Metabolic Pathway Analysis as Part of Systems Biology
Stefan SchusterDept. of Bioinformatics
Friedrich Schiller University Jena, Germany
Friedrich Schiller(1759-1805)
Famous people at Jena University:
Ernst Haeckel(1834-1919, Biogenetic rule)
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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:
RobustnessFlexibilityFragilityOptimalityModularity
Theoretical Methods
Dynamic SimulationStability and bifurcation analysesMetabolic Control Analysis (MCA)Metabolic Pathway AnalysisMetabolic Flux Analysis (MFA)Optimizationand others
Theoretical Methods
Dynamic SimulationStability and bifurcation analysesMetabolic Control Analysis (MCA)Metabolic Pathway AnalysisMetabolic Flux Analysis (MFA)Optimizationand 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“
S. Schuster und C. Hilgetag: J. Biol. Syst. 2 (1994) 165-182
non-elementary flux mode
elementary flux modes
An elementary mode is a minimal set of enzymes thatcan operate at steady state with all irreversible reactions used in the appropriate direction
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
All flux distributions in the living cell are non-negative linear combinations of elementary modes
Mathematical background
Steady-state condition NV = 0Sign 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)
flux1
flux2
flux3
generating vectors
NADP
NADPH
NADP
NADPH
NADHNAD
ADP
ATP
ADP
ATP
CO2
ATP ADP
G6P
X5P
Ru5P
R5P
S7P
GAP
GAP
6PG
GO6P
F6P FP2
F6P
DHAP
1.3BPG
3PG
2PG
PEP
E4P
Part of monosaccharide metabolism
Red: external metabolites
Pyr
NADHNAD
ADP
ATP
ADP
ATP
ATP ADP
G6P GAPF6P FP2
DHAP
1.3BPG
3PG
2PG
PEP
1st elementary mode: glycolysis
Pyr
2nd elementary mode: fructose-bisphosphate cycle
ATP ADP
F6P FP2
4 out of 7 elementary modes in glycolysis-pentose-phosphate system
NADP
NADPH
NADP
NADPH
NADHNAD
ADP
ATP
ADP
ATP
CO2
ATP ADP
G6P
X5P
Ru5P
R5P
S7P
GAP
GAP
6PG
GO6P
F6P FP2
F6P
DHAP
1.3BPG
3PG
2PG
PEP
E4P
S. Schuster, D.A. Fell, T. Dandekar:Nature Biotechnol. 18 (2000) 326-332
Pyr
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. Mendesand 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
NADP
NADPH
NADP
NADPH
NADHNAD
ADP
ATP
ADP
ATP
CO2
ATP ADP
G6P
X5P
Ru5P
R5P
S7P
GAP
GAP
6PG
GO6P
F6P FP2
F6P
DHAP
1.3BPG
3PG
2PG
PEP
E4P
Optimization: Maximizing molar yields
ATP:G6P yield = 3 ATP:G6P yield = 2
Pyr
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.
Glc
G6P
233
Anthr
Trp105
PEPPyr
3PGGAP
PrpP
S. Schuster, T. Dandekar, D.A. Fell,Trends Biotechnol. 17 (1999) 53
Optimality of metabolism Example of theoretical prediction: Maximization of
pathway flux subject to constant total enzyme concentration (Waley, 1964; Heinrich, Schuster
and Holzhütter, 1987)
1
1
r
jrtot
jq
qqEE
Position in the chain
Optimalenzymeconcn.
1 2 3 4
(q: equilibrium constant)
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
ADP ATP ADP ATPATP ADP
G6P F6P Pyr
ATP ADP
Gluc Ac.ald.
CO2
EtOH
Fermentation
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 shownfor bacterium Holophaga foetida growing on methoxylatedaromatic compounds (Kappler et al., 1997).
Game-theoretical problem
How to define the payoff?
We propose taking the steady-state population density as thepayoff. Particular meaningful in spatially distributed systemsbecause 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 asa 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
Cooperative strategy Competitive strategy
Cooperative 3.2 0.0 strategy larger than
in Nash equilibr.
Competitive 5.5 2.7strategy
This is equivalent to the „Prisoner‘s dilemma“
We take the steady-state population density as the payoff. Values calculated with parameter values from model in Pfeiffer et al. (2001).
Nash equilibrium
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 matrixfor the Prisoner‘s Dilemma
Cooperate Defect
Nash equilibrium
Cooperate
Defect
Escape/Escape
A B
10 years prison/Escape + Reward
Escape + Reward/10 years prison
5 years prison/5 years prison
Pareto optimum
)()( SJNSJNS SFF
SRR
RR
ATPRR
dNNScJN
FF
ATPFF
dNNScJN
Substrate level:
Population densities:
v, constant substrate input rate; JS, resource uptake rates;JATP, ATP production rates; d, death rate.
System equations
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
SK
SVSJ
Mi
iSi
max
Sii
ATPi
JyJ
(yi = ATP:glucose yield of pathway i)
Do we need anthropomorphic concepts?
…such as „strategy“, „cooperation“, „altruism“NO!! They are auxiliary means to understand co-
evolution more easilyThe 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 avillage or fish stock in the ocean. Each of n users of thecommons may think s/he could over-use it withoutdamaging 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 organismsFor 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 oflabour with neurons,which degrade lactate tocarbon 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
At low cell diffusion rates and low substrate input,respirators can win in the long run.
Blue: respirators
Red: fermenters
Black: empty sites
Yellow: both
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 speciesCompetition 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“
From: O. Pelz et al.,Environm. Microb.1 (1999), 167–174
Example: Degradation of 4-chlorosalicylate
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 decompositionScientists tend to analyse: „function of a
gene“, „role of an calcium oscillations“, „impact of an enzyme“
The ability of a steel ship to be afloat
cannot be explained by decomposition
However:
Analytical vs. holistic approaches
Decomposition should not be overdoneExample 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
•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
Cooperations