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Chromosomal origin of replication coordinates logically
distinct types of bacterial genetic regulation
Kosmas Kosmidis
1,2
, Kim Philipp Jablonski
3,5
, Georgi Muskhelishvili
4
and Marc-Thorsten Hütt
3
✉
For a long time it has been hypothesized that bacterial gene regulation involves an intricate interplay of the transcriptional
regulatory network (TRN) and the spatial organization of genes in the chromosome. Here we explore this hypothesis both on a
structural and on a functional level. On the structural level, we study the TRN as a spatially embedded network. On the functional
level, we analyze gene expression patterns from a network perspective (“digital control”), as well as from the perspective of the
spatial organization of the chromosome (“analog control”). Our structural analysis reveals the outstanding relevance of the
symmetry axis defined by the origin (Ori) and terminus (Ter) of replication for the network embedding and, thus, suggests the co-
evolution of two regulatory infrastructures, namely the transcriptional regulatory network and the spatial arrangement of genes on
the chromosome, to optimize the cross-talk between two fundamental biological processes: genomic expression and replication.
This observation is confirmed by the functional analysis based on the differential gene expression patterns of more than 4000 pairs
of microarray and RNA-Seq datasets for E. coli from the Colombos Database using complex network and machine learning methods.
This large-scale analysis supports the notion that two logically distinct types of genetic control are cooperating to regulate gene
expression in a complementary manner. Moreover, we find that the position of the gene relative to the Ori is a feature of very high
predictive value for gene expression, indicating that the Ori–Ter symmetry axis coordinates the action of distinct genetic control
mechanisms.
npj Systems Biology and Applications (2020) 6:5 ; https://doi.org/10.1038/s41540-020-0124-1
INTRODUCTION
In spite of the tremendous progress made in Systems Biology
1–3
and the construction of computational models of biological
cells,
4,5
we still lack the appropriate understanding of the
underlying principles of genetic regulation to predict, for example,
the gene expression pattern of a bacterium. Since the beginning
of Systems Biology, the investigation of bacterial gene regulation
has been an important source of hypotheses about the principles
of biological regulation.
6–9
The transcriptional regulatory network
(TRN) of the classical model organism Escherichia coli has been the
subject of a vast number of statistical analyses. In fact, this
network has been the first example of a complex network for
which a non-random network motif distribution (deviations from
randomness of the counts of small subgraphs) has been
reported.
6,10
In spite of its prominence and the diversity of
investigations, this network has been mostly studied in isolation.
It is becoming ever clearer that beyond network topology itself,
the spatial embedding of complex networks provides an
important additional layer of information for understanding a
network’s function.
11,12
While this aspect has been explored in
transportation networks,
13,14
brain networks
15,16
and a wide range
of other natural and technical systems,
17,18
it has not been studied
in much detail in the gene regulatory system. In particular, only
few aspects of the spatial embedding of the E. coli TRN have been
studied before, e.g., the spatial (i.e., chromosomal) distribution of
genes with and without a reported link in the TRN
19,20
and the
orientation of genes on the genome.
21
It is also intuitive (and in fact a prominent research trend of the
last years, see e.g.,
12
) that spatially embedded networks need to
be analyzed with a different set of tools than graphs without such
a spatial embedding. For example, the concept of a dimension,
which has been rarely discussed in complex network theory was
found to be an important property of spatially embedded
networks.
22
In a spatially embedded network typically long-
ranging links have a different systemic purpose than short-ranging
links. For example, in social networks most people have their
friends in their neighborhood, and the arrangement of connec-
tions in power grids and transportation networks obviously
depends on the distance between the connected units. Consider-
ing the network of passenger flights, it is systemically plausible
that such links occur only above a certain spatial distance. The
transcriptional regulatory network is a somewhat non-standard
example of a spatially embedded network, as the “space”, i.e., the
3D organization of the circular chromosome, is not immediately
obvious. We explore the hypothesis that bacterial gene regulation
is organized as an interplay of two distinct types of control—one
exerted by the TRN (“digital control”) and one arising from the
spatial organization of the chromosome (“analog control”). This
hypothesis has been formulated,
23,24
put into a broader con-
text
25,26
and supported by statistical analyses
27–29
in a range of
studies over the last decade, but has yet to be confirmed as a
consistent organizational principle across all layers of quantita-
tively assessable information.
Here we first address the interplay of digital and analog control
on a purely structural level, by analyzing the chromosomal
embedding of the TRN of E. coli. Next, we extend this investigation
to a functional level by employing a method proposed in the
ref.
27
to quantify the strengths of the two control types by using
data from the COLOMBOS
30
database and perform a large-scale
study of the interplay between digital and analog control.
1
Division of Theoretical Physics, Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece.
2
PharmaInformatics Unit, Research Center ATHENA, Athens,
Greece.
3
Department of Life Sciences and Chemistry, Jacobs University, Bremen, Germany.
4
Department of Biology, Agricultural University of Georgia, Tbilisi, Georgia.
5
Present
address: Department of Biosystems Science and Engineering, ETH Zürich, Zürich, Switzerland ✉email: m.huett@jacobs- university.de
www.nature.com/npjsba
Published in partnership with the Systems Biology Institute
1234567890():,;
COLOMBOS is a collection of expression data from published
microarrays and RNA-Seq experiments performed in E. coli (and
several other prokaryotes). COLOMBOS combines expression data
analyses across different research papers, labs, and platforms. A
key idea in COLOMBOS is to compare relative expression values to
a reference state as sets of “condition contrasts”. This should
correct for platform-dependent differences between studies. The
expression data contained within the database are also linked to a
manually curated, standardized condition annotation, and ontol-
ogy. Figures 1,2summarizes the design of our study.
By analyzing (i) the distribution statistics of links in the
transcriptional regulatory network, (ii) the agreement of gene
expression patterns with both, the TRN and the distribution of
genes in the genome, and (iii) the “learnability”of gene expression
patterns by a decision tree employing various chromosomal and
regulatory features we have been able to establish two main
components of the logic underlying bacterial gene expression: (1)
The Ori–Ter axis is a relevant organizer of gene expression; (2)
Chromosomal structure (“analog control”) and transcription
factors (“digital control”) contribute to regulation in an “either–or”
fashion with one level of control buffering the other.
RESULTS
Structural evidence for the interplay of digital and analog control
and the relevance of the Ori–Ter axis
We start by employing methods from statistical physics of
complex networks, in order to identify the non-random features
characterizing the chromosomal embedding of the transcriptional
regulatory network.
A key assumption of our investigation is that in spite of the
complex and spatiotemporally variable 3D organization of the E.
coli chromosome, the linear organization given by the positional
order of genes along the chromosome is a relevant coordinate
system for investigating a non-random spatial embedding of the
TRN. This assumption is strongly supported by the study of
distributions of genes with and without TRN participation,
20
the
statistical analysis of gene expression patterns along the
chromosomal coordinates
27,31
and the phenotypic changes
contingent on positional shifts of genes encoding the transcrip-
tion factors in the chromosome.
32,33
Perhaps unsurprisingly, application of standard tools for the
analysis of spatially embedded networks does not reveal striking
non-random features of the chromosomal embedding of the TRN
and only provides weak evidence for the co-evolution of these
two biological structures
34
(see Supplementary Figs 1, 2).
As a consequence, we develop and apply a set of methods
tailor-made for the biological system analyzed here, thus
addressing the core question: Is the transcriptional regulatory
network systematically shaped by the chromosomal embedding?
Given the known relevance of the Ori–Ter axis dividing the
circular chromosome into the right and left arms for genetic
regulation,
31
we can rephrase the question: Is the chromosomal
embedding of the transcriptional regulatory network particular
with respect to the Ori–Ter axis? Our analysis strategy in the
following is to compute network quantities under rotation of this
axis and see, whether the true axis stands out. The method,
termed EDURA (edge distribution under rotation of an axis; see
Fig. 2) is based on the principles described below.
Given the position of an axis, we distinguish between six
categories of edges, namely edges on the right chromosomal arm
pointing away from the origin of replication Ori, r
+
, or towards the
Ori, r
−
and the same on the left arm, l
+
and l
−
, respectively, as well
as edges across the two chromosomal arms, from right to left, rl,
and from left to right, lr. Figure 1illustrates these categories using
a small sample graph. The labels “left”and “right”are understood
looking from Ori to Ter. A schematic representation of the EDURA
method is given in Supplementary Fig. 3.
It is clear that, when a different axis is chosen, these edge
categories change. The counts n(r
+
), etc. can now be evaluated for
each position of an axis. Under rotation of the axis an edge will
undergo a systematic sequence of category transitions. Starting
from lr as an example, a typical sequence under axis rotation will
be lr →r
+
→rl →l
−
. As a consequence, counts of link types are
highly correlated and strongly dependent on gene density and
Fig. 1 Summary of our investigation and overview of the
workflow. On the structural level (obtained from RegulonDB,
55
),
the spatial embedding of the TRN within the circular chromosome is
evaluated via the EDURA (Edge Distribution Under Rotation of an
Axis) method. The functional level is contributed by the COLOMBOS
database
30
and analyzed jointly with the structural information
using the concepts of digital and analog control strengths,
27
as well
as decision trees.
Fig. 2 Illustration of the edge categories used in the subsequent
analysis. The light blue circle represents the circular chromosome,
while the dots represent genes (red: right chromosomal arm; blue:
left chromosomal arm). Directed edges indicate interactions
between genes. The dashed blue line denotes the axes used for
the assignment of edge categories (with the longer end
representing Ori).
K. Kosmidis et al.
2
npj Systems Biology and Applications (2020) 5 Published in partnership with the Systems Biology Institute
1234567890():,;
node degree. Figure 3shows the counts n(r
+
), etc. as a function of
the axis position for the real chromosomally embedded E. coli TRN.
The highly volatile nature of these counts, as well as the strong
influence of gene density, systematic transitions (leading to high
correlations among the curves) and contribution of hubs (e.g.,
dramatic changes in the curves due to many edges changing
category at the same time) are clearly visible.
In order to remove these direct effects on the edge categories,
we have to (1) consider asymmetries, rather than absolute counts,
of the edge categories and (2) subtract the average signal
observed in a randomized graph (see Methods section). The ±
asymmetry indicating a mismatch between edges going down
and going up for one chromosomal arm can be defined as
Ar
±¼nðrþÞnðrÞ
nðrþÞþnðrÞþnðrlÞ;(1)
and accordingly for Al
±. The “cross–along”asymmetry, measuring
the asymmetry between edges along the chromosomal arms and
across them, is defined as
A$l ¼nðlrÞþnðrlÞnðlþÞnðlÞnðrþÞnðrÞ
nðlrÞþnðrlÞþnðlþÞþnðlÞþnðrþÞþnðrÞ;(2)
which is the number of edges across the arms minus the number
of edges along the arms, normalized by the total number of
edges. Without any clear systematics with respect to a given axis,
the asymmetries will display strong correlations, due to the
transition rules outlined above. Any disruption of these correla-
tions at some axis position is an indicator of the non-random
features of the network for this axis.
Using randomly generated networks with a systematic edge
distribution with respect to an axis (systematic random networks;
see Methods section) we can test and calibrate the EDURA
method (see Supplementary Information). These tests show that,
indeed, a specific axis inscribed in the edge distribution is
detected via the EDURA method as drastic drops in correlation
among the edge category asymmetries for this axis position (see
Supplementary Fig. 4). In Fig. 4the same analysis is performed for
the real E. coli TRN.
The first statistical analysis supports the earlier findings,
20
where
via point process statistics it was found that genes under known
direct transcriptional regulation are systematically more distal on
the chromosome than genes without transcriptional regulation,
confirming the general idea that bacterial gene regulation is
organized as an interplay of network-based (digital) control and
(analog) control based on the spatial organization of the
chromosome. In order to go beyond the confirmation of the
previous finding
20
we resort to a common technique of network
science, the comparison with randomized graphs as a method for
identifying the higher-order non-random features of a given
network. In this way we find structural evidence for the
chromosomal embedding of the network being systematic with
respect to one characteristic spatial axis in the circular chromo-
some (Fig. 4). This axis is defined by the origin (Ori) and terminus
(Ter) of replication. Previously it was argued that the spatiotem-
poral organization of genomic transcription indeed follows the
two replichores as the main spatial organizers.
31
Here we find that
the network architecture itself carries an evolutionary imprint of
this bilinear space defined by the two replichores.
Functional evidence for the interplay of digital and analog control
In order to assess the functional implications of this structural
interdependence of the transcriptional regulatory network and
the spatial organization of the chromosome we resort to the
COLOMBOS representation of the Gene Expression Omnibus
(GEO) database. For a large number of gene expression datasets,
we measure the agreement of significant expression changes with
the network and with chromosomal neighborhoods by employing
the quantification methods for digital and analog control
strengths defined previously.
27
We start our investigation by creating the transcriptional
regulatory network (TRN) and the gene proximity network (GPN)
Fig. 3 Analysis of edge categories in the E. coli TRN. a
Representation of the chromosomally embedded E. coli TRN. As in
Fig. 1the large light blue circle represents the circular chromosome
and the blue line indicates the Ori–Ter axis. Black dashes on the
chromosome indicate genes. bEdge categories for the chromoso-
mally embedded E. coli TRN from aas a function of the axis position.
The true Ori and Ter positions are indicated as a reference.
Fig. 4 Edge category asymmetry analysis for the real E. coli TRN.
Asymmetries as a function of the assumed axis position (upper
panel). Correlation coefficient of Ar
±and Al
±as a function of the
assumed axis position (lower panel).
K. Kosmidis et al.
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of the E.coli genome. Details of these two networks are found in
the Methods section.
Then, for each of the ~4000 experimental datasets obtained
from the COLOMBOS database we generate “effective”TRN and
GPN networks by removing the nodes that are not significantly
differentially expressed as well as all their links.
Supplementary Fig. 5 (left) shows and example of such an
“effective TRN”. It depicts data from the experiment GSE10158
which contains microarray data on the expression profile of E. coli
treated with cefsulodin and mecillinam, both alone and in
combination. The figure shows the 22 genes whose expression
level was significantly altered comparing the contrasts with id’s
GSM256904_ch1 and GSM256868_ch1. Genes on the graph are
positioned on a circle according to their coordinates on the E.coli
chromosome. Supplementary Fig. 5 (right) presents a view of an
“extended”TRN subgraph which contains the differentially
expressed genes (blue points) plus all the genes that are
connected to the differentially expressed ones in the E. coli TRN
although without significantly altered expression levels (yellow
points). The extended network comprises 90 genes. A complete
understanding of regulatory control, about which the present
manuscript is a first step, should aim in explaining why the “blue”
genes were differentially expressed while the “yellow”ones were
not, despite their immediate connection on the TRN which
indicates a strong interaction between the two.
Figures 5,6show scatter plots of the digital vs. analog control
strengths of more than 4000 effective E. coli networks derived
from the COLOMBOS database (see Methods section and
particularly the Effective Networks subsection). Figure 5shows
data for 104 high quality RNA-Seq experiments. The results
demonstrate an anti-correlation between digital and analog
control strength with a Spearman correlation coefficient of −0.34.
Figure 6shows data for 3969 effective networks constructed
from contrasts of microarray experiments. The results demonstrate
once more an anti-correlation between digital and analog control
strengths with a Spearman correlation coefficient of −0.16. A
heatmap representation of the corresponding rank-based
scatterplots is given in Supplementary Figs 15 (RNA-Seq) and 16
(microarray). In line with the negative correlations discussed here,
these heatmap representations show the buffering relationship
between digital and analog control: high rank values of analog
control go along with low rank values of digital control and
vice versa.
Our analysis reveals the systematic anti-correlation of digital
and analog control as a large global trend in bacterial
transcriptomes. In this way, it confirms the buffering of these
two categories of bacterial gene regulation that was hypothesized
before
27
based on a set of transcriptome profiles obtained under a
dedicated experimental variation of both, the machinery of digital
control (via the analysis of hub mutants in the transcriptional
regulatory network) and analog control (via the alteration of
supercoiling energy in the genome induced by topoisomerase
poisons). Our new results show that the anti-correlation of these
distinct logical types of regulation is not limited to perturbations
of the regulatory machinery, but persists across a wide range of
experimental conditions (phenotypes) and genotypes.
Strikingly, the anti-correlation between digital and analog
control strengths is much stronger for significantly downregulated
than for upregulated genes, when these two categories are
analyzed separately (see Supplementary Figs 8, 9). This statistical
difference between downregulated and upregulated genes is in
line with the earlier observation
35
that the “ground state”(or
default state) in prokaryotic gene regulation is nonrestrictive (or
“on”), as opposed to eukaryotic gene regulation, where the
ground state is restrictive (or “off”). It is then intuitive that the
systematic interplay between digital and analog control reveals
itself in the pattern of deviations from the ground state, i.e., in the
downregulated genes.
We have re-computed our results varying the two main
parameters of our analysis, namely the logFC threshold for
determining differentially expressed genes and the distance
threshold defining links in the GPN (see Supplementary Figs 11,
12). This parameter variation confirms the robustness and strong
statistical validity of our findings. As an additional confirmation we
Fig. 5 Digital vs. analog control for gene-level RNA-Seq data. Data
for 104 effective networks resulting from contrasts of RNA-Seq
experiments have been analyzed. Central panel: Scatter plot of the
digital vs. analog control strengths. Top panel: Histogram of the
distribution of analog control strength. Right panel: Histogram of
the distribution of digital control strength.
Fig. 6 Digital vs. analog control for gene-level microarray data.
Data for 3969 effective networks resulting from contrasts of
microarray experiments have been analyzed. Central panel: Scatter
plot of the digital vs. analog control strengths. Top panel: Histogram
of the distribution of analog control strength. Right panel:
Histogram of the distribution of digital control strength.
K. Kosmidis et al.
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npj Systems Biology and Applications (2020) 5 Published in partnership with the Systems Biology Institute
computed the interplay of digital and analog control strengths
also on the operon level (see Supplementary Figs 13, 14), leading
qualitatively to the same results.
Summarizing, our results demonstrate for the first time that the
tight coupling between digital (network-based) and analog
(chromosomal) control goes far beyond the response to
perturbations specifically designed to affect one of the two
control types (as reported previously
27
), but is a universal property
of bacterial gene regulation.
Decision tree analysis of transcriptome profiles and the relevance
of the Ori–Ter axis
In order to ascertain that the anti-correlation observed in the large
set of transcriptome profiles is not dependent on our choice of
quantification method, namely the digital and analog control
strengths, we also used a machine learning framework in order to
measure, which structural features are employed to predict
significant expression changes from the database of transcriptome
profiles, when the feature set consists of nine quantitative
variables (see Methods section, Decision Trees) selected to
represent a wide range of network and chromosomal properties.
This set of features is specifically designed to highlight the
impacts of either digital or analog control in a given expression
profile.
Here we are not interested in the quality of the classification
(and, hence, do not separate the data into training and test data),
but rather in the features employed by the decision tree to split
the genes in an expression contrast into “differentially expressed”
and “not differentially expressed”. As our main goal is to assess the
interplay between digital and analog control at work in these
gene expression patterns, we use a set of features, which can
either be associated with digital control (number of differentially
expressed regulators of a gene in the TRN, hns regulating the
gene, fis regulating the gene, crp regulating the gene) or analog
control (number of differentially expressed neighbors in the GPN,
hns binding site density near a gene’s location, fis binding site
density, crp binding site density), as well as one feature not
directly classifiable as digital or analog control, namely the
position of a gene relative to the Ori. For each gene expression
contrast we can now compute the relative importance of each of
these features in classifying genes according to their differential
expression. The question here is, whether the decision tree
predominantly employs analog features in contrasts with high
analog control strength and, conversely, digital features in
contrasts with high digital control strength.
In this analysis, we use the binding sites only as a proxy for local
structural features of chromosome. Previous studies demonstrated
that the gene order along the Ori–Ter axis is highly conserved in
bacteria.
31
This spatial order is apparent not only for the principal
regulatory genes (such as e.g., RNA polymerase sigma factors and
nucleoid-associated proteins) but also for their targets. Further-
more, while the chromosomal position of a gene is thought to be
determinative for the gene copy number and expression level,
36–39
recent studies strongly suggest that it is also determinative for the
spatial location of the gene product in the cell. In particular, the
regulatory proteins were found to diffuse from their cognate sites
of production forming gradients.
40,41
This suggests that the
genomic distances between the transcriptional regulators and
their targets are subject to evolutionary constraints and that in
general, regulatory genes would be preferentially positioned in
the vicinity of target genes.
21
However, spatial considerations
imply a different effect in the case of highly abundant DNA
architectural proteins, such as e.g., the nucleoid-associated
proteins, that diffuse over relatively large distances, bind
cooperatively at hundreds of chromosomal sites and compact
the DNA by constraining DNA supercoils over extended chromo-
somal regions.
24,42–44
Variable spatial distributions of
nucleoprotein complexes formed by global regulators such as
e.g., FIS and H-NS modulate the structural dynamics of the
chromosome exerting continuous or analog effects on genetic
expression reflected in directionally coherent changes of tran-
script patterns involving neighboring genes
45,46
that can be
readily measured by estimating the analog control strength in the
effective networks.
We have generated decision trees for each of the microarray
and RNA-Seq effective networks in our possession and used them
to estimate the importance of all of the nine features in each case.
In order to exclude the effects of randomness in the estimation of
importance, the differentially expressed genes for each of the
individual effective networks were shuffled 100 times and decision
trees were used to estimate the feature importance of these
randomized cases. Subsequently, we subtracted the mean of the
randomized importances from the actual feature importance.
The results form a matrix of nine columns and 3969 rows for the
microarray data and 104 rows for the RNA-Seq data. This matrix
can be augmented, if we include the digitalCTC and the
analogCTC as two additional columns, especially since we are
interested in investigating how the proposed measures of
digitalCTC and analogCTC correlate with the features used to
characterize the expressed E. coli genes. As before, the RNA-Seq
and microarray experiments were analyzed separately. Figure 7
(left panel) shows the Spearman correlation coefficient between
analogCTC and each of the features for networks derived from the
RNA-Seq experiments. Figure 7(right panel) shows the same, but
for the digitalCTC. Similarly, Fig. 8(left panel) shows the Spearman
correlation coefficient between analogCTC and each of the
features for networks derived from the microarray experiments
and Fig. 8(right panel) shows the same for the digitalCTC.
In all cases we observe a high correlation between digitalCTC
and the “digital”features, i.e., trn cont,hns dig cont,fis dig cont and
crp dig cont. We also observe a high correlation between
analogCTC and gpn cont, which is a very characteristic analog
control feature. The overall trend is in agreement of what is
expected by the assumption of the existence of two complemen-
tary forms of transcriptional control and provides a proof that the
quantities of analogCTC and digitalCTC are a reliable means of
Fig. 7 Feature importance correlations for RNA-Seq data. (Left)
Spearman correlation coefficient between analogCTC and each of
the features for networks derived from the rnaseq experiments.
(Right) The same for the digitalCTC. The color code above each bar
is: blue—analog control feature, red—digital control feature, green
—dual feature (related to the Ori–Ter axis).
K. Kosmidis et al.
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Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2020) 5
measuring the impact of digital and analog control mechanisms of
gene regulation in the expression profiles.
The systematic anti-correlation between features associated
with digital control and features associated with analog control, as
well as the relevance of the Ori–Ter axis (via the relevance of the
distance from Ori as a feature integrated in the machine learning
analysis) confirm the results from the previous two sections.
More specifically, we find that the relative position of a gene
with regard to the chromosomal Ori, that is along the Ori–Ter axis,
is a feature of very high predictive value for gene expression.
Despite its clear impact, we cannot readily attribute the influence
of the Ori–Ter symmetry axis either to purely digital or to purely
analog type of control. Therefore, we consider this axis as a third
essential and distinct regulatory element of the system, i.e., a
coordinator of gene expression.
DISCUSSION
In this study we set out to integrate two different modes of
transcriptional regulation, one mediated by the TRN and another
by spatial organization of the chromosome. For this purpose we
applied a set of structural and functional analyses. We hypothe-
sized that the TRN is spatially embedded in the chromosome such
that the pattern of directed links is highly non-random with
respect to a single axis converting the circular space (i.e., the
circular chromosome) into two linear branches (the chromosomal
“arms”). We set out to identify this organizational principle, as well
as the position of the axis, by computing a set of statistical
quantifiers for each candidate position of such an axis and then
observing clear systematics in the behavior of these topological
features emerging when we approach the true axis position. This
novel data analysis is called EDURA (Edge Distribution Under
Rotation of an Axis). One counter-intuitive aspect of the EDURA
result is that the disruption of correlations is the relevant signal.
This follows from the transformation properties of link categories
indicated in the previous section with l
+
transforming first into rl
and then into r
−
upon rotation of the axis. Highly correlated link
counts are therefore the default, while a sudden drop in
correlation is indicative of a systematic arrangement of links with
respect to this position of the axis. We have tested and confirmed
this view by a detailed analysis of random graphs with a
systematic link distribution bias with respect to a randomly
selected axis (see Methods section, “Systematic random net-
works”; see Supplementary Fig. 4 for an example of EDURA for a
systematic random network). Beyond the set of findings on
bacterial gene regulation, we are convinced that the EDURA
method, together with the axis-systematic random networks, will
be of relevance for the analysis of a range of other spatially
embedded networks.
We discovered a systematic orientation of the network with
respect to the Ori–Ter axis indicative of an evolutionary co-
adaptation of replication and transcriptional regulation. Indeed, in
E. coli and other bacteria the collisions between the transcription
machinery and the replisomes progressing bi-directionally from
the Ori towards the Ter pose problems potentially leading to
genetic instability,
47
and this conflict has been widely studied
both in prokaryotes
48
and eukaryotes.
49
It is revealing that we find
an evidence for an evolutionary adjustment of these two
fundamental levels of cellular DNA transactions—replication and
gene regulation—on a purely structural level (via the embedding
of the network in the chromosome), as well as on a functional
level in gene expression profiles. This means that replication and
transcription are coordinated from the same assessment center
using the Ori–Ter axis as a system of coordinates, providing a new
rationale for understanding the evolution of chromosomal gene
organization.
Our results confirm previous observations of two logically
distinct—digital and analog—types of transcriptional regulation in
E. coli
20,27
and demonstrate an anti-correlation of digital and
analog control strengths across a wide range of genotypes and
phenotypes. Futhermore we clearly show the dualistic nature of
digital and analog control via feature selection in a classification of
transcriptome profiles based on machine learning, with additional
evidence for relevance of the Ori–Ter axis. This is clearly visible in
Fig. 7(RNA-Seq) and Fig. 8(microarray), which show the
correlation of each feature with analog (left) and digital (right)
control strengths. First of all, the previously discussed anti-
correlation of digital and analog control strengths is clearly visible.
Furthermore, one can see that, indeed, the analog features tend to
correlate with analog control strengths, while the digital features
rather correlate with digital control strength. Only the position
relative to the Ori stands out: It is (slightly) negatively correlated
with both, digital and analog control strengths. These systematics
of the correlations are the same for RNA-Seq data (Fig. 7) and
microarray data (Fig. 8). Hence we denote this symmetry axis as a
coordinator of genetic regulation. It is noteworthy that our data
predominantly consist of statistical signals made visible by
comparison with null models as well as methods from machine
learning. In all cases we average over a wide range of conditions
and individual cases (for example, the transcriptome profiles of
diverse origins or the high variation in gene density across the
chromosome). As a consequence of these averaging procedures
most of the signals will necessarily be rather faint. We would like
to emphasize, however, that each of the signals reported here is
highly significant and, in combination, the collection of statistical
signals from the structural investigation, the assessment of
transcriptome profiles and the machine learning classification
task furnish a structural and dynamical foundation of digital and
analog control in bacterial gene regulation.
Taken together, these data provide a very clear picture, where
the set of ideas about chromosomal DNA topology as a
fundamental level embedding the transcriptional regulation in
bacteria discussed in the literature already for several dec-
ades
23,24,26,27,50
is confirmed and the evidence for an evolutionary
alignment of two fundamental levels of cellular organization—
replication and gene regulation—is found on a purely structural
level (via the embedding of the network in the chromosome), as
Fig. 8 Feature importance correlations microarray data. (Left)
Spearman correlation coefficient between analogCTC and each of
the features for networks derived from the microarray experiments.
(Right) The same for the digitalCTC. The color code above each bar
is: blue—analog control feature, red—digital control feature, green
—dual feature (related to the Ori–Ter axis).
K. Kosmidis et al.
6
npj Systems Biology and Applications (2020) 5 Published in partnership with the Systems Biology Institute
well as on a functional level in the design of gene expression
patterns. Notably, the embedding of a network in space along a
systemically defined axis can potentially be of relevance for a wide
range of systems. Sensory systems for example have an axis along
the hierarchical depth from the input nodes to processing nodes
generating ever more abstract representations of the sensory
input.
51,52
The same is true for manufacturing systems with their
hierarchy of input, production and assembly/output layers.
53
The situation we face in our attempts to epitomize the
spatiotemporal constraints imposed on the emergence of gene
expression patterns is reminicent of the work by Brockmann and
Helbing
54
on the spread of epidemic diseases. They show that the
complex spatiotemporal pattern of disease occurrences becomes
a simple propagating wave on a tree graph derived from shortest
flight distances. Distances in this “re-arranged world”are much
more meaningful than geographic distances. Here, “space”is the
genome and the air traffic network is the TRN, which facilitates the
spreading of information across the genome. In that work
54
the
spatial distance was ignored. Adapting their formalism to the case,
where a mixture of spatial and network distances defines the re-
arranged “world”would allow a completely novel view on gene
expression profiles.
METHODS
Transcriptional regulatory network
In our investigation, a TRN is a graph whose nodes represent genes. If a
gene aencodes a transcription factor A, which regulates another gene b
then a link pointing from ato bis inserted in the graph. The E. coli TRN
used for the present paper was created using data from RegulonDB,
55
a
freely available database of the regulatory network of Escherichia coli K-12.
The TRN we have used has 1771 nodes and 3975 edges. Its minimum node
degree is equal to one, the maximum node degree is equal to 496 and the
average degree is equal to 4.49. The largest cluster of the TRN consists of
1678 nodes and has 3788 edges. It is a disassortative network with a
degree assortativity coefficient equal to −0.32 meaning that high degree
nodes tend to connect to low degree nodes and slightly avoid "hub”–"hub”
connections.
It is well known that genes are organized in operons i.e., groups of genes
sharing a regulatory domain. In order to check for and exclude the
contributions of the “operon”effect we have also performed our
investigations on a modified version of the TRN where the nodes are
operons instead of genes and a link between two operons is present if a
gene in one operon produces a transcription factor that regulates a gene
of the second operon. The largest cluster of this operon TRN consists of
816 nodes and 1551 edges with max degree equal to 220 and average
degree equal to 3.80.
Gene proximity network
The GPN is an undirected graph of 4609 nodes and 90,878 edges. It is a
formal representation of the spatial organization of the chromosome.
Following the prescription from earlier work,
27
nodes represent genes and
are connected to each other, if their “centers”are separated by a distance
less or equal to a distance threshold of T
GPN
=20 kilobase pairs (kbp) on
the circular DNA chromosome. The info required for constructing the GPN
i.e., gene names and their starting and ending positions on the E. coli
chromosome were again obtained from RegulonDB. As a gene’s“center”
position we have considered the average of its starting and ending
positions.
Transcriptome profiles and effective networks
COLOMBOS offers RNA-Seq and microarray experimental data containing
differentially expressed genes between pairs of experiments. Differentially
expressed genes are determined by computing the log-fold change
(logFC) between the two experimental conditions. We consider three
modes of differential expression depending on the logFC: “differentially
regulated”(absdge) (abs(logFC) > T
FC
), “upregulated”(posdge) (logFC >
T
FC
), “downregulated”(negdge) (logFC < −T
FC
).
We construct an effective TRN by taking the subgraph from the
complete TRN consisting of all differentialy expressed genes and the links
among them (see Supplementary Fig. 5 left for an example). Thus, an
effective TRN is a directed subgraph of the TRN where the nodes are only
the genes whose expression level has been significantly altered. Similarly,
we construct an effective GPN by taking the subgraph from the complete
GPN consisting of all differentialy expressed genes and the links among
them. Consequently, each pair of experiments has one effective TRN and
one effective GPN associated with it. In total we have analyzed 104
effective TRNs and effective GPNs from RNA-Seq data and 3969 effective
TRNs and effective GPN from microarray data.
Differential expression on the gene level is translated to the operon level
in the following way: an operon is considered differentially expressed, if
any gene in the operon is differentially expressed. The same rule is applied
for distinguishing between differentially upregulated and downregulated
operons. A potentially conflicting case, where an operon consists of both,
significantly upregulated and downregulated genes in the same experi-
ment, does not occur in the data sets we analyzed.
Unless indicated otherwise, results are shown for T
FC
=2.5 and T
GPN
=20
kbp. The robustness of the results under variation of T
FC
and T
GPN
is
demonstrated in Supplementary Figs 11–14.
Systematic random networks
A key component of the structural part of our analysis is the arrangement
of edges with respect to a given spatial axis. In order to interpret the
statistics observed in the real network, we employ a simple graph-
generation algorithm to create random networks with edge counts, which
are systematic with respect to one predefined axis. Parameters of this
algorithm are the number of nodes, N; the number of edges in each
category, n(r
+
), n(r
−
), n(l
+
), n(l
−
), n(rl), n(lr), with respect to the chosen axis
(see Fig. 1for an illustration of the edge categories); the position of the
axis, a*; the size of the genome, g. First, random positions for the Ngenes
are created (N/2 per chromosomal arm). Next, random links within each
category are created according to the axis a*. These networks can
subsequently be analyzed via the same analysis pipeline as the real
chromosomally embedded TRN.
Graph randomization
All the results for the edge category asymmetry analysis shown here are
differences between a given graph and a set of randomized graphs,
serving as a null model. Here we keep the gene positions fixed and
randomize the edges via switch randomization. For each randomized
graph, 5000 randomization steps are performed.
Control strengths
Qualitatively speaking, each control strength measures the agreement
between a set of genes and a given network. In the induced subgraph
spanned by the set of genes we compute the connectivity (specifically we
compute the number of nodes with non-zero degree in the subgraph).
Using a null model of randomly drawn gene sets, we then compute the z-
score of this connectivity. This z-score is the control strength. Applying this
procedure for the TRN yields the digital control strength; applying this
procedure to the GPN yields the analog control strength.
For each effective network the control ratio Ris calculated as the
number of connected nodes N
connected
(i.e., the size of the connected
subnet component) over the number of isolated nodes N
isolated
(i.e., the
size of the unconnected subnet component), R=N
connected
/N
isolated
. The
control type confidence, CTC
27
or control strength, is the z-score of R,
calculated from the mean Rand its standard deviation obtained from
10,000 runs of the corresponding null model. In the case of the digital null
model, the same number of affected nodes was mapped randomly on the
TRN. For the analog null model, the same number of affected genes was
mapped randomly on the positions in circular genome.
Decision trees
For the decision tree implementation we choose nine features which will
be the input of our machine learning model. Our decision tree model will
use these features to predict whether a gene will be differentially
expressed or not. These features are the following:
●PosOric =position relative to Ori.
●crp density =crp binding sites density i.e., number of cpr binding sites
in a distance +/−50,000 base pairs around the gene.
●hns density =hns binding sites density i.e., number of hns binding
K. Kosmidis et al.
7
Published in partnership with the Systems Biology Institute npj Systems Biology and Applications (2020) 5
sites in a distance +/−50,000 base pairs around the gene.
●fis density =fis binding sites density i.e., number of fis binding sites in
a distance +/−50,000 base pairs around the gene.
●gpn cont =number of affected neighbors in the GPN.
●trn cont =number of affected ancestors in the TRN.
●hns dig cont =binary variable; 1, if hns is in the gene’s direct TRN
predecessors, 0 otherwise.
●fis dig cont =binary variable; 1, if fis is in the gene’s TRN direct
predecessors, 0 otherwise.
●crp dig cont =binary variable; 1, if crp is in the gene’s TRN direct
predecessors, 0 otherwise.
In short, we assume that the differential expression of a gene is a
function fof the above nine variables. The range of fis the discrete set 0, 1
where the value 1 means that the gene is differentially expressed. Thus,
each of the 4602 E. coli genes is characterized by a nine-dimensional
“vector”with the values of these nine variables as coordinates. For each of
these genes the value of fis known (and that is true for each of the ~4000
experiments of the COLOMBOS database). Predicting the values of fand
comparing them to the known values can be seen as a supervised learning
problem. In fact, a decision tree represents a function that takes as input a
vector of attribute values and returns a “decision”i.e., a single output value.
A decision tree reaches its decision by performing a sequence of tests.
Each internal node in the tree corresponds to a test of the value of one of
the input attributes. The algorithm selects a variable and splits the data to
the value of the variable that maximizes the entropy gain (or equivalently
the Gini impurity gain) from the split.
56
In our case at each node which contains for example Ngenes we
calculate the value S¼ðp1lnðp1Þþp0lnðp0ÞÞ where p
1
is the fraction of
expressed genes to total genes Non the node and p
0
is the fraction of
silent genes to N. Then test splittings are performed and the quantity
G¼ð
nleft
NSleft þnright
NSrightÞis calculated. The split that maximizes the
difference S−Gis selected. The Gini impurity g=p
1
(1 −p
1
)+p
0
(1 −p
0
)
is a valid and often used alternative to the entropy S.
Then it does the same for all other variables, finally selecting the variable
and value that leads to the maximum gain among all possible choices.
Thus, the main nodes split in two nodes and the process is repeated for
each of them until a perfect classification is reached. Finally, we calculate
the importance of each feature (variable) used for the classification
process. The way to compute the feature importance values of a single tree
is by traversing the tree and for each internal node that splits on feature i
we compute the error reduction of that node multiplied by the number of
samples that were routed to the node and sum this quantity for all nodes
to estimate the feature importance of variable i. The error reduction
depends on the impurity criterion that you use (Gini or entropy). It is the
impurity of the set of examples that gets routed to the internal node minus
the sum of the impurities of the two partitions created by the split. This is
the way that regression trees are implemented in scikit-learn
57
which is
rapidly becoming a standard machine learning tool.
Reporting summary
Further information on research design is available in the Nature Research
Reporting Summary linked to this article.
DATA AVAILABILITY
All data analysed during this study are publicly available via the databases referenced
in the article.
CODE AVAILABILITY
The code used to perform the analyses presented in the current study is available
from the corresponding author on reasonable request.
Received: 30 August 2019; Accepted: 21 January 2020;
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ACKNOWLEDGEMENTS
M.H. and G.M. acknowledge support from Deutsche Forschungsgemeinschaft (grant
numbers HU 937/8, MU 1549/13).
AUTHOR CONTRIBUTIONS
K.K., G.M. and M.H. conceived the research. K.K., K.J. and M.H. developed the
computational framework. K.K. and K.J. analyzed the data. G.M. and M.H. contributed
to the results interpretation. K.K., G.M. and M.H. wrote the paper.
COMPETING INTERESTS
The authors declare no competing interests.
ADDITIONAL INFORMATION
Supplementary information is available for this paper at https://doi.org/10.1038/
s41540-020-0124-1.
Correspondence and requests for materials should be addressed to M.-T.H.
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