V21 Metabolic Pathway Analysis (MPA)

1
V21 Metabolic Pathway Analysis (MPA)
Metabolic Pathway Analysis searches for
meaningful structural and functional units in
metabolic networks. The most promising, very
similar approaches are based on convex analysis
and use the sets of elementary flux modes
(Schuster et al. 1999, 2000) and extreme pathways
(Schilling et al. 2000). Both sets span the
space of feasible steady-state flux distributions
by non-decomposable routes, i.e. no subset of
reactions involved in an EFM or EP can hold the
network balanced using non-trivial fluxes. MPA
can be used to study e.g. - routing
flexibility/redundancy of networks -
functionality of networks - idenfication of
futile cycles - gives all (sub)optimal pathways
with respect to product/biomass yield - can be
useful for calculability studies in MFA Klamt
et al. Bioinformatics 19, 261 (2003)
2
Metabolic Pathway Analysis Elementary Flux Modes
The technique of Elementary Flux Modes (EFM) was
developed prior to extreme pathways (EP) by
Stephan Schuster, Thomas Dandekar and
co-workers Pfeiffer et al. Bioinformatics, 15,
251 (1999) Schuster et al. Nature Biotech. 18,
326 (2000) The method is very similar to the
extreme pathway method to construct a basis for
metabolic flux states based on methods from
convex algebra. Extreme pathways are a subset of
elementary modes, and for many systems,
both methods coincide. Are the subtle
differences important?
3
Elementary Flux Modes
Start from list of reaction equations and a
declaration of reversible and irreversible
reactions and of internal and external
metabolites. E.g. reaction scheme of
monosaccharide Fig.1 metabolism. It includes
15 internal metabolites, and 19 reactions. ? S
has dimension 15 ? 19. It is convenient to
reduce this matrix by lumping those reactions
that necessarily operate together. ?
Gap,Pgk,Gpm,Eno,Pyk, ? Zwf,Pgl,Gnd Such
groups of enzymes can be detected
automatically. This reveals another two sequences
Fba,TpiA and 2 Rpe,TktI,Tal,TktII. Schuster
et al. Nature Biotech 18, 326 (2000)
4
Elementary Flux Modes
Lumping the reactions in any one sequence gives
the following reduced system Construct initial
tableau by combining S with identity matrix
Ru5P FP2 F6P GAP R5P
Pgi Fba,TpiA Rpi reversible 2Rpe,TktI,Tal,Tkt
II Gap,Pgk,Gpm,Eno,Pyk Zwf,Pgl,Gnd Pfk ir
reversible Fbp Prs_DeoB
1 0 ... 0 0 0 1 0 0
0 1 ... 0 0 -1 0 2 0
0 0 ... 0 -1 0 0 0 1
0 0 ... 0 -2 0 2 1 -1
0 0 ... 0 0 0 0 -1 0
0 0 ... 0 1 0 0 0 0
0 0 ... 0 0 1 -1 0 0
0 0 ... 0 0 -1 1 0 0
0 0 ... 1 0 0 0 0 -1
T(0)
Schuster et al. Nature Biotech 18, 326 (2000)
5
Elementary Flux Modes
Aim again bring all entries of right part of
matrix to 0. E.g. 2row3 - row4 gives
reversible row with 0 in column 10 New
irreversible rows with 0 entry in column 10 by
row3 row6 and by row4 row7. In general,
linear combinations of 2 rows corresponding to
the same type of directio- nality go into the
part of the respective type in the tableau.
Combinations by different types go into the
irreversible tableau because at least 1
reaction is irreversible. Irreversible
reactions can only combined using positive
coefficients.
1 0 0 1 0 0
1 0 -1 0 2 0
1 -1 0 0 0 1
1 -2 0 2 1 -1
1 0 0 0 -1 0
1 1 0 0 0 0
1 0 1 -1 0 0
1 0 -1 1 0 0
1 0 0 0 0 -1
T(0)
1 0 0 1 0 0
1 0 -1 0 2 0
2 -1 0 0 -2 -1 3
1 0 0 0 -1 0
1 0 1 -1 0 0
1 0 -1 1 0 0
1 0 0 0 0 -1
1 1 0 0 0 0 1
1 2 0 0 2 1 -1
T(1)
Schuster et al. Nature Biotech 18, 326 (2000)
6
Elementary Flux Modes
Aim zero column 11. Include all possible
(direction-wise allowed) linear combinations of
rows. continue with columns 12-14.
1 0 0 1 0 0
1 0 -1 0 2 0
2 -1 0 0 -2 -1 3
1 0 0 0 -1 0
1 0 1 -1 0 0
1 0 -1 1 0 0
1 0 0 0 0 -1
1 1 0 0 0 0 1
1 2 0 0 2 1 -1
T(1)
1 0 0 1 0 0
2 -1 0 0 -2 -1 3
1 0 0 0 -1 0
1 0 0 0 0 -1
1 1 0 0 0 0 1
1 2 0 0 2 1 -1
1 1 0 0 -1 2 0
-1 1 0 0 1 -2 0
1 1 0 0 0 0 0
T(2)
Schuster et al. Nature Biotech 18, 326 (2000)
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Elementary Flux Modes
In the course of the algorithm, one must avoid -
calculation of nonelementary modes (rows that
contain fewer zeros than the row already
present) - duplicate modes (a pair of rows is
only combined if it fulfills the condition
S(mi(j)) ? S(mk(j)) ? S(ml(j1)) where
S(ml(j1)) is the set of positions of 0 in this
row. - flux modes violating the sign restriction
for the irreversible reactions. Final
tableau T(5) This shows that the
number of rows may decrease or increase in the
course of the algorithm. All constructed
elementary modes are irreversible.
1 1 0 0 2 0 1 0 0 0 ... ... 0
-2 0 1 1 1 3 0 0 0 ... ...
0 2 1 1 5 3 2 0 0
0 0 1 0 0 1 0 0 1
5 1 4 -2 0 0 1 0 6
-5 -1 2 2 0 6 0 1 0 ... ...
0 0 0 0 0 0 1 1 0 0 ... ... 0
Schuster et al. Nature Biotech 18, 326 (2000)
8
Elementary Flux Modes
Graphical representation of the elementary flux
modes of the monosaccharide metabolism. The
numbers indicate the relative flux carried by the
enzymes. Fig. 2
Schuster et al. Nature Biotech 18, 326 (2000)
9
Two approaches for Metabolic Pathway Analysis?
The pathway P(v) is an elementary flux mode if it
fulfills conditions C1 C3. (C1) Pseudo
steady-state. S ? e 0. This ensures that none
of the metabolites is consumed or produced in the
overall stoichiometry. (C2) Feasibility rate ei
? 0 if reaction is irreversible. This demands
that only thermodynamically realizable fluxes are
contained in e. (C3) Non-decomposability there
is no vector v (unequal to the zero vector and to
e) fulfilling C1 and C2 and that P(v) is a proper
subset of P(e). This is the core characteristics
for EFMs and EPs and supplies the decomposition
of the network into smallest units (able to hold
the network in steady state). C3 is often called
genetic independence because it implies that
the enzymes in one EFM or EP are not a subset of
the enzymes from another EFM or EP. Klamt
Stelling Trends Biotech 21, 64 (2003)
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Two approaches for Metabolic Pathway Analysis?
The pathway P(e) is an extreme pathway if it
fulfills conditions C1 C3 AND conditions C4
C5. (C4) Network reconfiguration Each reaction
must be classified either as exchange flux or as
internal reaction. All reversible internal
reactions must be split up into two separate,
irreversible reactions (forward and backward
reaction). (C5) Systemic independence the set
of EPs in a network is the minimal set of EFMs
that can describe all feasible steady-state flux
distributions. Klamt Stelling Trends
Biotech 21, 64 (2003)
11
Two approaches for Metabolic Pathway Analysis?
A(ext)
B(ext)
C(ext)
R1
R2
R3
B
R4
R8
R7
R5
A
C
P
R9
D
R6
Klamt Stelling Trends Biotech 21, 64 (2003)
12
Reconfigured Network
A(ext)
B(ext)
C(ext)
R1
R2
R3
B
R4
R8
R7b
R7f
A
C
P
R5
R9
D
R6
3 EFMs are not systemically independent EFM1
EP4 EP5 EFM2 EP3 EP5 EFM4 EP2 EP3
Klamt Stelling Trends Biotech 21, 64 (2003)
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Property 1 of EFMs
The only difference in the set of EFMs emerging
upon reconfiguration consists in the two-cycles
that result from splitting up reversible
reactions. However, two-cycles are not considered
as meaningful pathways. Valid for any network
Property 1 Reconfiguring a network by splitting
up reversible reactions leads to the same set of
meaningful EFMs.
Klamt Stelling Trends Biotech 21, 64 (2003)
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Software FluxAnalyzer
What is the consequence of when all exchange
fluxes (and hence all reactions in the network)
are irreversible?
EFMs and EPs always co-incide!
Klamt Stelling Trends Biotech 21, 64 (2003)
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Property 2 of EFMs
Property 2 If all exchange reactions in a network
are irreversible then the sets of meaningful EFMs
(both in the original and in the reconfigured
network) and EPs coincide.
Klamt Stelling Trends Biotech 21, 64 (2003)
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Reconfigured Network
A(ext)
B(ext)
C(ext)
R1
R2
R3
B
R4
R8
R7b
R7f
A
C
P
R5
R9
D
R6
3 EFMs are not systemically independent EFM1
EP4 EP5 EFM2 EP3 EP5 EFM4 EP2 EP3
Klamt Stelling Trends Biotech 21, 64 (2003)
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Comparison of EFMs and EPs
Problem EFM (network N1) EP (network
N2) Recognition of 4 genetically indepen- Set
of EPs does not contain operational modes dent
routes all genetically independent routes for
converting (EFM1-EFM4) routes. Searching for
EPs exclusively A to P. leading from A to P
via B, no pathway would be found.
Klamt Stelling Trends Biotech 21, 64 (2003)
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Comparison of EFMs and EPs
Problem EFM (network N1) EP (network
N2) Finding all the EFM1 and EFM2 are One
would only find the optimal routes optimal
because they suboptimal EP1, not the optimal
pathways for yield one mole P per optimal routes
EFM1 and synthesizing P during mole substrate
A EFM2. growth on A alone. (i.e. R3/R1
1), whereas EFM3 and EFM4 are only
sub- optimal (R3/R1 0.5).
Klamt Stelling Trends Biotech 21, 64 (2003)
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Comparison of EFMs and EPs
EFM (network N1) 4 pathways convert A to P
(EFM1-EFM4), whereas for B only one route (EFM8)
exists. When one of the internal reactions
(R4-R9) fails, for production of P from A 2
pathways will always survive. By contrast,
removing reaction R8 already stops the production
of P from B alone.
EP (network N2) Only 1 EP exists for producing P
by substrate A alone, and 1 EP for synthesizing P
by (only) substrate B. One might suggest that
both substrates possess the same redundancy of
pathways, but as shown by EFM analysis, growth on
substrate A is much more flexible than on B.
Problem Analysis of network flexibility
(structural robustness, redundancy) relative
robustness of exclusive growth on A or B.
Klamt Stelling Trends Biotech 21, 64 (2003)
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Comparison of EFMs and EPs
EFM (network N1) R8 is essential for producing P
by substrate B, whereas for A there is no
structurally favored reaction (R4-R9 all occur
twice in EFM1-EFM4). However, considering the
optimal modes EFM1, EFM2, one recognizes the
importance of R8 also for growth on A.
EP (network N2) Consider again biosynthesis of P
from substrate A (EP1 only). Because R8 is not
involved in EP1 one might think that this
reaction is not important for synthesizing P from
A. However, without this reaction, it is
impossible to obtain optimal yields (1 P per A
EFM1 and EFM2).
Problem Relative importance of single
reactions relative importance of reaction R8.
Klamt Stelling Trends Biotech 21, 64 (2003)
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Comparison of EFMs and EPs
EFM (network N1) R6 and R9 are an enzyme subset.
By contrast, R6 and R9 never occur together with
R8 in an EFM. Thus (R6,R8) and (R8,R9) are
excluding reaction pairs. (In an arbitrary
composable steady-state flux distribution they
might occur together.)
EP (network N2) The EPs pretend R4 and R8 to be
an excluding reaction pair but they are not
(EFM2). The enzyme subsets would be correctly
identified. However, one can construct simple
examples where the EPs would also pretend wrong
enzyme subsets (not shown).
Problem Enzyme subsets and excluding reaction
pairs suggest regulatory structures or rules.
Klamt Stelling Trends Biotech 21, 64 (2003)
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Comparison of EFMs and EPs
EFM (network N1) The shortest pathway from A to
P needs 2 internal reactions (EFM2), the longest
4 (EFM4).
EP (network N2) Both the shortest (EFM2) and the
longest (EFM4) pathway from A to P are not
contained in the set of EPs.
Problem Pathway length shortest/longest
pathway for production of P from A.
Klamt Stelling Trends Biotech 21, 64 (2003)
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Comparison of EFMs and EPs
EFM (network N1) All EFMs not involving the
specific reactions build up the complete set of
EFMs in the new (smaller) sub-network. If R7 is
deleted, EFMs 2,3,6,8 survive. Hence the mutant
is viable.
EP (network N2) Analyzing a subnetwork implies
that the EPs must be newly computed. E.g. when
deleting R2, EFM2 would become an EP. For this
reason, mutation studies cannot be performed
easily.
Problem Removing a reaction and mutation
studies effect of deleting R7.
Klamt Stelling Trends Biotech 21, 64 (2003)
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Comparison of EFMs and EPs
EFM (network N1) For the case of R7, all EFMs
but EFM1 and EFM7 survive because the latter
ones utilize R7 with negative rate.
EP (network N2) In general, the set of EPs must
be recalculated compare the EPs in network N2
(R2 reversible) and N4 (R2 irreversible).
Problem Constraining reaction
reversibility effect of R7 limited to B ? C.
Klamt Stelling Trends Biotech 21, 64 (2003)
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Software FluxAnalyzer
FluxAnalyzer has both EPs and EFMs
implemented. Allows convenient studies of
metabolic systems. Klamt et al.
Bioinformatics 19, 261 (2003)
26
Summary
EFM are a robust method that offers great
opportunities for studying functional and
structural properties in metabolic
networks. Klamt Stelling suggest that the term
elementary flux modes should be used whenever
the sets of EFMs and EPs are identical. In cases
where they dont, EPs are a subset of EFMs. It
remains to be understood more thoroughly how much
valuable information about the pathway structure
is lost by using EPs. Ongoing Challenges -
study really large metabolic systems by
subdividing them - combine metabolic model with
model of cellular regulation.
Klamt Stelling Trends Biotech 21, 64 (2003)
27
Integrated Analysis of Metabolic and Regulatory
Networks
Sofar, studies of large-scale cellular networks
have focused on their connectivities. The
emerging picture shows a densely-woven web where
almost everything is connected to everything. In
the cells metabolic network, hundreds of
substrates are interconnected through biochemical
reactions. Although this could in principle lead
to the simultaneous flow of substrates in
numerous directions, in practice metabolic fluxes
pass through specific pathways (? high flux
backbone, V20).
Topological studies sofar did not consider how
the modulation of this connectivity might also
determine network properties.
Therefore it is important to correlate the
network topology (picture derived from EFMs and
EPs) with the expression of enzymes in the cell.
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Analyze transcriptional control in metabolic
networks
Regulatory and metabolic functions of cells are
mediated by networks of interacting biochemical
components. Metabolic flux is optimized to
maximize metabolic efficiency under different
conditions. Control of metabolic flow -
allosteric interactions - covalent modifications
involving enzymatic activity - transcription
(revealed by genome-wide expression
studies) Here N. Barkai and colleagues analyzed
published experimental expression data of
Saccharomyces cerevisae.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
29
Recurrence signature algorithm
Availability of DNA microarray data ? study
transcriptional response of a complete genome to
different experimental conditions. An essential
task in studying the global structure of
transcriptional networks is the gene
classification. Commonly used clustering
algorithms classify genes successfully when
applied to relatively small data sets, but their
application to large-scale expression data is
limited by 2 well-recognized drawbacks -
commonly used algorithms assign each gene to a
single cluster, whereas in fact genes may
participate in several functions and should thus
be included in several clusters - these
algorithms classify genes on the basis of their
expression under all experimental conditions,
whereas cellular processes are generally affected
only by a small subset of these conditions.
Ihmels et al. Nat Genetics 31, 370 (2002)
30
Recurrence signature algorithm
Aim identify transcription modules (TMs). ? a
set of randomly selected genes is unlikely to be
identical to the genes of any TM. Yet many such
sets do have some overlap with a specific TM. In
particular, sets of genes that are compiled
according to existing knowledge of their
functional (or regulatory) sequence similarity
may have a significant overlap with a
transcription module. Algorithm receives a gene
set that partially overlaps a TM and then
provides the complete module as output. Therefore
this algorithm is referred to as signature
algorithm.
Ihmels et al. Nat Genetics 31, 370 (2002)
31
Recurrence signature algorithm
normalization of data
identify modules
classify genes into modules
a, The signature algorithm. b , Recurrence as a
reliability measure. The signature algorithm is
applied to distinct input sets containing
different subsets of the postulated transcription
module. If the different input sets give rise to
the same module, it is considered reliable. c,
General application of the recurrent signature
method.
Ihmels et al. Nat Genetics 31, 370 (2002)
32
Normalize expression matrices
Collect from literature expression dataset
composed of over 1000 conditions, including
environmental stresses, profiles of deletion
mutants and natural processes such as cell
cycle. Element Egc of the gene expression matrix
contains the log-expression change of gene g ?1,
..., NG under the experimental conditions c ?1,
..., NC where NG and NC denote the total number
of genes and conditions, respectively. Introduce
2 normalized expression matrices EGgc and ECgc
with zero mean and unit variance with respect to
genes and conditions
where ?...?x denote the average with respect to x.
Ihmels et al. Nat Genetics 31, 370 (2002)
33
Experiment signature SC
The input set consists of NI genes Score each
experimental condition by the average expression
change over the genes of the input set. The
condition score is
The experiment signature SC contains those
conditions whose absolute score is statistically
significant
Here use tC 2.0 as the condition threshold
level and the standard deviation expected for
random fluctuations of
Ihmels et al. Nat Genetics 31, 370 (2002)
34
Gene Signature SG
In the next step, score all genes by the weighted
average change in the expression with the
experimental signature. The gene score is
The gene signature SG contains those genes whose
absolute score is statistically significant
Here use tG 3.0 as the gene threshold level and
the measured standard deviation ?G.
Ihmels et al. Nat Genetics 31, 370 (2002)
35
Fusion of signatures
Apply signature algorithm to reference input set
GIref and to a set of input sets GI(i) that are
obtained from GIref (? identify robust
modules!) Each set contains a fraction of the
wanted genes in GI(i) and some unrelated genes
that were selected at random. The result is a
reference signature Sref and a collection of
modified signatures Si. The overlap between
any of these signatures and the reference
signature is defined as
where ... refers to the size of a set and ?
denotes intersection.
Ihmels et al. Nat Genetics 31, 370 (2002)
36
Fusion of signatures
All signatures Si whose overlap with the
reference signature exceeds a certain threshold
are included in the set of recurrent signatures
The threshold tR must be chosen to be large
enough to discriminate against random
fluctuations, but small enough to include a
significant fraction of signatures. Here, tR
70. A module is obtained by selecting only
those genes that appear in at least 80 of all
signatures in R.
Ihmels et al. Nat Genetics 31, 370 (2002)
37
Fusion of signatures
Generate modules from recurrent signatures To
fuse pairs of recurrent signatures Si, Sj into
transcription modules For each pair, compute
the intersect Pij Si ? Sj of genes appearing in
both signatures as well as the overlap
Select the pair signature Pref with the largest
associated overlap OLref as the seed of a new
module. Assign all pair signatures Pij whose
overlap with Pref exceeded a certain fraction tR
of OLref to the set of recurrent signatures R
Ihmels et al. Nat Genetics 31, 370 (2002)
38
Fusion of signatures
Obtain gene content and scores of the associated
module from R. Remove the pairs that were
assigned to R from the total pool of pair
signatures Pij. To avoid identification of
more, less-coherent realizations of the same
module, remove also those pairs from R that would
have been assigned to R for a somewhat lower
value of threshold tR unless they had a
significant overlap (75) with any other pair
signature. This process is iterated until all
sets are assigned.
Ihmels et al. Nat Genetics 31, 370 (2002)
39
Numerical test
Apply algorithm to set of Ncore genes that are
known to be co-regulated. Then add Nrand randomly
selected genes. The addition of many random genes
leaves the output of the signature algorithm
essentially unchanged.
In detail A reference set of Ncore co-regulated
genes was composed of genes encoding either
ribosomal proteins (dashed lines) or proteins
involved in amino-acid biosynthesis
(dashed/dotted line). The recurrent signature
method was applied to this set as follows. First,
a collection of input sets was derived by
randomly adding genes to the reference set.
Second, the signature algorithm was applied to
the reference set and to the derived sets this
generates a reference signature and a collection
of perturbed signatures, respectively. Last, the
overlaps between the reference signature and the
perturbed signatures were calculated. Shown is
the average overlap as a function of the number
of genes added to the reference set. The
different lines correspond to different choices
of Ncore, shown in parentheses.
Ihmels et al. Nat Genetics 31, 370 (2002)
40
Correlation between genes of the same metabolic
pathway
Distribution of the average correlation between
genes assigned to the same metabolic pathway in
the KEGG database. The distribution
corresponding to random assignment of genes to
metabolic pathways of the same size is shown for
comparison. Importantly, only genes coding for
enzymes were used in the random control.
Interpretation pairs of genes associated with
the same metabolic pathway show a similar
expression pattern.
However, typically only a set of the genes
assigned to a given pathway are coregulated.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
41
Correlation between genes of the same metabolic
pathway
Genes of the glycolysis pathway (according KEGG)
were clustered and ordered based on the
correlation in their expression profiles. Shown
here is the matrix of their pair-wise
correlations. The cluster of highly correlated
genes (orange frame) corresponds to genes that
encode the central glycolysis enzymes. The
linear arrangement of these genes along the
pathway is shown at right.
Of the 46 genes assigned to the glycolysis
pathway in the KEGG database, only 24 show a
correlated expression pattern. In general, the
coregulated genes belong to the central pieces of
pathways.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
42
Coexpressed enzymes often catalyze linear chain
of reactions
Coregulation between enzymes associated with
central metabolic pathways. Each branch
corresponds to several enzymes. In the cases
shown, only one of the branches downstream of the
junction point is coregulated with upstream
genes. Interpretation coexpressed enzymes are
often arranged in a linear order, corresponding
to a metabolic flow that is directed in a
particular direction.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
43
Co-regulation at branch points
To examine more systematically whether
coregulation enhances the linearity of metabolic
flow, analyze the coregulation of enzymes at
metabolic branch-points. Search KEGG for
metabolic compounds that are involved in exactly
3 reactions. Only consider reactions that exist
in S.cerevisae. 3-junctions can integrate
metabolic flow (convergent junction) or allow
the flow to diverge in 2 directions (divergent
junction). In the cases where several reactions
are catalyzed by the same enzymes, choose one
representative so that all junctions considered
are composed of precisely 3 reactions catalyzed
by distinct enzymes. Each 3-junction is
categorized according to the correlation pattern
found between enzymes catalyzing its branches.
Correlation coefficients gt 0.25 are considered
significant.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
44
Coregulation pattern in three-point junctions
All junctions corresponding to metabolites that
participate in exactly 3 reactions (according to
KEGG) were identified and the correlations
between the genes associated with each such
junction were calculated. The junctions were
grouped according to the directionality of the
reactions, as shown. Divergent junctions, which
allow the flow of metabolites in two alternative
directions, predominantly show a linear
coregulation pattern, where one of the emanating
reaction is correlated with the incoming reaction
(linear regulatory pattern) or the two
alternative outgoing reactions are correlated in
a context-dependent manner with a distinct
isozyme catalyzing the incoming reaction (linear
switch). By contrast, the linear regulatory
pattern is significantly less abundant in
convergent junctions, where the outgoing flow
follows a unique direction, and in conflicting
junctions that do not support metabolic flow.
Most of the reversible junctions comply with
linear regulatory patterns. Indeed, similar to
divergent junctions, reversible junctions allow
metabolites to flow in two alternative
directions. Reactions were counted as coexpressed
if at least two of the associated genes were
significantly correlated (correlation coefficient
gt0.25). As a random control, we randomized the
identity of all metabolic genes and repeated the
analysis.
In the majority of divergent junctions, only one
of the emanating branches is significantly
coregulated with the incoming reaction that
synthesizes the metabolite.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
45
Co-regulation at branch points conclusions
The observed co-regulation patterns correspond to
a linear metabolic flow, whose directionality can
be switched in a condition-specific manner. When
analyzing junctions that allow metabolic flow in
a larger number of directions, there also only a
few important branches are coregulated with the
incoming branch. Therefore transcription
regulation is used to enhance the linearity of
metabolic flow, by biasing the flow toward only a
few of the possible routes.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
46
Connectivity of metabolites
The connectivity of a given metabolite is defined
as the number of reactions connecting it to other
metabolites. Shown are the distributions of
connectivity between metabolites in an
unrestricted network (?) and in a network where
only correlated reactions are considered (?). In
accordance with previous results (Jeong et al.
2000) , the connectivity distribution between
metabolites follows a power law (log-log plot).
In contrast, when coexpression is used as a
criterion to distinguish functional links, the
connectivity distribution becomes exponential
(log-linear plot).
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
47
Differential regulation of isozymes
Observe that isozymes at junction points are
often preferentially coexpressed with alternative
reactions. ? investigate their role in the
metabolic network more systematically. Two
possible functions of isozymes associated with
the same metabolic reaction. An isozyme pair
could provide redundancy which may be needed for
buffering genetic mutations or for amplifying
metabolite production. Redundant isozymes are
expected to be coregulated. Alternatively,
distinct isozymes could be dedicated to separate
biochemical pathways using the associated
reaction. Such isozymes are expected to be
differentially expressed with the two alternative
processes.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
48
Differential regulation of isozymes in central
metabolic PW
Arrows represent metabolic pathways composed of a
sequence of enzymes. Coregulation is indicated
with the same color (e.g., the isozyme
represented by the green arrow is coregulated
with the metabolic pathway represented by the
green arrow). ? Most members of isozyme pairs
are separately coregulated with alternative
processes.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
49
Differential regulation of isozymes
Regulatory pattern of all gene pairs associated
with a common metabolic reaction (according to
KEGG). All such pairs were classified into
several classes (1) parallel, where each gene
is correlated with a distinct connected reaction
(a reaction that shares a metabolite with the
reaction catalyzed by the respective gene pair)
(2) selective, where only one of the enzymes
shows a significant correlation with a connected
reaction and (3) converging, where both enzymes
were correlated with the same reaction.
Correlations coefficients gt0.25 were considered
significant. To be counted as parallel, rather
than converging, we demanded that the correlation
with the alternative reaction be lt80 of the
correlation with the preferred reaction.
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Differential regulation of isozymes
interpretation
The primary role of isozyme multiplicity is to
allow for differential regulation of reactions
that are shared by separated processes. Dedicatin
g a specific enzyme to each pathway may offer a
way of independently controlling the associated
reaction in response to pathway-specific
requirements, at both the transcriptional and the
post-transcriptional levels.
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51
Genes coexpressed with metabolic pathways
Identify the coregulated subparts of each
metabolic pathway and identify relevant
experimental conditions that induce or repress
the expression of the pathway genes. Also
associate additional genes showing similar
expression profiles with each pathway using the
signature algorithm. Input set of genes, some of
which are expected to be coregulated. Output
coregulated part of the input and additional
coregulated genes together with the set of
conditions where the coregulation is
realized. Numerous genes were found that are not
directly involved in enzymatic steps -
transporters - transcription factors
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
52
Co-expression of transporters
Transporter genes are co-expressed with the
relevant metabolic pathways providing the
pathways with its metabolites. Co-expression is
marked in green.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
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Co-regulation of transcription factors
Transcription factors are often co-regulated with
their regulated pathways. Shown here are
transcription factors which were found to be
co-regulated in the analysis. Co-regulation is
shown by color-coding such that the transcription
factor and the associated pathways are of the
same color.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
54
Hierarchical modularity in the metabolic network
Sofar co-expression analysis revealed a strong
tendency toward coordinated regulation of genes
involved in individual metabolic pathways.
Does transcription regulation also define a
higher-order metabolic organization, by
coordinated expression of distinct metabolic
pathways?
Based on observation that feeder pathways (which
synthesize metabolites) are frequently
coexpressed with pathways using the synthesized
metabolites.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
55
Feeder-pathways/enzymes
Feeder pathways or genes co-expressed with the
pathways they fuel. The feeder pathways (light
blue) provide the main pathway (dark blue) with
metabolites in order to assist the main pathway,
indicating that co-expression extends beyond the
level of individual pathways. These results can
be interpreted in the following way the organism
will produce those enzymes that are needed.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
56
Hierarchical modularity in the metabolic network
Derive hierarchy by applying an iterative
signature algorithm to the metabolic pathways,
and decreasing the resolution parameter
(coregulation stringency) in small steps. Each
box contains a group of coregulated genes
(transcription module). Strongly associated genes
(left) can be associated with a specific
function, whereas moderately correlated modules
(right) are larger and their function is less
coherent. The merging of 2 branches indicates
that the associated modules are induced by
similar conditions. All pathways converge to one
of 3 low-resolution modules amino acid
biosynthesis, protein synthesis, and stress.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
57
Hierarchical modularity in the metabolic network
Although amino acids serve as building blocks for
proteins, the expression of genes mediating these
2 processes is clearly uncoupled! This may
reflect the association of rapid cell growth
(which triggers enhanced protein synthesis) with
rich growth conditions, where amino acids are
readily available and do not need to be
synthesized. Amino acid biosynthesis genes are
only required when external amino acids are
scarce. In support of this view, a group of
amino acid transporters converged to the protein
synthesis module, together with other pathways
required for rapid cell growth (glucose
fermentation, nucleotide synthesis and fatty acid
synthesis).
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
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Global network properties
Jeong et al. showed that the structural
connectivity between metabolites imposes a
hierarchical organization of the metabolic
network. That analysis was based on connectivity
between substrates, considering all potential
connections. Here, analysis is based on
coexpression of enzymes. In both approaches,
related metabolic pathways were clustered
together!
There are, however, some differences in the
particular groupings (not discussed here), and
importantly, when including expression data the
connectivity pattern of metabolites changes from
a power-law dependence to an exponential one
corresponding to a network structure with a
defined scale of connectivity. This reflects the
reduction in the complexity of the network.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
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Summary

• Transcription regulation is prominently involved
  in shaping the metabolic network of S. cerevisae.
  
• Transcription leads the metabolic flow toward
  linearity.
• Individual isozymes are often separately
  coregulated with distinct processes, providing a
  means of reducing crosstalk between pathways
  using a common reaction.
• Transcription regulation entails a higher-order
  structure of the metabolic network.
• It exists a hierarchical organization of
  metabolic pathways into groups of decreasing
  expression coherence.

Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)