Elucidating the Roadmap of Metabolism by Pathway Analysis

1
Elucidating the Roadmap of Metabolism by Pathway
Analysis

• Stefan Schuster
• Friedrich Schiller University Jena
• Dept. of Bioinformatics

2
Topics of this talk
3
Introduction

• Metabolism is bridge between genotype and
  phenotype
• Networks of metabolic reactions are complex due
  to their size and the presence of bimolecular
  reactions
• Many kinetic parameters unknown. Maximal
  velocities depend on enzyme concentrations

4
Roadmap as a metaphor
Roads form simple graph
5
Metabolism is hypergraph
6
Technologically relevant metabolic syntheses

• Antibiotics by fungi
• Ethanol by yeast
• Amino acids by bacteria
• Dyes
• Perfumes
• etc. etc.

7
Theoretical Methods

• Dynamic Simulation
• Stability and bifurcation analyses
• Metabolic Control Analysis (MCA)
• Metabolic Pathway Analysis
• Metabolic Flux Analysis (MFA)
• Optimization, Evolutionary Game Theory
• and others

8
Theoretical Methods

• Dynamic Simulation
• Stability and bifurcation analyses
• Metabolic Control Analysis (MCA)
• Metabolic Pathway Analysis
• Metabolic Flux Analysis (MFA)
• Optimization, Evolutionary Game Theory
• and others

9
Metabolic Pathway Analysis (or Metabolic Network
Analysis)

• Decomposition of the network into the smallest
  functional entities (metabolic pathways)
• Does not require knowledge of kinetic
  parameters!!
• Uses stoichiometric coefficients and
  reversibility/irreversibility of reactions

10
History of pathway analysis

• Direct mechanisms in chemistry (Milner 1964,
  Happel Sellers 1982)
• Clarke 1980 extreme currents
• Seressiotis Bailey 1986 biochemical pathways
• Leiser Blum 1987 fundamental modes
• Mavrovouniotis et al. 1990 biochemical pathways
• Fell (1990) linearly independent basis vectors
• Schuster Hilgetag 1994 elementary flux modes
• Liao et al. 1996 basic reaction modes
• Schilling, Letscher and Palsson 2000 extreme
  pathways

11
Mathematical background
Steady-state condition NV(S) 0 If the kinetic
parameters were known, this could be solved for
S. If not, one can try to solve it for V. The
equation system is linear in V. However, usually
there is a manifold of solutions. Mathematically
kernel (null-space) of N. Spanned by
basis vectors. These are not unique.
12
P
S
4
3
non-elementary flux mode
1
1
P
1
3
S
S
1
2
2
2
S
4
P
P
2
1
P
S
4
3
1
1
P
3
1
S
S
S
S
1
2
1
2
1
1
1
1
S
S
4
4
P
P
P
P
2
1
2
1
elementary flux modes
S. Schuster et al. J. Biol. Syst. 2 (1994)
165-182 Trends Biotechnol. 17 (1999) 53-60
Nature Biotechnol. 18 (2000) 326-332
13
An elementary mode is a minimal set of enzymes
that can operate at steady state with all
irreversible reactions used in the appropriate
direction
All flux distributions in the living cell are
non-negative linear combinations of elementary
modes
Related concept Extreme pathway (C.H. Schilling,
D. Letscher and B.O. Palsson, J. theor. Biol.
203 (2000) 229) - distinction between internal
and exchange reactions, all internal reversible
reactions are split up into forward and reverse
steps
14
Mathematical background (2)
Steady-state condition NV 0 Sign restriction
for irreversible fluxes Virr 0 This
represents a linear equation/inequality
system. Solution is a convex region. All edges
correspond to elementary modes. In addition,
there may be elementary modes in the interior.
15
Geometrical interpretation
Elementary modes correspond to generating vectors
(edges) of a convex polyhedral cone ( pyramid)
in flux space (if all modes are irreversible)
16
Rate 3
Rate 2
generating vectors
Rate of enzyme 1
17
Software for computing elementary modes
EMPATH (in SmallTalk) - J. Woods
METATOOL (in C) - Th. Pfeiffer, F. Moldenhauer,
A. von Kamp
Included in GEPASI - P. Mendes
and JARNAC - H. Sauro
part of METAFLUX (in MAPLE) - K. Mauch
part of FluxAnalyzer (in MATLAB) - S. Klamt
part of ScrumPy (in Python) - M. Poolman
Alternative algorithm in MATLAB C. Wagner (Bern)
On-line computation
pHpMetatool - H. Höpfner, M. Lange
http//pgrc-03.ipk-gatersleben.de/tools/phpMetatoo
l/index.php
18
Biochemical Applications1. Can sugars be
produced from lipids?

• Known in biochemistry for a long time that many
  bacteria and plants can produce sugars from
  lipids (via C2 units) while animals cannot

19
AcCoA is linked with glucose by a chain of
reactions. However, no elementary mode realizes
this conversion in the absence of the glyoxylate
shunt.
Glucose
CO2
AcCoA
Pyr
PEP
Cit
Oxac
CO2
IsoCit
Mal
CO2
OG
Fum
SucCoA
Succ
CO2
20
Elementary mode representing conversion of AcCoA
into glucose. It requires the glyoxylate shunt.
Glucose
CO2
AcCoA
Pyr
PEP
Cit
Oxac
CO2
Mas
Icl
IsoCit
Gly
Mal
CO2
OG
Fum
CO2
SucCoA
Succ
21
The glyoxylate shunt is present in green plants
and many bacteria (e.g. E. coli). This
example shows that a description by usual graphs
in the sense of graph theory is
insufficient S. Schuster, D.A. Fell Modelling
and simulating metabolic networks. In
Bioinformatics From Genomes to Therapies (T.
Lengauer, ed.) Wiley-VCH, Weinheim, in press.
22
A successful theoretical prediction
Glucose
Red elementary mode Usual TCA cycle Green
elementary mode Catabolic pathway predicted in
Liao et al. (1996) and Schuster et al. (1999).
Experimental hints in Wick et al. (2001).
Experimental proof in
CO2
E. Fischer and U. Sauer A novel metabolic cycle
catalyzes glucose oxidation and anaplerosis in
hungry Escherichia coli,
AcCoA
Pyr
PEP
J. Biol. Chem. 278 (2003) 4644646451
Cit
Oxac
CO2
IsoCit
Gly
Mal
CO2
OG
Fum
Succ
CO2
SucCoA
23
2. Crassulacean Acid Metabolism (CAM)

• Variant of photosynthesis employed by a range of
  plants (e.g. cacti) as an adaptation to arid
  conditions
• To reduce water loss, stomata are closed during
  daytime
• At nighttime, PEP CO2 ? oxaloacetate ? malate
• At daytime, malate ? pyruvate (or PEP) CO2 ?
  carbohydrates

24
CAM metabolism during daytime
25
Elementary modes
A)
B)
Starch synthesis via malic enzyme as occurring
in Cactaceae and Crassulacea
Hexose synthesis via malic enzyme as occurring
in Agavaceae and Dracaenaceae
Dracaena
Ferocactus
26
C)
D)
Simultaneous starch and hexose synthesis via
malic enzyme as occurring in
Hexose synthesis via PEPCK as occurring in
Clusia rosea and in
Clusia minor
Ananus comosus pineapple
27
F)
E)
Starch synthesis via PEPCK as occurring in
Asclepadiaceae
Simultaneous starch and hexose synthesis via
PEPCK as occurring in
Caralluma hexagona
Aloe vera
28
Pure pathways

• In a review by Christopher and Holtum (1996),
  only cases A), B), D), and E) were given as
  pure functionalities. F) was considered as a
  superposition, and C) was not mentioned.
• However, F) is an elementary mode as well,
  although it produces two products. It does not
  use the triose phosphate transporter
• The systematic overview provided by elementary
  modes enables one to look for missing examples.
  Case C) is indeed realized in Clusia minor
  (Borland et al, 1994).
• Interestingly, (almost) pure elementary modes are
  realized here, although this should reduce
  robustness

S. Schuster, D.A. Fell Modelling and simulating
metabolic networks. In Bioinformatics From
Genomes to Therapies (T. Lengauer, ed.)
Wiley-VCH, Weinheim, in press.
29
3. Adenine and adenosine salvage pathways

• Human erythrocytes cannot synthesize nucleotide
  phosphates de novo
• They can recycle nucleotides to give nucleotide
  phosphates
• In particular, they can recycle adenine and
  adenosine, but not hypoxanthine

S. Schuster, D. Kenanov Adenine and adenosine
salvage pathways in erythrocytes and the role of
S-adenosylhomocysteine hydrolase A theoretical
study using elementary flux modes. FEBS J. 272
(2005) 5278-5290.
30
membrane
2,3DPG
DPGM
DPGase
HK
PGI
ALD
GAPDH
GLCim
PFK
PGK
GLCext
GA3P
FDP
1,3 DPG
GLC
G6P
F6P
3PG
TPI
NADH
ADP
ATP
NAD
ATP
ADP
ADP
ATP
PGM
DHAP
G6PDH
NADP
2GSH
2PG
GL6P
EN
PGLase
PEP
ADP
GSHox
GSSGR
GO6P
PK
PYRtrans
ATP
PYRext
PYR
GL6PDH
GSSG
NADH
NADPH
LDH
LACtrans
NAD
R5PI
F6P
LAC
LACext
CO
GA3P
S7P
R5P
2
TKI
TA
RU5P
TKII
Xu5PE
X5P
GA3P
E4P
R5P
PRM

Na leak
PRPPsyn


Na
Na
R1P
ATP
PRPP
HGPRT
ADP
HXtrans
HYPXext
HYPX
IMP
PRPP
NaK ATPase
3'KetoRibose
ADPRT
NUC
AMPDA
ATP
ADENINE
AMP
INO
PNPase
HCY
ADA
NUC

K

K
ADO

K leak
ATP
AMP
SAHH2
HCY
AK
ApK
S-AdoHcy
MetAcc
AMP
ADP
ADP
MT
Acc
SAHH1
SAM
SAMext
31
Question

• As salvage pathways use enzymes consuming ATP as
  well as enzymes producing ATP, it is not easy to
  see whether a net synthesis of ATP is possible.
• Invest ATP to gain ATP - Bootstrapping like Baron
  Münchhausen?

32
Goal

• Analyse theoretically how many salvage pathways
  exist
• Which enzymes involves each of these and in what
  flux proportions (i.e. relative fluxes)
• Compute the net overall stoichiometry of ATP
  anabolism
• Medical impact of enzyme deficiencies

33
External metabolites

• Adenine or adenosine depending on which salvage
  is analysed
• glucose, lactate, CO2, ATP
• hypoxanthine, sodium and potassium outside the
  cell

34
Adenine as a source

• 153 elementary modes
• 4 of these produce ATP
• ATP per adenine yield 11
• ATP per glucose yields 310, 27, 14, 16

35
membrane
2,3DPG
DPGM
DPGase
HK
PGI
ALD
GAPDH
GLCim
PFK
PGK
GLCext
GA3P
FDP
1,3 DPG
GLC
G6P
F6P
3PG
TPI
NADH
ADP
ATP
NAD
ATP
ADP
ADP
ATP
PGM
DHAP
G6PDH
NADP
2GSH
2PG
GL6P
EN
PGLase
PEP
ADP
GSHox
GSSGR
GO6P
PK
PYRtrans
ATP
PYRext
PYR
GL6PDH
GSSG
NADH
NADPH
LDH
LACtrans
NAD
R5PI
F6P
LAC
LACext
CO
GA3P
S7P
R5P
2
TKI
TA
RU5P
TKII
Xu5PE
X5P
GA3P
E4P
R5P
PRM

Na leak
PRPPsyn


Na
Na
R1P
ATP
PRPP
HGPRT
ADP
HXtrans
HYPXext
HYPX
IMP
PRPP
NaK ATPase
3'KetoRibose
ADPRT
NUC
AMPDA
ATP
ADENINE
AMP
INO
PNPase
HCY
ADA
NUC

K

K
ADO

K leak
ATP
AMP
SAHH2
HCY
AK
ApK
S-AdoHcy
MetAcc
AMP
ADP
ADP
MT
Acc
SAHH1
SAM
SAMext
Elementary mode with highest ATPglucose yield
(310)
36
membrane
2,3DPG
DPGM
DPGase
HK
PGI
ALD
GAPDH
GLCim
PFK
PGK
GLCext
GA3P
FDP
1,3 DPG
GLC
G6P
F6P
3PG
TPI
NADH
ADP
ATP
NAD
ATP
ADP
ADP
ATP
PGM
DHAP
G6PDH
NADP
2GSH
2PG
GL6P
EN
PGLase
PEP
ADP
GSHox
GSSGR
GO6P
PK
PYRtrans
ATP
PYRext
PYR
GL6PDH
GSSG
NADH
NADPH
LDH
LACtrans
NAD
R5PI
F6P
LAC
LACext
CO
GA3P
S7P
R5P
2
TKI
TA
RU5P
TKII
Xu5PE
X5P
GA3P
E4P
R5P
PRM

Na leak
PRPPsyn


Na
Na
R1P
ATP
PRPP
HGPRT
ADP
HXtrans
HYPXext
HYPX
IMP
PRPP
NaK ATPase
3'KetoRibose
ADPRT
NUC
AMPDA
ATP
ADENINE
AMP
INO
PNPase
HCY
ADA
NUC

K

K
ADO

K leak
ATP
AMP
SAHH2
HCY
AK
ApK
S-AdoHcy
MetAcc
AMP
ADP
ADP
MT
Acc
SAHH1
SAM
SAMext
Elementary mode with lowest ATPglucose yield
(16)
37
Adenosine as a source

• 97 elementary modes
• 12 of these produce ATP
• ATP per adenosine yield 11, 23, 58, 817,
  25, 514, and 14.
• ATP per glucose yields 11, 56, 23, 59, 13,
  16, and 10!!
• When ATP/glucose 10, then all adenosine is
  used as exclusive energy source

38
membrane
2,3DPG
DPGM
DPGase
HK
PGI
ALD
GAPDH
GLCim
PFK
PGK
GLCext
GA3P
FDP
1,3 DPG
GLC
G6P
F6P
3PG
TPI
NADH
ADP
ATP
NAD
ATP
ADP
ADP
ATP
PGM
DHAP
G6PDH
NADP
2GSH
2PG
GL6P
EN
PGLase
PEP
ADP
GSHox
GSSGR
GO6P
PK
PYRtrans
ATP
PYRext
PYR
GL6PDH
GSSG
NADH
NADPH
LDH
LACtrans
NAD
R5PI
F6P
LAC
LACext
CO
GA3P
S7P
R5P
2
TKI
TA
RU5P
TKII
Xu5PE
X5P
GA3P
E4P
R5P
PRM

Na leak
PRPPsyn


Na
Na
R1P
ATP
PRPP
HGPRT
ADP
HXtrans
HYPXext
HYPX
IMP
PRPP
NaK ATPase
3'KetoRibose
ADPRT
NUC
AMPDA
ATP
ADENINE
AMP
INO
PNPase
HCY
ADA
NUC

K

K
ADO

K leak
ATP
AMP
SAHH2
HCY
AK
ApK
S-AdoHcy
MetAcc
AMP
ADP
ADP
MT
Acc
SAHH1
SAM
SAMext
One elementary mode using adenosine as energy and
nucleotide source
39
2.3-Diphosphoglycerate bypass

• Neither for adenine nor adenosine salvage, any
  elementary mode involves the 2.3DPG bypass
• ATP balance would not be positive anymore

40
Molar investment ratio

• moles of ATP consumed
• moles of ATP produced - moles of ATP consumed
• In elementary mode 1 of adenine salvage, this
  ratio is 18(20-18)  91.
• S. Schuster, D. Kenanov FEBS J. 272 (2005)
  5278-5290.

2 4-2
In glycolysis
1
41
Maximization of tryptophanglucose yield
Model of 65 reactions in the central metabolism
of E. coli. 26 elementary modes. 2 modes with
highest tryptophan glucose yield 0.451.
S. Schuster, T. Dandekar, D.A. Fell, Trends
Biotechnol. 17 (1999) 53
Glc
PEP
233
Pyr
G6P
Anthr
3PG
PrpP
105
GAP
Trp
42
Conclusions

• Elementary modes are an appropriate concept to
  describe biochemical pathways
• Information about network structure can be used
  to derive far-reaching conclusions about
  performance of metabolism
• Elementary modes reflect specific characteristics
  of metabolic networks such as steady-state mass
  flow, thermodynamic constraints and and the
  systemic interactions (Systems Biology)

43
Conclusions (2)

• It can be tested whether connected routes can
  function at steady state
• A complete list of potential pathways can be
  generated. Thereafter, experimental search for
  realized pathways.
• Pathway analysis is well-suited for computing
  maximal and submaximal molar yields

44
Cooperations

• Steffen Klamt, Jörg Stelling, Ernst Dieter Gilles
  
• (MPI Magdeburg)
• Thomas Dandekar (U Würzburg)
• David Fell (Brookes U Oxford)
• Thomas Pfeiffer, Sebastian Bonhoeffer (ETH
  Zürich)
• Thomas Wilhelm (IMB Jena)
• Reinhart Heinrich, Thomas Höfer (HU Berlin)
• Marko Marhl (U Maribor, Slovenia)
• Hans Westerhoff (VU Amsterdam)
• and others
• Acknowledgement to DFG and BMBF for financial
  support

45
Current group members

• Dr. Axel von Kamp
• Dr. Ina Weiß
• Dimitar Kenanov
• Jörn Behre
• Beate Knoke
• Ralf Bortfeldt
• Gunter Neumann