METHODOLOGY ARTICLEOpen Access
Improving metabolic flux predictions using
absolute gene expression data
Dave Lee1†, Kieran Smallbone1†, Warwick B Dunn1, Ettore Murabito1, Catherine L Winder1, Douglas B Kell1,2,
Pedro Mendes1,3and Neil Swainston1*
Background: Constraint-based analysis of genome-scale metabolic models typically relies upon maximisation of a
cellular objective function such as the rate or efficiency of biomass production. Whilst this assumption may be valid
in the case of microorganisms growing under certain conditions, it is likely invalid in general, and especially for
multicellular organisms, where cellular objectives differ greatly both between and within cell types. Moreover, for
the purposes of biotechnological applications, it is normally the flux to a specific metabolite or product that is of
interest rather than the rate of production of biomass per se.
Results: An alternative objective function is presented, that is based upon maximising the correlation between
experimentally measured absolute gene expression data and predicted internal reaction fluxes. Using quantitative
transcriptomics data acquired from Saccharomyces cerevisiae cultures under two growth conditions, the method
outperforms traditional approaches for predicting experimentally measured exometabolic flux that are reliant upon
maximisation of the rate of biomass production.
Conclusion: Due to its improved prediction of experimentally measured metabolic fluxes, and of its lack of a
requirement for knowledge of the biomass composition of the organism under the conditions of interest, the
approach is likely to be of rather general utility. The method has been shown to predict fluxes reliably in single
cellular systems. Subsequent work will investigate the method’s ability to generate condition- and tissue-specific
flux predictions in multicellular organisms.
Keywords: Flux balance analysis, Metabolic flux, Metabolic networks, Transcriptomics, RNA-Seq, Exometabolomics
The applications of genome-scale metabolic modelling
have increased over recent years, as have the number of
metabolic models available and the diversity of organ-
isms that such reconstructions cover . Traditional
approaches to analysing such models have focused on
constraint-based modelling, including widely used tech-
niques such as flux balance analysis (FBA) . FBA relies
upon specification of an objective function that the cell
is assumed to optimise. Objective functions can cover a
range of cellular objectives , such as maximisation /
minimisation of ATP consumption, but frequently (and
particularly in the case of microorganisms) take the form
of an assumed “biomass” function; a hypothetical reac-
tion that mimics cell growth rate . Such a biomass
function is used to account for the flow of materials that
are necessary for building new cells, and is commonly
required in constraint-based models even when maxi-
mising variables other than growth rate.
Maximisation of biomass yield is not generally consid-
ered a valid principle in microbiology ; however, it is
commonly assumed to be the optimality criterion driv-
ing the evolution of microorganisms . The premise is
that an organism that acquires and/or redistributes
resources to outgrow its competitors will be in the best
position to survive [7,8]. Assumption of growth rate
maximisation in FBA studies has led to successful pre-
dictions of the actual growth rate in a number of organ-
isms [4,9]. Such an assumption, however, is likely to be
invalid for individual cell types in multicellular organ-
isms, where cellular objectives may differ greatly both
* Correspondence: email@example.com
1Manchester Institute of Biotechnology, University of Manchester, 131
Princess Street, Manchester M1 7DN, UK
Full list of author information is available at the end of the article
© 2012 Lee et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
Lee et al. BMC Systems Biology 2012, 6:73
between and within tissues. The assumption of maximal
rates of biomass production involves an objective at the
cellular level, whereas in multicellular organisms a given
cell’s objective is likely to be realised via survival at the
organism level, which may not necessarily be dependent
upon the growth of the cell. Moreover, signals from the
extracellular environment may trigger different cellular
priorities and objectives. These issues have been demon-
strated by the work of Gille et al. , who modelled the
metabolism ofhuman hepatocyte, indicating
objective is to preserve homeostasis of blood com-
pounds, a process that is modulated by the extracellular
availability of oxygen and other nutrients.
Another concern when applying FBA is the inad-
equacy of the biomass definition itself. Typically, the
assumed composition of E. coli is used as a template to
define the biomass of the organism of interest . To do
this, a cell’s macromolecular composition (in terms of
protein, RNA, DNA, carbohydrate and lipid content),
the metabolite content of each macromolecular class,
and the biosynthetic and maintenance costs for various
cellular processes are required . Not only are such
numbers difficult to determine, but it is also to be
expected that they would change drastically under differ-
ent environmental conditions. Problems associated with
reliance on a biomass objective function have led to a
number of studies that focus on the determination of a
suitable objective function [10–12].
This work therefore focuses on another approach, in-
vestigating the use of ‘omics data to act as a guide for
the prediction of the intracellular metabolic fluxes that a
given cell exhibits. A priori it may be supposed that en-
zymatic transcript concentrations and metabolic fluxes
can be related to each other, albeit in a complex manner,
since fluxes are clearly dependent on the concentrations
of enzymes and/or their encoding transcripts . Draw-
ing upon previous work [14–17], this approach investi-
gates how relating metabolic fluxes to enzyme-encoding
gene expression levels affects the predictive power of
constraint-based analysis. The hypothesis is that doing
so would provide a comparable, or better, representation
of intracellular fluxes than does reliance upon an
assumed biomass objective alone. As stated in related
work by Becker et al. , “the statement of an
[assumed] objective introduces a ‘user-bias’ and such ob-
jective may not be relevant to the true physiological
state.” It is the removal of this user-bias, through the ap-
plication of a purely data-driven objective, that this work
attempts to address.
This study involves the acquisition and analysis of ab-
solute quantitative transcriptomics data from Saccharo-
myces cerevisiae, and the subsequent use of these
data to constrain an existing genome-scale metabolic
model . A comparison between FBA results
generated through this approach and those generated
from applying a more traditional biomass objective is
Such an approach may have ramifications for the
genome-scale modelling of human metabolism ,
where tissue-specific microarray data are publicly avail-
able and have been exploited in the development of
tissue-specific models of human metabolism by Shlomi
et al. . The approach of Shlomi et al. categorises nu-
merous tissue-specific relative gene expression data sets
into high, medium and low expression, with the goal of
limiting the tissue-specific network to contain only those
reactions for which consistent high gene expression has
been observed. A disadvantage of this work is that it was
performed upon a “consensus” of gene expression data,
generated under a range of physiological and experimen-
tal conditions. Furthermore, the data used are generated
from microarrays, which provide relative expression
ratios of the same gene under different conditions.
Microarrays are applicable to comparative studies, and
as such, the data that they produce do not allow for
comparison of absolute expression levels across genes, pri-
marily due to differences in hybridisation efficiency .
In addition, microarray data is associated with a number
issues, limited dynamic detection range, presence of back-
ground noise and the detection of transcripts being lim-
ited to sequences printed on the array .
The approach provided here relies upon absolute gene
expression data generated under the condition of inter-
est, using RNA-Seq. RNA-Seq provides expression levels
in terms of counts of expressed transcripts that can be
related to transcripts per cell and thus an absolute level.
Therefore, the expression levels generated are compar-
able across the transcriptome and have been shown to
be more indicative of protein concentrations than gene
expression levels generated from microarrays [21,23]. By
extension, RNA-Seq data is likely to provide a more reli-
able indication of enzymatic activity than that generated
through relative expression techniques. Furthermore,
RNA-Seq mitigates many of the limitations inherent in
the use of microarrays .
Results and discussion
The methodology involves a number of steps. Specifically,
these are i) providing gene-protein-reaction (GPR) rela-
tionships in the metabolic model; ii) mapping of gene
expression data to individual reactions; iii) correlating
gene expression data to the predicted metabolic flux; and
iv) validating the metabolic flux predictions through com-
parison of predicted values against those determined
experimentally. It is important to note that the model is
not constrained with experimentally measured flux para-
meters. These values are subsequently used to validate the
Lee et al. BMC Systems Biology 2012, 6:73
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flux predictions generated solely from gene expression
data. The steps involved in the method are described in
detail below and summarised in Figure 1.
Mapping gene expression data to metabolic reactions
Previous approaches to applying gene-level data to meta-
bolic maps have involved thresholding; the gene can be
defined as having two states: on or off , or three
states: low, medium or high expression . Here a dif-
ferent approach is used, where the absolute gene expres-
sion data are used to create continuous, rather than
discrete, reaction weightings.
The method is applied to the genome-scale model of
yeast metabolism, Yeast 5 , an extension of earlier
community-driven yeast metabolic reconstructions [24,25].
RNA-Seq data are used to constrain the reconstruction,
providing an absolute measurement of gene expression that
is comparable across all genes in the data set. The hypoth-
esis is that absolute and comparable measurements of gene
expression can be used to infer activity of the encoded
enzymes. Although it is recognised that there is overall
poor correlation between gene and protein expression ,
recent studies have indicated an increased correlation be-
tween mRNA and protein concentrations than was
reported previously [23,27]. The assumption behind the
method is that gene expression levels can be used to infer
metabolic fluxes with reasonable accuracy, provided that
they are applied on a genome-scale, and provided that the
predicted metabolic flux pattern adheres to the normal
stoichiometric and thermodynamic constraints that are ap-
plied to constraint-based modelling. By applying gene ex-
pression levels on such a scale, and by adhering to such
constraints, it is hoped that effects such as experimental
error, differing protein translation rates, differing transcript
and protein stabilities, and differing enzymatic activities,
will be reduced. Whilst the procedure is here applied to
transcriptomics data, future work will investigate whether
the method would be improved by integration with abso-
lute proteomics data .
The assignment of gene expression data to individual
metabolic reactions is complicated by the fact that there
is not a one-to-one mapping between gene and reaction.
The presence of promiscuous enzymes , isoenzymes
and enzymatic complexes underscores the requirement
for a careful mapping of gene expression data to meta-
bolic reactions. Details of the approach undertaken here
are provided in the Methods section.
From metabolic reactions to flux predictions
Constraint-based analysis [30,31] uses physicochemical
constraints such as mass and charge balance, energy bal-
ance, and flux limitations to describe the potential
behaviour of an organism.
The basic biochemical structure of the metabolic path-
ways is generally of sufficient granularity to allow deduc-
tionof the underlying network
addition, the flux of each reaction through the system
may be constrained through, for example, knowledge of
enzyme maximal activities (vmax) or irreversibility con-
siderations . Given a typical genome-scale metabolic
model such as Yeast 5, at steady state these constraints
may be written as:
Nv ¼ 0
where N is the stoichiometric matrix, v a steady state
flux pattern, and Li and Ui the lower and upper flux
bounds respectively for each reaction i.
A number of techniques have been proposed to de-
duce the network behaviour from this minimal set of in-
formation, including FBA and extreme pathway  or
elementary mode analysis . In particular, FBA high-
lights the most effective and efficient paths through the
network in order to optimise a particular objective func-
tion . Genome-scale reconstructions typically con-
tain a pseudoreaction representing growth (a “biomass
reaction”) and FBA is typically used to identify a pattern
Figure 1 Steps undertaken in constraining metabolic models with gene expression data. The approach is applicable to genome-scale
metabolic model that contain gene-protein-reaction (GPR) relationships. Absolute gene-expression data is mapped to individual reactions
following the Boolean logic described in the “Mapping gene expression data to metabolic reactions” section of the Methods. Correlation
between this gene-expression data and metabolic fluxes is maximised by following a three step algorithm comprising of: i) maximising the
correlation between the initial set of irreversible reactions and the experimental data; ii) performing flux variability to determine additional
reactions that must now be unidirectional; iii) repeating this cycle of maximising correlation until no extra irreversible reactions are found through
flux variability analysis. The solution predicts exometabolic fluxes that can then be compared to those generated experimentally.
Lee et al. BMC Systems Biology 2012, 6:73
Page 3 of 9
of fluxes at steady state that maximise the rate of this re-
action. This is seen as corresponding to maximising the
rate of biomass production with respect to a nutrient of
reference (usually glucose), with other necessary nutri-
ents assumed to be in excess. This is unlikely to be
applicable to turbidostat cultures where growth rates are
maximised but where their efficiencies in terms of mass
of cells per mass of glucose may be low.
In this study, the rate of biomass production is not the
function that is maximised explicitly. Instead, the focus
is on maximising the correlation between the steady-
state pattern of the predicted fluxes and the correspond-
ing gene expression data at the biochemical level. This is
achieved through minimising:
where the sum is taken over all reactions i for which re-
action data diare available, in this case, all reactions with
an associated gene. σiis the error in data point i as cal-
culated in the mapping of gene expression data to indi-
vidual reactions (see Methods). Thus the objective is to
predict a flux that is as close as possible to the reaction
estimate, weighted according to the confidence in that
estimate. The function Z is convex in v, and this allows
the use of the powerful tools of convex programming
. Convexity is normally required to solve optimisa-
tion problems involving thousands of variables and is
certainly to be preferred from the point of view of com-
putational performance. This is the reason that a pos-
sibly more natural function such as the Pearson
product-moment correlation coefficient is not used in
its place. Moreover, Z may be linearised through
decomposing v into components greater than, or less
vi¼ diþ dþ
for each i. Hence the fast and robust tools of linear
programming  may be utilised.
One remaining problem is that the direction of revers-
ible reactions (defined operationally as those whose net
fluxes may be in either direction in the organism of
interest) is potentially arbitrary. The aim is to maximise
correlation between the absolute flux and reaction data,
but replacing v with |v| in the definition of Z would re-
move its convexity. Instead, an iterative process is used
to assign the data to the model:
1. Maximise the correlation between the initial set of
irreversible reactions and the experimental data. The
sum in Z is taken only over irreversible reactions
(i.e. those with a known direction of flux).
2. Perform flux variability analysis (FVA)  to
determine which further reactions in the network
must thus be unidirectional, i.e. they cannot carry a
flux in the other direction without decreasing the
correlation coefficient found in point 1.
3. A new larger set of irreversible reactions is defined.
The cycle between FVA and maximising correlation
is continued until no extra irreversible reactions are
found through variability analysis. As the number of
irreversible reactions will never decrease, the
algorithm terminates in a finite number of steps.
Comparison of predicted and measured exometabolome
Fluxes were predicted by following two approaches:
standard FBA (i.e. maximisation of cellular biomass),
and maximisation of the correlation between specific
metabolic fluxes and gene expression data, as described
here. In the latter case, gene expression data were col-
lected under two growth conditions: at 75% and 85% of
the maximum biomass levels attainable for this strain
with the utilised growth medium. In general FBA pro-
blems are underdetermined, i.e. there is an infinite num-
ber of solutions satisfying the criterion of optimality.
The innumerable set of these equally optimal solutions
is known as the solution space and is in the shape of a
multi-dimensional polytope. Different algorithms have
been proposed to explore the solution space of an FBA
problem and enumerate its edges (the alternate optima)
[33,39]. The approach followed here is to identify one sin-
gle solution for each FBA formulation that is representa-
tive of the entire solution space. This is achieved by
applying geometric FBA, a method that identifies the FBA
solution that lies in the centre of the solution space .
The exometabolome or “metabolic footprint” of an or-
ganism provides a quick and convenient summary of its
metabolic activities, especially under unbalanced growth
conditions [41,42]. The predicted exometabolome fluxes
from both methods were compared against experimen-
tally measured fluxes. The coefficient of determination
R2was used to test the goodness of fit of the predictions;
R2=1 means a perfect match between model and data,
whilst R2=0 is the value obtained by simply predicting
the mean of the data for each point. Thus R2<0 denotes
a very poor prediction.
The results for the flux to exit of six metabolites -
carbon dioxide, ethanol, glycerol, acetate, lactate and tre-
halose - are presented in Tables 1 and 2. These exchange
fluxes were normalised according to the measured glucose
uptake flux of their respective growth condition. The
standard FBA method of maximising growth predicts that
all glucose is converted to carbon dioxide, and provides a
Lee et al. BMC Systems Biology 2012, 6:73
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very poor fit to the data (R2<0). The best fit possible
under the assumption of maximal biomass prediction is
R2=0.20 and R2=0.58, respectively. In contrast, a good fit
is found by applying the method described here to gene
expression data gathered at both the 75% and 85% bio-
mass level R2=0.87 and R2=0.96, respectively).
It is recognised that the gene expression correlation
method failed to predict glycerol transport at the 75% max-
imal biomass level, and underestimates this at the 85%
maximal biomass level. Furthermore, acetate exchange is
underestimated under both conditions. However, the gene
expression method is capable of predicting low-level exo-
metabolic fluxes of lactate and trehalose, and it is noticed
that existing methods also investigated (GIMME  and
iMAT ) did not predict anything other than carbon di-
oxide excretion when applied to the same model and gene
In this paper, a methodology for using absolute quantita-
tive gene expression data to predict genome-scale flux
patterns has been defined. Unlike standard constraint-
based analysis approaches such as biomass maximisa-
tion, this method is able to provide accurate predictions
of the major exometabolome fluxes in Saccharomyces
cerevisiae under the measured experimental conditions.
Both transcriptome and exometabolome data from
steady state cultures grown under specific conditions of
interest are generated. The acquisition of data from
defined and controlled cultures allows the direct compari-
son of the two data sets. The relatively easy generation of
data - commercial kits were used to extract the RNA from
the cell - negates the need to use a “consensus” set of pub-
licly available transcriptomics data. Moreover, with calibra-
tion it allows for absolute quantification, rather than the
use of relative values as typically output in microarray
experiments. Advancements in analytical technologies
within the metabolomics field and the development of
defined methodologies and tools have facilitated the gen-
eration of robust and reproducible data for systems biol-
The method described here does not rely on the defin-
ition, and assumed maximisation, of a biomass function
that is often uncertain and necessarily depends on the spe-
cific growth conditions. It is notable that the proposed
approach provides prediction of exometabolome fluxes
under two growth conditions, whereas the standard FBA
formulation provides a single prediction that is unable to
distinguish between conditions. Tailoring the standard
FBA approach to deal with different growth conditions
would require the specification of individual biomass func-
tions for each condition. This time-consuming task
requires knowledge of the cell composition and energetic
Table 1 Comparison of experimental with predicted exometabolome fluxes, at 75% maximal biomass level
Experiment Predicted: Gene expressionPredicted: Standard FBA Predicted: Fitted FBA Predicted: GIMMEPredicted: iMAT
22.7 31.5 37.622.731.5 48.5
0.87 -0.100.200.01 -0.71
Table 2 Comparison of experimental with predicted exometabolome fluxes, at 85% maximal biomass level
Experiment Predicted: Gene expressionPredicted: Standard FBA Predicted: Fitted FBAPredicted: GIMME Predicted: iMAT
21.0 20.125.0 21.0 16.032.2
0.96 0.540.580.52 0.28
Fluxes are reported in units of mmoles/hr/g dry weight (DW), and are scaled by measured glucose uptake flux [see additional file – exometabolomics.xls].
Predicted fluxes are given for the gene expression constrained approach, introduced here, and the standard FBA method that relies upon maximisation of
biomass. As standard FBA generates a number of feasible solutions, the “best” solution (the one which minimises the taxicab distance between prediction and
data) is reported as “Fitted FBA”. Additionally, the existing algorithms GIMME  and iMAT  are applied, using the same model and gene expression data as
was used to generate the gene expression constrained results.
Lee et al. BMC Systems Biology 2012, 6:73
Page 5 of 9
requirements under the growth condition of interest. The
approach described here thus provides an easier means of
determining metabolic fluxes under a range of conditions
than relying on the standard method of biomass
The gene expression constraining approach can also
be considered as a filter: given that the experimental
data can be taken as representative of the fluxes, the
random errors associated with such data should cancel
out at a genome-wide level. Because the FBA solution
needs to satisfy the steady-state assumption, the pre-
dicted fluxes must be consistent with the mass conserva-
tion of each metabolite. If the topology of the network
encompasses the whole system metabolism, the noise of
the data should subside in favour of the real signal.
Moreover it allows changes in ‘omics data from the per-
spective of their influence on the system as a whole to
be viewed. Although transcriptomics data are not neces-
sarily representative of the protein levels, their use in
metabolic constraint-based modelling provides much
better predictive power than does the standard FBA
method. Specifically, the gene expression constrained
method provides good fits to the measured flux to exit
data at both 75% and 85% growth level R2=0.87 and
R2=0.96 respectively), while the standard FBA method
provides a much poorer fit.
Typically, gene knockouts are modelled under the
assumption that there is no downstream effect on gene
regulation, and that there is a minimum change at the flux
level (for example using minimisation of metabolic adjust-
ment (MoMA) ). Rather than simply making such an
assumption, this work suggests a better approach would
be to effect the (relatively easy) measurement of gene ex-
pression data after knockout, and subsequent use of this
data to predict the new flux pattern. It is envisaged that
the same approach could be used to retrieve flux patterns
in cells under different physiological conditions, or during
the progression of metabolic diseases such as cancer and
diabetes. Furthermore, methods that predict exometabolo-
mic fluxes are of particular use in ‘white’ biotechnology
Continuous cultures of Saccharomyces cerevisiae
Steady-state cultures of Saccharomyces cerevisiae (BY4743
hoΔ/HO, (YDL227C; MATa/MATα;
leu2Δ0/leu2Δ0; met15Δ0/MET15; LYS2/lys2Δ0; ura3Δ0/
ura3Δ0) were established using a permittistat approach
[46, 47], in which the electrical capacitance of the culture
was monitored by a probe inserted into the vessel con-
nected to a Biomass Monitor 220 (Aber Instruments, UK).
The cultures were grown in F1 media  with a working
volume of 2l in a 3l vessel (Applikon Biotechnology,
temperature of 30°C, 650 rpm agitation control, pH 4.5 and
1.5 ml min-1air supply, under the control of the operating
software BioXpert (Applikon Biotechnology, Netherlands).
A feedback loop was programmed to regulate the media
pump and maintain the culture at the desired set point
(either 75% or 85% of the maximum achievable biomass
levels known for this strain in the growth media used). As
usual in a turbidostat, the growth rate of the culture was at
μmaxand without nutrient limitation. Off-gas analysis of O2
and CO2 was measured using a tandem gas analyser
(Magellan Instruments, Sweden). Further details of the ex-
perimental procedure are outlined in .
Samples were collected for transcriptome and exome-
tabolome analysis from three independent (biological)
replicates operated under identical conditions. The
growth parameters turbidity (OD680nm), dry weight,
culture purity, extracellular glucose concentration and
total cell count (determined with a Cellometer Auto
M10, Nexcelem Biosciences, USA) were monitored to
assess the reproducibility of the replicates.
Generation and analysis of RNA-Seq data
The RNA was extracted from the Saccharomyces cerevi-
siae samples using a RiboPure yeast kit (Ambion Life
Sciences, USA). Total RNA samples were depleted of
abundant ribosomal RNA molecules using the RiboMi-
nus eukaryote kit for RNA-Seq (Invitrogen, USA). The
RNA transcripts were converted into a cDNA library
using the SOLiD total RNA-Seq Kit (Applied Biosys-
tems, USA). Analysis of the library was performed using
a SOLiD sequencing system (Applied Biosystems, USA)
for the whole transcriptome library, generating millions
of short reads of sequence. Counts for each transcript
were generated by first aligning sequence reads were
aligned onto a yeast reference genome (SGD/sacCer2
assembly, downloaded 09/02/2011 from the UCSC Gen-
ome Browser ) using Bowtie, version 0.12.7 .
After alignment, the Cufflinks algorithm , version
1.02, was employed to infer the gene transcripts most
likely present according to the aligned reads. Once
assigned to their most likely source genes, Cufflinks was
employed to calculate transcript abundance in terms of
RPKM , an estimate of transcript counts normalised
both locally (according to the length of the assigned
transcript) and globally (the number of total mapped
reads per million).
Generation and analysis of exometabolome data
Exometabolome samples were collected by syringe filtra-
tion (0.2μm pore filter) of the culture to rapidly remove
the biomass from the culture. The resulting filtrate was
snap-frozen in liquid nitrogen for further analysis. The
concentrations of acetate and ethanol were perfor-
med by enzymatic assays (Megazyme, Ireland). Gas
Lee et al. BMC Systems Biology 2012, 6:73
Page 6 of 9
chromatography mass spectrometry (GC-MS) quantified
the remaining metabolites detected in the exometabolome.
The chromatographic peak areas for the metabolites
detected in the samples were compared to an externally
constructed calibration curve. A stock solution containing
glycerol, trehalose, glucose and fructose was prepared at a
concentration of 10 mmol l-1. The stock solution was seri-
ally diluted to provide calibration standards in the range
of 0.1-1000 μmol l-1. Aliquots of the calibration standards
and exometabolome samples were lyophilised (HETO VR
MAXI vacuum centrifuge attached to a RVT4104 cooling
trap; Thermo Life Sciences, UK).
The lyophilised samples and standards were derivatised
for GC-MS analysis. An aliquot (50μl 20 mgml-1O-
methylhydroxylamine solution was added to each sample
and heated at 40°C for 90 minutes. 50μl N-acetyl-N-
(trimethylsilyl)-trifluoroacetamide (MSTFA) was added to
the samples and heated at 40°C. Samples were analysed on
an Agilent 6890N gas chromatograph and 7683 autosam-
pler (Agilent Technologies, UK) coupled to a LECO Pega-
sus III electron impact time-of-flight mass spectrometer
(LECO Corporation, USA). 1μl of the sample was rapidly
introduced in to an injector operating at 250°C, with a
split ratio of 1:10 and a helium flow rate of 0.8ml min-1
in constant flow mode. Metabolites were separated
on a SPB50 phase column (30m x 0.25mm x 0.25μm;
Supelco, UK) with a 50 min temperature gradient (initial
temperature of 70°C was held for 4 min followed by a 5°C
min-1temperature ramp to 290°C which was held con-
stant for 2 min). The chromatographic eluent was intro-
duced to an electron impact mass spectrometer. The
transfer line and ion source temperatures were 250°C.
Mass spectral data was acquired in the range 70-600 Da
with an acquisition rate of 10Hz. Processing of the raw
data was performed with LECO ChromaTof v2.25 soft-
ware to construct a data matrix (metabolite peak vs. sam-
ple number) including the chromatographic peak areas.
Calibration curves were constructed for each metabolite
to determine the concentration of the metabolites in the
Carbon balancing was achieved to 97% and 95% for
the 75% and 85% maximum achievable biomass growth
conditions, respectively [see Additional file 1 – exometa-
Mapping gene expression data to metabolic reactions
The model, Yeast 5, is encoded and distributed in the
Systems Biology Markup Language (SBML) . Follow-
ing the conventions implemented by many genome-scale
metabolic models , many reactions in Yeast 5 are asso-
ciated with genes and proteins via gene-protein-reaction
(GPR) associations: Boolean statements connecting genes
to reactions. For example, reaction r_0003 ((R,R)-butane-
diol dehydrogenase) is annotated with:
Given this simple mapping from gene to reaction, the
gene expression count of YAL060W=0.0152±0.00757
can be used to directly give a reaction weighting of
However, in general, GPR associations are not so sim-
ple, and there is a many-to-many mapping from gene to
reaction. For example, reaction r_0250 (carbamoyl phos-
phate synthase) is annotated as:
GENE_ASSOCIATION: (YJR109C and YOR303W) or
with associated gene expression data YJR109C=0.156±
0.083, YOR303W=0.0976±0.033 and YJL130C=0.126
±0.013. Consider first the Boolean AND relationship
above; this means that the reaction is catalysed by a
complex between the two gene products. Since the max-
imum complex concentration is given by the minimum
concentration of its components, the weighting of the
complex is defined as:
The OR relationship allows for alternative catalysts to
each reaction; as such the total capacity is given by the
sum of its components, so:
Note that the standard deviation above is estimated
through the assumption that the variables are uncorre-
lated, allowing variances to be added.
All scripts required to map gene expression data to a
metabolic model, and to generate flux predictions from
the model are available as additional files. In addition,
the metabolic model Yeast 5 and the experimental gene
expression data used in this study are provided as add-
itional files. The Cobra Toolbox for Matlab  is
required to run the scripts. Results generated in this
study used the Gurobi Optimizer 4.5.1 linear solver
(Gurobi Optimization, USA).
Additional file 1: Exometabolomics data. Experimentally measured
exometabolomic flux data, both unscaled and carbon-scaled. Data
generated from cellular culture grown at both 75% and 85% maximum
biomass level, in units of mmoles/hr/g dry weight.
Lee et al. BMC Systems Biology 2012, 6:73
Page 7 of 9
Additional file 2: Yeast 5. Genome-scale metabolic model of
metabolism in Saccharomyces cerevisiae.
Additional file 3: Gene data 75%. Gene expression data, generated by
RNA-Seq, on cellular culture grown at 75% maximum biomass level, in
units of reads per kilobase of transcript per million mapped reads (RPKM).
Additional file 4: Gene data 85%. Gene expression data, generated by
RNA-Seq, on cellular culture grown at 85% maximum biomass level, in
units of RPKM.
Additional file 5: Results. Matlab script that runs the analysis function,
using the above model and gene expression data. Generates flux
predictions and compares these to the above experimentally measured
exometabolomic flux data.
Additional file 6: Analysis. Matlab function that performs the method
described in this work. Additionally provides implementations of the
existing algorithms GIMME  and iMAT .
Additional file 7: Gene expression mapper for enzymatic
complexes (A and B). Helper Matlab function that is used in mapping
gene expression data to individual reactions. Called by analysis function.
Additional file 8: Gene expression mapper for isoenzymes (A or B).
Helper Matlab function that is used in mapping gene expression data to
individual reactions. Called by analysis function.
The authors declare that they have no competing interests.
NS conceived the idea and led the project. CW performed the continuous
culture. DL and CW generated the gene expression data. WD generated the
exometabolome results. DL, KS and EM developed and implemented the
algorithm. KS produced the results. KS and NS developed the Matlab scripts.
All authors read and approved the final manuscript.
This work was supported by the EU FP7 through the UNICELLSYS project
(grant 201142), the BBSRC and EPSRC through the Manchester Centre for
Integrative Systems Biology (grant BB/C008219/1) and the Doctoral Training
Centre ISBML (grant EP/F500009/1). The authors are grateful to Michael
Howard, along with Leo Zeef, Andy Hayes and others at the Genomic
Technologies Core Facility at the University of Manchester for the generation
of the RNA-Seq data.
1Manchester Institute of Biotechnology, University of Manchester, 131
Princess Street, Manchester M1 7DN, UK.2School of Chemistry, University of
Manchester, Manchester M13 9PL, UK.3Virginia Bioinformatics Institute,
Virginia Tech, Washington St. 0477, Blacksburg, Virginia 24060, USA.
Received: 11 January 2012 Accepted: 5 June 2012
Published: 19 June 2012
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Cite this article as: Lee et al.: Improving metabolic flux predictions using
absolute gene expression data. BMC Systems Biology 2012 6:73.
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