Decoupling Environment-Dependent and Independent Genetic Robustness across Bacterial Species Shiri Freilich *

Decoupling Environment-Dependent and Independent Genetic Robustness across Bacterial Species Shiri Freilich *
Decoupling Environment-Dependent and Independent
Genetic Robustness across Bacterial Species
Shiri Freilich1,2*., Anat Kreimer3,5., Elhanan Borenstein6,7, Uri Gophna4, Roded Sharan1, Eytan
Ruppin1,2*
1 The Blavatnik School of Computer Sciences, Faculty of Life Sciences, Ramat Aviv, Israel, 2 Sackler School of Medicine, Faculty of Life Sciences, Ramat Aviv, Israel, 3 School
of Mathematical Science, Faculty of Life Sciences, Ramat Aviv, Israel, 4 Department of Molecular Microbiology and Biotechnology, Faculty of Life Sciences, Ramat Aviv,
Israel, 5 Department of Biomedical Informatics, Columbia University, New York, New York, United States of America, 6 Department of Biological Sciences, Stanford
University, Stanford, California, United States of America, 7 Santa Fe Institute, Santa Fe, New Mexico, United States of America
Abstract
The evolutionary origins of genetic robustness are still under debate: it may arise as a consequence of requirements
imposed by varying environmental conditions, due to intrinsic factors such as metabolic requirements, or directly due to an
adaptive selection in favor of genes that allow a species to endure genetic perturbations. Stratifying the individual effects of
each origin requires one to study the pertaining evolutionary forces across many species under diverse conditions. Here we
conduct the first large-scale computational study charting the level of robustness of metabolic networks of hundreds of
bacterial species across many simulated growth environments. We provide evidence that variations among species in their
level of robustness reflect ecological adaptations. We decouple metabolic robustness into two components and quantify
the extents of each: the first, environmental-dependent, is responsible for at least 20% of the non-essential reactions and its
extent is associated with the species’ lifestyle (specialized/generalist); the second, environmental-independent, is associated
(correlation = ,0.6) with the intrinsic metabolic capacities of a species—higher robustness is observed in fast growers or in
organisms with an extensive production of secondary metabolites. Finally, we identify reactions that are uniquely
susceptible to perturbations in human pathogens, potentially serving as novel drug-targets.
Citation: Freilich S, Kreimer A, Borenstein E, Gophna U, Sharan R, et al. (2010) Decoupling Environment-Dependent and Independent Genetic Robustness across
Bacterial Species. PLoS Comput Biol 6(2): e1000690. doi:10.1371/journal.pcbi.1000690
Editor: Herbert M. Sauro, University of Washington, United States of America
Received May 22, 2009; Accepted January 26, 2010; Published February 26, 2010
Copyright: ß 2010 Freilich et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was supported by grants from the Israeli Science Foundation (ISF), the German-Israel Foundation (GIF), the ERA-NET PathoGenoMics and
Tauber Fund to ER. SF is a fellow of the Edmond J. Safra Program in Tel-Aviv University. EB is supported by the Morrison Institute for Population and Resource
Studies, a grant to the Santa Fe Institute from the James S. McDonnell Foundation 21st Century Collaborative Award Studying Complex Systems and by NIH Grant
GM28016. RS was supported by grants from the German-Israel Foundation for Research and Development and ERA-NET PathoGenoMics. UG was supported by
the Bi-national Science Foundation and the German-Israeli Foundation for Research and Development. The funders had no role in study design, data collection
and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: [email protected] (SF); [email protected] (ER)
. These authors contributed equally to this work.
a wide spectrum of habitats, others demonstrate highly specialized
nutritional requirements. In free-living organisms, new pathways
have evolved by acquiring reactions that put external nutrients
into metabolic use allowing species a greater choice in their
metabolic requests [5]. The genetic implications of the selective
pressure to increase the nutritional repertoire make environmental
robustness and genetic robustness intertwined. The contribution of
environmental robustness to genetic robustness is demonstrated by
the following example: the evolution of a new metabolic pathway
allows a species to put a new external metabolite (metabolite A)
into metabolic use as an alternative to an existing pathway making
use of metabolite B, hence promoting environmental robustness.
Under such conditions where both A and B are available (nutrientrich conditions), the species will also gain genetic robustness in
front of mutations in one of the corresponding pathways (in case of
a mutation preventing the use of metabolite B the species can use
the alternative pathway utilizing A and vice versa). The effect of
environmental robustness on genetic robustness in metabolic
networks was studied in detail in yeast [6,7]: more than half of the
genes that were nonessential for growth under nutrient-rich
Introduction
Systematic deletion studies have shown that under laboratory
conditions the large majority of genes in the genome are
dispensable, and that in many cases dispensability depends on
the experimental setting [1]. These studies have reinforced the
notion of robustness of biological systems, which denotes the
invariance of phenotypes in the face of perturbations [2]. Two
types of perturbations are encountered by biological systems:
genetic alterations and environmental variations. Genetic robustness of a biological system is viewed as its ability to continue
functioning following mutations [3,4], while environmental
robustness refers to buffering against external changes (e.g.,
changes in temperature and salinity, or in the availability of
nutrients). Genetic robustness can be studied at various levels of
biological organization, from the molecular level to the organism
level, where a state is considered to be robust if a mutation has an
insignificant effect on the trait examined [2].
Environmental robustness differs greatly across bacterial species:
whereas some species exhibit an impressive ability to proliferate in
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Environment-Dependent and Independent Robustness
expanded under different collection of metabolites, were shown
to be highly robust against the elimination of mutations [16,17].
The network expansion method has been helpful in uncovering
the role played by some specific metabolites on the evolution of
metabolic networks. The introduction of oxygen to the
atmosphere, for example, was demonstrated to be coupled with
the appearance of many new pathways and reactions, considerably increasing the complexity of the metabolic networks of
aerobic species beyond that reachable by any anoxic network
[18]. Studying the species-specific expansion of networks given
various metabolite combinations has permitted the grouping
together of organisms with similar metabolic capabilities [19].
Following the introduction of the expansion method, other
related topological approaches have been developed to provide
predictions for the network-specific set of externally consumed
metabolites, as inferred by the structure of the corresponding
metabolic network [20,21]. These methods aim to define the
minimal set of externally acquired compounds – i.e., these
metabolites that cannot be synthesized from other compounds
and permit the production of all other compounds in the
network. Here, we combined the expansion algorithm and an
algorithm for predicting species-specific metabolic environments
(The seed algorithm [20]). By integrating these two algorithms,
we provide a new model that not only predicts robustness across
species (as was previously done using the expansion method
[17]), but also examines robustness across environments and
hence provides predictions for condition-dependent and independent reactions. Taking this integrative approach, we aim to
characterize the level of species-specific robustness and, for each
species individually, to decouple between robustness which is
condition-dependent (due to reactions which are essential in
some environments but not in other) and robustness which is
condition-independent. We start by describing our model and
testing its biological plausibility. We then use it to systematically
characterize the level of robustness across bacterial species
(condition dependent and independent). Finally, we apply the
model for studying whether dispensability is a directly selected
feature.
Author Summary
When a species is grown under optimal conditions the
single-knockout of most of its genes is not likely to affect
its viability. The resilience of biological systems to
mutations is termed genetic robustness and its extent
across different species has not yet been systematically
described. Since the deletion of a gene can have varying
consequences depending on the environmental conditions, the extent of species’ genetic robustness reflects
both the range of conditions (or environments) in which it
can survive as well as the availability of alternative cellular
routes (compensating for a gene’s loss of function). Here,
we developed a computational model for estimating the
essentiality of metabolic reactions across natural-like
environments and applied it to chart species’ level of
genetic robustness, providing the first systematic description of genetic robustness across species. Studying
robustness across a wide collection of natural-like environments enables one to stratify, for each species
individually, the extent of environmental-dependant and
independent robustness and hence advances our understanding of its evolutionary origins. Our main finding is
that the level of environmental dependent robustness is
associated with the lifestyle of a species (i.e., specialists
versus generalist), whereas the level of environmentalindependent robustness is associated with its metabolic
production capacities.
conditions were found to be active under eight restricting growth
conditions [7]. However, as environmental robustness cannot fully
explain the dispensability of genes, two other hypotheses have
been proposed for the evolution of genetic robustness [2]: First, an
adaptive origin – i.e., a direct, natural selection in favor of genes
which allow a species to endure genetic perturbations (initially
suggested by Fisher to explain the observed dominance of wildtype alleles to the overwhelming majority of deleterious mutations
[8]). Second, an intrinsic origin– i.e., genetic robustness has evolved
as a byproduct of natural selection in favor of other, adaptive,
traits. In the context of dominance, selection for increased
metabolic flux is a widely accepted explanation for the recessive
nature of most mutations [9–11]. Since metabolic enzymes act as
part of large, multi-enzymes, networks, single-loci mutations
(resulting in 50% activity of the corresponding enzyme in the
heterozygote) are not expected to affect the overall behavior of the
system. Hence such mutations are not detectable at the phenotypic
level and mutants are considered to be recessive [12]. For genetic
robustness, one can similarly argue that robustness is intrinsic to
the optimization of some phenotypes, and has evolved as a
byproduct of a selective pressure for increasing steady-state
metabolic fluxes via the incorporation of alternative metabolic
pathways [2,13,14]. Notably, there is an essential difference
between man-made systems, where robustness is built in on
purpose, and biological systems that are shaped by natural
selection at the population level, in which non robust systems can
survive if reproduction rate compensates failure rate.
Few recently developed methods allow one to systematically
address the influence of the environment on metabolic network
structure. The network expansion method – a method for
generating the set of all possible metabolites that can be
produced from a set of compounds - permits the reconstruction
of networks in different metabolic environments [15]. Using the
network expansion approach, generic sub-networks (describing
a collection of metabolic reactions across known genomes rather
than the reactions tenable within any specific organism),
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Results
The buffering capacity of metabolic networks was previously
predicted using in silico metabolic flux analysis approaches [22–32]
but the underlying stoichiometric metabolic models (providing the
quantitative relationships between the reactants and the products
of each reaction) are available for only a few selected species.
Topology-driven approaches (requiring only the network topological backbone and not a full blown stoichiometric model), although
providing only qualitative predictions for the activity of a reaction
(active/not active) rather than a quantitative estimate of the fluxes
it carries, have been previously shown to predict the in vivo
essentiality of genes with considerable accuracy [33,34]. Such
methods unravel topological, network genetic robustness (NGR), which
refers to the network’s ability to buffer mutations via the existence
of alternative pathways, and is distinct from robustness that arises
from the presence of alternative genes (duplicates or functional
analogs) [4,16,29,30]. Here, we studied species-specific topological
robustness by applying a topology-driven computational approach
for predicting an organism’s viability in a given environment,
estimated according to its ability to produce a set of essential
biomass metabolites (Figure 1). Taking a similar approach to [21],
these metabolites were chosen because they are deemed essential
for life in all known bacteria and include amino acids, nucleotides
and essential co-factors (Methods).
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Figure 1. Illustration of a simple metabolic network producing an essential constituent of biomass on different growth media.
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We quantify metabolic NGR in 487 bacterial organisms. For
each species we simulate its growth on a rich medium and
systematically delete each reaction in turn. Under each deletion,
we test the ability of the metabolic network to produce key biomass
metabolites (Methods). A specific rich medium was individually
computed for each species by employing a previously developed
‘reverse ecology’ algorithm [20] that computes the full set of
metabolites that an organism extracts from its environment
(Methods). Growth simulation was done by using the expansion
method [15] – an approach where networks of increasing size are
constructed starting from an initial set of substrates (the seed) by
stepwise addition of those reactions whose substrates are produced
in the current core network (i.e., compounds present in the seed or
provided as product by reactions incorporated in earlier steps).
Here, the expansion method was used to construct the speciesspecific metabolic networks following each deletion, given the
species-specific rich environment. In the toy example illustrated in
Figure 1 this procedure leads to the identification of the two
external metabolites, based on the topology of the metabolic
network. NGR is calculated as the fraction of non-essential
reactions (i.e., those reactions whose absence is compensated by
the presence of alternative routes) out of all network reactions. In
Figure 1, g is the only essential reaction out of 7 reactions and the
NGR of the network is 6/7. The topological-based essentiality
predictions show good agreement in two species where essentiality
data has been assembled via experimental knock-out studies –
Escherichia coli and Bacillus subtilis – yielding an accuracy of 0.86 and
0.85 respectively (Methods). Taken together, the computation of
species-specific rich growth media results in an ensemble of 487
environments, representing a sample of the ecological niches that
different bacterial species can inhabit.
To elucidate the contribution of environmental robustness to
genetic robustness across species and lifestyles, we first assess the
viability of all 487 species across these 487 sample environments
(in Figure 1, for example, we identify two viable environments –
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environments II and III). We consider the fraction of the
environments in which a given species is viable as a measure of
its environmental robustnesss [35]. This measure significantly correlates
with two (general, non-metabolic) established measures of
variability of species’ habitats (Fraction of regulatory genes: 0.44,
P = 9e-8 [36]; Environmental complexity: 0.33, P = 3e-4 [37],
Spearman correlations; Methods), showing that as a general trend
(though not in all cases) high environmental robustness in observed
in generalist species. As expected (according to [38]), the
environmental robustness of species also significantly correlates
with the modularity of their metabolic networks (20.43, P,2e-16,
Methods).
Following using the collection of 487 environments (constructed
by calculating the optimal metabolic environment of each species
in the analysis and hence representing a sample of the ecological
niches that different bacterial species can inhabit, Methods) for
predicting species-specific environmental robustness, we use it for
the identification of conditionally essential reactions. In every
viable environment of a given organism (that is, a collection of
metabolites that allows the production of all target metabolites of a
given species) we systematically delete all its metabolic reactions
(single reaction at a time). This leads to the identification of
conditionally essential/non-essential reactions – reactions that are
essential in some viable growth environment of the organism but
are non-essential under other, more favorable, conditions such as
its own species-specific rich medium (reactions a and b in Figure 1;
Methods). The resulting matrix, describing the essentiality of all
metabolic reactions across the 487 by 487 species and environments, is given in Text S1 note 1. The metabolic reactions of each
species can hence be divided into three non-overlapping groups: (i)
(unconditionally) essential reactions – i.e., reactions that are essential
over all growth media (reaction g in Figure 1); (ii) conditionally
essential/non-essential reactions (reactions a and b in Figure 1); and (iii)
(unconditionally) non-essential reactions – that are backed-up over all
growth media (reactions c, d, e and f in Figure 1, and see Text S1
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related to network robustness and that the structure of the
network, and not only its size, has functional significance. The
associations between condition-dependent NGR, centrality and
connectivity remain significant when controlling for the effect of
network size (Text S1 note 3), providing a system-level support to
the view that network connectivity contributes towards a better
compensation for loss-of-function mutations [41,42]. The association between topological properties, robustness, and species’
lifestyle is visualized in Figure 3 where we show two metabolic
networks of similar size (,200 reactions) that greatly differ in both
their topological properties and their robustness. The metabolic
network of the free-living Clostridium botulinum is more central and
connected than the network of the host-associated Helicobacter
acinonychis, and correspondingly exhibits a remarkably higher
robustness.
Next we quantified the robustness of each reaction in each
species as the fraction of its non-essential entries across all viable
environments, marking its degree of conditional-essentiality in
each species (from 0 – essential across all environments, to 1 – nonessential across all environments). For each species, we studied the
association between the species-specific level of reaction’s
essentiality and other topological and evolutionary characteristics.
In accordance with experimental data from yeast [41], nonessential reactions tend to be more central and highly connected
than essential reactions (Methods; Text S1 Note 4). Hence, our
data provide a large-scale, cross-species support to findings
observed at the single-species level. The robustness of reactions
is also associated with evolutionary conservation: in the large
majority of species (83%) we find a significant positive correlation
(P,0.05) between a reaction’s robustness and its conservation, as
inferred from the phylogenetic distribution of reactions across
species (mean correlation – 0.21, maximal correlation – 0.37; Text
S1 Figure 2). At the species level, this correlation is absent
note 2 for evidence that we recover the large majority of
conditionally essential genes). For each network we compute a
condition-independent NGR score (ciNGR) that denotes the fraction of
the non-essential reactions (group iii) out of all reactions and a
condition-dependent NGR score (cdNGR) which denotes the fraction of
the non-essential and conditionally-essential/non-essential reactions (group iii and group ii) out of all reactions. The fraction of
each reaction’s group (non-essential, essential, conditionallyessential/non-essential) over all species is shown in Figure 2. In
Escherichia coli, where 83% of the genes were experimentally shown
to be dispensable under aerobic growth in rich medium [39,40],
we observe a corresponding fraction of 0.78 non-essential
reactions (Table S1). In host-dependent species the observed
fraction of non-essential reactions (ciNGR) is typically markedly
lower (0.35 in Mycoplasma genitalium for example), in accordance
with the experimentally observed range of 20% to 60%
dispensable genes [39]. Overall, in most species we observe a
large fraction of non-essential reactions closely scattered around a
mean of 0.75 (Table S1, Figure 2).
We further studied how the topology of the metabolic networks
relates to their level of observed robustness. For this, we looked at
two topological characteristics measured for each network:
network connectivity – describing the average number of
neighbors each protein-node has, and network centrality –
describing the average centrality of its node members where the
centrality of each individual node is determined by calculating the
mean shortest path between the node and all other nodes in the
network (Methods). The overall robustness of the network
(cdNGR) is positively correlated with its topological properties
including network size, network connectivity and network
centrality (size of network: 0.61, P = 0; connectivity: 0.77, P = 0;
mean shortest path: 20.65, P = 0; Spearman correlations;
Methods). This shows that an array of topological properties is
Figure 2. The distribution of non-essential, essential and conditionally-essential/non-essential reactions versus environmental
diversity across the 487 organisms studied. Lines represent the linear regression calculated for each group.
doi:10.1371/journal.pcbi.1000690.g002
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Figure 3. The metabolic networks of species with similar network size and different topological properties. (A) Clostridium botulinum:
Network size, 189; connectivity, 5.2; centrality (mean shortest path), 3.7; robustness (NGR), 0.85. (B) Helicobacter acinonychis: Network size, 191;
connectivity, 4.1; centrality (mean shortest path), 5.4; robustness (NGR), 0.56. Red circles - essential reactions; green circles - non-essential reactions.
doi:10.1371/journal.pcbi.1000690.g003
primarily in host-associated species, where the robustness of
reactions is likely to be affected by the host-microbe interactions
(Text S1 Figure 2). Notably, when considering the robustness of
reactions across all species and environments (i.e., a reactionspecific score describing its mean level of essentiality across all
species) the correlations between essentiality and conservation is
markedly higher than that observed when considering each species
alone (0.58 P,2.2e-16, Spearman, and compare with Text S1
Figure 2) further testifying to the utility of the large scale
investigation performed here.
Examining the distribution of the reaction categories within
major metabolic classes reveals two metabolic categories that are
highly enriched in non-essential reactions: nucleotide metabolism
and carbohydrate metabolism (P = 0, Fisher test) (Text S1 note 5).
Conversely, reactions functioning in amino-acid biosynthesis
contain significantly more essential reactions (conditionally and
un-conditionally) than expected by chance (P = 0, Fisher test),
hence, due to the over-representation of essential reactions,
comprising a particularly non-robust to mutations functional
category. The level of essentiality of reactions associated with two
very basic metabolites, oxygen and ATP, is an interesting case of
marked dissociation. We find that oxygen-utilizing reactions are
highly backed-up (fraction of non-essential appearances in oxygenutilizing reactions versus all reactions: 0.96 and 0.88 respectively; P
value 5e-5 in a Wilcoxon test; Text S1 Note 6 and 7, Table S4).
There are several possible explanations for the high level of
redundancy of oxygen utilizing reactions: First oxygen was
introduced into the atmosphere after the appearance of cellular
life forms, where oxygen-dependant reactions were shown to
augment more ancient, pre-oxygen reactions [18]. Second, oxygen
is a limiting factor across many environments and hence the
availability of alternative pathways allows species to alternate
between pathways, according to the environmental conditions at a
given time. Notably, reactions utilizing other redox molecules such
as NAD also show high level of redundancy (fraction of backed
appearances in NAD-utilizing reactions: 0.93; P value 5e-3 in a
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Wilcoxon test; Text S1 Note 6), possibly due to the occurrence of
alternative pathways using NADP or other electron acceptors.
However, oxygen-utilizing reactions are still significantly more
backed-up (i.e., non-essential) than NAD utilizing reactions (P
value 0.017 in a Wilcoxon test; Text S1 Note 6). ATP-dependent
reactions, on the other hand, have significantly low levels of
robustness (fraction of backed appearances in ATP-utilizing
reactions: 0.79; P value 1e-4 in a Wilcoxon test; Text S1 Note
6). The least robust (most essential) reactions across bacterial
species are those performed by ATP-dependent amino-acyl tRNA
synthethases (Table S2), a class of highly conserved enzymes [43]
that are known to be essential across species [44]. One potential
explanation for the high level of essentiality of ATP-dependent
reactions may be that such reactions, being thermodynamically
unfavorable in the forward direction when not coupled to ATP
hydrolysis, are not likely to have other, spontaneous, alternatives.
Figure 2 displays the correlation between the species distribution of the reaction types (non-essential, essential and conditionally
essential/non-essential) with environmental robustness. Notably,
the fraction of ciNGR (unconditionally non-essential reactions green dots in Figure 2) is not strongly affected by the species’ level
of environmental robustness (the number of environments in
which it is viable). In contrast, the fraction of conditionallyessential/non-essential reactions exhibits a remarkably high
correlation with environmental robustness (0.81, P,2e-16,
Spearman), which remains significant when controlling for the
effect of network size (Text S1 Note 8). A strong correlation
between the fraction of conditionally-essential/non-essential
reactions and environmental robustness is also observed when
using an alternative set of 20,000 environments constructed by
random shuffling of the seeds from the original environments
while maintaining their original distribution (0.76, P,2e-16,
Spearman; Text S1 Note 2). Our findings thus provide direct
large-scale evidence that genetic robustness is associated with
environmental robustness. Although such association is expected
considering both the nature of the model as well as the biological
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has been a driving force in the evolution of genetic robustness in
bacterial metabolic networks [2]. Unlike the correlation between
metabolic activity and condition-independent robustness reported
above, the correlation between metabolic activity and conditiondependent robustness is insignificant when controlling for the
effect of other co-associated factors (Text S1 Note 10). Interestingly, the predictor provides a good approximation for the level of
genetic robustness in facultative bacteria and a more moderate
approximation in aerobic bacteria (facultative: 0.70 P 5e-7;
aerobic: 0.43 P 0.007; Pearson correlations), but an insignificant
one for anaerobic bacteria (Figure 4). Indeed, it has been
previously suggested that oxygen-tolerant bacteria (facultative
and aerobic) have developed an array of alternative metabolic
pathways of different energetic costs, whose activity they delicately
balance to optimize their metabolic yield given the environmental
conditions [47,48]. Notably, information on the rate of growth is
only available to less than fourth of the species examined, and
many pathways involved in secondary metabolism are yet to be
revealed. Hence our estimate of metabolic capacity only reflects
current state of knowledge. The availability of growth rate
information for additional species, as well as the characterization
of additional secondary pathways will allow more accurate
predictions of species’ metabolic capacities.
To study whether genetic robustness has evolved directly in an
adaptive manner we use an approach suggested by [7] and
examine the association between network-level robustness (the
existence of alternative pathways) and gene-level robustness (the
existence of a duplicate gene or of a functional analogs) [2,42,45]
across all species studied. If the network dispensability of reactions
would have adaptively evolved to provide resilience to mutations,
one would expect that duplicate genes of non-essential reactions
would be preferentially lost while duplicate gene copies of essential
genes would be preferentially maintained, as they provide genelevel back-up to essential reactions. Yet, in accordance with
previous findings in yeast [7], we find that essential reactions are
not more enriched in multi-copy genes (Text S1 Note 11). We
further looked the level of genetic robustness at Rubrobacter
xylanophilus and Deinococcus radiodurans - extermophyls which are
exposed to high levels of radiation (Text S1 Notes 1). The NGR
values of both species do not significantly differ from those
observed in other bacteria. (0.74 and 0.77 respectively, compared
with a mean value of 0.75 over all species), and hence do not
support an association between high level of genetic robustness
and high rate of genetic perturbations, as can be expected in case
of adaptive origin of robustness.
Beyond evolutionary insights about the extent and origins of
metabolic robustness, our approach permits the high-throughput
identification of essential reactions across species and can be
applied for delineating species-specific (or group-specific) essentiality. Potential antibiotic drug targets, for example, can be
identified by revealing reactions that are backed up in commensal
human bacteria while essential in human pathogens. Methenyltetrahydrofolate cyclohydrolase (EC 3.5.4.9) is an example for a
widely distributed reaction (present in most species) that is nonessential across all non-pathogenic human bacteria in our data,
while essential in many human pathogens (Figure 5). In many
pathogenic species methenyltetrahydrofolate cyclohydrolase catalyses the only reaction for the production of 10-formyltetrahydrofolate, an essential metabolite for the translation process in
bacteria [49,50]. In human commensal organisms, an alternative
route for the production of 10-formyltetrahydrofolate is available
via a reaction catalyzed by Formyltetrahydrofolate synthetase
(6.3.4.3). Notably, methenyltetrahydrofolate cyclohydrolase has
known inhibitors, which have little activity in mammalian cells and
setting it aims to recapture, the use of the approach for the
characterization of condition-essential/non-essential reactions
demonstrates that environmental diversity by itself cannot fully
account for the level of robustness observed, whereas conditionalindependent robustness is observed across all species examined
including the most specialized and most diverse ones (Figure 2).
Notably, the fraction of conditionally-essential/non-essential
reactions almost invariably does not exceed 20% of the total
metabolic reactions in the dataset, in line with previous
experimental findings indicating that niche-specificity by itself
cannot explain the dispensability of a significant fraction of the
genes [6,7,45]. While these results provide a fair estimate of the
contribution of nutritional factors, other environmental factors
(e.g., temperature, salinity, etc.) that go beyond the current model
probably lead to an overall larger environmental contribution.
As environmental diversity mainly affect the robustness of
condition-dependent reactions and not condition-independent
reactions (Figure 2), we turn to study the level of association
between metabolic activity and the level of robustness of the latter
group (ciNGR), aiming at revealing its pattern of association with
other phenotypic characteristics. Notably, no correlation is
observed between the fraction of ciNGR and the fraction of
conditional-essential/non-essential reactions, further supporting
the view that the evolution of the condition-independent
component of genetic robustness is derived by different selective
forces than the condition-dependent component. We use growth
rate data to account for the growth capacity of an organism and
additionally measure the fraction of metabolic reactions dedicated
to the production of its secondary metabolites (Methods) [46]. A
generalized linear model based on both measures is employed to
predict network robustness values and yields a fairly marked
correlation with the observed NGR scores (0.59 Pearson, P = 1e11, Figure 4), providing a significantly improved fit over the results
obtained while using each measure individually (Text S1 Note 9).
This association, though by itself cannot infer causality, provides
support to the notion that a need to increase metabolic capacities
Figure 4. Observed versus predicted NGR. Predicted values are
derived from a generalized linear predicting NGR from the growth rate
and fraction of secondary metabolites of each species. Growth rate data
was available for 109 species including 17 anaerobic (red), 37 aerobic
(blue), 40 facultative (green), 4 microaerophilic, and 11 unknown.
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network increases [17]. Here, we introduce a computational
approach that integrates together algorithms which were
previously used individually for studying the structure and
evolution of metabolic network: The expansion algorithm was
used for studying robustness under different environments and
in different species (though in a given environment); The seed
algorithms were used to predict the nutritional environment of
species [20,21]. By integrating these two algorithms, we provide
a new model that provides predictions for condition-dependent
and independent robustness across many species and environments. By conducting a large-scale comparative study we
provide evidence that variations among species in their level
of network genetic robustness (condition-dependent and independent) reflect adaptations to different ecological niches and
lifestyles. Notably, beyond robustness, other features of metabolic networks such as the collection of enzymatic functions [53]
and the ability to utilize external nutrients [19] also reflect
environmental adaptations, where in many cases the metabolic
capacities of species are better associated with their lifestyle than
with their phylogeny. Alternative lifestyle characteristics are
associated with the two types of robustness: the extent of
conditional-dependent robustness is strongly associated with the
environmental diversity of species (specialized or generalist), and
the extent of condition-independent robustness is associated
with the corresponding metabolic capacities. Importantly, our
model only considers qualitative conditions, i.e., the actual
availability of metabolites, whereas the choice between alternative pathways can reflect adaptations to quantitative conditions,
i.e., the concentration of metabolites [14,47]. Considering this
qualitative description of conditional-dependence of reactions,
the association between the level of condition-dependent
robustness and species’ environmental diversity suggests that
the former evolve as a result of a selection for alternating
between nutritional sources. For most species examined the
range of nutrients that can be consumed by a species can only
partially explain the corresponding level of robustness (only
about 20 percent of the reactions), where the complementary
non condition-dependent robustness has arisen mainly to meet
the metabolic requirements of a species. The association
between the level of robustness and the corresponding metabolic
capacity of a species can be explained either by a selection to
increase flux – similarly to the effect of gene dosage [7] – or by
selection to optimize the metabolic efficiency under given
conditions, for example by alternating between routes in
accordance with the corresponding substrate concentrations
[47,48]. Thus, the design of metabolic networks (as viewed by
the presence of alternative pathways) represents a speciesspecific adaptation to both its needs and its environment.
Beyond the evolutionary implications of this study, additional
applications can be withdrawn from the association between
growth rate and topological properties (i.e., network robustness),
as reported here. The observed association suggests that
topological models can be used for predicting growth rate (for
a broader spectrum of species than is currently possible with the
existing range of stochiometeric models). An intriguing challenge is to develop supervised learning techniques to learn a
predictive function for condition-dependent growth rate, given
the topological characteristics of that environment-specific
network and the species-specific growth potential under optimal
conditions. Currently, there is a lack of systematic data of
growth rate across media for a wide collection of species [54],
needed for building the growth rate predictor suggested above.
Hopefully, the future accumulation of such data will allow
conducting such study.
Figure 5. Distribution of pathways for the synthesis of 10formyltetrahydrofolate in human pathogens and human
commensal organisms. Maroon squares: metabolites; blue squares:
reactions. MCH: methenyltetrahydrofolate cyclohydrolase; FTL: formyltetrahydrofolate synthetase; HC: human commensals; HP: human
pathogens. 10-Formyltetrahydrofolate acts as a formyl donor in purine
biosynthesis, and for formylation of methionyl-tRNA required for
producing fMet-tRNA – a molecule required in most bacterial species
for initiating protein synthesis. All human commensals (7/7) contains
two alternative routes for the production of 10-formyltetrahydrofolate.
Only 28 out of 73 human pathogens which have MCH contain the
alternative route, making MCH essential in the remaining 45 organisms.
These 45 pathogenic organisms include several Shigella, Salmonella and
Mycobacterium species (the full list of species and the essentiality of
MCH and FTL is provided in Text S1 Note 13 and in Table S5). The
approach presented here can easily be generalized for highlighting
essentiality in other groups of medical, ecological or agricultural
interest.
doi:10.1371/journal.pcbi.1000690.g005
are therefore selective [50]. Additional examples of pathogenicspecific essential reactions are provided in Text S1 Note 13 and in
Table S6.
Discussion
Overall, our analysis charts out the robustness of the metabolic
system across a wide variety of bacterial species and growth media.
Several limitation of this analysis should yet be acknowledged. The
predictions for the essentiality of reactions, as well as the set of
growth environments, are based on a topological network-based
computation. Hence, this analysis ignores many other properties of
metabolic reactions such as stochiometry, rate, and dynamics.
Incorporating these properties into the metabolic network model
can potentially yield more accurate results [51]. Nevertheless,
metabolic network topologies can readily be obtained for hundreds
of species, allowing a phylogenetic, large-scale analysis [37] and
may thus delineate emerging patterns in the metabolic data. This
broad perspective enables the elucidation of general principles
underlying the structure and evolution of metabolic networks
[16,17,52]. Finally, our predictions of reactions’ essentiality are
shown to be in general agreement with experimental observations,
in the few cases where the latter exist.
Several recent studies have used topological-based approaches for systematically revealing the structural properties of
metabolic networks. The expansion algorithm was applied for
estimating the level of robustness in reference sub-networks,
comprising all reactions present in the KEGG database
(irrespective of the organism in which they have been found)
[16], as well as for conducting a comparative study of the level
of robustness in species-specific sub-networks produced by the
expansion algorithm under a given combination of external
resources [17]. These studies clearly testify for the high
robustness of metabolic sub-networks, where the sensitivity
following deletion of reactions decreases as the size of the subPLoS Computational Biology | www.ploscompbiol.org
7
February 2010 | Volume 6 | Issue 2 | e1000690
Environment-Dependent and Independent Robustness
Methods
Computing topological network genetic robustness
(NGR)
Construction of species-specific metabolic networks and
environments
For each metabolic network (i.e., species), we compute conditiondependent and independent NGR. The species-specific NGR score is
computed as follows: using its species-specific metabolic rich
environment as the species’ growth medium, each enzyme in the
network examined is knocked out in turn and the expansion
algorithm is used to evaluate if all target metabolites are produced
in the perturbed network. If the whole list is still successfully
produced, this enzyme is scored 1 (non-essential) and otherwise it
is scored 0 (essential). The fraction of non-essential enzymes in the
network is the network’s NGR score. Condition-independent NGR is
computed using the ensemble of all viable environments of a given
species; i.e., we repeat the same knockout procedure in each viable
environment. Subsequently, an enzyme is scored 1 if it is backedup across all environments (non-essential) and 0 otherwise. The
enzymes that are non-essential under all conditions are termed
condition-independent and their fraction denotes the network’s overall
condition-independent NGR score. Enzymes are termed conditiondependent if they are found to be backed-up in some (but not all) of
the viable media examined, per species, and their fraction in a
given species is their condition-dependent NGR score. Notably, the
species-specific rich media refers to the most optimal metabolic
environment a species can have, i.e., an environment where all of
its metabolic pathways have the potential to be active. Hence,
reactions that are essential when the metabolic network works at
full capacity will also be essential under less favorable conditions.
The species-specific condition-dependent and independent NGR scores are
listed in Table S1.
Metabolic data on the enzymes and reactions in each species
were collected from KEGG 24 (release 46) [55] for 487 bacterial
organisms. The reaction scheme describing the substrates and
products in each reaction was retrieved from the reaction_
mapformula.lst file, describing only the main metabolites in
each reaction (as in the KEGG pathway diagrams) and not the
co-factors (e.g., H2O molecules). Metabolic networks were
constructed as follows: Each enzyme is represented as a node
in the network. Let E1 = e11, e21, … , en1 denote the set of
enzymes that catalyze reaction R1, and E2 = e12, e22, … , em2
denote the set of enzymes that catalyze reaction R2. If a product
of R1 is a substrate of R2, then edges are assigned between all
nodes of E1 and all nodes of E2. Edges are also assigned within
E1 nodes and within E2 nodes. A list of 86 target metabolites
(Table S3) – that is, metabolites that are likely to be essential for
growth in most species [56–58], was used for constructing
species-specific target metabolite lists according to the intersection between the generic target metabolites and the metabolites
that each species produces. Enzymes that are not relevant for
the production of biomass metabolites were omitted from the
networks. Such enzymes were identified by repeating the
expansion of the network in a reverse manner, using the full
networks and the set of biomass metabolites as seeds. Each
reaction that participated in the production of biomass
metabolites was added to the network. Thus, only reactions
that had no part (direct or indirect) in the production of the
biomass metabolites were omitted from the network. In the
approach taken here, reactions that are not involved in the
production of the biomass metabolites will have no effect on the
network’s viability following a deletion, hence would have no
effect on our results. Using these effective reactions, we
constructed the effective network further used throughout the
analysis. For each network we computed modularity, centrality
and connectivity. Modularity was computed using Newman’s
algorithm [59] as described in [60]. Centrality is computed by
first determining all pairwise shortest paths using the Floyd–
Warshall algorithm [61] and then calculating, for each node, its
mean shortest path (MSP) distance to all other nodes in the
network, denoting the node’s centrality (within a specific
network). In cases where the network has more than one
connected component, nodes from two different components
are assumed to have a distance of twice the maximal distance
obtained within the components. The centrality of the network
is the minimal MSP across all nodes.
Metabolic growth environments (rich media) were inferred for
each species individually using the seed algorithm developed by
[20], retrieving an ensemble of 487 species-specific rich growth
media (one for each species). Other approaches for the
construction of metabolic environments were additionally employed (Text S1 Note 2). To compute the species viability across all
environments we tested the viability of each species over the set of
487 metabolic growth environments as follows: given a specific
organism and an environment (set of external metabolites), an
organism is considered viable in this environment if all its essential
target metabolites are produced – this is examined by using a
network expansion algorithm [15] that outputs an activated
metabolic sub-network, and verifying that the expanded subnetwork produces all target metabolites. The Environmental robustness of
each network is calculated as the corresponding fraction of viable
environments.
PLoS Computational Biology | www.ploscompbiol.org
Benchmarking the topology-driven predictions for
reactions’ essentiality against experimental data
Using the procedure described above we classify each reaction
in each species as non-essential, essential or conditionaldependent (essential/non-essential). Non-essential and essential
reactions (scoring either 1 or 0, respectively, i.e., non-essential or
essential across all environments) of E. coli and Bacillus subtilis were
assigned to the corresponding genes by parsing the KEGG
‘enzyme’ file (downloaded from ftp://ftp.genome.jp/pub/kegg/).
The essentiality predictions for 327 (out of 530) E. coli reactions
and 250 (out of 397) Bacillus subtilis reactions which are assigned
to a single gene were compared with the pertaining experimental
data. Experimental data from systematic gene knock-out studies
of E. coli genes were retrieved from [62] and for the essentiality of
Bacillus subtilis genes were retrieved from [63]. Accuracy was
calculated as the fraction of true positives and true negatives out
of all observations.
Retrieving species-specific measures
Fractions of regulatory genes were taken from [36], describing
the fraction of transcription factors out of the total number of
genes in the organism as an indicator of transcriptional complexity
(indirectly testifying to environmental variability) [37]. This is also
the measure of transcriptional complexity. Environmental complexity values were obtained from [37], where the natural
environments of 117 bacterial species were ranked based on the
NCBI classification for bacterial lifestyle [64]. Growth rate:
minimal duplication-time data, available for 109 species in the
dataset were retrieved from [65]. Secondary metabolism: the
fractions of enzymes involved in secondary metabolites were
constructed by parsing KEGG data and counting for each species
the number of enzymes which participate in pathways of
secondary metabolism.
8
February 2010 | Volume 6 | Issue 2 | e1000690
Environment-Dependent and Independent Robustness
Table S3 Full description and KEGG ID of the 86 target
metabolites.
Found at: doi:10.1371/journal.pcbi.1000690.s004 (0.01 MB PDF)
Supporting Information
Text S1 Supplementary Notes, Tables and Figures.
Found at: doi:10.1371/journal.pcbi.1000690.s001 (0.53 MB PDF)
Table S4 List of all species which have an enzymes catalyzing
Genomic and ecological attributes of species in the
analysis. This table displays the following attributes for the 487
bacterial species studied here: KEGG label, name, network size
(number of reaction-nodes participating in the production of
biomass metabolites), environmental robustness, condition-dependent NGR, condition-independent NGR (across 487 environments), condition-independent NGR (across 487+200000 environments), fraction of regulatory genes, environmental complexity
score, lifestyle description, doubling time, oxygen requirements,
centrality of the network, connectivity (mean rank) an modularity,
correlation between reactions’ essentiality and reactions’ conservation, centrality and connectivity and the P-value for the
correlation (spearman) . Values were computed and retrieved as
described in the Methods section.
Found at: doi:10.1371/journal.pcbi.1000690.s002 (0.09 MB
TXT)
Table S1
reaction 1.14.16.1 (Phenylalanine 4-monooxygenase).
Found at: doi:10.1371/journal.pcbi.1000690.s005 (0.03 MB PDF)
Table S5 List of human commensal and pathogens and the
distribution and essentiality of Methenyltetrahydrofolate cyclohydrolase (EC 3.5.4.9) and Formyltetrahydrofolate synthetase
(6.3.4.3) across these species.
Found at: doi:10.1371/journal.pcbi.1000690.s006 (0.03 MB XLS)
Table S6 Distribution and essentiality of reactions across human
commensal and pathogens organisms.
Found at: doi:10.1371/journal.pcbi.1000690.s007 (0.06 MB XLS)
Acknowledgments
We thank Stefan Schuster, Martin Kupiec and Tomer Shlomi for reading
the manuscript and providing helpful feedback and Moshe Mevarech for
his comments on the data.
Table S2 Levels of evolutionary conservation (phylogenetic/
phyletic distributions) and essentiality of reactions across species
and environments.
Found at: doi:10.1371/journal.pcbi.1000690.s003 (0.35 MB XLS)
Author Contributions
Conceived and designed the experiments: SF ER. Performed the
experiments: SF AK. Analyzed the data: SF AK UG RS ER. Contributed
reagents/materials/analysis tools: EB. Wrote the paper: SF ER.
References
24. Fell DA, Sauro HM (1990) Metabolic control analysis by computer: progress and
prospects. Biomed Biochim Acta 49: 811–816.
25. Fell DA (1992) Metabolic control analysis: a survey of its theoretical and
experimental development. Biochem J 286 (Pt 2): 313–330.
26. Edwards JS, Palsson BO (2000) The Escherichia coli MG1655 in silico metabolic
genotype: its definition, characteristics, and capabilities. Proc Natl Acad Sci U S A
97: 5528–5533.
27. Klamt S, Gilles ED (2004) Minimal cut sets in biochemical reaction networks.
Bioinformatics 20: 226–234.
28. Stelling J, Klamt S, Bettenbrock K, Schuster S, Gilles ED (2002) Metabolic
network structure determines key aspects of functionality and regulation. Nature
420: 190–193.
29. Stelling J, Sauer U, Szallasi Z, Doyle FJ 3rd, Doyle J (2004) Robustness of
cellular functions. Cell 118: 675–685.
30. Deutscher D, Meilijson I, Kupiec M, Ruppin E (2006) Multiple knockout
analysis of genetic robustness in the yeast metabolic network. Nat Genet 38:
993–998.
31. Behre J, Wilhelm T, von Kamp A, Ruppin E, Schuster S (2008) Structural
robustness of metabolic networks with respect to multiple knockouts. J Theor
Biol 252: 433–441.
32. Bergmann FT, Sauro HM (2008) Comparing simulation results of SBML
capable simulators. Bioinformatics 24: 1963–1965.
33. Lemke N, Heredia F, Barcellos CK, Dos Reis AN, Mombach JC (2004)
Essentiality and damage in metabolic networks. Bioinformatics 20: 115–119.
34. Wunderlich Z, Mirny LA (2006) Using the topology of metabolic networks to
predict viability of mutant strains. Biophys J 91: 2304–2311.
35. Freilich S, Kreimer A, Borenstein E, Yosef N, Sharan R, et al. (2009) Metabolicnetwork driven analysis of bacterial ecological strategies. Genome Biol 10(6):
R61.
36. Madan Babu M, Teichmann SA, Aravind L (2006) Evolutionary dynamics of
prokaryotic transcriptional regulatory networks. J Mol Biol 358: 614–633.
37. Parter M, Kashtan N, Alon U (2007) Environmental variability and modularity
of bacterial metabolic networks. BMC Evol Biol 7: 169.
38. Kashtan N, Alon U (2005) Spontaneous evolution of modularity and network
motifs. Proc Natl Acad Sci U S A 102: 13773–13778.
39. Koonin EV (2003) Comparative genomics, minimal gene-sets and the last
universal common ancestor. Nat Rev Microbiol 1: 127–136.
40. Gerdes SY, Scholle MD, Campbell JW, Balazsi G, Ravasz E, et al. (2003)
Experimental determination and system level analysis of essential genes in
Escherichia coli MG1655. J Bacteriol 185: 5673–5684.
41. Vitkup D, Kharchenko P, Wagner A (2006) Influence of metabolic network
structure and function on enzyme evolution. Genome Biol 7: R39.
42. Wagner A (2000) Robustness against mutations in genetic networks of yeast. Nat
Genet 24: 355–361.
43. Brown JR, Doolittle WF (1995) Root of the universal tree of life based on ancient
aminoacyl-tRNA synthetase gene duplications. Proc Natl Acad Sci U S A 92:
2441–2445.
1. Thatcher JW, Shaw JM, Dickinson WJ (1998) Marginal fitness contributions of
nonessential genes in yeast. Proc Natl Acad Sci U S A 95: 253–257.
2. de Visser JA, Hermisson J, Wagner GP, Ancel Meyers L, Bagheri-Chaichian H,
et al. (2003) Perspective: Evolution and detection of genetic robustness.
Evolution 57: 1959–1972.
3. Wagner A (2005) Distributed robustness versus redundancy as causes of
mutational robustness. Bioessays 27: 176–188.
4. Kitano H (2004) Biological robustness. Nat Rev Genet 5: 826–837.
5. Pal C, Papp B, Lercher MJ (2005) Adaptive evolution of bacterial metabolic
networks by horizontal gene transfer. Nat Genet 37: 1372–1375.
6. Blank LM, Kuepfer L, Sauer U (2005) Large-scale 13C-flux analysis reveals
mechanistic principles of metabolic network robustness to null mutations in
yeast. Genome Biol 6: R49.
7. Papp B, Pal C, Hurst LD (2004) Metabolic network analysis of the causes and
evolution of enzyme dispensability in yeast. Nature 429: 661–664.
8. Fisher RA (1928) The Possible Modification of the Response of the Wild Type to
Recurrent Mutations. The American Naturalist 62: 115–126.
9. Bourguet D (1999) The evolution of dominance. Heredity 83 (Pt 1): 1–4.
10. Orr HA (1991) A test of Fisher’s theory of dominance. Proc Natl Acad Sci U S A
88: 11413–11415.
11. Wright S (1934) Physiological and evolutionary theories of dominance. The
American Naturalist 68: 25–53.
12. Kacser H, Burns JA (1981) The molecular basis of dominance. Genetics 97:
639–666.
13. Kafri R, Springer M, Pilpel Y (2009) Genetic redundancy: new tricks for old
genes. Cell 136: 389–392.
14. Papp B, Teusink B, Notebaart RA (2009) A critical view of metabolic network
adaptations. HFSP Journal 3: 24–35.
15. Ebenhoh O, Handorf T, Heinrich R (2004) Structural analysis of expanding
metabolic networks. Genome Inform 15: 35–45.
16. Handorf T, Ebenhoh O, Heinrich R (2005) Expanding metabolic networks:
scopes of compounds, robustness, and evolution. J Mol Evol 61: 498–512.
17. Ebenhoh O, Handorf T, Heinrich R (2005) A cross species comparison of
metabolic network functions. Genome Inform 16: 203–213.
18. Raymond J, Segre D (2006) The effect of oxygen on biochemical networks and
the evolution of complex life. Science 311: 1764–1767.
19. Ebenhoh O, Handorf T (2009) Functional classification of genome-scale
metabolic networks. EURASIP J Bioinform Syst Biol. 570456 p.
20. Borenstein E, Kupiec M, Feldman MW, Ruppin E (2008) Large-scale
reconstruction and phylogenetic analysis of metabolic environments. Proc Natl
Acad Sci U S A 105: 14482–14487.
21. Handorf T, Christian N, Ebenhoh O, Kahn D (2008) An environmental
perspective on metabolism. J Theor Biol 252: 530–537.
22. Kacser H, Burns JA (1973) The control of flux. Symp Soc Exp Biol 27: 65–104.
23. Sauro HM, Small JR, Fell DA (1987) Metabolic control and its analysis.
Extensions to the theory and matrix method. Eur J Biochem 165: 215–221.
PLoS Computational Biology | www.ploscompbiol.org
9
February 2010 | Volume 6 | Issue 2 | e1000690
Environment-Dependent and Independent Robustness
55. Kanehisa M, Goto S (2000) KEGG: kyoto encyclopedia of genes and genomes.
Nucleic Acids Res 28: 27–30.
56. Becker SA, Palsson BO (2005) Genome-scale reconstruction of the metabolic
network in Staphylococcus aureus N315: an initial draft to the two-dimensional
annotation. BMC Microbiol 5: 8.
57. Feist AM, Henry CS, Reed JL, Krummenacker M, Joyce AR, et al. (2007) A
genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that
accounts for 1260 ORFs and thermodynamic information. Mol Syst Biol 3: 121.
58. Oh YK, Palsson BO, Park SM, Schilling CH, Mahadevan R (2007) Genomescale reconstruction of metabolic network in Bacillus subtilis based on highthroughput phenotyping and gene essentiality data. J Biol Chem 282:
28791–28799.
59. Newman ME (2006) Modularity and community structure in networks. Proc
Natl Acad Sci U S A 103: 8577–8582.
60. Kreimer A, Borenstein E, Gophna U, Ruppin E (2008) The evolution of
modularity in bacterial metabolic networks. Proc Natl Acad Sci U S A 105:
6976–6981.
61. Cormen TH, Leiserson CE, Rivest RL (1990) Introduction to algorithms.
Cambridge, Mass. ; London New York: MIT Press; McGraw-Hill. xvii, 1028 p.
62. Yamazaki Y, Niki H, Kato J (2008) Profiling of Escherichia coli Chromosome
database. Methods Mol Biol 416: 385–389.
63. Kobayashi K, Ehrlich SD, Albertini A, Amati G, Andersen KK, et al. (2003)
Essential Bacillus subtilis genes. Proc Natl Acad Sci U S A 100: 4678–4683.
64. [http://www.ncbi.nlm.nih.gov/genomes/lproks.cgi]. EGP.
65. Couturier E, Rocha EP (2006) Replication-associated gene dosage effects shape
the genomes of fast-growing bacteria but only for transcription and translation
genes. Mol Microbiol 59: 1506–1518.
44. Ochsner UA, Sun X, Jarvis T, Critchley I, Janjic N (2007) Aminoacyl-tRNA
synthetases: essential and still promising targets for new anti-infective agents.
Expert Opin Investig Drugs 16: 573–593.
45. Gu Z, Steinmetz LM, Gu X, Scharfe C, Davis RW, et al. (2003) Role of
duplicate genes in genetic robustness against null mutations. Nature 421: 63–66.
46. Martin JF, Demain AL (1980) Control of antibiotic biosynthesis. Microbiol Rev
44: 230–251.
47. Helling RB (1994) Why does Escherichia coli have two primary pathways for
synthesis of glutamate? J Bacteriol 176: 4664–4668.
48. Pfeiffer T, Schuster S, Bonhoeffer S (2001) Cooperation and competition in the
evolution of ATP-producing pathways. Science 292: 504–507.
49. Newton DT, Creuzenet C, Mangroo D (1999) Formylation is not essential for
initiation of protein synthesis in all eubacteria. J Biol Chem 274: 22143–22146.
50. Murta SM, Vickers TJ, Scott DA, Beverley SM (2009) Methylene tetrahydrofolate dehydrogenase/cyclohydrolase and the synthesis of 10-CHO-THF are
essential in Leishmania major. Mol Microbiol.
51. Rokhlenko O, Shlomi T, Sharan R, Ruppin E, Pinter RY (2007) Constraintbased functional similarity of metabolic genes: going beyond network topology.
Bioinformatics 23: 2139–2146.
52. Janga SC, Babu MM (2008) Network-based approaches for linking metabolism
with environment. Genome Biol 9: 239.
53. Aguilar D, Aviles FX, Querol E, Sternberg MJ (2004) Analysis of phenetic trees
based on metabolic capabilites across the three domains of life. J Mol Biol 340:
491–512.
54. Follows MJ, Dutkiewicz S, Grant S, Chisholm SW (2007) Emergent
biogeography of microbial communities in a model ocean. Science 315:
1843–1846.
PLoS Computational Biology | www.ploscompbiol.org
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