Transcript ppt - Chair of Computational Biology

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 cell‘s metabolic network, hundreds of substrates are interconnected through
biochemical reactions. Although this could could in principle lead to the
simultaneous flow of substrates in numerous directions, in practice metabolic
fluxes pass through specific pathways.
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.
Start with review of last lecture‘s final point about coupling of metabolic and
regulatory networks.
22. Lecture WS 2003/04
Bioinformatics III
1
Application of elementary modes
Metabolic network structure of E.coli determines
key aspects of functionality and regulation
Compute EFMs for central
metabolism of E.coli.
Catabolic part: substrate uptake
reactions, glycolysis, pentose
phosphate pathway, TCA cycle,
excretion of by-products (acetate,
formate, lactate, ethanol)
Anabolic part: conversions of
precursors into building blocks like
amino acids, to macromolecules,
and to biomass.
Stelling et al. Nature 420, 190 (2002)
22. Lecture WS 2003/04
Bioinformatics III
2
Robustness analysis
The # of EFMs qualitatively indicates whether a mutant is viable or not, but does
not describe quantitatively how well a mutant grows.
Define maximal biomass yield Ymass as the optimum of:
Yi , X / Si
ei
 Sk
ei
ei is the single reaction rate (growth and substrate uptake) in EFM i selected for
utilization of substrate Sk.
Stelling et al. Nature 420, 190 (2002)
22. Lecture WS 2003/04
Bioinformatics III
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Can regulation be predicted by EFM analysis?
Compute control-effective fluxes for each reaction l by determining the efficiency of any EFM
ei by relating the system‘s output  to the substrate uptake and to the sum of all absolute
fluxes.
With flux modes normalized to the total substrate uptake, efficiencies i(Sk, ) for
the targets for optimization -growth and ATP generation, are defined as:
ei
eiATP
 i S k ,  
and  i S k , ATP 
l
 ei
 eil
l
l
Control-effective fluxes vl(Sk) are obtained by averaged weighting of the product of reactionspecific fluxes and mode-specific efficiencies over all EFMs using the substrate under
consideration:
vl S k  
1
max
X / Sk
Y

l



S
,

e
i k i
i
  S ,  
i
k

1
max
A / Sk
Y
l

l



S
,
ATP
e
i k
i
i
  S , ATP
i
k
l
YmaxX/Si and YmaxA/Si are optimal yields of biomass production and of ATP synthesis.
Control-effective fluxes represent the importance of each reaction for efficient and flexible
operation of the entire network.
Stelling et al. Nature 420, 190 (2002)
22. Lecture WS 2003/04
Bioinformatics III
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Prediction of gene expression patterns
As cellular control on longer timescales
is predominantly achieved by genetic
regulation, the control-effective fluxes
should correlate with messenger RNA
levels.
Compute theoretical transcript ratios
(S1,S2) for growth on two alternative
substrates S1 and S2 as ratios of
control-effective fluxes.
Compare to exp. DNA-microarray data
for E.coli growing on glucose and
acetate.
Excellent correlation!
Stelling et al. Nature 420, 190 (2002)
22. Lecture WS 2003/04
Calculated ratios between gene expression levels
during exponential growth on acetate and
exponential growth on glucose (filled circles
indicate outliers) based on all elementary modes
versus experimentally determined transcript
ratios. Lines indicate 95% confidence intervals
for experimental data (horizontal lines), linear
regression (solid line), perfect match (dashed
line) and two-fold deviation (dotted line).
Bioinformatics III
5
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)
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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)
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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)
22. Lecture WS 2003/04
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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)
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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} at 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
EGgc
E 
gc 2
G
gG
gG
0
ECgc
1
E 
where ...x denote the average with respect to x.
gc 2
C
cC
cC
0
1
Ihmels et al. Nat Genetics 31, 370 (2002)
22. Lecture WS 2003/04
Bioinformatics III
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Experiment signature SC
The input set consists of NI genes:


GI  g1 ,..., g N I  G
Score each experimental condition by the average expression change over the
genes of the input set. The condition score is:
gc
sc  EG
gG I
The experiment signature SC contains those conditions whose absolute score is
statistically significant:

S C  c  C : sc  s c
cC
 t C C

Here use tC = 2.0 as the condition threshold level and the standard deviation
expected for random fluctuations of
C 
1
NI
Ihmels et al. Nat Genetics 31, 370 (2002)
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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:
s g  sc ECgc
cS c
The gene signature SG contains those genes whose absolute score is statistically
significant:

SG  g  G : s g  s g
gG
 tG G

Here use tG = 3.0 as the gene threshold level and the measured standard deviation
G.
Ihmels et al. Nat Genetics 31, 370 (2002)
22. Lecture WS 2003/04
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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
S S
OLref

i
i
ref
S i  S ref
where |...| refers to the size of a set and  denotes intersection.
Ihmels et al. Nat Genetics 31, 370 (2002)
22. Lecture WS 2003/04
Bioinformatics III
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Fusion of signatures
All signatures Si whose overlap with the reference signature exceeds a certain
threshold are included in the set of recurrent signatures

R  Si : OLref
 tR
i

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)
22. Lecture WS 2003/04
Bioinformatics III
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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
OLij 
Pij
Si  S j
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 :
R  Pij : OL Pij , Pref   t R OLref 
Ihmels et al. Nat Genetics 31, 370 (2002)
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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)
22. Lecture WS 2003/04
Bioinformatics III
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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)
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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)
22. Lecture WS 2003/04
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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)
22. Lecture WS 2003/04
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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)
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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 > 0.25 are considered
significant.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
22. Lecture WS 2003/04
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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 >0.25). As a random
control, we randomized the identity of all metabolic genes and repeated
the analysis.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
22. Lecture WS 2003/04
Bioinformatics III
In the majority of divergent
junctions, only one of the
emanating branches is significantly
coregulated with the incoming
reaction that synthesizes the
metabolite.
22
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)
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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)
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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)
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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)
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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 >0.25 were
considered significant. To be
counted as parallel, rather than
converging, we demanded that the
correlation with the alternative
reaction be <80% of the correlation
with the preferred reaction.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
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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.
Dedicating 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.
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
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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)
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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)
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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)
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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 coexpression 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.
22. Lecture WS 2003/04
Ihmels, Levy, Barkai, Nat. Biotech 22, 86 (2004)
Bioinformatics III
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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)
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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.
1
Transcription leads the metabolic flow toward linearity.
2
Individual isozymes are often separately coregulated with distinct processes,
providing a means of reducing crosstalk between pathways using a common
reaction.
3
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)
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