Metabolic Pathway Analysis: Principles,
Examples and Application
Zhen Chen
Institute of Bioprocess and Biosystems Engineering
Hamburg University of Technology, Germany
Hongjuan Liu, Jianan Zhang
Institute of Nuclear and New Energy Technology
Tsinghua University, China
Dehua Liu
Institute of Applied Chemistry, Department of Chemical Engineering
Tsinghua University, China
1
Introduction
For the further understanding of the metabolic systems functionality, the structure, pathways and flux
distributions analysis in metabolic networks has become an important approach (Stefan et al., 2012;
Trang et al., 2012; Kurata et al., 2007; Chen et al. 2009). The ever-increasing genome sequencing has
exposed us to a large amount of information (Ostrander & Beale, 2012; Wajid & Serpedin, 2012; Bras et
al., 2012). These genomic information are the basis for our systematic understanding on the cellular behavior and helpful for the further modification of genome sequences for various applications, such as
metabolic engineering of strains for bioprocesses and therapeutics, bioremediation, etc. Clarification of
the linkage between genotype and phenotype, however, is highly complicated because of various interactions between metabolites and proteins, metabolic pathways and cellular regulations. Direct modeling of
cellular kinetics at genomic level is still highly challenging based on current techniques.
In view of the complicated interactions, metabolic pathway analysis (MPA) has provided a simplified approach for analyzing functionality and regulation of metabolic networks. Based on the stoichiometric rather than kinetic properties of metabolic networks, MPA aims to discover and analyze meaningful routes involved in the metabolic networks, linking the cellular behavior with its inherent metabolic
network structure (Kremling et al., 2000; Covert et al., 2001).
MPA can be used to study the functionality of metabolic networks, the flexibility/redundancy of
metabolic pathways (Papin et al., 2002; Stellling et al., 2002). The futile cycles and optimal pathways
with respect to product/biomass yield also can be easily identified (Schuster et al., 2000), thus enabling
the search of promising targets of genetic manipulations for industrial strain development (Wiechert et
al., 2002). Furthermore, MPA is useful in metabolic flux analysis, considering that all of the flux distributions are the linear combinations of elementary flux modes (Klamt et al., 2002).
In MPA, two approaches, called as elementary flux modes and extreme pathways, have mostly
been used for the study of the pathway structure in biochemical networks. These two approaches are very
similar, and thus they are often difficult to be differentiated and implemented properly. In this chapter,
the method of MPA is introduced. The elementary flux modes and extreme pathways are described and
compared. Furthermore, the detailed examples are also illustrated for the practical application of elementary flux analysis.
2
Theoretical Aspects of Metabolic Pathway Analysis
2.1
Network Structure and Pathway Analysis
A well-built metabolic network is the base of MPA, which can be the biochemically defined maps or reconstructed network derived from genome annotation. It should be mentioned that the structure of metabolic network directly affects the results of MPA. On the other hand, the results of MPA can also be used
to evaluate the rationality of the network.
For a given metabolic network, the system boundaries should be defined firstly. The metabolites
outside the system boundary are ‘external metabolites’, such as nutrients, excreted products. The ‘internal
metabolites’ are located inside the cell and participate in the biochemical reactions of the metabolic network. The metabolite fluxes across system boundaries, connecting external metabolites and internal me-
tabolites through enzymatic reactions or transport process, are called as exchange fluxes. For an internal
metabolite Xi, following equation is given based on the mass balance:
dX i
dt
= ∑ Si, j v j
(1)
j
where vj and Si,j are the metabolic flux of reaction j and stoichiometric coefficient of metabolite Xi in reaction j, respectively. Si,j is negative when Xi is consumed and positive when Xi is produced. At steady
state, the concentrations of all internal metabolites are constant dXi / dt = 0.The mass balance of the systems can be simplified as linear equations:
Sv = 0
(2)
where S is an m×n stoichiometric matrix and vj is the metabolic fluxes. The rows of S correspond to the
internal metabolites in a reaction network and the columns of S correspond to the stoichiometric coefficients of internal metabolites in the associated reactions. The stoichiometric matrix S contains all of the
information about how substances are linked through reactions within the network and thus it indicates
the topological structure and architecture of the network. All of the possible solutions of Equation (2)
within the null space represent the capabilities of a given metabolic genotype. Exploring the null space
thus allows us to predict several inherently important properties of a metabolic network, such as the critical links of two metabolites in the network, the efficiency of energy extraction and material conversion
for a given substrate, the potential substrate and building blocks that cell can use or manufacture (Schilling et al., 1999).
With the further consideration of inequality constraints on the irreversible reactions (reversible reactions can be decomposed as irreversible forward and backward reactions),
vi ≥ 0
(3)
Equation 2 can be described as a high-dimensional cone that is located in a space where each axis corresponds to a reaction flux (Figure 1). The solution space with the shape of a convex polyhedral cone has a
finite number of edges. The edges of the cone are unique for a given metabolic network and correspond
to biochemically feasible pathways, called as extreme pathways. Any vector within the cone can be represented as a nonnegative linear combination of the extreme pathways:
v = ∑α k f k , α k ≥ 0
(4)
k
where fk is fluxes of extreme pathways.
2.2
Extreme Pathways
As mentioned above, the extreme pathways (EPs) correspond to the edges of the high-dimensional convex solution space of a biochemical network. Extreme pathways (EPs) share three important properties.
Firstly, EPs are unique for a given metabolic network which means that EPs are invariant property of the
network. Furthermore, each EP consists of the minimum set of enzymes (or reactions) that needs to build
as a functional unit. Finally and most importantly, EPs are the systemically independent flux modes. No
extreme pathway can be represented as a nonnegative linear combination of any other extreme pathways
(Papin et al., 2004).
Figure 1: Convex flux cone defines the feasible solution space of metabolic systems at
steady state. The edges of the convex flux cone are extreme pathways (EP). All steady
state flux vectors (V) are non-negative linear combinations of extreme pathways.
2.3
Elementary Flux Mode
The concept of elementary flux mode (EFM) also derives from convex analysis of null solution space of
Equation 2. Generally speaking, elementary modes are a superset of the extreme pathways that fulfill the
request of “genetic independence” and “non-decomposability”, which means that removal of any reaction
in an elementary mode would destroy the functional unit. In other words, extreme pathways are a subset
of elementary flux modes and the number of extreme pathways is less than or equal to the number of elementary modes. For a given metabolic network, there is also only one unique set of elementary flux
modes.
The difference between elementary flux modes and extreme pathways can be illustrated in Figure
2. For a small system composed of three internal metabolites and three external metabolites (Figure 2a),
there exist four EFMs (Figure 2b) and three EPs (Figure 2c). The elementary mode EFM 4 is not systematically independent with other modes because it is a nonnegative linear combination of EFM1 and
EFM2, corresponding to the extreme pathways EP 1 and EP 2. However, EFM1 fulfills the requirement
of genetic independence and deletion of any genes in the system could destroy the functional unit. The
difference between the two sets of pathways is derived from the use of the reversible exchange flux for
the metabolite A which can be canceled out by linear combination of EP 1 and EP 2. If all of the exchange fluxes in the systems are irreversible, the elementary modes and extreme pathways are equivalent.
If a system existing large number of reversible exchange reactions, the number of extreme pathways
would be significantly less than elementary modes.
(a)
(b)
(c)
Figure 2: Example of a simple metabolic network, containing the elementary flux modes (EFM) and
extreme pathways (EP). (a) Configuration of the biological network. The system boundary defines the
concept of external metabolites (ext) and internal metabolites, exchange fluxes and internal fluxes. (b)
Four elementary flux modes of the biological network which are genetic independent. (c) Three extreme pathways which are systemically independent. The difference between the two sets of pathways
derived from the use of reversible exchange flux for the metabolite A. The elementary flux mode
EFM4 is a non-negative linear combination of the extreme pathways EP1 and EP2.
Since the calculation of extreme pathways would potentially eliminate the reversible exchange
fluxes, application of extreme pathways for the interpretation of system properties should be carefully
used. Therefore, elementary mode analysis is more generally used for the full evaluation of network
properties. However, it should be noted that the number of elementary flux modes exponentially increased with the enhancement of network complexity. Although the algorithm has been optimized during
the past years, it is still impossible to calculate all elementary modes in genome-wide networks.
3
Example-elementary Flux Mode Analysis of Glycerol Metabolic Network
The general procedure of elementary flux mode analysis is depicted in Figure 3. As mentioned above, the
first step of elementary flux mode analysis is to set up a proper metabolic network. The metabolic network can be built up based on genome information or pathway database like Kyoto Encyclopedia of
Genes and Genomes (KEGG). Since it is still impossible to calculate all elementary modes in genome
level, the metabolic work should be simplified to the suitable scale. For example, the biomass synthetic
pathways are often simplified to a reaction composed of different metabolic precursors. After setting up a
starting metabolic network, the system boundary can be defined and steady state assumption will be applied to constraint the mass balance of internal metabolites. The reversibility of bio-reactions also can be
used to introduce inequality constraints (Equation 3). The biological network is represented by stoichiometric matrix and the elementary flux modes are calculated. The desired information from the elementary
flux modes can be obtained through different analysis. The example of elementary flux modes analysis of
glycerol metabolic network under both anaerobic and aerobic conditions is discussed in the following
section (This example was revised from the authors’ publication: Chen et al. Journal of Biomedicine and
Biotechnology 2010, Article ID 518743, doi:10.1155/2010/518743).
Reconstruct metabolic network
Define system boudaries
internal and external metabolites, reversibility of bioreactions
!
Represent the biological network by stoichiometrics matrix
Calculate the element flux modes
!
Analyze the distribution and correlation of different flux modes
Figure 3: Flow chart of anelementary flux analysis process
3.1
Glycerol Metabolism
Glycerol has aroused people’s attention due to its low price as the byproduct of biodiesel production and
can be turned to high value added products (Yazdani & Gonzalez, 2007; Yang & Turon, 2012; Abad et
al. 2012; Liu et al. 2007; Xu et al., 2009). Succinate is traditionally produced from sugars under anaerobic conditions. This process, however, is not optimal succinate production due to the limited availability
of reducing equivalents (Zeikus & Jain, 1999; Litsanov et al., 2012a; Litsanov et al., 2011). The byproduct glycerol is a potential substrate for the succinate production because glycerol has a higher reduced
state compared with glucose and several microorganisms such as E. coli can transform glycerol into succinate (Booth et al., 2005). However, no industrially competitive organisms can effectively produce succinate from glycerol so far. Based on the technology of metabolic engineering, E. coli can be developed
to utilize glycerol for succinate production effectively for its clear inheritance background (Lin et al.,
2005; Litsanov et al. 2012b; Litsanov et al., 2012c; Kang et al., 2011).
In E.coli, glycerol is firstly phosphorylated into glycerol 3-phophate (G3P) by ATP-dependent
glycerol kinase encodedby glpK gene, and then glycerol 3-phophate is converted into dihydroxyacetone
phosphate (DHAP) by aerobic G3Pdehydrogenase encoded by glpD gene (Figure 4) under aerobic condition (Freedberg & Lin, 1973; Sweet et al. 1990). The anaerobic fermentative pathway of glycerol has just
been clarified in recent years (Dharmadi et al., 2006; Murarka et al., 2008) although the aerobic dissimilation of glycerol by E.coli has already been known for a long time. In this pathway, glycerol is converted to dihydroxyacetone (DHA) by NAD+ linked glycerol dehydrogenase (GDH), and the DHA is phosphorylated to DHAP via the ATP-dependent or phosphoenolpyruvate (PEP)-dependent DHA kinase
(DHAK). DHAP is then reduced into 1,2-propanediol or enter glycolysis (Altarasn & Camerond, 1999).
E. coli can utilize glycerol in both aerobic and anaerobic conditions, the potential and the feasibility of engineered E. coli for the succinate production in aerobic and anaerobic condition can be analyzed
through elementary flux analysis. The rational strain development strategy also can be put forward based
on the elementary flux analysis.
3.2
Metabolic Network Construction of Glycerol Metabolism in Escherichia coli
The glycerol metabolic network of E. coli was constructed1 (Fig. 4) containing glycerol dissimilation
pathways, glycolysis pathway (EMP), pentose phosphate pathway (PPP), tricarboxylic acid (TCA) cycle,
biosynthesis pathway, anaplerosis, and respiratory chain based on some literatures (Zhang & Xiu, 2009;
Sauer et al., 2004; Carlson & Srienc, 2004; Edwards & Palsson, 2000).
Under aerobic condition, glycerol is firstly phosphorylated into G3P by ATP-dependent glycerol
kinase and then G3P is transferred into DHAP by NAD+-dependent G3P dehydrogenase (Freedberg &
Lin, 1973; Sweet et al., 1990). The 1, 2-propanediol pathway is assumed to be inactive. Pyruvate oxidase
is active under aerobic condition which will transfer pyruvate into acetate. The detailed description of the
model is listed in Appendices A1 and A3.
Under anaerobic condition, glycerol is assumed to be dissimilated into DHA by NAD+-dependent
glycerol dehydrogenase and then DHA is phosphorylated into DHAP by ATP-dependent or PEPdependent DHA kinase (Dharmadi et al., 2006; Murarka et al., 2008). The pathway from DHAP to 1,2propanediol is considered to be active under anaerobic condition (Dharmadi et al., 2006). The pyruvate
1
http://www.genome.jp/kegg/metabolism.html
dehydrogenase complex and the respiratory chain are inactive under anaerobic condition (Hasona et al.,
2004; Berg et al., 2002). The detail description of the model is listed in Appendix A1 and A2.
Glycerol_ext
R1
glpF
CO2
Glucose-6-P
Glycerol
ATP
gldA
R4 glpK
Biomass
R60
ATP
NADPH
NADH+2ADP
R14
fpe
R33
tkt
GA-3-P
Sed-7-P
R34
tkt
Erythrose-4-P
Fructrose-6-P
R85
1,2-PDO_ext
PEP
R40
CO2
pck
R41
pykAF
R17
ATP
NADH
R51
Pyruvate
pdh
NADPH
2NADH
NADH
Oxaloacetate
mdh
Malate
aceB
R28
R44
Glyoxylate
Fumarate
R81
Acetate
Ethanol
R82
R83
Lactate_ext
Formate_ext
Acetate_ext
Ethanol_ext
R50
Citrate
acnB
icd
sdhABCD
R23
Isocitrate
R43
aceA
R24
CO2
NADPH
α-Ketoglutarate
Succinate
R26
sucAB
sucCD
Succinyl-CoA
ATP
adhE
R80
R22
gltA
R29
fumABC
Lactate
ldhA
pfl
poxB
R20
R52
Formate
NADH
R21
ATP
CO
2
CO2
pta, ackA R53
ATP Acetyl-CoA
R42
R84
tkt
R35
R16
NAD+2ATP
R27
Ribose-5-P
Xylulose-5-P
Fructrose-6-P
fpiA
ppc
NADH
NADH
R32
R31
gpi
NADH
R2
ADP
R72
Ribulose-5-P
R30
DHA
Glycerol-3-P
R13 fbp
GA-3-P
dhaK
dhaKLM
glpD
PG
Fructrose-1,6-P
R7
R3 PEP
Pyruvate
ATP
NADH
PEP
PYR
R5
R11
Oxaloacetate
fba
tpi12
Acetyl-CoA
DHAP
GA-3-P
α-Ketoglutarate
R10
2NADH
Glucose-6-P
NADH
R15
R6
Erythrose-4-P
ATP
Ribose-5-P
1,2-PDO
Glucose-6-P
PG
R70
R71
2NADPH
R25 CO2
NADH
Succinate_ext
Figure 4: Central metabolic network of glycerol in wild type E.coli. The dashed arrows represent the particular pathways in anaerobic conditions. Reversible reactions are represented by a
double-headed arrow. Key genes associated with the pathway are included.
Then, the elementary mode analysis was carried out for studying the metabolism of glycerol in
E.coli by using METATOOL 5.1 (http://pinguin.biologie.unijena.de/bioinformatik/networks/metatool/
metatool5.1/metatool5.1.html) (Kamp & Schuster, 2006). Metabolic pathway analysis resulted in tens to
hundreds of elementary flux modes for each situation investigated. The fluxes were calculated as relative
molar values normalized to the glycerol uptake rate and were defined as mol/mol (glycerol).
3.3
Elementary Mode Analysis of Glycerol Metabolism under Aerobic Condition
1.2
1.2
1
1
0.8
0.8
Lactate(mol mol-1)
Succinate(mol mol-1)
The aerobic metabolic network model got 259 elementary flux modes. The relationship between the
yields of products and biomass is shown in Figure 5. The enclosed regions represent the possible solution
space. The fluxes were normalized by glycerol uptake rate and defined as mol/mol (glycerol).
It was indicated that the maximum molar yield of biomass under aerobic condition was 0.725
mol/mol (only CO2 was produced). The results suggested that aerobic condition and the TCA cycle was
effective for biomass formation. The succinate production modes were diversely distributed throughout
the feasible solution space and the high potential of succinate production is associated with the cell
growth by metabolic modification under aerobic condition. The maximum succinate yield under aerobic
condition (an aerobic mode suggests oxygen consumption) is 1.0 mol/mol which requires the cosubstrates added such as CO2 or carbonate salts. The optimal flux distribution for succinate production is
shown in Figure 6.
0.6
0.4
0.6
0.4
0.2
0.2
0
0
0
0.2
0.4
0.6
0
0.8
0.2
0.6
0.8
0.6
0.8
Biomass(mol mol-1)
Biomass(mol mol-1)
(a)
(b)
1.2
1.2
1
1
Ethanol(mol mol-1)
Acetate(mol mol-1)
0.4
0.8
0.6
0.4
0.2
0
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Biomass(mol mol-1)
(c)
0.8
0
0.2
0.4
Biomass(mol mol-1)
(d)
Figure 5: Relationship between the yields of biomass and byproducts for the obtained elementary
modes of E.coli under aerobic conditions. (a) Succinate; (b) Lactate; (c) Acetate; (d)Ethanol.
Glycerol_ext
100
CO2
2NADPH
Glucose-6-P
Glycerol
Ribulose-5-P
ATP
100
Fructrose-6-P
Xylulose-5-P
Fructrose-1,6-P
Sed-7-P
Ribose-5-P
Glycerol-3-P
NADH
GA-3-P
100
DHAP
ATP
NADH
ADP
NADPH
GA-3-P
100
Fructrose-6-P
100
ATP
NADH
PG
NAD++2ATP
NADH+2ATP+1/2O2
Erythrose-4-P
100
100
CO2
PEP
ATP
NADH
Pyruvate
Lactate
Formate
NADH
CO2
Formate_ext
Acetyl-CoA
NADH
ATP
Acetate
Acetate_ext
Ethanol
Ethanol_ext
2NADH
Oxaloacetate
100
Citrate
Malate
100
Fumarate
NADH
Isocitrate
Glyoxylate
100
CO2
Succinyl-CoA
100
NADPH
α-Ketoglutarate
Succinate
CO2
Lactate_ext
NADH
Succinate_ext
Figure 6: The optimum flux distribution of glycerol metabolism for
succinate production in E.coli under aerobic conditions.
Under the optimal flux distribution mode, PEP was totally carboxylated into oxaloacetate by PEP
carboxylase, and the latter was further transferred into succinate. This is the key point for obtaining high
succinate yield, and thus PEP carboxylase with high activity is needed. The network robustness and its
sensitivity to perturbation were critical to the optimal metabolic pathway. The sensitivity of succinate
yield to the flux ratios at the key branch nodes PEP and acetyl-CoA was considered. PEP was consumed
in reactions R40 and R17 which are catalyzed by PEP carboxylase and pyruvate kinase, respectively. The
flux ratio was denoted as
R(40,17) =
R40
.
(R40 + R17)
(5)
The influence of flux distribution at PEP node is shown in Figure 7(a). The succinate yield increased
from 0.5 mol/mol to 1.0 mol/mol when R(40, 17) increased from 0 to 1.0. The results showed that increasing the flux distribution from PEP to oxaloacetate was beneficial for succinate production. For acetyl-CoA node, it was consumed in reactions R22, R44, R50, and R53 which are catalyzed by citrate synthase, aldehyde dehydrogenase, malate synthase, and phosphate acetyltransferase, respectively. The flux
ratio was denoted as
R(22,44,50,53) =
R22
.
(R22 + R44 + R50 + R53)
(6)
1.2
1.2
1
1
Succinate(mol mol-1)
Succinate(mol mol-1)
The influence of flux distribution at acetyl-CoA node is shown in Figure 7(b). The succinate yield decreased from 1.0 mol/mol to 0.75 mol/mol when R(22, 44, 50, 53) increased from 0 to 1.0. The results
indicated that decreasing the flux distribution from acetyl to TCA cycle was beneficial for succinate production since the carbon would be lost during the TCA cycle.
0.8
0.6
0.4
0.2
0.8
0.6
0.4
0.2
0
0
0
0.2
0.4
0.6
R40/(R40+R17)
(a)
0.8
1
0
0.2
0.4
0.6
0.8
R22/(R22+R50+R44+R53)
(b)
Figure 7: Sensitivity of succinate yield to the relative fluxes at the (a) PEP node, (b) AcCoA
node under aerobic conditions. The PEP node involves the catabolic reactions of R40 and R17
which are catalyzed by PEP carboxylase and Pyruvate kinase respectively. The AcCoA node involves the catabolic reactions of R22, R50, R44 and R53 which are catalyzed by citrate synthase,
aldehyde dehydrogenase, malate synthase and phosphate acetyltransferase respectively.
1
3.4
Elementary Mode Analysis of Glycerol Metabolism under Anaerobic Condition
55 elementary flux modes were obtained under anaerobic condition. The relationship between the yields
of products and biomass was shown in Figure 8. The production of 1,2-propanediol, ethanol and formate
was necessary for the biomass synthesis because the cell growth was always associated with the production of 1,2-propandediol, ethanol and formate.
The maximum molar yield of biomass under anaerobic condition is 0.187 mol/mol with the respective yields of 1,2-propanediol, ethanol and formate were 0.248 mol/mol, 0.495 mol/mol, 0.57
mol/mol. Under this condition, no succinate, acetate and lactate were produced. The biomass synthesis
process consumes ATP and produces reducing equivalents (NADH). Both ATP and NAD need to be regenerated through the production of other byproducts (the biomass synthesis equation in Appendix A2).
The maximum succinate yield under anaerobic condition is 1.0 mol/mol when CO2 or carbonate
salts are added as co-substrates and the optimal flux distribution for succinate production was shown in
Figure 9.
In this case, there were no production of biomass and other byproducts. The key points for this
mode were that the phosphorylation of DHA was only catalyzed by ATP-dependent DHA kinase and
PEP was totally carboxylated into oxaloacetate by PEP carboxylase and the latter was further transferred
into succinate. This required a very high activity of ATP-dependent DHA kinase and PEP carboxylase.
However, it was reported that the PEP-dependent DHA kinase plays the main role in E.coli which dramatically reduced the yield of succinate. With single PEP-dependent DHA kinase function, there will be
no succinate production (Murarkaet al. 2008). Thus the PEP-dependent DHA kinase is the bottleneck of
succinate production under anaerobic condition.
Comparing the results of elementary flux mode analysis above, the aerobic condition seemed to be
more favorable for succinate production although the maximum succinate yields were the same
(1.0mol/mol) under both anaerobic and aerobic conditions.Under anaerobic conditions, the cell grows
slowly and the cell growth is associated with the 1,2-propanediol, ethanol and formateproduction. That
inhibitsthe practical application of succinate production from glycerol(Trinh and Srienc, 2009).
3.5
The strategy for enhancing succinate production based on elementary flux analysis
The maximum succinate yields were 1.0 mol/mol under aerobic condition from the above results of elementary flux mode analysis. The possible design for the improving succinate producer to enhance the
butanol yield could be overexpressing the PEP carboxylase or expressing pyruvate carboxylase. Knocking down of the isocitratedehydrogenase gene (icd) also would enhance the succinate production because
the flux flowed from isocitrate to alpha-ketoglutarate and succinyl-CoA would result in the carbon lost.
Since acetate is the main byproduct under aerobic condition (Lina et al., 2005), knocking out the pyruvate oxidase gene (poxB) and phosphate acetyltransferase gene (pta) also is expected to increase the
succinate yield.
Under anaerobic condition, overexpressing the PEP carboxylase and substitution of PEPdependent DHA kinase into ATP-dependent DHA kinase would be prior consideration. An alternative
choice is to express the heterogeneous pyruvate carboxylase in E.coli. The overexpression of pyruvate
carboxylase could redistribute the flux of pyruvate into oxaloacetate for succinate production. The optimal flux distribution for succinate production in such case could also reach 1.0 mol/mol.
0.6
0.5
1
Lactate(mol mol-1)
Succinate(mol mol-1)
1.2
0.8
0.6
0.4
0.4
0.3
0.2
0.1
0.2
0
0
0
0.05
0.1
0.15
Biomass(mol mol-1)
0
0.2
0.05
0.2
0.7
1,2-propanediol(mol mol-1 )
0.35
0.3
Acetate(mol mol-1)
0.15
(b)
(a)
0.25
0.2
0.15
0.1
0.05
0
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.05
0.1
0.15
Biomass(mol mol-1)
0.2
0
0.05
(c)
0.1
0.15
Biomass(mol mol-1)
0.2
(d)
1.2
1.2
1
1
Ethanol(mol mol-1)
Formate(mol mol-1)
0.1
Biomass(mol mol-1)
0.8
0.6
0.4
0.2
0
0.8
0.6
0.4
0.2
0
0
0.05
0.1
Biomass(mol mol-1)
(e)
0.15
0.2
0
0.05
0.1
0.15
Biomass(mol mol-1)
(f)
Figure 8: Relationship between the yields of biomass and byproducts for the obtained elementary modes of E.coli under anaerobic conditions. (a) Succinate; (b) Lactate; (c) Acetate; (d) 1,2Propanediol; (e) Formate; (f) Ethanol. The enclosed regions represent the possible solution
space. The fluxes was normalized by glycerol uptake rate and expressed as mol/mol (glycerol).
0.2
Glycerol_ext
100
CO2
2NADPH
Glucose-6-P
Glycerol
Ribulose-5-P
NADH
100
Xylulose-5-P
Fructrose-6-P
Ribose-5-P
DHA
ATP
Fructrose-1,6-P
PEP
Sed-7-P
GA-3-P
Pyruvate
100
DHAP
ATP
NADH
ADP
NADPH
GA-3-P
100
Fructrose-6-P
100
ATP
NADH
PG
NAD++2ATP
NADH+2ATP+1/2O2
Erythrose-4-P
100
100
CO2
PEP
ATP
NADH
Pyruvate
Lactate
Formate
NADH
CO2
Acetyl-CoA
NADH
Lactate_ext
Formate_ext
ATP
Acetate
Acetate_ext
Ethanol
Ethanol_ext
2NADH
Oxaloacetate
100
Citrate
Malate
100
Fumarate
NADH
Isocitrate
Glyoxylate
100
CO2
Succinyl-CoA
100
NADPH
α-Ketoglutarate
Succinate
CO2
NADH
Succinate_ext
Figure 9: The optimum flux distribution of glycerol metabolism for succinate
production in E.coli under anaerobic conditions when only ATP-dependent DHA
kinase plays function.
It has been reported that expressing the ATP-dependent DHA kinase and pyruvate carboxylase
could both increase the yield of succinate (Murarka et al., 2008). Another consideration to increase the
succinate yield is reducing the byproducts production. Since the production of 1,2-propanediol, ethanol
and formate is necessary for biomass synthesis, the possible strategy is knocking out the phosphate
acetyltransferase gene (pta) and lactate dehydrogenase gene (ldh) to increase the succinate production.
This example indicated that elementary flux analysis provided not only the possible optimal pathway, but also the proper genetic modification strategy.
4
4.1
Other Applications of Metabolic Pathway Analysis in Systems Biology and Metabolic Engineering
Calculation of Optimal Conversion Yield for Guiding Metabolic Engineering
As discussed above, MPA can be used to determine the overall capacity ortheoretical maximum yield of
a cellular system and study the effects of strain genetic modification. Knowledge of the theoretical maximum yield allows estimating the potential economic efficiency of a process. Moreover, rational design
can be obtained for the efficient production and genetic modification. Liao et al. (Liao et al., 1996) reported utilizing MPA for the development of high-efficiency producer of aromatic amino acids for the
first time. By examining all of the optimal and suboptimal flux distributions and elementary modes directing carbon flow to the pathways for targeted metabolites, an E. coli strain that channeled substrates to
the aromatic pathway at theoretical yields have been constructed successfully. Recently, elementary flux
mode analysis also has been used for genome scale metabolic studies dealing with, for example, the rational design of methionine production in E. coli and C. glutamicum (Krömer et al., 2006), and the production of polyhydroxybutanoate in yeast (Carlson et al., 2002).
It should be mentioned that there are other approaches which could also be utilized to calculate
theoretical maximum yield, such as flux balance analysis. However, these methods are often based on
different sets of constraints for getting the optimal solution under a given condition. MPA, however, can
predict all of the possible solution space and give correlation of different fluxes variants. This significantly enlarges the application scope of MPA.
4.2
Evaluation of the Constructed Network from Genomic Data
As mentioned above, the results of MPA is significantly dependent on the initially constructed metabolic
network. Thus it is important to have confidence in the functional assignments of the genome. Any errors
exist in this functional assignment or annotation of genes would change the structure metabolic network
and result in different sets of elementary flux pathways. On the other hand, the results of pathway analysis can be used to evaluate the genome annotation of an organism. For example, if the pathway analysis
shows that the organism is unable to synthesize an experimentally proved molecule, and then a functional
assignment maybe concluded being missing.
5
Concluding Remarks
In this chapter, the basic principles of metabolic pathway analysis are introduced. The differences between extreme pathway and elementary flux mode are compared. With the increase of genome data and
reconstructed metabolic network, metabolic pathway analysis would have more applications for exploring the inherent properties of metabolic systems, helping us for further understanding of the cellular behavior and designing more efficient cell factories. The scaling up of elementary flux mode analysis in
genome scale would be the future directions for metabolic pathway analysis.
Appendix A1
Reactions
R1
R2
R3
R4
R5
R6
R7
R10
R11
R13
R14
R15
R16
R17
R20
R21
R22
R23
R24
R25
R26
R27
R28
R29
R30
R31
R32
R33
R34
R35
R40
R41
R42
R43
R44
R50
R51
R52
R53
R60
R70
R71
R72
R80
R81
R82
Genes
glpF
gldA
dhaKLM
glpK
glpD
dhaK
tpi12
fba
fbp
gpi
pykAF
pdh
pfl
gltA
acnB
icd
sucAB
sucCD
sdhABCD
fumABC
mdh
rpe
rpiA
tkt
tkt
tkt
ppc
pck
malE
aceA
aceB
adhE
ldhA
poxB
pta,ackA
Reactions and Enzymes
Enzymes
Aerobic/anaerobic specificitity
glycerol facilitator
Glycerol dehydrogenase II
anaerobic
PTS-depedentDihydroxyacetone kinase anaerobic
glycerol kinase
aerobic
Glycerol-3-phosphate dehydrogenase
aerobic
sets of reactions
anaerobic
ATP-depedentDihydroxyacetone kinase
Triose-phosphate isomerase
Fructose-bisphosphatealdolase
Fructose-bisphosphatase
Glucose-6-phosphate isomerase
sets of reactions
sets of reactions
Pyruvate kinase
Pyruvate dehydrogenase
aerobic
Pyruvate formate-lyase
anaerobic
Citrate synthase
Aconitatehydratase
Isocitrate dehydrogenase
Oxoglutarate dehydrogenase
aerobic
Succinate-CoA ligase
aerobic
Succinate dehydrogenase
Fumaratehydratase
Malate dehydrogenase
sets of reactions
Ribulose-phosphate 3-epimerase
Ribose-5-phosphate isomerase
Transketolase
Transaldolase
Transketolase
PEP carboxylase
PEP carboxykinase
malic enzyme
Isocitratelyase
Malate synthase
Aldehyde dehydrogenase
Lactate dehydrogenase
pyruvate oxidase
aerobic
Phosphate acetyltransferase,Acetate kinase
Biomass formation
ATP-hydrolysis
Transhydrogenase
respiratory chain 1
aerobic
Membrane transport reaction
Membrane transport reaction
Membrane transport reaction
References
1
2
2
1
1
2
2
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
3
4
KEGG
KEGG
KEGG
5
5
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
KEGG
6
KEGG
7
7
7
7
R83
R84
R85
Membrane transport reaction
Membrane transport reaction
Membrane transport reaction
Appendix A2 – The anaerobic metabolic network model input file used for
the program METATOOL.
-ENZREV (reversible reactions)
R10r R11r R14r R15r R16r R23r R26r R27r R28r R29r R31r R32r R33r R34r R35r R71r R86r
-ENZIRREV (irreversible reactions)
R1 R2 R3 R6 R7 R13 R17 R21 R22 R24 R30 R40 R41 R42 R43 R44 R50 R51 R53 R60 R70 R80
R81 R82 R83 R84 R85
-METINT (internal metabolite declaration)
Glycerol DHA DHAP GA-3-P propanediol PG PEP Pyruvate Acetyl-CoA CoASH Oxaloacetate Citrate
Isocitrate a-Ketoglutarate Succinate Fumarate Malate Glyoxylate Glucose-6-P Fructrose-6-P Fructrose-16-P
Ribulose-5-P Xylulose-5-P Ribose-5-P Sed-7-P Erythrose-4-P Lactate Formate Acetate Ethanol NAD NADH
ATP ADP NADP NADPH CO2
-METEXT (external metabolite declaration)
Glycerol_extEthanol_extAcetate_ext CO2_ext Lactate_extSuccinate_extFormate_ext BIOMASS propanediol_ext
-CAT
Reactions:
-Glycerol specific metabolisms
R1: Glycerol_ext = Glycerol.
R2: Glycerol + NAD = DHA + NADH.
R3: PEP+DHA = DHAP + Pyruvate.
R6: DHAP+2NADH=propanediol+NAD.
R7: DHA+ATP=DHAP+ADP
-Glycolysis
R10r: DHAP = GA-3-P.
R11r: DHAP + GA-3-P = Fructrose-16-P.
R13: Fructrose-16-P = Fructrose-6-P.
R14r: Fructrose-6-P=Glucose-6-P.
R15r: GA-3-P + ADP + NAD = PG + ATP + NADH.
R16r: PG=PEP.
R17: PEP +ADP = PYR+ ATP
-TCA cycle
R21: PYR + CoASH = Acetyl-CoA + FORMATE.
R22: Oxaloacetate + Acetyl-CoA = Citrate + CoASH.
R23r: Citrate = Isocitrate.
R24: Isocitrate + NADP = a-Ketoglutarate + NADPH + CO2.
R27r: Succinate + NAD = Fumarate + NADH.
R28r: Fumarate = Malate.
R29r: Malate + NAD = Oxaloacetate + NADH.
-Pentose Phosphate Pathway
R30: Glucose-6-P + 2NADP = Ribulose-5-P + 2NADPH + CO2.
R31r: Ribulose-5-P = Xylulose-5-P.
R32r: Ribulose-5-P = Ribose_5_P.
R33r: Ribose-5-P + Xylulose-5-P = Sed-7-P + GA-3-P.
R34r: GA-3-P + Sed-7-P = Erythrose-4-P + Fructrose-6-P.
R35r: Erythrose-4-P + Xylulose-5-P = GA-3-P + Fructrose-6-P.
-Anapleurotic reactions
R40: PEP + CO2 = Oxaloacetate.
R41: Oxaloacetate + ATP = PEP + ADP + CO2.
R42: MALATE + NADP = Pyruvate + NADPH + CO2.
R43: Isocitrate = Glyoxylate + Succinate .
R44: Glyoxylate + Acetyl-CoA = Malate + CoASH .
-Redox-associated reactions
R50: Acetyl-CoA + 2NADH = Ethanol + 2NAD + CoASH.
R51: Pyruvate + NADH = Lactate + NAD.
R53: Acetyl-CoA + ADP = Acetate + CoASH + ATP.
-Biomass formation
R60:
0.0206Glucose-6-P+0.0072Fructrose-6-P+0.0627Ribose-5-P+0.0361
Erythrose-4-P+
P+0.1338PG+0.0720PEP+0.2861Pyruvate+0.2930Acetyl-CoA+0.1481
Oxaloacetate+0.1078
+1.6548 NADPH+1.7821ATP+0.3548 NAD =2.87 BIOMASS+1.6548 NADP+0.2930
CO2+1.7821 ADP+0.3548 NADH.
-Oxidative phosphorylation/maintenance energy:
R70: ATP = ADP.
R71r: NADPH + NAD = NADH + NADP.
-Membrane transport reactions
R80: Lactate = Lactate_ext.
R81: Formate = Formate_ext.
R82: Acetate = Acetate_ext.
R83: Ethanol = Ethanol_ext.
R84: Succinate = Succinate_ext.
R85: propanediol=propanediol_ext.
R86r: CO2=CO2_ext.
+0.0129GA-3a-Ketoglutarate
CoASH+0.1678
Appendix A3 – The aerobic metabolic network model input file used for
the program METATOOL.
-ENZREV (reversible reactions)
R10r R11r R14r R15r R16r R23r R26r R27r R28r R29r R31r R32r R33r R34r R35r R71r R86r
-ENZIRREV (irreversible reactions)
R1 R4 R5 R13 R17 R20 R22 R24 R25 R30 R40 R41 R42 R43 R44 R50 R51 R53 R60 R70 R72 R80
R81 R82 R83 R84 R87
-METINT (internal metabolite declaration)
Glycerol Glycerol-3-P DHAP GA-3-P PG PEP Pyruvate Acetyl-CoA CoASH Oxaloacetate Citrate Isocitrate
a-KetoglutarateSuccinyl-CoA Succinate Fumarate Malate Glyoxylate Glucose-6-P Fructrose-6-P Fructrose-16P Ribulose-5-P Xylulose-5-P Ribose-5-P Sed-7-P Erythrose-4-P Lactate Acetate Ethanol NAD NADH ATP
ADP NADP NADPH CO2 O2
-METEXT (external metabolite declaration)
Glycerol_extEthanol_extAcetate_ext CO2_ext Lactate_extSuccinate_ext BIOMASS O2_ext
-CAT
Reactions:
-Glycerol specific metabolisms
R1: Glycerol_ext = Glycerol.
R4: Glycerol+ATP = Glycerol-3-P + ADP.
R5: Glycerol-3-P + NAD = DHAP + NADH.
-Glycolysis
R10r: DHAP = GA-3-P.
R11r: DHAP + GA-3-P = Fructrose-16-P.
R13: Fructrose-16-P = Fructrose-6-P.
R14r: Fructrose-6-P = Glucose-6-P.
R15r: GA-3-P + ADP + NAD = PG + ATP + NADH.
R16r: PG = PEP.
R17: PEP+ADP = Pyruvate + ATP.
-TCA cycle
R20: Pyruvate + CoASH +NAD = Acetyl-CoA + CO2 +NADH.
R22: Oxaloacetate + Acetyl-CoA = Citrate + CoASH.
R23r: Citrate = Isocitrate.
R24: Isocitrate + NADP = a-Ketoglutarate + NADPH + CO2.
R25: a-Ketoglutarate+NAD+CoASH = Succinyl-CoA+NADH+CO2.
R26r: Succinyl-CoA+ADP=Succinate+ATP+CoASH.
R27r: Succinate + NAD = Fumarate + NADH.
R28r: Fumarate = Malate.
R29r: Malate + NAD = Oxaloacetate + NADH.
-Pentose Phosphate Pathway
R30: Glucose-6-P + 2NADP = Ribulose-5-P + 2NADPH + CO2.
R31r: Ribulose-5-P = Xylulose-5-P.
R32r: Ribulose-5-P = Ribose_5_P.
R33r: Ribose-5-P + Xylulose-5-P = Sed-7-P + GA-3-P.
R34r: GA-3-P + Sed-7-P = Erythrose-4-P + Fructrose-6-P.
R35r: Erythrose-4-P + Xylulose-5-P = GA-3-P + Fructrose-6-P.
-Anapleurotic reactions
R40: PEP + CO2 = Oxaloacetate.
R41: Oxaloacetate + ATP = PEP + ADP + CO2.
R42: MALATE + NADP = Pyruvate + NADPH + CO2.
R43 :Isocitrate = Glyoxylate + Succinate .
R44 :Glyoxylate + Acetyl-CoA = Malate + CoASH .
-Redox-associated reactions
R50: Acetyl-CoA + 2NADH = Ethanol + 2NAD + CoASH.
R51: Pyruvate + NADH = Lactate + NAD.
R52: Pyruvate=CO2+Acetate.
R53: Acetyl-CoA + ADP = Acetate + CoASH + ATP.
-Biomass formation
R60:
0.0206Glucose-6-P+0.0072Fructrose-6-P+0.0627Ribose-5-P+0.0361
Erythrose-4-P+
P+0.1338PG+0.0720PEP+0.2861Pyruvate+0.2930Acetyl-CoA+0.1481
Oxaloacetate+0.1078
+1.6548 NADPH+1.7821ATP+0.3548 NAD =2.87 BIOMASS+1.6548 NADP+0.2930
CO2+1.7821 ADP+0.3548 NADH.
-Oxidative phosphorylation/maintenance energy:
+0.0129GA-3a-Ketoglutarate
CoASH+0.1678
R70: ATP = ADP.
R71r: NADPH + NAD = NADH + NADP.
R72: NADH+2ADP+1/2O2=NAD+2ATP.
-Membrane transport reactions
R80: Lactate = Lactate_ext.
R82: Acetate = Acetate_ext.
R83: Ethanol = Ethanol_ext.
R84: Succinate = Succinate_ext.
R86r: CO2=CO2_ext.
R87: O2_ext=O2
Acknowledgments
The authors would appreciate the financial support by Tsinghua University Initiative Scientific Research
Program (No. 2012Z02144) and the National Natural Science Funds (No. 21106078).
The corresponding author is Hongjuan Liu. Tel: +86-10-89796086, Fax: +86-10-89796086; E-mail:
[email protected]
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