Metabolic Pathway Analysis as Part of Systems Biology

1
Metabolic Pathway Analysis as Part of Systems
Biology

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

2
Famous people at Jena University
Friedrich Schiller (1759-1805)
Ernst Haeckel (1834-1919, Biogenetic rule)
3
From ExPASy
4
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

• 1960s Dynamic simulation of biochemical systems
• by David Garfinkel

• Metabolic Control Analysis (1973 H. Kacser/J.
  Burns,
• R. Heinrich/T.A. Rapoport, 1980s Hans
  Westerhoff)

• Biochemical Systems Theory (1970s Michael
• Savageau)

5

• Since end 1990s 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

6
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

7
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

8
Features often studied in Systems Biology

• Robustness
• Flexibility
• Fragility
• Optimality
• Modularity

9
Theoretical Methods

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

10
Theoretical Methods

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

11
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

12
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

13
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 und C. Hilgetag J. Biol. Syst. 2
(1994) 165-182
14
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
15
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.
16
Geometrical interpretation
Elementary modes correspond to generating vectors
(edges) of a convex polyhedral cone ( pyramid)
in flux space (if all modes are irreversible)
17
flux3
flux2
generating vectors
flux1
18
Pyr
ATP
X5P
S7P
E4P
ADP
Ru5P
CO2
PEP
NADPH
GAP
F6P
R5P
NADP
6PG
2PG
3PG
GO6P
ATP
NADPH
ADP
NADP
G6P
GAP
F6P
FP
1.3BPG
2
NADH
NAD
DHAP
ATP
ADP
Part of monosaccharide metabolism
Red external metabolites
19
Pyr
ATP
2
ADP
PEP
2
2PG
2
3PG
ATP
2
ADP
G6P
GAP
F6P
FP
1.3BPG
2
2
NADH
NAD
DHAP
ATP
ADP
1st elementary mode glycolysis
20
F6P
FP
2
ATP
ADP
2nd elementary mode fructose-bisphosphate cycle
21
Pyr
ATP
X5P
2
S7P
E4P
2
2
2
4
ADP
Ru5P
CO2
PEP
NADPH
GAP
F6P
2
R5P
6
3
2
NADP
2
6PG
2PG
3
2
6
3PG
GO6P
ATP
NADPH
2
6
ADP
3
5
NADP
GAP
F6P
FP
1.3BPG
G6P
2
2
2
NADH
NAD
DHAP
ATP
ADP
4 out of 7 elementary modes in glycolysis- pentose
-phosphate system
S. Schuster, D.A. Fell, T. Dandekar Nature
Biotechnol. 18 (2000) 326-332
22
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/phpMetatoo
l/index.php
23
Optimization Maximizing molar yields
Pyr
ATP
X5P
2
S7P
E4P
2
ADP
Ru5P
CO2
PEP
NADPH
GAP
F6P
R5P
3
2
NADP
6PG
2PG
3
2
3PG
GO6P
ATP
NADPH
2
ADP
3
NADP
GAP
F6P
FP
1.3BPG
G6P
2
2
2
NADH
NAD
DHAP
ATP
ADP
ATPG6P yield 3 ATPG6P yield 2
24
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
25
Optimality of metabolism

• Example of theoretical prediction
  Maximization of pathway flux subject to constant
  total enzyme concentration (Waley, 1964
  Heinrich, Schuster
• and Holzhütter, 1987)

(q equilibrium constant)
Optimal enzyme concn.
1
2
3
4
Position in the chain
26

• 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

27
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 (gt30 moles ATP per
  mole of glucose) but low ATP production rate

28
Two possible strategies
Fermentation
Glucose
Ethanol
(Pyruvate,
Lactate)
Respiration
2 ATP
H2O CO2
32 ATP
cell A
cell B
respiration or fermentation?
respiration or fermentation?
29
Fermentation
CO2
Gluc
EtOH
Pyr
Ac.ald.
G6P
F6P
2
2
ADP
ATP
ADP
ATP
ATP
ADP
ATP
ADP
30
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).
31
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.
32
Population payoffs and resource level
T. Frick, S. Schuster An example of the
prisoner's dilemma in biochemistry.
Naturwissenschaften 90 (2003) 327-331.
33
Payoff matrix of the gameof 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 Competitive strategy
Cooperative 3.2
0.0 strategy
larger than in Nash
equilibr. Competitive 5.5
2.7 strategy This
is equivalent to the Prisoners dilemma
Nash equilibrium
34
Prisoners 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.

35
Payoff matrixfor the Prisoners Dilemma
B
Cooperate Defect
A
Pareto optimum
10 years prison/ Escape Reward
Cooperate
Escape/Escape
5 years prison/ 5 years prison
Escape Reward/ 10 years prison
Defect
Nash equilibrium
36
System equations
Substrate level
Population densities
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.
37
Michaelis-Menten rate laws
(yi ATPglucose yield of pathway i)
38
Do we need anthropomorphic concepts?

• such as strategy, cooperation, altruism
• NO!! They are auxiliary means to understand
  co-evolution more easily
• The game-theoretical problem can alternatively be
  described by differential equation systems. Nash
  equilibrium is asymptotically stable steady state

39
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!
40
n-Player games
Tragedy of the commons - Generalization of the
prisoners 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
41
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.

42
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.

43
Healthy exceptions

• Cells using fermentation in multicellular
  organisms

Striated muscle during heavy exercise -
diffusion of oxygen not fast enough.
Erythrocytes - small volume prevents
mitochondria.
Astrocytes division of labour with
neurons, which degrade lactate to carbon dioxide
and water.
44
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.

45
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.
46
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

47
Example Degradation of 4-chlorosalicylate
From O. Pelz et al., Environm. Microb. 1 (1999),
167174
48
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

49
Conclusions

• Analysis (Greek) means decomposition
• Scientists tend to analyse function of a gene,
  role of an calcium oscillations, impact of an
  enzyme

50
The ability of a steel ship to be afloat cannot
be explained by decomposition
However
51
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

52
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