0.2
0
9
6
12
15
18
Time (h)
0.35
(b)
Specific growth rate (h−1)
0.3
0.25
0.2
0.15
0.1
0.05
0
6
8
10
12
14
16
18
Time (h)
Figure 5. (a) Histogram of fraction of cells having
greater and less than incident surface area of 1.6 mm2
for the case of normal growth. Dark boxes indicate cells
with greater than 1.6 mm2, while white boxes represent
fraction of cells with less than 1.6 mm2 (b) Predicted
specific growth rate for normal growth from the
frequency of cells having greater than 1.6 mm2 (as
obtained from Fig. 5a). ‘K’ shows the specific growth
rate obtained from image analysis and ‘m’ shows the
specific growth rates from data shown in Fig. 1 for normal
growth.
Based on the above fraction, the average growth
rate was estimated on the assumption that the cells
with surface area greater than 1.6 mm2 will have a
specific rate of division equal to 0.67 h1 (i.e. the
maximum specific growth rate for the cells growth
obtained through serial dilution). For example, at
t ¼ 6 h since 36% of cells were dividing at the
maximum rate (see Fig. 5a), the growth rate of the
overall population can be estimated to be 0.24 h1
(i.e. 0.36 0.67 h1, also see Fig. 5b). The average
specific growth rate can also be obtained from the
slope of the growth curve for the normal growth (see
in Fig. 1) at t ¼ 6 h. Figure 5b shows a comparison
between estimated specific growth rates obtained
from the image analysis to that obtained from growth
experiments. The average specific growth rate of the
culture estimated from the image analysis matched
the values obtained from the growth curve. The error
between the average growth rate, estimated from
image analysis and from the growth experiment was
in the range of 1–15%.
A similar analysis for the cells growth obtained
through serial dilution (see Fig. 6a) indicate that
82% of the cells have surface area greater than
1.6 mm2 at t ¼ 6 h. This fraction decreases to 7% at
t ¼ 12 h. There are two points to be noted: (i) cells
with surface area higher than 1.6 mm2 at t ¼ 6 h
obtained through growth from serial dilution of
seed culture was higher (by about 55%) as compared to that observed for the normal growth; (ii)
the shift from dividing to nondividing occurred
during a shorter duration of time (approximately
6 h) as compared to that of the normal growth (12 h
Fig. 6b shows a comparison between estimated
growth rates obtained from image analysis to that
obtained from growth experiment for cells growth
obtained through serial dilution. In this case, image
analysis had a closer match to the rate obtained
from OD measurement. This was indicated by only a
maximum error of 12%. The average growth rate
was not only higher, but also steeper for the culture
growth obtained through serial dilution indicating
that the cells underwent the shift to the nondividing in a very short period.
The above assumption of dividing cells having
incident surface area greater than 1.6 mm2 was
verified by obtaining histogram for other incident
surface area. Therefore, the above analysis was
repeated for the incident surface area equal to 1.5
and 1.7 mm2. The estimated specific growth rates
from such an analysis yielded higher errors implying
that the 1.6 mm2 was an optimal value of incident
surface area above which cell division take place
(results not shown). Thus, the analysis also estimated the average cell size necessary for cell
division to occur for C. glutamicum.
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Fraction of cells
1
(a)
0.8
0.6
0.4
0.2
0
6
7.5
9
10.5
12
Time (h)
0.7
(b)
Specific growth rate (h−1)
0.6
0.5
0.4
0.3
0.2
0.1
0
6
7
8
9
10
11
12
Time (h)
Figure 6. (a) Histogram of fraction of cells having
greater and less than incident surface area of 1.6 mm2
for cells obtained through serial dilution. Dark boxes
indicate surface area greater than 1.6 mm2, while white
boxes represent fraction of cells with less than 1.6 mm2.
(b) Predicted specific growth rate for cells obtained
through serial dilution from the frequency of cells having
greater than 1.6 mm2 (as obtained from Fig. 6a). ‘K’
shows the specific growth rate obtained from image
analysis and ‘m’ shows the specific growth rates from
data shown in Fig. 1 for cells obtained through serial
dilution.
analysis yielded the cumulative distribution of cells
with different incident surface area for cells
obtained through normal growth and through serial
dilution of seed culture. The orientation of the cells
is an important issue and to counter the same
several images at a given time has been used to
yield an average normalized cumulative distribution. As expected, the growth obtained through
serial dilution yielded a steeper cell distribution
indicating that most of the cells were in a similar
state of division. Whereas, in the normal growth,
cells had more variation represented by a lower
value of the exponent ‘a’. More cells were in the
nondividing state during the course of the fermentation, which implied that the cell distribution was
becoming more uniform. This was represented with
an increase in the value of exponent ‘a’. It was also
noted that the average cell size as measured by
incident surface area was larger in exponential
growth phase than in the stationary phase. The
shift between these stages was shorter for the cells
growth obtained through serial dilution as compared to normal growth. The cell division can also
be used to yield average cell property in time. We
show that the normalized cell distribution can be
used to evaluate the percentage of cells that are
dividing in a population.
Acknowledgements
The authors are thankful to Mr. R. Aravindan for
his support in conducting part of experiments and
to Miss Rajitha Vupulla for her help during manuscript writing.
Conclusion
Cell size distribution is known to play an
important role in the physiological state of cells.
Past studies have shown that cell division is
initiated at a critical size (Grewal and Edgar,
2003). Although coulter counter, flow cytometry
and image analysis have been used to measure the
cell size distribution based on size and surface
area, quantification of such a data is scarce. We
present a quantification methodology of cell
distribution based on incident surface area by using
image analysis. We, further, use a distribution
function to predict the possible variation in growth
rate due to different seed-culturing states of the
culture.
We have used a cumulative distribution function
to quantify the growth of C. glutamicum. Image
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