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Dynamic clustering of bacterial population
a __
PINEA D
fl5l p3
Physica
ELSEVIER
D 75 (1994)
81-88
Dynamic clustering of bacterial population Elizabeth Department
of Biotechnology,
P. Ko, Tetsuya Yomo, Itaru Urabe
Faculty of Engineering,
Osaka University, 2-1 Yamadaoka,
Suita, Osaka 565, Japan
Abstract Bacterial cells having the same genotype were observed to split into a few clusters of phenotypes with various levels of enzyme activity. When the mixture of these phenotypically heterogeneous but genotypically homogeneous cells was cultivated in a liquid medium, the distribution of the population size of each cluster of phenotypes showed various kinds of dynamic oscillations. In addition, when this dynamic behavior was examined for the cells of the single colony, various patterns of shifting of homogeneous to heterogeneous lineage and vice versa were observed in the population. The results imply that differentiation of the cells with the same genotype can occur without spatial information and even under the same environment where the cells interact globally without spatial constraint. This interesting phenomenon totally contradicts the conventional biology that the genotype of a cell uniquely determines the phenotype of the cell and its progeny, but is consistent with the theoretical model of cell differentiation presented in the following paper. The sources of discrepancy between the existing theory in molecular biology and our results were discussed and it is concluded that in understanding a complex living system, a simple model consisting of the essence of the complex system can be constructed justifying the observed properties of the molecules in the system which provide free interactions.
1. Introduction
genotype
It is generally believed that the life of a cell is determined by its genome and environment, and that the genome is accurately duplicated and transmitted to the progeny. In short, the genotype of a cell uniquely determines the phenotype of the cell and its progeny in an environment, except for the occurrence of mutation on the genome. This concept has been applied most explicitly in the system of bacteria such as the Escherichia coli. In the higher organisms, cell differentiation is a well-known phenomenon, in which cells starting from a single cell become to have different phenotypes without changing the 0167-2789/94/$07.00 0 1994 Elsevier SSDZ 0167-2789(94)00068-2
Science
B.V. All rights
(in some cases as shown
in the immune
system the change in the genotype is also observed). This phenomenon was justified to be the cause of the differences in the microenvironment of each cell, and therefore did not violate the above conventional concept. However, it was shown by Kaneko [l] that the complex metabolic system in a living cell may lead the cell to differentiate into cells of different phenotypes through a globally coupled dynamic system. The present paper shows experimental results which cannot be explained by the existing theory in molecular biology and which even contradicts the above mentioned conventional concept. Nevertheless, the results imply that dynamic reserved
82
E.P. Ko et al. I Physica D 75 (1994) 81-88
clustering and differentiation of the cells can occur without any spatial information under the same environment where cells interact globally. Previously we had obtained a gene coding for xylanase, an enzyme catalyzing the hydrolysis of xylan (a polysaccharide) from the bacterium, Bacillus pumilus [2]. Inherently, an enteric bacteria called Escherichia coli (E. coli) does not have the xylanase. Therefore, the xylanase gene obtained was first inserted into a vector plasmid (a small extrachromosomal DNA used as a vehicle for carrying a foreign gene into a microbial cell), and the resulting modified plasmid was then introduced into E. cob. Thus, the modified E. coli produces xylanase through the gene carried on the plasmid [3]. Such modified bacterial cell is generally called a transformed cell or simply a transformat. Six kinds of the mutant genes of xylanase were prepared by replacing one of its amino acid residues with a different one through site directed mutagenesis [3]. Introduction of each of these mutant genes carried by the plasmid vector into E. coli revealed an interesting phenomenon violating the said concept above. In contrast to other cases, only the E. cofi transformants containing a plasmid carrying either one of the two genes coding for mutant xylanases named E182D and E182S exhibited different levels of enzyme activity as shown by the varying halo sizes in the Congo Red plate assay [3,4] (see Fig. lb). These results mean that bacterial cells having the same enzyme gene give rise to different phenotypes. It was confirmed that this unexpected phenomenon is not due to the heterogeneity in the genotype of the transformants as described below. Accordingly, these results revealed that the above conventional concept, where cells having the same genotype give rise to the same phenotype, is not always followed even in a simple system, such as the E. coli, among organisms. Indeed, this interesting phenomenon may imply that E. coli cells carrying a particular gene differentiate into various phenotypes. Here, we will show the dynamic behavior of this phenotypically
heterogeneous population during cultivation shaken liquid medium wherein all cells allowed to grow in the same environment interact freely with each other without constraint.
in a are and any
2. Results and discussion Transformants obtained after a single mutation of the xylanase gene at El82 were found to express different levels of enzyme activity [3]. Though single colony isolation of the transformants was performed, heterogeneity in enzyme activity was still observed. Therefore, the possibility exists that the heterogeneity observed in the population of the transformants with regards to enzyme activity may be due to spontaneous mutation which occurred during the manipulation of the gene. However, when the structural genes harbored in the plasmids of the 15 randomly chosen original transformants expressing different levels of activity were sequenced, it was found that these transformants possessed precisely the same structural gene. The same results were observed with the 14 randomly chosen progenies obtained after single colony isolation. Hence, it was confirmed that the heterogeneity in enzyme activity of the population of transformants is not due to differences in the nucleotide sequence of the gene. Accordingly, this result eliminates the probability that the heterogeneity in enzyme activity is due to contamination. The same mutant gene coding for E182D was again prepared as described previously [3]. E. coli cells were transformed by introducing the plasmid DNA containing both the mutant gene and an ampicillin resistant gene. Therefore, only cells that contain the said plasmid DNA can grow in a medium containing ampicillin (selection medium) owing to the ampicillin resistant gene. This follows that, with the use of this selection medium, any cells without ampicillin
E.P. Ko et al. I Physica D 75 (1994) 81-88
resistance can be eliminated from the population of the transformants. The transformants showed heterogeneity in the colony size as well as in the level of the enzyme activity (Fig. l), confirming the previous
83
observation [3]. According to the category described in the legend of Fig. 1, the transformants were classified into four groups (++, +, +, and -) based on the level of the enzyme activity as determined qualitatively and into three groups
Fig. 1. Heterogeneity in colony size (a) and enzyme activity (b) of E. coli transformants. (a) E. coli transformants containing a plasmid carrying a gene coding for the mutant xylanase (E182D) were prepared by the method described previously [3], and were grown overnight in the selection medium containing Luria-Bertani broth and 50 uglml ampicillin. An aliquot of the diluted overnight culture of the transformants were grown at 37°C for 17-18 h on an agar plate containing the same selection medium and 1.4% agar before measuring the size of the colony. Colonies were then classified according to their sizes into large (2.0-2.7 mm), medium (1.0-1.5 mm), and small (0.35-0.5 mm). (b) The cells taken from each colony were replica plated on the agar plate as stated above containing 0.5% xylan in potassium phosphate buffer (pH 6.5), and were grown at 37°C for 24 h. Enzyme activity was qualitatively screened by the Congo Red plate assay [3,4] where the haloes visualized as shown above are indicative of the activity level, i.e., a larger halo corresponds to a higher enzyme activity exhibited by the colony. Haloes were classified into the following four groups by the size and appearance: (+ +), 3.0-7.1 mm, bright or shiny; (+), 1.0-3.0 mm, dull; (+), blurred; and (-), no halo at all. Below the picture is the designation of the halo sizes observed.
84
E.P. Ko et al. I Physica D 7.5 (1994) 81-88
(large,
medium, and small) based on their size. It was confirmed that the difference
colony between
the groups
macroscopically biguous
case.
This result
cells in the population clusters
there
it should
exhibit
properties, including
various
be discriminated
oscillate
rarely
plitude
clearly
is an am-
shows
that
of the transformants
based on the property
retrospect, cells
can easily
and that
frequency of occurrence of the two groups sisting of the medium and the small colony
form
they possessed.
be emphasized but clustered
that levels
the In
these of the
albeit possessing the same genome the plasmid carrying the mutant en-
zyme gene. Successive culture of the mixture of the phenotypically heterogeneous but genotypically homogeneous transformants obtained above was done for 30 days (Fig. 2). The distribution of the cells with respect to the properties, i.e., the enzyme activity and colony size, in the 24 h culture was determined (see Fig. 1, legend). The results show that the frequency of each cluster exhibiting different levels of the enzyme activity within 30 days of successive cultivation has a dynamic irregular oscillation (Fig. 3a), while the
synchronously
with
(Fig. 3b). Therefore,
a
consizes
constant
whether
am-
this oscilla-
tion observed arises from the behavior of the cells in the liquid medium or from their instability on the plate or from the plate assay itself was considered. erty
The population
in each
different
of the
frequency
10 plates
days were then classified
of a prop-
assayed
in
10
in the form of
a 10 x 10 contingency table where one-way ANOVA was conducted. One-way ANOVA was carried out with the null hypothesis that there is no difference in the variance of the population frequency between the different days. The results show that the dynamic oscillation of the different
groups is statistically significant (4t.05.9,90 = 1.88) except in the case of the large size of the colony. Hence, it is concluded that the oscillation observed is a characteristic of the behavior of the cells in the liquid medium. Theoretically, in the biological point of view, all cells of the same genotype will have the same
Transformants 0 Day
Fig. 2. Scheme of the successive liquid culture for 30 days. An aliquot of 50 ~1 from the culture of E. coli transformants obtained, as described in the caption of Fig. 1, was inoculated into a fresh 5 ml selection medium contained in a test tube. Cells were cultivated at 37°C for 24 h with reciprocal shaking, after which sampling was done at a definite time. Successive cultivation of the transformants for 30 days was performed by transferring about lo4 cells from the one-day culture into the fresh selection medium and cultivated in the same way. The distributions of enzyme activity and colony size in the one-day culture were assessed by the method described in the caption of Fig. 1. The cell density at the end of the one-day culture was in the range of IO’-IO’.
E. P. Ko et al. I Physica
Days
Days
Fig. 3. Frequency distribution of the enzyme activity (a) and the colony size (b) among the 1000 randomly each day’s culture during the 30 days successive liquid culture (a): (B), ++; (A), +; (O), 2; (El), -. medium; (W), small.
growth rate in the same environment. Therefore, the distribution pattern of the phenotypes in the population will not deviate and remains at a constant level. However, in the case when different phenotypes have variable growth rate, the group of phenotypes having the fastest growth rate will slowly dominate the population during the course of successive culture, and therefore, in the long run will lead to a monotonous increase in their frequency in the population. Accordingly, the dynamic changes observed in the distribution of each group in the population cannot simply be explained by the growth rate of the phenotypes as stated conventionally. Another possible cause for the dynamic change in the frequency of each group is the frequent mutations occurring in the genome leading to the occurrence of different phenotypes that were observed. However, this possibility can be ruled out by the fact, as will be shown in the latter part of the text, that the bacterial population grown from some of the single cells after transformation were found to be homogeneous in their phenotype for at least 3 days under the same experimental procedures as the above 30 days successive cultivation. In other words, if the occurring mutations were frequent enough that it can explain the dynamic oscillations observed, then the chance for obtaining a homogeneous lineage or stable clone would be nil. Therefore, the observed dynamic oscillation is not due to
85
D 75 (1994) 81-88
chosen colonies from (b): (A),
large; (O),
any mutation in the genome including the chromosome and the region of the plasmid other than the structural gene, which was confirmed to be the same even with different phenotypes. It is to be noted that the transformants are grown in the liquid medium allowing the cells to interact freely without any spatial constraint. Therefore, we cannot disregard the possibility that the growth rate of each cell changes and that the property of each cell may shift from a certain level to another during the course of cultivation. These assumptions seem to be justifiable by the new model of Kaneko and Yomo [5] regarding cell differentiation which was based on the former theory of Kaneko [l] showing that many identical elements with chaotic dynamics differentiate into some clusters by interacting globally through a mean field and that the elements in each cluster oscillate in a different way [l]. Indeed, the complex-III stage of the new model corresponds to the dynamic clustering and oscillations observed in the population of the transformants (Fig. 3). To observe more directly the dynamic shifting of one individual phenotype into another, many lines of lineages starting from the single colony of the transformants with different properties defined above were examined. An aliquot culture of the transformants prepared as described above were spread on agar plates to obtain single colonies grown from a single cell. Out of these
86
E.P. Ko et al. i Physica
A.
D 7S (1994) 81-88
Transformants
Heterogeneous
lineage
(ii&
@ Homogeneous
lineage
Heterogeneous
lineage
Fig. 4. Illustration of the S-days successive liquid culture of the different lineages. The one-day liquid culture described in Fig. 2 was done successively for 3 days starting from single colonies. For the A series, the single colonies were obtained from the original culture of the transformants prepared as described in the legend of Fig. 1. For the B series, the single colonies were obtained from the end of the first-day culture showing heterogeneity in the A series. At the end of each day’s culture, heterogeneity of the cell population in the level of the enzyme activity was judged by the Congo Red plate assay [3,4]. For the A series, the heterogeneity of the first inoculum was also assessed.
colonies, 25 were chosen and cultivated successively for 3 days (Fig. 4). Simultaneously, the level of the enzyme activity of the cells in the first inoculum of the 24 h cultures were checked and the results were summarized in Table 1, series A. The first inoculum of the 25 colonies showed that only four were homogeneous while the others were heterogeneous. The level of the
between each enzyme activity is different homogeneous lineage (data not shown). The fact that the inocula contained a heterogeneous cell population indicates that even the cells in the single colony originating from a single cell differentiate and form clusters on the agar plate, while the inocula containing a homogeneous cell population indicates that differentiation may not
E.P. Ko et al. I Physica D 75 (1994) 81-88
Table 1 Distribution of switching pattern between heterogeneous and homogeneous populations in each line of lineages. The cell population was regarded as either heterogeneous (Hetero) or homogeneous (Homo) based on the level of the enzyme activity. For the A series, the judgement was done at the first inoculum and at the end of each day’s culture; for the B series, the judgement was done at the end of each day’s culture. No. of lineages
Series
Type of lineage
A
Hetero+ Hetero-t HeteroHetero+Hetero+Hetero+Homo Homo+ Hetero+ Hetero+ Homo--+Homo+HomoAHomo
B
Hetero-, HeteroHetero+ Homo+ Homo + Homo+ Homo+
Hetero Hetero
Hetero-, Hetero Hetero-, Homo Homo+ Homo HeteroA Hetero Homo + Hetero Hetero-+ Homo Homo+ Homo
19 2 2 2 21 2 1 2 1 1 2
have occurred, thereby showing the heritability of the level of property in the lineage. It should be pointed out that the level of the property of a cell in the liquid medium was examined through the halo size created by the colony grown from a single cell. The above result showed that such colony often contains a heterogeneous cell population and that the evaluation is done not directly on the property of the cell but on the property of the colony. As stated earlier, it was confirmed that through one-way ANOVA, the oscillation of the frequency population of each group between the days is not due to the instability of the cell that multiplies and forms a colony on the plate. The results from the 24 h cultures showed that out of the 21 lineages that were heterogeneous in population from the start, 19 continued to be heterogeneous, but interestingly, two turned into homogeneous on the third day. This indicates that the level of the property of all cells in the culture spontaneously shifted to a uniform level in some cases. In the case of the four lineages having a homogeneous population from the start, two lineages remain to be homogeneous in the population throughout the 3 days successive
87
culture, while the other two turned into a heterogeneous population after 24 h cultivation. These results clearly show that the cells change the levels of their property during the liquid culture where they interact freely. To further observe these dynamic behaviors, 30 colonies were chosen from the heterogeneous population of the 24 h culture of the first-day stage described above, and again, each was cultivated successively in the liquid culture for 3 days. As shown in Table 1 (series B), more varied patterns were observed including the shifting of heterogeneous to homogeneous population and vice versa within one lineage during the span of 3 days. These results indicate that shifting between homogeneous and heterogeneous populations occurs randomly. As mentioned above, there are 4 colonies, numbered 8, 14, 37 and 42, with homogeneous lineage. Qualitative screening of the enzyme activity showed that colonies no. 8 and 42 produced no halo at all, while colonies no. 14 and 37 produced halo sizes of 2.3 mm and 2.1 mm, respectively (data not shown). It was again confirmed that the nucleotide sequence of the structural gene of xylanase in the plasmids of these colonies are precisely the same. The experimental results presented so far clearly show that bacterial cells having the same genotype form various clusters of phenotypes having different levels of property, and that there is dynamic oscillation in the frequency of each cluster in the population during the growth in the liquid culture where the cells can freely interact with each other without any spatial constraint. Clustering of the phenotypes in the liquid culture implies that differentiation can occur and can be observed without any spatial information. The model presented by Kaneko and Yomo [5] coincides well with the results stated above, thereby providing an explanation for the behavior observed with the bacterial cell. The model is based on a globally coupled dynamic system where simple metabolic chemical reactions were introduced into the system of the
88
E.P. Ko et al. I Physica D 75 (1994) 81-88
cell which
are of chaotic
this new model the population
elements.
[5], the temporal of the bacterial
Indeed,
in
oscillation
of
cells shown
in this
paper was found in the complex-III stage of their simulation. Therefore, the living cells, even with the same genotype, with
different
phenotypes
information by liquid medium. From
the
can differentiate interacting
existing
into clusters
without
any
globally
a
is always
to the
present
complexity
biologists
explanatory
framework
in
as large and marked
as the
of the living
have
been
system,
exploring
it
the properties of a purified molecule from the system which instituted the concepts.
on the real behavior
the field of molecular biology, no answer can be drawn for the experimental results described above. So far, in contrast to the results presented here, most of the experimental data reported in the journals of biochemistry and molecular biology do not violate the existing theoretical framework. This may be due to the possibility that these data depict only the average behavior of a system, thereby leveling or even concealing any unusual chaotic behavior characteristic to the individual cells or proteins in the system. In addition, the possibility also exists that many random-looking informations or results gathered in the past are just shelved or even ignored. In contrast, we now report the chaotic behavior of the bacterial cells having the same genotype which could not have been revealed without exploring the phenotype of the individual cell under the same environment. In this case, the behavior of the phenotype of the individual cell in the liquid medium was observed through the colony originated from a single cell on the plate. Hence, each cell was considered as an entity. Briefly, what we advocate here is not that the difference in phenotype of the individual cell in a population
Due molecular through isolated
spatial
through
one shown in our results, but simply that each cell has its own individual character which needs to be considered.
This
way neglects
of the molecule
some
facts
in the living
system where complex interactions with other molecules exist. Therefore, understanding the living system cannot truly be achieved. To attain such goal, studies on the molecule of the living system should be done in its natural environment after which a simple model or concept can be constructed. That is, as shown in this paper, the phenotype of the individual cell was observed through the cells in the liquid medium where they can interact freely without spatial constraint. The results obtained were then justified by the simple model of Kaneko and Yomo [5] regarding dynamic clustering and cell differentiation as based on a globally coupled dynamic system.
References [l] K. Kaneko, Physica D 41 (1990) 137. [2] W. Panbangred, T. Kondo, S. Negoro, A. Shinmyo and H. Okada, Mol. Gen. Genet. 192 (1983) 335-341. [3] E.P. Ko, H. Akatsuka, H. Moriyama, A. Shinmyo. Y. Hata, Y. Katsube, I. Urabe and H. Okada, Biochem. J. 288 (1992) 117-121. [4] R.M. Teather and P.J. Wood, Appl. Env. Microbial. 43 (1982) 777-780. [5] K. Kaneko and T. Yomo, Cell division, differentiation and dynamic clustering, to appear.
PINEA D
fl5l p3
Physica
ELSEVIER
D 75 (1994)
81-88
Dynamic clustering of bacterial population Elizabeth Department
of Biotechnology,
P. Ko, Tetsuya Yomo, Itaru Urabe
Faculty of Engineering,
Osaka University, 2-1 Yamadaoka,
Suita, Osaka 565, Japan
Abstract Bacterial cells having the same genotype were observed to split into a few clusters of phenotypes with various levels of enzyme activity. When the mixture of these phenotypically heterogeneous but genotypically homogeneous cells was cultivated in a liquid medium, the distribution of the population size of each cluster of phenotypes showed various kinds of dynamic oscillations. In addition, when this dynamic behavior was examined for the cells of the single colony, various patterns of shifting of homogeneous to heterogeneous lineage and vice versa were observed in the population. The results imply that differentiation of the cells with the same genotype can occur without spatial information and even under the same environment where the cells interact globally without spatial constraint. This interesting phenomenon totally contradicts the conventional biology that the genotype of a cell uniquely determines the phenotype of the cell and its progeny, but is consistent with the theoretical model of cell differentiation presented in the following paper. The sources of discrepancy between the existing theory in molecular biology and our results were discussed and it is concluded that in understanding a complex living system, a simple model consisting of the essence of the complex system can be constructed justifying the observed properties of the molecules in the system which provide free interactions.
1. Introduction
genotype
It is generally believed that the life of a cell is determined by its genome and environment, and that the genome is accurately duplicated and transmitted to the progeny. In short, the genotype of a cell uniquely determines the phenotype of the cell and its progeny in an environment, except for the occurrence of mutation on the genome. This concept has been applied most explicitly in the system of bacteria such as the Escherichia coli. In the higher organisms, cell differentiation is a well-known phenomenon, in which cells starting from a single cell become to have different phenotypes without changing the 0167-2789/94/$07.00 0 1994 Elsevier SSDZ 0167-2789(94)00068-2
Science
B.V. All rights
(in some cases as shown
in the immune
system the change in the genotype is also observed). This phenomenon was justified to be the cause of the differences in the microenvironment of each cell, and therefore did not violate the above conventional concept. However, it was shown by Kaneko [l] that the complex metabolic system in a living cell may lead the cell to differentiate into cells of different phenotypes through a globally coupled dynamic system. The present paper shows experimental results which cannot be explained by the existing theory in molecular biology and which even contradicts the above mentioned conventional concept. Nevertheless, the results imply that dynamic reserved
82
E.P. Ko et al. I Physica D 75 (1994) 81-88
clustering and differentiation of the cells can occur without any spatial information under the same environment where cells interact globally. Previously we had obtained a gene coding for xylanase, an enzyme catalyzing the hydrolysis of xylan (a polysaccharide) from the bacterium, Bacillus pumilus [2]. Inherently, an enteric bacteria called Escherichia coli (E. coli) does not have the xylanase. Therefore, the xylanase gene obtained was first inserted into a vector plasmid (a small extrachromosomal DNA used as a vehicle for carrying a foreign gene into a microbial cell), and the resulting modified plasmid was then introduced into E. cob. Thus, the modified E. coli produces xylanase through the gene carried on the plasmid [3]. Such modified bacterial cell is generally called a transformed cell or simply a transformat. Six kinds of the mutant genes of xylanase were prepared by replacing one of its amino acid residues with a different one through site directed mutagenesis [3]. Introduction of each of these mutant genes carried by the plasmid vector into E. coli revealed an interesting phenomenon violating the said concept above. In contrast to other cases, only the E. cofi transformants containing a plasmid carrying either one of the two genes coding for mutant xylanases named E182D and E182S exhibited different levels of enzyme activity as shown by the varying halo sizes in the Congo Red plate assay [3,4] (see Fig. lb). These results mean that bacterial cells having the same enzyme gene give rise to different phenotypes. It was confirmed that this unexpected phenomenon is not due to the heterogeneity in the genotype of the transformants as described below. Accordingly, these results revealed that the above conventional concept, where cells having the same genotype give rise to the same phenotype, is not always followed even in a simple system, such as the E. coli, among organisms. Indeed, this interesting phenomenon may imply that E. coli cells carrying a particular gene differentiate into various phenotypes. Here, we will show the dynamic behavior of this phenotypically
heterogeneous population during cultivation shaken liquid medium wherein all cells allowed to grow in the same environment interact freely with each other without constraint.
in a are and any
2. Results and discussion Transformants obtained after a single mutation of the xylanase gene at El82 were found to express different levels of enzyme activity [3]. Though single colony isolation of the transformants was performed, heterogeneity in enzyme activity was still observed. Therefore, the possibility exists that the heterogeneity observed in the population of the transformants with regards to enzyme activity may be due to spontaneous mutation which occurred during the manipulation of the gene. However, when the structural genes harbored in the plasmids of the 15 randomly chosen original transformants expressing different levels of activity were sequenced, it was found that these transformants possessed precisely the same structural gene. The same results were observed with the 14 randomly chosen progenies obtained after single colony isolation. Hence, it was confirmed that the heterogeneity in enzyme activity of the population of transformants is not due to differences in the nucleotide sequence of the gene. Accordingly, this result eliminates the probability that the heterogeneity in enzyme activity is due to contamination. The same mutant gene coding for E182D was again prepared as described previously [3]. E. coli cells were transformed by introducing the plasmid DNA containing both the mutant gene and an ampicillin resistant gene. Therefore, only cells that contain the said plasmid DNA can grow in a medium containing ampicillin (selection medium) owing to the ampicillin resistant gene. This follows that, with the use of this selection medium, any cells without ampicillin
E.P. Ko et al. I Physica D 75 (1994) 81-88
resistance can be eliminated from the population of the transformants. The transformants showed heterogeneity in the colony size as well as in the level of the enzyme activity (Fig. l), confirming the previous
83
observation [3]. According to the category described in the legend of Fig. 1, the transformants were classified into four groups (++, +, +, and -) based on the level of the enzyme activity as determined qualitatively and into three groups
Fig. 1. Heterogeneity in colony size (a) and enzyme activity (b) of E. coli transformants. (a) E. coli transformants containing a plasmid carrying a gene coding for the mutant xylanase (E182D) were prepared by the method described previously [3], and were grown overnight in the selection medium containing Luria-Bertani broth and 50 uglml ampicillin. An aliquot of the diluted overnight culture of the transformants were grown at 37°C for 17-18 h on an agar plate containing the same selection medium and 1.4% agar before measuring the size of the colony. Colonies were then classified according to their sizes into large (2.0-2.7 mm), medium (1.0-1.5 mm), and small (0.35-0.5 mm). (b) The cells taken from each colony were replica plated on the agar plate as stated above containing 0.5% xylan in potassium phosphate buffer (pH 6.5), and were grown at 37°C for 24 h. Enzyme activity was qualitatively screened by the Congo Red plate assay [3,4] where the haloes visualized as shown above are indicative of the activity level, i.e., a larger halo corresponds to a higher enzyme activity exhibited by the colony. Haloes were classified into the following four groups by the size and appearance: (+ +), 3.0-7.1 mm, bright or shiny; (+), 1.0-3.0 mm, dull; (+), blurred; and (-), no halo at all. Below the picture is the designation of the halo sizes observed.
84
E.P. Ko et al. I Physica D 7.5 (1994) 81-88
(large,
medium, and small) based on their size. It was confirmed that the difference
colony between
the groups
macroscopically biguous
case.
This result
cells in the population clusters
there
it should
exhibit
properties, including
various
be discriminated
oscillate
rarely
plitude
clearly
is an am-
shows
that
of the transformants
based on the property
retrospect, cells
can easily
and that
frequency of occurrence of the two groups sisting of the medium and the small colony
form
they possessed.
be emphasized but clustered
that levels
the In
these of the
albeit possessing the same genome the plasmid carrying the mutant en-
zyme gene. Successive culture of the mixture of the phenotypically heterogeneous but genotypically homogeneous transformants obtained above was done for 30 days (Fig. 2). The distribution of the cells with respect to the properties, i.e., the enzyme activity and colony size, in the 24 h culture was determined (see Fig. 1, legend). The results show that the frequency of each cluster exhibiting different levels of the enzyme activity within 30 days of successive cultivation has a dynamic irregular oscillation (Fig. 3a), while the
synchronously
with
(Fig. 3b). Therefore,
a
consizes
constant
whether
am-
this oscilla-
tion observed arises from the behavior of the cells in the liquid medium or from their instability on the plate or from the plate assay itself was considered. erty
The population
in each
different
of the
frequency
10 plates
days were then classified
of a prop-
assayed
in
10
in the form of
a 10 x 10 contingency table where one-way ANOVA was conducted. One-way ANOVA was carried out with the null hypothesis that there is no difference in the variance of the population frequency between the different days. The results show that the dynamic oscillation of the different
groups is statistically significant (4t.05.9,90 = 1.88) except in the case of the large size of the colony. Hence, it is concluded that the oscillation observed is a characteristic of the behavior of the cells in the liquid medium. Theoretically, in the biological point of view, all cells of the same genotype will have the same
Transformants 0 Day
Fig. 2. Scheme of the successive liquid culture for 30 days. An aliquot of 50 ~1 from the culture of E. coli transformants obtained, as described in the caption of Fig. 1, was inoculated into a fresh 5 ml selection medium contained in a test tube. Cells were cultivated at 37°C for 24 h with reciprocal shaking, after which sampling was done at a definite time. Successive cultivation of the transformants for 30 days was performed by transferring about lo4 cells from the one-day culture into the fresh selection medium and cultivated in the same way. The distributions of enzyme activity and colony size in the one-day culture were assessed by the method described in the caption of Fig. 1. The cell density at the end of the one-day culture was in the range of IO’-IO’.
E. P. Ko et al. I Physica
Days
Days
Fig. 3. Frequency distribution of the enzyme activity (a) and the colony size (b) among the 1000 randomly each day’s culture during the 30 days successive liquid culture (a): (B), ++; (A), +; (O), 2; (El), -. medium; (W), small.
growth rate in the same environment. Therefore, the distribution pattern of the phenotypes in the population will not deviate and remains at a constant level. However, in the case when different phenotypes have variable growth rate, the group of phenotypes having the fastest growth rate will slowly dominate the population during the course of successive culture, and therefore, in the long run will lead to a monotonous increase in their frequency in the population. Accordingly, the dynamic changes observed in the distribution of each group in the population cannot simply be explained by the growth rate of the phenotypes as stated conventionally. Another possible cause for the dynamic change in the frequency of each group is the frequent mutations occurring in the genome leading to the occurrence of different phenotypes that were observed. However, this possibility can be ruled out by the fact, as will be shown in the latter part of the text, that the bacterial population grown from some of the single cells after transformation were found to be homogeneous in their phenotype for at least 3 days under the same experimental procedures as the above 30 days successive cultivation. In other words, if the occurring mutations were frequent enough that it can explain the dynamic oscillations observed, then the chance for obtaining a homogeneous lineage or stable clone would be nil. Therefore, the observed dynamic oscillation is not due to
85
D 75 (1994) 81-88
chosen colonies from (b): (A),
large; (O),
any mutation in the genome including the chromosome and the region of the plasmid other than the structural gene, which was confirmed to be the same even with different phenotypes. It is to be noted that the transformants are grown in the liquid medium allowing the cells to interact freely without any spatial constraint. Therefore, we cannot disregard the possibility that the growth rate of each cell changes and that the property of each cell may shift from a certain level to another during the course of cultivation. These assumptions seem to be justifiable by the new model of Kaneko and Yomo [5] regarding cell differentiation which was based on the former theory of Kaneko [l] showing that many identical elements with chaotic dynamics differentiate into some clusters by interacting globally through a mean field and that the elements in each cluster oscillate in a different way [l]. Indeed, the complex-III stage of the new model corresponds to the dynamic clustering and oscillations observed in the population of the transformants (Fig. 3). To observe more directly the dynamic shifting of one individual phenotype into another, many lines of lineages starting from the single colony of the transformants with different properties defined above were examined. An aliquot culture of the transformants prepared as described above were spread on agar plates to obtain single colonies grown from a single cell. Out of these
86
E.P. Ko et al. i Physica
A.
D 7S (1994) 81-88
Transformants
Heterogeneous
lineage
(ii&
@ Homogeneous
lineage
Heterogeneous
lineage
Fig. 4. Illustration of the S-days successive liquid culture of the different lineages. The one-day liquid culture described in Fig. 2 was done successively for 3 days starting from single colonies. For the A series, the single colonies were obtained from the original culture of the transformants prepared as described in the legend of Fig. 1. For the B series, the single colonies were obtained from the end of the first-day culture showing heterogeneity in the A series. At the end of each day’s culture, heterogeneity of the cell population in the level of the enzyme activity was judged by the Congo Red plate assay [3,4]. For the A series, the heterogeneity of the first inoculum was also assessed.
colonies, 25 were chosen and cultivated successively for 3 days (Fig. 4). Simultaneously, the level of the enzyme activity of the cells in the first inoculum of the 24 h cultures were checked and the results were summarized in Table 1, series A. The first inoculum of the 25 colonies showed that only four were homogeneous while the others were heterogeneous. The level of the
between each enzyme activity is different homogeneous lineage (data not shown). The fact that the inocula contained a heterogeneous cell population indicates that even the cells in the single colony originating from a single cell differentiate and form clusters on the agar plate, while the inocula containing a homogeneous cell population indicates that differentiation may not
E.P. Ko et al. I Physica D 75 (1994) 81-88
Table 1 Distribution of switching pattern between heterogeneous and homogeneous populations in each line of lineages. The cell population was regarded as either heterogeneous (Hetero) or homogeneous (Homo) based on the level of the enzyme activity. For the A series, the judgement was done at the first inoculum and at the end of each day’s culture; for the B series, the judgement was done at the end of each day’s culture. No. of lineages
Series
Type of lineage
A
Hetero+ Hetero-t HeteroHetero+Hetero+Hetero+Homo Homo+ Hetero+ Hetero+ Homo--+Homo+HomoAHomo
B
Hetero-, HeteroHetero+ Homo+ Homo + Homo+ Homo+
Hetero Hetero
Hetero-, Hetero Hetero-, Homo Homo+ Homo HeteroA Hetero Homo + Hetero Hetero-+ Homo Homo+ Homo
19 2 2 2 21 2 1 2 1 1 2
have occurred, thereby showing the heritability of the level of property in the lineage. It should be pointed out that the level of the property of a cell in the liquid medium was examined through the halo size created by the colony grown from a single cell. The above result showed that such colony often contains a heterogeneous cell population and that the evaluation is done not directly on the property of the cell but on the property of the colony. As stated earlier, it was confirmed that through one-way ANOVA, the oscillation of the frequency population of each group between the days is not due to the instability of the cell that multiplies and forms a colony on the plate. The results from the 24 h cultures showed that out of the 21 lineages that were heterogeneous in population from the start, 19 continued to be heterogeneous, but interestingly, two turned into homogeneous on the third day. This indicates that the level of the property of all cells in the culture spontaneously shifted to a uniform level in some cases. In the case of the four lineages having a homogeneous population from the start, two lineages remain to be homogeneous in the population throughout the 3 days successive
87
culture, while the other two turned into a heterogeneous population after 24 h cultivation. These results clearly show that the cells change the levels of their property during the liquid culture where they interact freely. To further observe these dynamic behaviors, 30 colonies were chosen from the heterogeneous population of the 24 h culture of the first-day stage described above, and again, each was cultivated successively in the liquid culture for 3 days. As shown in Table 1 (series B), more varied patterns were observed including the shifting of heterogeneous to homogeneous population and vice versa within one lineage during the span of 3 days. These results indicate that shifting between homogeneous and heterogeneous populations occurs randomly. As mentioned above, there are 4 colonies, numbered 8, 14, 37 and 42, with homogeneous lineage. Qualitative screening of the enzyme activity showed that colonies no. 8 and 42 produced no halo at all, while colonies no. 14 and 37 produced halo sizes of 2.3 mm and 2.1 mm, respectively (data not shown). It was again confirmed that the nucleotide sequence of the structural gene of xylanase in the plasmids of these colonies are precisely the same. The experimental results presented so far clearly show that bacterial cells having the same genotype form various clusters of phenotypes having different levels of property, and that there is dynamic oscillation in the frequency of each cluster in the population during the growth in the liquid culture where the cells can freely interact with each other without any spatial constraint. Clustering of the phenotypes in the liquid culture implies that differentiation can occur and can be observed without any spatial information. The model presented by Kaneko and Yomo [5] coincides well with the results stated above, thereby providing an explanation for the behavior observed with the bacterial cell. The model is based on a globally coupled dynamic system where simple metabolic chemical reactions were introduced into the system of the
88
E.P. Ko et al. I Physica D 75 (1994) 81-88
cell which
are of chaotic
this new model the population
elements.
[5], the temporal of the bacterial
Indeed,
in
oscillation
of
cells shown
in this
paper was found in the complex-III stage of their simulation. Therefore, the living cells, even with the same genotype, with
different
phenotypes
information by liquid medium. From
the
can differentiate interacting
existing
into clusters
without
any
globally
a
is always
to the
present
complexity
biologists
explanatory
framework
in
as large and marked
as the
of the living
have
been
system,
exploring
it
the properties of a purified molecule from the system which instituted the concepts.
on the real behavior
the field of molecular biology, no answer can be drawn for the experimental results described above. So far, in contrast to the results presented here, most of the experimental data reported in the journals of biochemistry and molecular biology do not violate the existing theoretical framework. This may be due to the possibility that these data depict only the average behavior of a system, thereby leveling or even concealing any unusual chaotic behavior characteristic to the individual cells or proteins in the system. In addition, the possibility also exists that many random-looking informations or results gathered in the past are just shelved or even ignored. In contrast, we now report the chaotic behavior of the bacterial cells having the same genotype which could not have been revealed without exploring the phenotype of the individual cell under the same environment. In this case, the behavior of the phenotype of the individual cell in the liquid medium was observed through the colony originated from a single cell on the plate. Hence, each cell was considered as an entity. Briefly, what we advocate here is not that the difference in phenotype of the individual cell in a population
Due molecular through isolated
spatial
through
one shown in our results, but simply that each cell has its own individual character which needs to be considered.
This
way neglects
of the molecule
some
facts
in the living
system where complex interactions with other molecules exist. Therefore, understanding the living system cannot truly be achieved. To attain such goal, studies on the molecule of the living system should be done in its natural environment after which a simple model or concept can be constructed. That is, as shown in this paper, the phenotype of the individual cell was observed through the cells in the liquid medium where they can interact freely without spatial constraint. The results obtained were then justified by the simple model of Kaneko and Yomo [5] regarding dynamic clustering and cell differentiation as based on a globally coupled dynamic system.
References [l] K. Kaneko, Physica D 41 (1990) 137. [2] W. Panbangred, T. Kondo, S. Negoro, A. Shinmyo and H. Okada, Mol. Gen. Genet. 192 (1983) 335-341. [3] E.P. Ko, H. Akatsuka, H. Moriyama, A. Shinmyo. Y. Hata, Y. Katsube, I. Urabe and H. Okada, Biochem. J. 288 (1992) 117-121. [4] R.M. Teather and P.J. Wood, Appl. Env. Microbial. 43 (1982) 777-780. [5] K. Kaneko and T. Yomo, Cell division, differentiation and dynamic clustering, to appear.