Metabolic Pathway Analysis as
Part of Systems Biology
Stefan Schuster
Dept. of Bioinformatics
Friedrich Schiller University Jena,
Germany
Famous people at Jena University:
Friedrich Schiller
(1759-1805)
Ernst Haeckel
(1834-1919, Biogenetic rule)
From: ExPASy
Introduction
 Analysis of metabolic systems requires
theoretical methods due to high complexity
 Systems theoretical approaches used in this
field for a long time, for example:
•1960‘s Dynamic simulation of biochemical systems
by David Garfinkel
•Metabolic Control Analysis (1973 H. Kacser/J. Burns,
R. Heinrich/T.A. Rapoport, 1980‘s Hans Westerhoff)
•„Biochemical Systems Theory“ (1970‘s Michael
Savageau)
 Since end 1990‘s: New quality due to high
throughput experiments and on-line databases
(e.g. KEGG, ExPASy, BRENDA)
 „Metabolomics“ is a growing field besides
„genomics“, „proteomics“...
 Major challenge: clarify relationship between
structure and function in complex intracellular
networks
Motivation for the modelling of metabolism
 Functional genomics – assignment of gene
functions can be improved by consideration of
interplay between gene products
 Study of robustness to enzyme deficiencies and
knock-out mutations is of high medical and
biotechnological relevance
 Increase of rate and yield of bioprocesses
important in biotechnology
The evolutionary aspect
 Metabolic pathways result from biological
evolution
 Evolution is actually co-evolution because various
species interact
 Each species tends to optimize its properties; the
outcome depends also on the properties of the
other species
Features often studied
in Systems Biology:
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Robustness
Flexibility
Fragility
Optimality
Modularity
Theoretical Methods







Dynamic Simulation
Stability and bifurcation analyses
Metabolic Control Analysis (MCA)
Metabolic Pathway Analysis
Metabolic Flux Analysis (MFA)
Optimization
and others
Theoretical Methods



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


Dynamic Simulation
Stability and bifurcation analyses
Metabolic Control Analysis (MCA)
Metabolic Pathway Analysis
Metabolic Flux Analysis (MFA)
Optimization
and others
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
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“
non-elementary flux mode
elementary flux modes
S. Schuster und C. Hilgetag: J. Biol. Syst. 2 (1994) 165-182
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
Mathematical background
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.
Geometrical interpretation
Elementary modes correspond to generating vectors
(edges) of a convex polyhedral cone (= pyramid)
in flux space (if all modes are irreversible)
flux3
flux2
generating vectors
flux1
ATP
X5P
CO2 Ru5P
NADPH
NADP
S7P
Pyr
E4P
ADP
R5P
GAP
PEP
F6P
6PG
2PG
GO6P
3PG
ATP
NADPH
NADP G6P
ADP
F6P
FP
2
GAP
DHAP
ATP
NAD
1.3BPG
NADH
ADP
Part of monosaccharide metabolism
Red: external metabolites
ATP
Pyr
ADP
PEP
2PG
ATP
3PG
ADP
G6P
F6P
FP
GAP
2
DHAP
ATP
ADP
1st elementary mode: glycolysis
NAD
1.3BPG
NADH
F6P
ATP
FP2
ADP
2nd elementary mode: fructose-bisphosphate cycle
ATP
X5P
CO2 Ru5P
NADPH
NADP
S7P
E4P
ADP
GAP
R5P
PEP
F6P
6PG
2PG
GO6P
3PG
ATP
NADPH
NADP
Pyr
ADP
G6P
F6P
FP
2
GAP
DHAP
ATP
NAD
1.3BPG
NADH
ADP
4 out of 7 elementary modes in glycolysispentose-phosphate system
S. Schuster, D.A. Fell, T. Dandekar:
Nature Biotechnol. 18 (2000) 326-332
Software for computing elementary modes
ELMO (in Turbo-Pascal) - C. Hilgetag
EMPATH (in SmallTalk) - J. Woods
METATOOL (in C) - Th. Pfeiffer, F. Moldenhauer,
A. von Kamp, M. Pachkov
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
On-line computation:
pHpMetatool - H. Höpfner, M. Lange
http://pgrc-03.ipk-gatersleben.de/tools/phpMetatool/index.php
Optimization: Maximizing molar yields
ATP
X5P
CO2 Ru5P
NADPH
NADP
S7P
E4P
ADP
GAP
R5P
PEP
F6P
6PG
2PG
GO6P
3PG
ATP
NADPH
NADP
Pyr
ADP
G6P
F6P
FP
2
GAP
DHAP
ATP
NAD
1.3BPG
NADH
ADP
ATP:G6P yield = 3 ATP:G6P yield = 2
Maximization of tryptophan:glucose yield
Model of 65 reactions in the central metabolism of E. coli.
26 elementary modes. 2 modes with highest tryptophan:
glucose yield: 0.451.
PEP
Pyr
S. Schuster, T. Dandekar, D.A. Fell,
Trends Biotechnol. 17 (1999) 53
Glc
233
G6P
Anthr
3PG
PrpP
GAP
105
Trp
Optimality of metabolism
Example of theoretical prediction: Maximization of
pathway flux subject to constant total enzyme
concentration (Waley, 1964; Heinrich, Schuster
and Holzhütter, 1987)
Ej 
Etot


q  1 q r  j 
qr 1
(q: equilibrium constant)
Optimal
enzyme
concn.
1
2
3
4
Position in the chain
 However, there are more objective functions
besides maximization of pathway flux
 Maximum stability and other criteria have been
suggested (Savageau, Heinrich, Schuster, …)
 Optimality criterion for a particular species need
not coincide with optimality criterion for a
community of species
 Optimization theory needs to be extended to
cope with this problem  Game theory
Maximum flux vs.
maximum molar yield
Example: Fermentation has a low yield
(2 moles ATP per mole of glucose) but high
ATP production rate (cf. striated muscle);
respiration has a high yield (>30 moles
ATP per mole of glucose) but low ATP
production rate
Two possible strategies
Fermentation
CO2
Gluc
G6P
ATP ADP
F6P
ATP
Pyr
ADP ADP ATP ADP ATP
Ac.ald.
EtOH
Game-theoretical problem
The two cells (strains, species) have two strategies.
The outcome for each of them depends on their own
strategy as well as on that of the competitor.
Respiration can be considered as a cooperative strategy
because it uses the resource more efficiently.
By contrast, fermentation is a competitive strategy.
Switch between high yield and high rate has been shown
for bacterium Holophaga foetida growing on methoxylated
aromatic compounds (Kappler et al., 1997).
How to define the payoff?
We propose taking the steady-state population density as the
payoff. Particular meaningful in spatially distributed systems
because spreading of strain depends on population density.
Dependence of the payoff on the strategy of the other species
via the steady-state substrate level. This may also be used as
a source of information about the strategy of the other species.
Population payoffs and resource level
T. Frick, S. Schuster: An example of the prisoner's dilemma in biochemistry.
Naturwissenschaften 90 (2003) 327-331.
Payoff matrix of the „game“
of two species feeding on the same resource
We take the steady-state population density as the payoff.
Values calculated with parameter values from model in Pfeiffer et al. (2001).
Cooperative strategy
Cooperative
strategy
3.2
Competitive
strategy
5.5
Competitive strategy
0.0
larger than
in Nash equilibr.
2.7
Nash equilibrium
This is equivalent to the „Prisoner‘s dilemma“
Prisoner‘s dilemma
 If prisoner A reveals the plan of escape to the jail
director, while prisoner B does not, A is set free and
gets a reward of 1000 ₤. B is kept in prison for 10
years.
 The same vice versa.
 If none of them betrays, both can escape.
 If both betray, they are kept in prison for 5 years.
 They are allowed to know what the other one does.
Payoff matrix
for the Prisoner‘s Dilemma
A
B
Cooperate
Pareto optimum
Cooperate
Defect
Escape/Escape
Escape + Reward/
10 years prison
Defect
10 years prison/
Escape + Reward
5 years prison/
5 years prison
Nash equilibrium
System equations
Substrate level:
S   N R J RS (S )  N F J FS (S )
Population densities:
N R  cJRATP S NR  dNR
N F  cJFATP S NF  dNF
v, constant substrate input rate; JS, resource uptake rates;
JATP, ATP production rates; d, death rate.
T. Pfeiffer, S. Schuster, S. Bonhoeffer: Cooperation and
Competition in the Evolution of ATP Producing Pathways.
Science 292 (2001) 504-507.
Michaelis-Menten rate laws
J S  
S
i
J
ATP
i
Vi maxS
K S
M
i
 yi J
S
i
(yi = ATP:glucose yield of pathway i)
Do we need anthropomorphic concepts?
 …such as „strategy“, „cooperation“, „altruism“
 NO!! They are auxiliary means to understand coevolution more easily
 The game-theoretical problem can alternatively be
described by differential equation systems. Nash
equilibrium is asymptotically stable steady state
A paradoxical situation:
 Both species tend to maximize their
population densities.
 However, the resultant effect of these two
tendencies is that their population densities
decrease.
The whole can be worse
then the sum of its parts!
n-Player games
„Tragedy of the commons“ - Generalization of the
prisoner‘s dilemma to n players
Commons: common possession such as the pasture of a
village or fish stock in the ocean. Each of n users of the
commons may think s/he could over-use it without
damaging the others too much. However, when all of
them think so…
Biological examples
 S. cerevisiae and Lactobacilli use
fermentation even under aerobiosis, if
sufficient glucose is available. They behave
„egotistically“.
 Other micro-organisms, such as
Kluyverymyces, use respiration.
Multicellular organisms
 For multicellular organisms, it would be
disadvantageous if their cells competed against
each other.
 In fact, most cell types in multicellular organisms
use respiration.
 Exception: cancer cells. Perhaps, their „egotistic“
behaviour is one of the causes of their pathological
effects.
„Healthy“ exceptions:
 Cells using fermentation in multicellular
organisms
Erythrocytes small volume
prevents mitochondria.
Striated muscle during heavy
exercise - diffusion of oxygen
not fast enough.
Astrocytes – division of
labour with neurons,
which degrade lactate to
carbon dioxide and water.
How did cooperation evolve?
 Deterministic system equations: fermenters
always win.
 However, they can only sustain low population
densities. Susceptible to stochastic extinction.
 Further effects in spatially distributed systems.
Cooperating cells can form aggregates.
Possible way out of the dilemma: Evolution in a
2D (or 3D) habitat with stochastic effects
Blue: respirators
Red: fermenters
Yellow: both
Black: empty sites
At low cell diffusion rates and low substrate input,
respirators can win in the long run.
Aggregates of cooperating cells can be seen as an
important step towards multicellularity.
T. Pfeiffer, S. Schuster, S. Bonhoeffer: Cooperation and
Competition in the Evolution of ATP Producing Pathways.
Science 292 (2001) 504-507.
Biotechnological relevance
 Communities of different bacteria species
 Competition for the same substrate or
division of labour so that the product of one
bacterium is used as a substrate by another
one (crossfeeding, like in astrocytes and
neurons)
 Pathways operating in microbial
communities = „consortium pathways“
Example: Degradation
of 4-chlorosalicylate
From: O. Pelz et al.,
Environm. Microb.
1 (1999), 167–174
Another example: E. coli
 E. coli in continuous culture (chemostat)
evolves, over many generations, so as to
show stable polymorphism (Helling et al.,
1987)
 One resulting strain degrades glucose to
acetate, another degrades acetate to CO2 and
water
 Example of intra-species crossfeeding
Conclusions
 „Analysis“ (Greek) means decomposition
 Scientists tend to analyse: „function of a
gene“, „role of an calcium oscillations“,
„impact of an enzyme“
However:
The ability of a steel ship to be afloat
cannot be explained by decomposition
Analytical vs. holistic approaches
 Decomposition should not be overdone
 Example elementary flux modes: smallest
functional units, rather than decomposition into
enzymes
 It depends on the question at which level the
description should be made
 Systems biology motivated by reasoning that the
whole is more than the sum of ist parts (sometimes
worse than…)
 Game theory is one possible holistic approach
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)
•Peer Bork (EMBL Heidelberg)
•Reinhart Heinrich, Thomas Höfer (HU Berlin)
•I. Zevedei-Oancea (formerly my group, now HU Berlin)
•Hans Westerhoff (VU Amsterdam)
• and others
•Acknowledgement to DFG for financial support