Two-stage flux balance analysis of metabolic networks for drug target identification.

Abstract

Efficient identification of drug targets is one of major challenges for drug discovery and drug development. Traditional approaches to drug target identification include literature search-based target prioritization and in vitro binding assays which are both time-consuming and labor intensive. Computational integration of different knowledge sources is a more effective alternative. Wealth of omics data generated from genomic, proteomic and metabolomic techniques changes the way researchers view drug targets and provides unprecedent opportunities for drug target identification.
In this paper, we develop a method based on flux balance analysis (FBA) of metabolic networks to identify potential drug targets. This method consists of two linear programming (LP) models, which first finds the steady optimal fluxes of reactions and the mass flows of metabolites in the pathologic state and then determines the fluxes and mass flows in the medication state with the minimal side effect caused by the medication. Drug targets are identified by comparing the fluxes of reactions in both states and examining the change of reaction fluxes. We give an illustrative example to show that the drug target identification problem can be solved effectively by our method, then apply it to a hyperuricemia-related purine metabolic pathway. Known drug targets for hyperuricemia are correctly identified by our two-stage FBA method, and the side effects of these targets are also taken into account. A number of other promising drug targets are found to be both effective and safe.
Our method is an efficient procedure for drug target identification through flux balance analysis of large-scale metabolic networks. It can generate testable predictions, provide insights into drug action mechanisms and guide experimental design of drug discovery.

Full text

Page 1

REPORTOpen Access
Two-stage flux balance analysis of metabolic
networks for drug target identification
Zhenping Li1†, Rui-Sheng Wang2†, Xiang-Sun Zhang3*
From The 4th International Conference on Computational Systems Biology (ISB 2010)
Suzhou, P. R. China. 9-11 September 2010
Abstract
Background: Efficient identification of drug targets is one of major challenges for drug discovery and drug
development. Traditional approaches to drug target identification include literature search-based target
prioritization and in vitro binding assays which are both time-consuming and labor intensive. Computational
integration of different knowledge sources is a more effective alternative. Wealth of omics data generated from
genomic, proteomic and metabolomic techniques changes the way researchers view drug targets and provides
unprecedent opportunities for drug target identification.
Results: In this paper, we develop a method based on flux balance analysis (FBA) of metabolic networks to
identify potential drug targets. This method consists of two linear programming (LP) models, which first finds the
steady optimal fluxes of reactions and the mass flows of metabolites in the pathologic state and then determines
the fluxes and mass flows in the medication state with the minimal side effect caused by the medication. Drug
targets are identified by comparing the fluxes of reactions in both states and examining the change of reaction
fluxes. We give an illustrative example to show that the drug target identification problem can be solved
effectively by our method, then apply it to a hyperuricemia-related purine metabolic pathway. Known drug targets
for hyperuricemia are correctly identified by our two-stage FBA method, and the side effects of these targets are
also taken into account. A number of other promising drug targets are found to be both effective and safe.
Conclusions: Our method is an efficient procedure for drug target identification through flux balance analysis of
large-scale metabolic networks. It can generate testable predictions, provide insights into drug action mechanisms
and guide experimental design of drug discovery.
Background
Drug target is a key molecule involved in a particular
metabolic or signaling pathway that is specific to a dis-
ease condition or the survival of a microbial pathogen
[1,2]. Identification and validation of drug target is the
essential first step in new drug discovery and develop-
ment. Drugs can be designed to modify the functioning
of the pathway in the diseased state by inhibiting a key
molecule, or to enhance the normal pathway by promot-
ing specific molecules that may have been affected in
the diseased state. For the diseases caused by microbial
pathogen, drugs usually are designed to inhibit the
essential components of the pathogen to disrupt its sur-
vival. In all the cases, drugs should be designed in such
a way as not to affect any other important molecules,
since modification of non-disease-causing molecules
may lead to undesirable side effects [3].
In pharmaceutics, drugs generally fail in the clinic for
two reasons: they either do not work or are proved to
be unsafe [1]. For example, if components other than
disease-causing compounds are affected by a drug, toxi-
city or side effect will arise; on the other hand, if dis-
ease-causing compounds are not inhibited by a drug,
then lack of efficacy will arise. Both of these problems
have been attributed to sloppy early target discovery and
are among the main challenges in developing new
* Correspondence: zxs@amt.ac.cn
† Contributed equally
3Academy of Mathematics and Systems Science, CAS, Beijing 100190, China
Full list of author information is available at the end of the article
Li et al. BMC Systems Biology 2011, 5(Suppl 1):S11
http://www.biomedcentral.com/1752-0509/5/S1/S11
© 2011 Li 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.

Page 2

drugs. Traditional drug development approaches focused
more on the efficacy of drugs than their toxicity, which
does not meet the increasing demand of public health
on new drug development. On the other hand, recent
drug research in post-genomic era stresses on the iden-
tification of specific biological targets such as enzymes
or proteins for drugs, which can be manipulated to pro-
duce the desired effect of curing a disease with mini-
mum disruptive side effects [1,4]. With the complete
sequencing of human and bacterial genomes and the
subsequent accumulation of genomic, proteomic, and
metabolomic data, systems biology approaches or net-
work-based analyses hold great promise for identifying
drug targets by utilizing biological networks, such as
gene regulatory networks, metabolic networks and pro-
tein interaction networks [5-16]. Among these methods,
one class is to identify drug targets by analyzing the
topological feature of protein interaction networks or
metabolic networks [6,8,9,17]. For example, Guimerà et
al. proposed a module-based approach to characterize
the roles of enzymes according to the modular structure
of metabolic networks, which is promising for identifica-
tion of drug targets [6]. Hormozdiari et al. proposed
sparest cut strategies to identify potential multiple-drug
targets in pathogenic protein-protein interaction net-
works with goal of disrupting known essential pathways
or complexes in pathogens [8]. In addition, flux balance
analysis (FBA) of genome-scale metabolic networks is
another important class of methods for drug target iden-
tification. Usually methods in this category aim to pre-
dict essential enzymes which are critical to the survival
and growth of pathogens [15,18-21]. Raman et al. con-
structed a comprehensive model of mycolic acid synth-
esis metabolic pathway in the pathogen Mycobacterium
tuberculosis and used FBA to do in silico systematic
gene deletions which identify proteins essential for this
pathway and lead to identification of anti-tubercular
drug targets [18]. Plasmodium falciparum is the primary
agent of the best-known tropical disease malaria. Plata
et al. reconstructed a genome-scale metabolic network
of P. falciparum and did FBA for simulating gene dele-
tion [20]. Their model reproduced the phenotypes of
experimental gene knockouts and drug inhibition assays
with high accuracy and identified 40 essential genes as
enzymatic drug targets. Recently, a few studies have
been done on prediction of drug-target interaction by
integration of chemical, genomic and pharmacological
data[11-13,22]. In short, wealth of various types of
omics data are changing the way researchers view drug
targets and provides unprecedent opportunities for drug
target identification.
For pathogenic diseases, drugs are designed to act on
the pathogen directly, and drug targets are those
enzymes crucial for the survival and growth of the
pathogen, which can be identified by FBA-based growth
simulation or sparse cut strategies [8,18,20]. The patho-
genic diseases are cured by inhibiting essential enzymes
(drug targets) using drugs. For nonpathogenic diseases,
drugs act on human enzymes and adjust the reactions
catalyzed by these enzymes to make metabolism normal
and cure the diseases caused by metabolic disorders
[7,14]. Although many methods have been developed for
drug target identification, most of them do not consider
the factor of side effects, which may be the main reason
why only modest results have been obtained so far.
Recently, a new drug target identification model based
on metabolic networks has been proposed by Sridhar et
al. [23,24], in which a set of enzymes (drug targets) is to
be found to inhibit disease-causing compounds through
drugs’ action on these enzymes and meanwhile reduce
the side effects caused to non-disease-causing com-
pounds as much as possible. In other words, inhibition
of the identified drug targets will stop the production of
a given set of disease-causing compounds, and mean-
while eliminate a minimum number of non-disease-
causing compounds. In their models, the side effect of a
drug is defined as the number of non-disease-causing
compounds eliminated while drugs inhibit the disease-
causing compounds. They presented a scalable heuristic
iterative algorithm as well as a branch-and-bound exact
algorithm for solving the formulated drug target identifi-
cation problem [23,24]. Song et al. developed a double
iterative optimization algorithm for the same problem
[25]. Li et al. further formulated this metabolic network-
based drug target identification model as an integer lin-
ear programming (ILP) which ensures that optimal solu-
tions can be exactly and efficiently obtained without any
heuristic manipulation [26]. Instead of using flux bal-
ance analysis, the drug target discovery model in this
class is based on the logic biochemical relationships
between reactions, enzymes and compounds: a reaction
is inhibited if and only if at least one of its reactant
metabolites is inhibited, and a product metabolite is
inhibited if and only if all reactions producing this meta-
bolite are inhibited [27]. Aiming at minimizing the side
effects of drug targets, this model does not need to
determine biological objective functions for optimizing
flux distribution.
The drug target identification model mentioned above
is qualitative and explores properties of metabolic net-
works from a topological view. However, although the
definition of damage in such a model reflects side effects
to some extent, it is still too coarse and cannot capture
the quantitative relationships among reactions, metabo-
lites and enzymes. In the process of metabolism, the
mass flows of metabolites and the fluxes of reactions
satisfy balance relationships. If disease-causing com-
pounds are completely inhibited by manipulating drug
Li et al. BMC Systems Biology 2011, 5(Suppl 1):S11
http://www.biomedcentral.com/1752-0509/5/S1/S11
Page 2 of 11

Page 3

targets, some non-disease-causing compounds may also
be eliminated, which may change the concentration or
mass flow of some other non-disease-causing com-
pounds. If the changed concentration or mass flow of
these non-disease-causing compounds is out of a healthy
range, some symptoms of side effects will appear. In
fact, although the accumulation of disease-causing com-
pounds in a sophisticated metabolic system may result
in diseases, it is not reasonable to inhibit them comple-
tely. We only need to adjust their concentration or mass
flow to a healthy range by certain medication strategies.
For example, the healthy range of normal empty blood
sugar concentration of a person is [0, 6.11] mmol/L. If
his empty blood sugar concentration is larger than 7.0
mmol/L, then he may be diagnosed to be a diabetes
patient. To cure diabetes, we need to reduce their
empty blood sugar concentration to a healthy range.
Sridhar et al.’s qualitative drug target identification
model cannot handle this case. In [7], Vera et al. pro-
posed a method called optimization program for drug
discovery (OPDD) to identify enzyme targets in enzymo-
pathies by integration of metabolic models and biomedi-
cal data. An existing S-system model and literature
information about the human hyperuricemia were used
to detect single-enzyme targets and two-enzyme targets.
This method needs to solve a large number of optimiza-
tion programs and select the most feasible solution by
additional criteria. Furthermore, side effects are not
taken into account. In this paper, we propose a method
to identify drug target based on flux balance analysis
(FBA), in which we consider a quantitative and more
reasonable definition of damage to reflect side effects of
drug action, that is, the deviation of the mass flow of
non-disease-causing metabolites from their health range.
Our method consists of two linear programming mod-
els: one is to find the optimal fluxes of reactions and the
mass flows of metabolites in the pathologic state, and
the other is to determine the fluxes and mass flows in
the medication state with the minimal side effect caused
by the medication. Then drug targets are identified by
comparing the fluxes of reactions in both states and
checking the reactions whose fluxes are changed. An
illustrative example is given to show that the drug target
identification problem can be solved effectively by our
method. We also apply our method to a hyperuricemia-
related purine metabolic pathway. Known drug targets
for hyperuricemia are correctly identified by our two-
stage FBA method, and the side effects of these targets
are also taken into account. A number of other promis-
ing drug targets are found to be both effective and safe.
Methods
Metabolism, which comprises the complete set of bio-
chemical reactions in a living cell, is one of the most
complex cellular processes. Metabolic networks connect
biochemical reactions via substrate and product sub-
stances called metabolites. In a metabolic network,
enzymes catalyze reactions which take substrates and
produce metabolites. Such processes constitute the
whole metabolism system of a living organism. However,
the malfunctions of some enzymes may lead to produc-
tion of excessive concentration or mass flow of certain
compounds in a sophisticated metabolic system, and
thereby may result in diseases [28]. Such compounds
are generally considered as disease-causing compounds
because they are directly relevant to the diseases. The
remaining compounds in the metabolic system are all
considered as non-disease-causing compounds. On the
other hand, those enzymes are considered as drug tar-
gets, if manipulating them by drugs the concentration
or mass flow of disease-causing compounds can be
adjusted to a healthy range. Hence, the drug target iden-
tification problem is to identify such an enzyme set that
can be manipulated by drugs to adjust the mass flow of
all disease-causing compounds to a healthy range, and
meanwhile reduce the gap between the mass flow of
non-disease-causing compounds after medication and
their healthy range as much as possible. The sum of
gaps between the mass flow of all non-disease-causing
compounds and their healthy state range is defined as
the side effects (of the drug targets).
Metabolic network representation
A metabolic network is generally a biochemical network,
in which chemical compounds and metabolites are
represented by nodes and reactions catalyzed by one or
several certain enzymes are denoted by directed edges.
In order to make drug target identification easily under-
stood, we use another graphical representation of meta-
bolic networks [29], in which a metabolic network is
built up of substrates that are connected to one another
not through single links, but through physical entities
denoting reactions (enzymes). A metabolic network in
this type of representation is a directed bipartite graph
and has two types of nodes. One type represents chemi-
cal reactions and the other metabolites. A directed edge
from a reaction to a metabolite means that the metabo-
lite is a product of the reaction. A directed edge from a
metabolite to a reaction represents that the metabolite
is a reactant of the reaction. A reversible reaction is
considered as two separate reactions corresponding to
forward and backward reactions. This representation
allows us conveniently to express the relations between
substrates, reactions and products by the topology of
metabolic networks.
Suppose that there are m metabolites {C1, C2, …,Cm}
and n reactions {R1, R2, …, Rn} in a metabolic network.
S = [si,j]m×nand T = [tj,i]n×mare the stoichiometric
Li et al. BMC Systems Biology 2011, 5(Suppl 1):S11
http://www.biomedcentral.com/1752-0509/5/S1/S11
Page 3 of 11

Page 4

coefficient matrices of reactions. The kth column of
matrix S denotes the coefficients of reactants in reaction
Rk, while the kth row of matrix T denotes the coeffi-
cients of metabolites produced by reaction Rk. We can
obtain the kth column of matrix S and the kth row of
matrix T from the chemical equation of reaction Rk.
Conversely, the chemical equation of reaction Rkcan be
deduced from the kth column of matrix S and the kth
row of matrix T. For example, the chemical equation of
reaction Rkis
2C1+ 3C2®C5+ 2C6
Then sl,k= 2, s2,k= 3, si,k= 0,i ≠ 1, 2 and tk,5= 1,
tk,6= 2, tk,j= 0, j ≠ 5,6.
After formulating a metabolic network into a bipartite
digraph as described above, our method for drug target
identification, called as two-stage FBA method, is
formulated into two linear programming models. The
general scheme is shown in Figure 1, which we will
introduce step by step in the following subsections.
Determining pathologic metabolite mass flows and
reaction fluxes
Kinetic modeling of large-scale metabolic networks is
often impossible due to lack of specific enzyme rate
data. A simple and useful alternative for analysis of
metabolic capabilities of cellular systems is flux balance
analysis (FBA) [30]. FBA ignores metabolite mass flow,
enzyme activity and transient dynamics and focuses on
stoichiometry of metabolic reactions, mass balance and
steady state, which makes it able to analyze large-scale
Medica?on model
Pathological model
Flux comparison
(a)
(b)
(c)
(d)
Target determina?on
Figure 1 General scheme of the two-stage flux balance analysis (FBA) method for drug target identification. Given a metabolic pathway
related to a disease (a), our two-stage FBA method first calculates optimal fluxes of reactions and mass flows of metabolites in the pathologic
state (b). Then, assuming some medication strategy can adjust the abnormal level of the disease-causing compound (the node marked in
yellow), the two-stage FBA method determines the fluxes of reactions and the mass flows of metabolites with minimum side effects in the
medication state (b). Different colors of the edges in (b) represent different fluxes. By comparing the reaction fluxes in the pathologic state and
medication state (c), a sub-network is constructed and potential drug targets (the node marked in red) are identified (d).
Li et al. BMC Systems Biology 2011, 5(Suppl 1):S11
http://www.biomedcentral.com/1752-0509/5/S1/S11
Page 4 of 11

Page 5

metabolic systems in complex organisms [27]. In FBA
models, the concentration change of each species over
time follows mass balance and can be defined in terms
of the flux (reaction rate) and stoichiometry of each
reaction in which the species participates. The transient
mass balance can be further simplified to only consider
the steady state, which leads to S · v = 0, where v = (v1,
v2, … ,vn)Tdenotes the flux vector of the reactions in
the stoichiometric matrix S = -S + TT. In metabolic sys-
tems, the feasible region in the steady-state flux space
may be too large to be meaningful. FBA overcomes this
by adding biologically meaningful objectives into the
model, such as maximization of growth rate, maximiza-
tion of ATP production, and minimization of nutrient
uptake. These objectives can be represented by a linear
combination of reaction fluxes of interest, which results
in a linear programming model:
max cT·v (1)
s.t. S · v = 0 (2)
Vmin≤ v ≤ vmax(3)
where c in the objective function (1) is a vector of
weights for the fluxes v, (2) is the set of mass balance
constraints, and (3) is the set of enzymatic capacity
constraints. FBA has been widely used for in silico
phenotype prediction. For more methodological details
of FBA, one can refer to [31,32].
Given a metabolic network in the pathologic state, we
delete the reactions that cannot take place because its
catalyzing enzyme is inhibited in the disease state.
Although the metabolic network is in the pathologic
state, it still can produce as much biomass or energy
(e.g. ATP) as possible so as to maintain tissue growth.
So we can determine the flux of each reaction and the
mass flow of each metabolite in the pathologic state by
a FBA optimization model. Let vjdenote the flux of
reaction Rj, xidenote the mass flow of metabolite Ci,
that is, the mass flow of metabolite Ciproduced (or
consumed) by all the reactions it involves in the meta-
bolic network. We use the following linear programming
model to determine the mass flows of metabolites and
the fluxes of reactions in the pathologic state:
max
,
z c x
j i i
i
m
j
n
=∑
1
=
=
∑
1
∑
(4)
s.t. for metabolite
s v
ij
t v
ji
C
j
j
n
j
j
n
i
==
∑
=
11
(5)
x s v
ij
C
ij
j
n
i
=
=∑
1
for metabolite
(6)
x t v
ji
C
ij
j
n
i
=
=∑
1
for metabolite
(7)
0 ≤ vj≤ Uj,j = 1,2, … , n (8)
0 ≤ xi≤ qi,i= 1,2, … , m (9)
The objective function denotes the maximization of
mass flows of certain metabolites. For example, if we
want to maximize the mass flows of metabolites in the
biomass reaction, we can set cbiomass,i= 1 and Cj,i= 0,
j ≠ biomass. Eq. (5) is the mass balance constraint of
each intermediate metabolite. Constraint (6) defines
that the mass flow of each metabolite is equal to the
weighted sum of the fluxes of all reactions (if any) that
consume this metabolite. Similarly, constraint (7) guar-
antees that the mass flow of each metabolite is equal
to the weighted sum of the fluxes of all reactions (if
any) that produce this metabolite. Constraints (14) and
(15) represent the capacity limits of reaction flux and
metabolite mass flow in the pathologic state, where Uj
and qiare the upper bounds of variables vjand xi
respectively.
Determining medication metabolite mass flows and
reaction fluxes
In the pathologic state, the mass flows of some meta-
bolites are out of healthy ranges which directly result
in the disease symptoms. For example, if the healthy
range of the jth metabolite’s mass flow is [ai,bj], it
means that xjshould satisfy aj≤ xj≤ bj. If xj>bjor xj
<aj, some fluxes of biochemical reactions should be
adjusted by using drugs so that xjÎ [aj, bj]. At this
time, the metabolite Cjis the disease-causing com-
pound, other metabolites are non-disease-causing com-
pounds, and the biochemical reactions whose fluxes
are to be enzymatically adjusted by using drugs are
viewed as drug targets. In this adjustment process, the
mass flows of some other non-disease-causing com-
pounds may change to be out of their health ranges,
which we define as the side effects of the drugs. A
good drug should be potent and have minimal side
effects. Aiming to minimize the side effects, we can
find the mass flows of metabolites and the fluxes of
reactions in the medication state by using the follow-
ing linear programming model:
∑
min()
dd
ii
i N
∈
∑
+−
+
(10)
s.t. for metabolite
s v
ij
t v
ji
C
j
j
n
j
j
n
i
==
∑
=
11
(11)
x s v
ij
C
ij
j
n
i
=
=∑
1
for methaolite
(12)
x t v
ji
C
ij
j
n
i
=
=∑
1
for metabolite
(13)
Li et al. BMC Systems Biology 2011, 5(Suppl 1):S11
http://www.biomedcentral.com/1752-0509/5/S1/S11
Page 5 of 11