Journal of Experimental Botany, Vol. 63, No. 6, pp. 2259–2274, 2012
doi:10.1093/jxb/ers018
REVIEW PAPER
Modelling cyanobacteria: from metabolism to integrative
models of phototrophic growth
Ralf Steuer1,
*, Henning Knoop1
and Rainer Machne´ 2
1
Institute of Theoretical Biology, Humboldt-University Berlin, Invalidenstr. 43, D-10115 Berlin, Germany
2
Institute for Theoretical Chemistry, University of Vienna, Austria
* To whom correspondence should be addressed. E-mail: ralf.steuer@hu-berlin.de
Received 18 October 2011; Revised 12 January 2012; Accepted 13 January 2012
Abstract
Cyanobacteria are phototrophic microorganisms of global importance and have recently attracted increasing
attention due to their capability to convert sunlight and atmospheric CO2 directly into organic compounds, including
carbon-based biofuels. The utilization of cyanobacteria as a biological chassis to generate third-generation biofuels
would greatly beneﬁt from an increased understanding of cyanobacterial metabolism and its interplay with other
cellular processes. In this respect, metabolic modelling has been proposed as a way to overcome the traditional trial
and error methodology that is often employed to introduce novel pathways. In particular, ﬂux balance analysis and
related methods have proved to be powerful tools to investigate the organization of large-scale metabolic
networks—with the prospect of predicting modiﬁcations that are likely to increase the yield of a desired product
and thereby to streamline the experimental progress and avoid futile avenues. This contribution seeks to describe
the utilization of metabolic modelling as a research tool to understand the metabolism and phototrophic growth of
cyanobacteria. The focus of the contribution is on a mathematical description of the metabolic network
of Synechocystis sp. PCC 6803 and its analysis using constraint-based methods. A particular challenge is to
integrate the description of the metabolic network with other cellular processes, such as the circadian clock,
the photosynthetic light reactions, carbon concentration mechanism, and transcriptional regulation—aiming at
a predictive model of a cyanobacterium in silico.
Key words: Ecosystems biology, ﬂux balance analysis (FBA), network reconstruction, photosynthesis, quantitative modelling,
systems biology.
Introduction
Cyanobacteria are phototrophic microorganisms and the
only known prokaryotes capable of oxygenic photosynthesis.
Having evolved possibly as early as 3.5 billion years ago
(Des Marais, 2000), cyanobacteria are of global importance
for almost all geochemical cycles and had profound impact
on life on Earth. Today, cyanobacteria are still responsible
for a signiﬁcant fraction of global primary productivity and
remain major players in global oxygen supply, carbon
sequestration, and nitrogen ﬁxation.
From a metabolic perspective, cyanobacteria are highly
versatile organisms and occupy almost every environment
where light is available. Renewed attention on the organization
of cyanobacterial metabolism is driven by their
capability to convert sunlight and atmospheric CO2 directly
into carbon-based compounds, therefore providing an opportune
biological chassis to generate third-generation biofuels
(Atsumi et al., 2009; Ducat et al., 2011; Hess, 2011;
Quintana et al., 2011). Indeed, biofuels derived from
cyanobacteria offer several potential advantages, as compared
with fuels derived from land-based plants or other
renewable sources. Cultivation of cyanobacteria does not
require large amounts of arable land and is therefore not in
direct competition with agricultural food production. Rather,
cyanobacteria can be grown in large quantities relying only
on water, including salt water, some minerals, CO2, and
sunlight. Several cyanobacteria also possess the capability to
ﬁx atmospheric nitrogen, with the potential to reduce costs of
fertilizer that may otherwise signiﬁcantly affect the economic
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and energetic feasibility of biofuel production from algae and
other organisms.
Most successful efforts to modify cyanobacterial metabolism
currently rely on a trial-and-error methodology to
introduce novel pathways and to increase the yield of
desired products (Atsumi et al., 2009; Bandyopadhyay
et al., 2010; Liu et al., 2011). In this respect, one of the
promises of Systems Biology is that computational modelling
will allow the prediction of targeted modiﬁcations of
metabolism, with the potential to streamline the experimental
progress and to avoid futile avenues. While the question
of whether Systems Biology can live up to its expectations is
still open, large-scale models of cellular metabolism are
indeed increasingly predictive and allow anticipation of
beneﬁcial modiﬁcations within the metabolic networks of
many organisms. In particular, ﬂux balance analysis (FBA),
and related methods, have proven to be powerful tools to
understand the organization of large-scale metabolic networks
(Orth et al., 2010; Sweetlove and Ratcliffe, 2011).
This contribution seeks to provide an overview on
existing modelling strategies of the metabolic network of
phototrophic cyanobacteria. In the ﬁrst section, a brief
introduction to metabolic modelling is given and a hierarchy
of descriptions is introduced that is suitable to represent
metabolic networks and pathways. Subsequently, a stoichiometric
model of the unicellular cyanobacterium Synechocystis
sp. PCC 6803 is described, including applications of FBA,
and several caveats and pitfalls in the process of reconstructing
metabolic networks are discussed. The ﬁnal section
provides an outlook on the integration of different cellular
processes within a common modelling framework, towards
a cyanobacterial cell in silico.
Computational models of metabolism
Computational modelling is increasingly recognized as an
expedient research tool to understand the organization of
biological systems. Nonetheless, the methods and practices
of mathematical modelling are highly diverse and no single
methodology alone is able to cover the diverse temporal and
spatial scales observed in biological systems. Therefore, the
future of modelling resides in the utilization of a combination
of methods, each suited to describe a particular aspect
of biological reality—giving rise to the challenge to combine
these diverse conceptual and computational pictures into
a coherent whole.
Common to almost all methods of modelling is that they
seek to translate a given biological process into a formal
language. According to the view put forward here, this
translation of biological reality into the mathematical realm
serves two distinct purposes (Steuer and Junker, 2009;
Steuer, 2011): ﬁrst, the translation of an assumed functional
interaction into a mathematical representation allows
researchers to communicate knowledge in a way that is not
possible by mere verbal description. Paradigmatic examples
are already provided by simple enzyme kinetics for which
the formulation of models allows communication of complex
patterns of interactions with only a few parameters. By
describing assumed molecular mechanisms, such as competitive
inhibition, using a mathematical representation allows
other researchers to contrast their own results in a precise
and well-deﬁned way. Secondly, once the interactions
underlying a biological process are cast into a mathematical
form, mathematical theory and computational methods
provide powerful tools to predict the emergent outcome of
any particular set of interactions—again signiﬁcantly surpassing
the scope of human intuitive reasoning. A paradigmatic
example is the emergence of oscillatory behaviour in
biochemical reaction networks. Once translated into an
appropriate mathematical representation, the answer to the
question of whether a given reaction mechanism allows for
sustained oscillations is little more than a technical formality.
Mathematical modelling therefore allows the study of
the consequences and outcomes of assumed interactions
using computational or analytical techniques. As will be
emphasized below, both of these aspects stand on their own
and are equally important to understand the functioning of
biological systems. Importantly, the use of a mathematical
language, in the sense outlined above, does not pre-suppose
or require trueness of the mathematical description.
While most techniques of modelling apply in a similar
way to a variety of cellular processes, the focus of this
review is foremost a description of models of cyanobacterial
metabolism. In many aspects, metabolic networks of prokaryotic
organisms are speciﬁcally suited for computational
modelling. This advantage can be attributed to three
characteristics that distinguish most prokaryotic metabolic
networks from other networks of cellular interactions
(Steuer, 2011): ﬁrst, the function of many biochemical
pathways resides in the mass transfer and synthesis of
metabolic compounds. This fact can be exploited to resolve
the topological organization of metabolic networks, for
example by isotopic labelling techniques. In contrast,
a similar technique that is able to trace functioning pathways
does not exist for cellular information processing
networks. Likewise, biochemical reaction networks are
subject to constraints with respect to physicochemical and
thermodynamic feasibility. Correspondingly, the topology
of central metabolism is reasonably well understood, at
least for many prokaryotic organisms. Secondly, the modes
of action of the building blocks of metabolic networks,
enzymes that catalyse biochemical reactions, have been
studied for more than a century. Most enzymes are
reasonably well described by conventional chemical kinetics
and their action can often be replicated in vitro. Therefore,
the local dynamics of enzymatic reactions are reasonably
well understood. Thirdly, and probably most important, the
metabolic network of prokaryotic organisms can usually be
assigned a well-deﬁned functionality, namely the synthesis
of cellular building blocks to support cellular growth and
the provision of ATP and other ‘currency metabolites’ for
cellular maintenance (Ibarra et al., 2002; Lewis et al., 2010).
These rather clear-cut objectives of metabolic pathways
form the basis of the success of the various optimization
techniques applied to large-scale metabolic networks.
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Although there are several caveats with respect to the
arguments outlined above, a known topology, reasonably
well understood modes of local action, and a clear-cut
functionality offer a good starting point for the construction
of models of cellular metabolism.
A hierarchy of computational description
In practice, metabolic models take a variety of forms and
no single computational methodology is able to describe all
possible aspects of metabolic functioning (Steuer and
Junker, 2009). Rather, a hierarchy of mathematical description
or frameworks exists, each with particular
strengths and weaknesses. An overview is given in Fig. 1.
Currently, there is a dichotomy between small-scale
models, usually involving a high level of detail with respect
to the interacting compounds on the one hand and largescale
models of cellular networks on the other hand.
Located on the right side within the continuum shown in
Fig. 1 are detailed kinetic models of cellular pathways.
Detailed kinetic models are usually implemented as a set of
ordinary differential equations for all biochemical compounds
within a pathway. Typically, the construction of
such models makes use of aggregated biochemical rate laws,
such as Michaelis–Menten kinetics, to describe biochemical
interconversions of compounds. Multiple repositories and
simulation tools exist that allow on- and ofﬂine analysis of
kinetic models (Olivier and Snoep, 2004; Hoops et al., 2006;
Machne´ et al., 2006; van Gend et al, 2007; Li et al., 2010).
However, the availability of detailed kinetic models of
cellular pathways, in particular for cyanobacteria or other
phototrophic organisms, is still extremely limited. One
reason for this scarcity is due to the fact that detailed
kinetic models put extensive demands on data availability.
Their construction usually requires explicit knowledge of all
involved rate constants and kinetic parameters. For cyanobacteria,
detailed kinetic models are mostly available for
selected subsystems, such as the cyanobacterial circadian
clock (Miyoshi et al., 2007; Rust et al., 2007; Cerveny´
and Nedbal, 2009; Brettschneider et al., 2010), photosystem
II (Jablonsky and Lazar, 2008), carbon-concentrating
mechanisms (Badger et al., 1985; Fridlyand et al., 1996),
as well as for selected metabolic pathways, such as the
Calvin–Benson cycle (Jablonsky et al., 2011). Kinetic
models often also rely on kinetic parameters and data
from plants and other related organisms. Small quasiautonomous
subsystems, such as the circadian clock, are
particularly suited for kinetic modelling as they typically
involve only few interacting partners that operate in
a manner sufﬁciently isolated from other cellular networks
and therefore allow a data-driven construction of detailed
kinetic models.
Given the difﬁculties associated with the construction of
detailed kinetic models, most current efforts towards
modelling cellular metabolism are located on the left side
within the continuum shown in Fig. 1. Topological methods
are understood here as methods that represent cellular
metabolism as a, usually bipartite, graph. Such graph-based
descriptions of metabolism, while popular in many areas of
interdisciplinary sciences (Baraba´si and Oltvai, 2004),
usually do not incorporate genuine biochemical quantities,
such as reaction stoichiometries, in the description of the
network—a shortcoming that signiﬁcantly limits their
potential to resolve genuine biological questions (Steuer
Fig. 1. A hierarchy of computational representations. Current approaches to metabolic modelling range from graph-based methods to
detailed kinetic models of cellular pathways. Methods that aim at large-scale description are typically less quantitative. Of particular
interest are also intermediate methods that seek to bridge the gap from detailed kinetic to large-scale models of cellular metabolism.
Adapted and redrawn from Steuer R and Junker BH. 2009. Computational models of metabolism: stability and regulation in metabolic
networks. In: Advances in chemical physics. This material is reproduced with permission of John Wiley & Sons, Inc.
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and Zamora Lopez, 2008). A better choice for the description
of biochemical networks are usually stoichiometric
models. Stoichiometric models explicitly take the physicochemical
nature of biochemical reaction networks into
account, but their analysis does not yet require kinetic
parameters or detailed knowledge of the properties of the
involved enzymes. Prominent applications of stoichiometric
modelling are the concept of elementary ﬂux modes
(EFMs), as well as FBA. In particular, FBA has become an
important tool to analyse the properties of large-scale
metabolic networks. FBA is entirely based on constraints
imposed by mass conservation and is able to incorporate
thermodynamic (Beard et al., 2004; Ku¨mmel et al., 2006;
Henry et al., 2007; Hoppe et al., 2007) and other constraints
(Zhuang et al., 2011).
Of particular interest are also intermediate methods that
seek to bridge the gap from stoichiometric to explicit kinetic
models of cellular pathways. Intermediate methods may, for
example, take the form of hybrid models, coupling a smallscale
kinetic model to a large-scale stoichiometric model of
metabolism (Mahadevan et al., 2002; Luo et al., 2006), or
aim to derive dynamic properties of large reaction networks
without requiring detailed knowledge of kinetic parameters.
The latter approach typically makes use of Monte Carlo
sampling of the parameter space to obtain a probabilistic
understanding of the dynamic properties of the respective
system (Wang et al, 2004; Steuer et al., 2006; Tran et al.,
2008; Steuer, 2011). It is expected that such methods will be
of importance for the further development of models of
phototrophic metabolism. In particular, several characteristic
properties of cyanobacterial metabolism differ from their
counterparts in conventional heterotrophic bacteria. These
differences include the utlilization of light as a resource,
which necessitates the consideration of the fast and intrinsically
dynamic light reactions as part of the metabolic
network. Likewise, several dominant metabolic processes,
such as the costs of uptake and cycling of inorganic carbon
(Tchernov et al., 2001, 2003), as well as the inhibition of
Rubisco by molecular oxygen, are highly dependent on
concentrations and their gradients—and therefore difﬁcult
to capture within a framework predominantly based on
stoichiometric relationships.
Fig. 2. Gene–protein–reaction associations for a selected subset of genes of the unicellular cyanobacterium Synechocystis sp. PCC
6803. Enzymes may be composed of several subunits and single genes may encode multifunctional enzymes.
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A stoichiometric reconstruction of
Synechocystis sp. PCC 6803
Large-scale stoichiometric modelling of metabolic networks
relies entirely on a high-quality reconstruction of the
underlying set of reactions. The aim of such a metabolic
reconstruction is to give a comprehensive account of all
biochemical conversions taking place within a living cell or
organism, including transport and non-enzymatic reactions.
The reconstruction process itself increasingly follows standard
procedures and is described in detail in the literature
(Feist et al., 2009; Thiele and Palsson, 2010a). Here, the
focus is on a recently published reconstruction of the
cyanobacterium Synechocystis sp. PCC 6803 (Knoop et al.,
2010). The reconstruction process typically comprises four
steps. The starting point is the annotated genome, as
obtained from the CyanoBase Web site (Nakamura et al.,
1998, 1999; Nakao et al., 2010), together with pathway
repositories such as the Kyoto Encyclopedia of Genes and
Genomes (KEGG; http://www.kegg.com/; Kanehisa et al.,
2006) or MetaCyc (www.metacyc.org; Caspi et al., 2010).
These resources are combined to provide an initial draft
network that consists of gene–protein–reaction associations
for each annotated gene, in addition to a number of nonenzymatic
(spontaneous) reactions and transport processes.
A small-scale example is shown in Fig. 2, and the
corresponding stoichiometric matrix is shown in Fig. 3.
Based on the draft reconstruction, an iterative process of
gap ﬁnding and network curation begins. In particular, the
draft network allows veriﬁcation of whether all known
metabolic intermediates of the respective organism can be
synthesized using the set of reactions assigned to the
organism. Usually, this is not the case and additional
reactions have to be included in the model. For example,
for the reconstruction of Synechocystis sp. PCC 6803
(Knoop et al., 2010), the draft network did not support the
synthesis of the amino acids glycine, serine, cysteine,
methionine, asparagine, and histidine. To complete the
network and to account for missing steps, different strategies
may be followed. To this end, an increasing number of
algorithms is available that aim to identify missing steps
within metabolic networks computationally and offer automated
schemes to provide suggestions for missing enzymes
(Kumar et al., 2007). These algorithms are usually based on
shortest-path or minimal extension criteria to complete the
metabolic network and to establish a deﬁned metabolic
functionality. However, it needs to be emphasized that such
automated schemes do not always lead to meaningful
results, owing to the fact that nature itself often does not
follow a logic of minimal extensions but may choose
seemingly capricious and non-optimal solutions for metabolic
interconversion routes. Therefore, in particular for
prokaryotic networks of smaller size, manual curation
remains the most important step in metabolic network
reconstruction. The knowledge accumulated in the biochemical
literature on selected pathways often provides
a crucial resource to re-annotate enzymes and to provide
a correct picture of biochemical interconversions. For
Synechocystis sp. PCC 6803, an example of the necessity of
incorporating literature knowledge is given by the detailed
Fig. 3. The stoichiometric matrix corresponding to the gene–reaction associations given in Fig. 2. Columns correspond to reactions, and
rows to metabolites.
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elucidation of the photorespiratory pathways (Eisenhut
et al., 2008) that were, at the time of reconstruction, not
part of any pathway database. It is noted that tests for
completeness and subsequent gap ﬁlling also must take into
account various non-enzymatic reactions, including possible
degradation reactions.
From network to model
Once the reconstruction can account for all relevant
synthesis routes of metabolic intermediates, the network is
converted into a mathematical model. This step involves the
inclusion of several pseudo-reactions that account for
cellular maintenance and growth, as well as the conversion
of the set of reactions into a computer-readable format.
Cellular maintenance is usually accounted for by adding an
additional ATP drain. However, utilization of NADPH,
independent of the synthesis reactions, and dilution of
metabolites by growth may also be considered. Of particular
importance is the biomass objective function (BOF) that
represents an overall pseudo-reaction to describe cellular
growth in terms of the required metabolic precursors. It is
assumed that for growth and replication a speciﬁed set of
metabolic precursors needs to be synthesized in ﬁxed
stoichiometric ratios. The BOF therefore describes a cellular
demand that the remaining synthesis reactions have to
satisfy in order to achieve cellular growth. It is noted that
the BOF may change depending on experimental conditions.
For cyanobacteria, different BOFs are usually
assigned to heterotrophic, mixotrophic and phototrophic
conditions, reﬂecting differences in cellular composition
(Shastri and Morgan, 2005). It is noted that a mathematical
model differs from a mere list of reactions in its scope to
assign a particular functionality to any set of reactions, such
as the capability to synthesize certain metabolic intermedi-
ates.
Finally, given a mathematical respresentation of the
network, preferably using a deﬁned exchange format such
as SBML (Systems Biology Markup Language; Hucka
et al., 2003), the model can be investigated using standard
methods for stoichiometric analysis. To this end, an increasing
number of software packages are available to
facilitate large-scale network analysis (Becker et al., 2007;
Klamt et al., 2007; Hoppe et al., 2011; Schellenberger et al.,
2011). The entire process is highly iterative, and is
summarized in Fig. 4. It is noted that at this stage, the
model itself is not expected to be a fully veriﬁed and errorfree
representation of the respective metabolic network.
Rather, its purpose is to provide a starting point to allow
systematic functional veriﬁcation, to identify uncertain and
possibly misannotated enzymatic steps, and therefore to
guide further experimentation.
It should be emphasized that the standardized reconstruction
process, followed by stoichiometric analysis, was
mainly developed to describe heterotrophic growth of
Fig. 4. The process of network reconstruction typically comprises four steps. Starting with a draft metabolic network (Step 1), the
network is contrasted and extended with data from the literature (Step 2) and transformed into a mathematical model (Step 3). The
resulting model is subject to computational analysis and further tested against available phenotypic data (Step 4). The process is iterative
and proceeds with Steps 2 to extend the reconstruction and to reconcile inconsistent information.
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various microorganisms. For example, within a recent effort
to generate automatically 130 genome-scale metabolic
models representing a taxonomically diverse set of bacteria
(Henry et al., 2010), only a single cyanobacterium was
included. A conspicuous lack of phototrophic metabolic
reconstructions was also noted in a recent overview on
applications of genome-scale reconstructions (Oberhardt
et al., 2009). Indeed, several aspects of phototrophic
metabolism can, as yet, only be inadequately represented
by stoichiometric models. For example, light is typically
represented as a single metabolic compound (photon) that
participates in stoichiometric reactions along with other
metabolites. Only recently, a ﬁrst attempt at a novel light
modelling approach that allows resolution of wavelength
and photon ﬂux has been proposed (Chang et al., 2011).
Problems in network reconstruction
In practice, a considerable number of further difﬁculties
complicate the process of network reconstruction outlined
above. Even for well-annotated organisms, such as Synechocystis
sp. PCC 6803, errors in gene annotation are not
uncommon. Likewise, integration of multiple reaction repositories
and literature research is considerably hampered
by different and often inconsistent naming schemes of
metabolic intermediates (Radrich et al., 2007). For example,
within KEGG, the metabolite 2-oxoisovalerate (COMPOUND:
C00141) is listed with no less than nine synoyms
(3-methyl-2-oxobutanoic acid, 3-methyl-2-oxobutyric
acid, 3-methyl-2-oxobutanoate, 2-oxo-3-methylbutanoate,
2-oxoisovalerate, 2-oxoisopentanoate, a-ketovaline, 2ketovaline,
and 2-keto-3-methylbutyric acid), each of which
may also be used within the literature and may therefore
confuse results when researching the corresponding bibliome.
Adding to the complexity of metabolite annotation,
metabolites usually also co-exist in different protonation
states depending on the intracellular milieu—a fact that
must be taken into account when reactions from different
sources are combined. Such inconsistent annotation may
lead to erroneous gaps within the network, as pathways
may no longer be connected. While most of these issues are
straightforwardly resolved using manual inspection and
expert knowledge, the large size of many metabolic networks
often requires automated solutions. To this end,
researchers working on metabolic network reconstructions
increasingly recommend the utilization of a controlled
vocabulary that allows consistent naming of metabolites to
facilitate cross-database comparison. Such a controlled
vocabulary usually refers to databases and web repositories,
such as ChEBI (Chemical Entities of Biological Interest),
a freely available dictionary of metabolic compounds
(de Matos et al., 2010). As a further advantage, consistent
and computer-readable naming allows software tools to
recognize the annotated compound and therefore allows
automated quality checks on the reconstructed networks to
be performed. Even if sourced from curated pathway
databases, reactions may not always be balanced with
respect to elements and charge, resulting in metabolic cycles
that can generate metabolic compounds without input. For
example, Yoshikawa et al. (2011) reported that they failed
to simulate a previously published model of Synechocystis
sp. PCC 6803 (Montagud et al., 2010) because the
reconstruction contained inadequate reaction loops. It is
therefore strongly recommended to perform automated
charge and elemental balancing at the end of the
reconstruction process, as, for example, facilitated by
COBRA 2 (Schellenberger et al., 2011) or the freely
available toolbox SuBliMinaL (Swainston et al., 2011).
It should be mentioned that during network reconstruction
not all identiﬁed missing steps correspond to erroneous
gaps within the respective metabolic network. Cyanobacteria
are known for highly streamlined genomes, in particular
the genus Prochlorococcus (Partensky and Garczarek
et al., 2010). For example, it was recently shown that
Prochlorococcus, whose genomes lack catalase and therefore
should be highly susceptible to damage from hydrogen
peroxide, are protected by an extant HOOH-consuming
microbial community in the surface mixed layer of the
oligotrophic ocean (Morris et al., 2011). Likewise, recently
a globally distributed marine cyanobacterium, UCYN-A,
was described that lacks the oxygen-producing photosystem
II complex. Instead, UCYN-A exhibits a strongly restricted
photofermentative metabolism and is probably dependent
on other organisms for essential compounds (Tripp et al.,
2010). In such cases, unsupervised automated reconstruction
may yield erroneous solutions that account for
metabolic pathways that are not present in the respective
organism.
Network size and quality criteria
One of the most persistent problems in current network
reconstructions is that clear-cut criteria whose properties
constitute a good reconstruction are still missing. While
stoichiometric consistency and other formal aspects can be
tested rather straightforwardly, the reconstruction process
itself still allows for miscellaneous choices of criteria for
inclusion or exclusion of speciﬁc reactions. This shortcoming
is particularly relevant for enzymes with unclear
speciﬁcity. In this case, a single enzyme might be annotated
for a large number of possible interconversions,
whereas in practice the enzyme is often for a smaller, but
unknown, subset of interconversions. Common cases also
include generic annotations in which enzymes, for example,
require a ‘reduced acceptor’ or ‘hydrogen donor’ (both
KEGG Compound C00030). Since current ﬂux balance
software can usually only deal with speciﬁc metabolites,
not classes of metabolites, such generic terms may lead to
a combinatorial inﬂation of the number of possible
reactions. A computational representation of enzymes
acting on polydisperse substrates, such as many storage
compounds, also remains a challenging task (Kartal et al.,
2011). Likewise, cofactor requirements of most reactions
are often unknown. For example, within the
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reconstruction of Synechocystis sp. PCC 6803, many
reactions are included as NAD/NADH- and NADP/
NADPH-dependent variants, as the actual speciﬁcities of
those reactions are unknown.
In general, a large number of current reconstructions opt
for the inclusion of as many reactions as possible, even at
the expense of overestimating the number of actual
interconversions for most enzymes. On the other hand,
several recent studies also deliberately only focus on
a selected subset of reactions, usually central carbon
metabolism and adjacent pathways. It was observed previously
(Sweetlove and Ratcliffe, 2011) that both
approaches often give rise to an almost identical number of
active reactions; that is, the number of reactions that carry
non-zero metabolic ﬂux under any condition is usually
similar. While both approaches have their merits, it must be
emphasized that the size of a reconstruction is only rarely
an indicator of quality and usually does not increase the
predictive power of a model. Indeed large size, in particular
for poorly characterized organisms, often indicates indiscriminate
inclusion of vaguely annotated enzymes.
A way to overcome some of these problems again resides
in consistent annotation. In this respect, a ﬁrst step is to
assign a level of conﬁdence with each included reaction,
such that other researchers can clearly identify on which
evidence any particular reaction was included within the
network. Such consistent annotation allows the discernment
of whether a particular reaction was included on the
basis of sound biochemical evidence, or whether, for
example, it was included to restore a certain metabolic
functionality whose absence would otherwise preclude
further analysis. Likewise, there is increasing agreement
that a complete reconstruction of any single organism and
its validation is beyond the means of a single research
group. Therefore, increasing emphasis is put on community
efforts, such as network reconstruction jamborees
that aim at a consensus reconstruction to reconcile and
reﬁne knowledge about the respective organism (Herrga˚rd
et al., 2008; Thiele and Palsson, 2010b). Such reconstruction
jamborees were already successfully undertaken for
several common organisms, including Saccharomyces
cerevisiae, Salmonella typhimurium, and Homo sapiens,
but, as yet, not for higher plants or cyanobacteria. Finally,
successful reconstructions should be made available on
dedicated exchange platforms, such as biomodels.org
(Li et al., 2010) or MemoSys (Pabinger et al., 2011),
to facilitate further improvement and utilization of the
reconstruction.
Flux balance analysis
Once a faithful reconstruction of the metabolic network is
available, the corresponding model is ready to be evaluated
using constraint-based analysis and other computational
methods. A method of choice is FBA, a computational
approach that has emerged as a numerically feasible
and highly predictive approach to study the properties of
large-scale metabolic networks. Crucial to its success, FBA
is based on only a few reasonable principles and assumptions,
most of which are likely to hold for prokaryotic
metabolic networks under many physiological conditions.
To apply FBA, metabolites are subdivided into a set of
compounds whose concentrations are assumed to be
stationary (internal metabolites) and a set of compounds
that may vary over time or are external to the network
(external metabolites). Examples of the latter include
external nutrients or certain cofactors whose concentrations
are assumed to be constant. FBA then makes use of the
fact that the set of stationary internal metabolites puts
constraints on the stationary ﬂux distributions within
the network. In particular, any unchanged metabolite
concentration over a given period of time implies that the
sum of ﬂuxes producing this metabolite equals the sum of
ﬂuxes consuming this metabolite. On the network
level, this mass balance constraint reduces the admissible
ﬂux space, such that only certain combinations of ﬂux
values are feasible. It is noted that the mass balance
constraint does not necessarily imply that the system is
at steady state. An identical reasoning holds, for example,
for oscillating networks—provided that the metabolite
concentration is unchanged after a deﬁned period of time,
such as a full diurnal cycle. In this case, the ﬂux values must
be understood as an integrated ﬂux over the respective
period.
Usually, the mass balance constraint itself does not give
rise to a speciﬁc ﬂux distribution. Within FBA it is therefore
assumed that cells have evolved such that their metabolic
ﬂux distribution satisﬁes one or more optimality criteria.
For single-celled organisms, such as cyanobacteria, the most
common optimality criterion is maximal biomass yield.
That is, the metabolic ﬂuxes are assumed to be distributed
such that they allow a maximal synthesis yield of all
metabolic precursors required for cellular growth. The
respective stoichiometric ratios of precursors are provided
by the BOF as part of the reconstruction process. It is noted
that the optimization process does not consider growth rate,
even though the results are usually stated in units of inverse
time. In particular, an alternative ﬂux solution that is
energetically less favourable but would allow for faster
interconversion rates is not selected by FBA (Schuster et al.,
2008). An illustration of FBA as a two-step process of
constraint and optimization is provided in Fig. 5. A simple
example is given in Fig. 6.
Besides the BOF, other cellular objectives can also be
explored. In particular, a straightforward optimization of
the BOF does not necessarily give rise to a unique ﬂux
solution. In this case, additional secondary objectives may
be included, such as the minimization of total ﬂux—usually
understood as a proxy for the minimization of enzyme
synthesis costs required to sustain a particular solution
(Holzhu¨tter, 2004). Since its initial formulation, a plethora
of reﬁnements and additions have been proposed for FBA.
In particular, great strides have been made to include
a variety of physicochemical constraints, such as thermodynamic
feasibility.
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Fig. 5. The principles of ﬂux balance analysis (FBA) as a two-stage constraint optimization: initially, all ﬂux values are constraint by
individual upper and lower bounds. Then, assuming stationary conditions, the mass balance constraint is applied, resulting in
relationships between intracellular ﬂuxes: the feasible ﬂux cone. A particular solution can be identiﬁed by applying optimization criteria,
such as the optimization of biomass yield (BOF). The optimal solution is not necessarily unique.
Fig. 6. The principles of FBA: a simple example. The starting point is a reaction network (upper left panel) encoded as a stoichiometric
matrix (upper right panel). Given a certain maximal utilization that satisﬁes the mass balance constraint and results in an optimal yield of
biomass formation, as predicted by the biomass objective function, BOF (lower left panel), the problem can be cast into a linear
optimization problem and is solved using standard methods of linear programming. A solution for the simple example is provided in the
lower right panel. In general, the solution is not unique.
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Properties of phototrophic metabolism
While large-scale models of phototrophic and cyanobacterial
metabolism are still scarce compared with those of
other organisms, a number of theoretical studies of
cyanobacterial metabolism have become available over the
past years. Preceded by several experimental studies on
cyanobacterial metabolism (Yang et al., 2002; Cogne et al.,
2003), the ﬁrst computational analysis based on FBA was
performed by Shastri and Morgan (2005), who studied
a stoichiometric model of Synechocystis sp. PCC 6803
under various growth conditions. The model was later
extended by Hong and Lee (2007) and augmented by gene–
reaction associations. Subsequently, Fu (2009) presented
a genome-scale reconstruction of Synechocystis sp. PCC
6803, involving, however, only minimal manual curation.
A manually curated model focused on the central metabolism
and phototrophic growth was presented by Knoop
et al. (2010). Later, two additional models were published
(Montagud et al., 2010; Yoshikawa et al., 2011), the latter
also conducting a comparison of their own model with the
results of ‘Montagud et al. (2010) and Knoop et al. (2010).
Interestingly, all models differ with respect to several key
pathways. An example is the alleged glyoxylate shunt that
is present in all previous reconstructions, except in the
reconstruction of Knoop et al. (2010). The presence of
such a shunt currently awaits experimental veriﬁcation.
Recent non-stationary ﬂux analysis does not support the
presence of the shunt (Young et al., 2011) and there is, to
the authors’ knowledge, no convincing experimental evidence
of its existence in cyanobacteria. However, the
recent discovery of missing enzymes in the citric acid cycle
(Zhang and Bryant, 2011) exempliﬁes that even core
metabolic pathways may not be completely described yet.
It is noted that none of the models, with the exception of
that of Knoop et al. (2010), fulﬁls current standards of
model annotation as requested by MIRIAM (Minimum
information requested in the annotation of biochemical
models; Le Nove`re et al., 2005). The lack of such unifying
nomenclature makes systematic comparisons unnecessarily
difﬁcult.
Similar to genome annotation, large-scale reconstructions
of cellular metabolism require continuous revision, extension,
and updating. The model originally presented by
Knoop et al. (2010) currently includes 608 genes, corresponding
to 633 metabolic reactions and 451 metabolites.
The focus of the model is a high quality description of
cyanobacterial central metabolism, rather than to account
for a maximal number of, mostly unveriﬁed, reactions.
External parameters include maximal photon inﬂux, maximal
carbon uptake, as well as possible constraints on the
supply of sulphur, nitrate, and inorganic phosphate. Based
on a given set of external parameters, the maximal growth
yield as well as a, not necessarily unique, ﬂux distribution
can be estimated.
Figure 7 shows an estimated ﬂux map for phototrophic
growth using a maximal light input of 7.7 mmol photons
g DWÀ1
hÀ1
. The growth yield was maximized with respect
to light input using the COBRA toolbox (Schellenberger
et al., 2011); other nutrients were not limiting. In addition,
cellular maintenance was accounted for by a basal ATPase
activity of 0.26 mmol g DWÀ1
hÀ1
. The ﬂux solution shown
in Fig. 7 corresponds to an average doubling time of ;12 h
in constant light. Figure 7 also provides an estimated
solution for storage-dependent night metabolism. However,
the choice of an appropriate objective function under this
condition is unclear, as Synechocystis sp. PCC 6803 does not
exhibit an extensive increase of biomass overnight. This
reﬂects an intrinsic problem of FBA, especially relevant for
temporally dynamic systems. Cyanobacterial metabolism is
subject not only to external (diurnal) light variation but also
to extensive transcriptional remodelling of metabolism via
a circadian clock. It is an open and exciting question for
modelling of cyanobacteria, how such temporal dynamics
can be integrated. In Fig. 7, as a proxy for night metabolism,
it is therefore assumed that the metabolism is dominated by
glycogen utilization to match cellular maintenance requirements,
again implemented as a basal ATP activity. In
addition, a small turnover of cellular components is assumed
that is proportional to the BOF. The solutions obtained by
FBA can be contrasted with measurements of phototrophic
ﬂux distributions (Young et al., 2011).
Photorespiration revisited
Importantly, FBA can result in experimentally testable
predictions about the functional role of certain reactions.
For example, the model of Knoop et al. (2010), and
likewise the ﬂux distribution shown in Fig. 7, predicts
a non-zero rate for the Rubisco oxygenase (EC 4.1.1.39),
a seemingly wasteful side reaction of the Calvin–Benson
cycle. This non-zero activity is due to the fact that two
enzymes necessary to synthesize the amino acid serine
from 3-phosphoglycerate via 3-phosphohydroxypyruvate
(EC 2.6.1.52 and EC 3.1.3.3, respectively) are not annotated
in the genome of Synechocystis sp. PCC 6803.
Lacking the conventional synthesis steps, photorespiration
provides an alternative pathway to synthesize the amino
acids glycine and serine. In particular, using the reconstruction
and conditions as deﬁned above, photorespiration
leads to a higher yield of serine and glycine per
photon than all annotated alternative pathways that could
likewise compensate for the absence of the phosphoserine
pathway (Knoop et al., 2010).
These ﬁndings illustrate several facts about FBA and its
utility in the analysis of cellular metabolism: The reconstruction
is based on current gene annotation and therefore
does not include the phosphoserine pathway. Nonetheless,
the respective enzymes may be present in the organism,
albeit, as yet, not recognized. Consequences of possible
alternative pathways can be tested by adding the respective
reactions to the reconstruction – resulting in veriﬁable
predictions about the possible functional role of putative
alternative pathways.
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Extensions of FBA
While the model of Knoop et al. (2010) and other models
have already offered varying degrees of novel insight into
the organization of phototrophic metabolism, all studies
were as yet limited to fairly standard applications of FBA.
However, it must be conceded that the metabolic lifestyle of
cyanobacteria grossly differs from the lifestyle of most of
those prokaryotic organisms that made applications of FBA
popular. Unlike most laboratory or industrial heterotrophic
bacteria, cyanobacteria follow a diurnal rhythm that
involves drastic changes and re-organizations within its
metabolic network. While differences between phototrophic
and heterotrophic growth have been frequently studied, the
transition from storage-based night metabolism to phototrophic
day metabolism exhibits far greater subtlety than
Fig. 7. A map of the central metabolic pathways of Synechocystis sp. PCC 6803. The map provides estimated ﬂux values using an
updated reconstruction of the cyanobacterium (Knoop et al., 2010). The boxes give ﬂux values (in 10À2
mmol g DWÀ1
hÀ1
) for day
conditions (light boxes) and night conditions (dark boxes). Day metabolism is characterized by ﬂux through the Calvin–Benson cycle and
an incomplete TCA cycle. Night metabolism is characterized by glycogen consumption and cyclic ﬂux throught the TCA cycle, mediated
by two recently identiﬁed enzymes (Zhang and Bryant, 2011). For reversible reactions, positive ﬂux values indicate downward ﬂux. Fluxes
marked with an asterisk are not unique.
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can currently be captured by conventional FBA. One can
envisage a complex temporal coordination of metabolism,
such that the biomass function itself is time dependent.
Indeed, studies of the cyanobacterial transcriptome (Sto¨ckel
et al., 2008) and proteome (Sto¨ckel et al., 2011) suggest
a highly coordinated transcriptional programme that is not
compatible with current representation of cellular growth
by a static BOF. Following the work of Asato (2003, 2006),
distinct sequential macromolecular synthesis periods can be
deﬁned that are aligned with the diurnal cycle, as well as the
cell division cycle (Yang et al., 2010).
Outlook: towards integrative models
Cellular metabolism does not operate isolated but is
embedded within a network of highly interconnected
cellular processes that inﬂuence, and are inﬂuenced by, the
metabolic state of a cell. One of the great challenges of
computational modelling is therefore to integrate these
diverse processes into a coherent computational framework
and to describe cellular interactions on the level of the
organism—towards a cyanobacterium in silico.
Processes that directly interact with, or mutually inﬂuence,
cyanobacterial metabolism include carbon-concentrating
mechanisms, the photosynthetic light reactions, the
circadian clock, cellular signal transduction, phototaxis,
transcriptional regulation, and chromosome organization,
as well as the properties of the environment. For several of
these processes, computational models already exist, albeit
incorporating different levels of detail and representing
different levels of reliability. Furthermore, as outlined in
the ﬁrst section, speciﬁc processes often require a speciﬁc
mathematical representation, making the integration of
these diverse computational techniques also a considerable
technical challenge.
Of primary importance to models of cyanobacterial
metabolism is the integration with the photosynthetic light
reactions. Photosynthesis itself is reasonably well understood,
and several kinetic models have been proposed that
describe various aspects of the photosynthetic apparatus in
considerable detail. These models are typically based on
biophysical principles and aim to incorporate the supramolecular
organization and internal states of protein complexes.
Detailed models of photosynthesis, such as the
model of Jablonsky and Lazar (2008), typically involve
a large number of state variables, making integration of
such models with metabolism a demanding task. Due to this
difﬁculty, most available kinetic models of the Calvin cycle
only employ highly simpliﬁed light reactions, such as the
direct regeneration of ATP and NADPH by light (Poolman
et al., 2000). Nonetheless, efforts to couple both processes
already exist (Laisk et al., 2006; Safra´nek et al., 2011). It
should be noted that one of the conclusions drawn from the
model of Laisk et al. (2008), a detailed kinetic model that
includes light reactions, electron–proton transport, enzymatic
reactions, and regulatory functions of C3 photosynthesis,
is that the model is nonetheless insufﬁcient to
reproduce the dark–light induction of photosynthesis.
Of similar importance for global regulation of metabolism
is the cyanobacterial circadian clock. The cyanobacterial
clock consists of a post-translational oscillator
(PTO), based on interactions of only three proteins (KaiA,
KaiB, and KaiC), coupled to a transcriptional/translational
feedback loop (TTFL). As a unique property of the clock,
the PTO can be reconstituted in vitro by mixing puriﬁed
proteins and ATP (Nakajima et al., 2005), and therefore
represents a highly attractive guinea pig for the development
of detailed computational models. Indeed, a large
number of kinetic models were developed over the past
years, mostly focusing on intermolecuar dynamics of interaction
among Kai proteins, entrainment, robustness, and
temperature compensation of the clock. In contrast, details
of the interaction between the clock, metabolism, and gene
expression are largely unknown. Not surprisingly, the clock
can be entrained by intracellular levels of ATP (Rust et al.,
2011) and, vice versa, the clock seems to exert global
control over cellular processes, including global gene
expression and the cell cycle (Yang et al., 2010; Johnson
et al., 2011). The clock therefore may represent a hinge that
allows integration and coordination of different cellular
processes.
What should an integrative cyanobacterial model look
like? In general, two different approaches are conceivable.
On the one hand, a top-down approach can be employed,
starting from a black-box view of cellular growth in
a photobioreactor that involves only major exchange ﬂuxes.
Such models are commonly employed in ecology and
biotechnology, and are often based on extensions of
Monod’s classic growth equations (Monod, 1949). Topdown
models of cyanobacterial growth are usually highly
predictive with respect to environmental interactions and do
not require detailed knowledge of intracellular states or
dynamics. A lucid review on the hurdles and challenges of
top-down modelling of phototrophc microorganisms was
recently given by Bernard (2011). On the other hand,
a modular bottom-up strategy may be employed (Snoep
et al., 2006). Here, individual computational models of
cellular processes, such as models for the light reactions and
the circadian clock, are combined into a coherent whole.
The modular approach offers the advantage that individual
expert groups can work on, and improve, detailed models of
cellular subprocesses, while simultaneously testing the
consequence on phototrophic growth by incorporating the
respective model into a cellular context. Only such integration
will allow an understanding of the multiple
feedbacks that arise from interaction of the various
subprocesses and deﬁne the physiological behaviour of
cyanobacteria in their environment. A ﬁrst example of such
an integrative model was recently proposed by Hellweger
(2010). Therein a conceptual model of Synechococcus
elongatus PCC 7942 was developed that includes the
photosynthetic light reactions, the post-translational oscillator,
a minimal metabolism, and a coarse-grained gene
expression machinery. The integrated model was used to
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investigate the ﬁtness effect of the circadian clock in
cyanobacteria in silico, again highlighting that complex
physiological traits, such as an enhanced ﬁtness of an
organism with a resonating clock, cannot be understood in
terms of individual molecular subprocesses alone.
It should be emphasized that top-down and bottom-up
approaches are not mutually exclusive but should be
considered complementary, and can be merged into intermediate
coarse-grained representations of cyanobacterial
cells. Such coarse-grained representations would allow the
gradual replacement of a Monod-type growth rate function.
In this sense, both strategies outlined above have strong
potential to contribute towards the long-term goal of in
silico models of cyanobacterial cells and communities in
complex environments. Such a step towards a computational
ecosystems biology will be instrumental in advancing our
understanding of environmental adaptations, complex microbial
communities, global carbon and nitrogen cycles, as
well as having the potential to facilitate and guide biotechnological
applications. Clearly, model integration goes
beyond the capabilities of any single research group and will
require increased collaboration and exchange between the
different areas of research that together deﬁne our knowledge
of cyanobacterial physiology.
Acknowledgements
The authors wish to thank the various colleagues and
researcher who provided crucial input on the life of
cyanobacteria and aspects of computational modelling, in
particular Wolfgang Lockau, Yvonne Zilliges, Ilka M.
Axmann, Christian Beck, Thomas Boerner, Wolfgang Hess,
Annegret Wilde, Sabrina Hoffmann, Hans Westerhoff,
Patrik Jones, and Ladislav Nedbal. Some of the ideas
towards cyanobacteria in silico were ﬁrst discussed at
a workshop in Mikulov, Czech Republic, November 10–13,
2010. RS and HK acknowledge ﬁnancial support by the
programm FORSYS-Partner of the German Bundesministerium
fu¨r Bildung und Forschung (Foerderkennzeichen
grant no. 0315274B). RM is grateful for ﬁnancial support
by the SFB 618 Theoretical Biology and by HARVEST
Marie Curie Actions Network project 238017.
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