Design principles
of metabolic networks
An extremely simplified representation
of a cellular metabolism
…which you will have to memorize
for this course, not!
The primary functions
of metabolism
Use the resources available in the environment
in order to provide energy, redox equivalents
and building materials for maintaining an
organism and building a new one
Synthesis and turnover of macromolecules and
structural components
Damage prevention/repair
Other services (synthesis of “messengers” and toxins,
movement, etc.)
… goal has to be achieved while
attending to many constraints
Stoichiometric & balancing
Thermodynamic
Osmotic pressure & solvent capacity
Physical-chemical properties of metabolites
Permeability
Solubility
Non-enzymatic reactivity
Topological
Dynamic and system-operational
Stability
Responsiveness
Robustness
…
The constraints
on metabolism
1. Stoichiometric constraints
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
Most metabolic processes have well-defined, known
stoichiometries, which reflect atom and charge balancing:
Ex: 1 GSSG + 1 NADPH + 1 H+ 2 GSH + 1 NADP+
Stoichiometric coefficients
C20H30N6O12S22- + C21H26N7O17P34- + H+ 2 C10H16N3O6S- + C21H25N7O17P33-
41 C, 57 H, 13 N, 29 O, 3 P, -5 41 C, 57 H, 13 N, 29 O, 3 P, -5
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
v12 X2
v41 dX 1
X4 X1 v 41 (2v 12 v 13 )
v13
X3
dt
Instantaneous rate of X1 accumulation =
Instantaneous rate of X4 conversion into X1 –
(Instantaneous rate of X1 conversion into X2 +
Instantaneous rate of X1 conversion into X3)
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
Not all combinations of fluxes can be indefinitely sustained
v12 X2 v12 X2 v12 X2
v41 v41 v41
X4 X1 X4 X1 X4 X1
v13 v13 v13
X3 X3 X3
X1 X1 X1
t t t
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
Steady state: No net accumulation or dilution of metabolites
v12 X2
v41 dX 1
X4 X1 0 v 41 (2v 12 v 13 )
v13
X3
dt
0=
Instantaneous rate of X4 conversion into X1 –
(Instantaneous rate of X1 conversion into X2 +
Instantaneous rate of X1 conversion into X3)
Stoichiometry defines relationships between fluxes at steady state
Elemental balancing
Avg. elemental comp. of S. cerevisiae: CH1.75N0.15O0.60P0.009S0.0019M0.018
Constituent/Nutrient Elemental composition
Protein CH1.58N0.27O0.32S0.003
Carbohydrate CH1.67O0.83
Lipids CH1.87N0.01O0.14P0.01
RNA CH1.23N0.39O0.74P0.1
DNA CH1.25N0.38O0.61P0.1
Glucose CH2O1
Glutamine CH2N0.4O0.6
Phosphate HO4 P
Sulphate O4S
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
Q: What combinations of fluxes are possible
for the network below at steady state ?
v4 v6
X1 X5
v1
v2 v3
2 inputs 2 outputs
X2 X6
X3
v5 v7
X4
Are these fluxes independent?
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
What combinations of fluxes are possible
for the network below at steady state ?
v4 v6 dX 1
v 4 v1 0
X1 X5 dt
dX 2
v1 v 5 v1 0
v2 v3 dt
dX 3
v5 v7 0
dt
X2 X6 dX 4
v7 v5 0
X3 dt
v5 v7 dX 5
v 1 (v 2 v 3 ) v 6 0
X4 dt
dX 6
v 1 (v 2 v 3 ) v 7 0
v 4 v 5 v 6 v 7 v1! dt
v2 v3 Only 2 degrees of freedom!
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
How can the network be made more versatile?
v4 v6 dX 1
v 4 v1 0
X1 X5 dt
dX 2
v1 v 5 v1 0
v2 v3 dt
dX 3
v5 v7 0
dt dX 3 dX 4 d (X 3 X 4 )
X2 X6 0
dX 4 dt dt dt
v7 v5 0
X3 dt
v5 v7 dX 5
v 1 (v 2 v 3 ) v 6 0
X4 dt
dX 6
v 1 (v 2 v 3 ) v 7 0
dt
Degrees of freedom = fluxes - (metabolites - conserv. relatships)
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
How can the network be made more versatile?
By connecting metabolites through additional pathways!
v4 v6 dX 1
v 4 v1 0
X1 X5 dt
dX 2
v1 v 5 v1 v 8 0
v2 v3 dt v1 v 6 v 4
dX 3
v5 v7 0 v7 v5
v8 dt
X2 X6 dX 4 v2 v3
v7 v5 0
X3 dt
v8 v5 v4
v5 v7 dX 5
v 1 (v 2 v 3 ) v 6 0
X4 dt
dX 6
v 1 (v 2 v 3 ) v 7 v 8 0
dt
v6v7, v4v5 are now possible
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
Multiple modes of functioning
v4 v6 v4 v6
X1 X5 X1 X5
v1 v1
v2 v3 v2 v3
v8 v8
X2 X6 X2 X6
X3 X3
v5 v7 v5 v7
X4 X4
One pathway, multiple functions
Stoichiometric constraints
Multiple modes of functioning in the pentose phosphate pathway
Stoichiometric constraints
Multiple modes of functioning in the pentose phosphate pathway
Stoichiometric constraints
Multiple modes of functioning in the pentose phosphate pathway
Cell requires both RIBOSE and NADPH
6 Glucose-6-P + 12 NADP+ + 6 H2O 6 Ribose-5-P + 12 NADPH + 12 H+ + 6 CO2
Glucose-6-P + 2 NADP+ + H2O Ribose-5-P + 2 NADPH + 2 H+ + CO2
Stoichiometric constraints
Chemical reactions do not create, destroy or transmute atoms
Redundant pathways also make metabolism more robust!
v4 v6
X1 X5
v1
v2 v3
Presence of enzyme catalyzing v8 makes
v8
X2 X6 possible to produce X5 and X6 even if
X3 enzyme catalyzing v1 is missing.
v5 v7
X4
Stoichiometric constraints
Key points:
Adaptation to changing environment
requires versatile metabolism
Metabolic versatility requires highly
connected networks (“redundant”
pathways)
“Redundant” pathways make metabolism
more robust against enzyme inactivation
Elemental balancing
Avg. elemental comp. of S. cerevisiae: CH1.75N0.15O0.60P0.009S0.0019M0.018
Constituent/Nutrient Elemental composition
Protein CH1.58N0.27O0.32S0.003
Carbohydrate CH1.67O0.83
Lipids CH1.87N0.01O0.14P0.01
RNA CH1.23N0.39O0.74P0.1
DNA CH1.25N0.38O0.61P0.1
Glucose CH2O1
Glutamine CH2N0.4O0.6
Phosphate HO4 P
Sulphate O4S
Stoichiometric constraints
Letters, syllables, words and sentences
in the biochemical text
NADPH Phosphates
Nicotinamide
Adenine
Ribose
AMP NMP
Large metabolites and macromolecules are
built from a hierarchy of molecular modules
Stoichiometric constraints
Letters, syllables, words and sentences
in the biochemical text
Complex nutrients Simple nutrients
Low probability of being High probability of being
similar to needed identical to needed
molecular modules molecular modules
Direct assimilation would Simple to recognize and
require expensive specific internalize
recognition and
internalization system
Assimilated intact, may
also be disassembled for
Disassembled upon energy production & supply of
assimilation simpler molecular modules
Stoichiometric constraints
Letters, syllables, words and sentences
in the biochemical text
NADPH Phosphates
Nicotinamide
Adenine
Ribose
AMP NMP
Large metabolites and macromolecules are
built from a hierarchy of molecular modules
Stoichiometric constraints
Letters, syllables, words and sentences
in the biochemical text
Complex nutrients Simple nutrients
Low probability of being High probability of being
similar to needed identical to needed
molecular modules molecular modules
Direct assimilation would Simple to recognize and
require expensive specific internalize
recognition and
internalization system
Assimilated intact, may
also be disassembled for
Disassembled upon energy production & supply of
assimilation simpler molecular modules
Stoichiometric constraints
Letters, syllables, words and sentences
in the biochemical text
Metabolism has a bow-tie architecture
- Highly connected (hubs)
Metabolic “currencies”
Macromolecules
- Possibly complex
- Possibly complex
- Very diverse
- Very diverse
Catabolism
Anabolism
- Simple, but…
- Low diversity
Nutrients
(Disassembly,
(Assembly)
energy)
Stoichiometric constraints
Hubs in metabolism
Comprehensive reconstructions of metabolism
Genome sequence
Escherichia coli – a bacterium
Gene list
Forster et al. (2003). Genome Res. 13: 244-53
Enzymes Saccharomyces cerevisiae – yeast
Edwards & Palsson (2000). PNAS 97: 5528-33
Reactions
Stoichiometric constraints
Hubs in metabolism
Most metabolites participate in cerevisiae (1123 reactions)
E. coli (1167 reactions) S. few
reactions (pathway intermediates)
# metabolites
200 200
100 100
50 50
20 20
10 10
5 A few metabolites participate
5
2 in many reactions (hubs)
2
1 1
1 5 10 50 100 500 1 2 5 10 20 50 100
# reactions entered # reactions entered
“Small world” network
Stoichiometric constraints
Hubs in metabolism
E. coli (1167 reactions) S. cerevisiae (1123 reactions)
Metabolite Consumed Produced Metabolite Consumed Produced
H+ 225 370 H+ ? ?
H2 O 229 82 H2 O ? ?
ATP 173 38 ATP 138 36
Pi 35 142 Pi 37 106
ADP 35 140 ADP 40 103
NAD+ 49 42 CO2 15 76
NADH 39 47 NADP+ 19 62
PPi 8 72 NADPH 60 17
CO2 8 58 PPi 10 63
NADP+ 19 45 NAD+ 43 26
NADPH 44 18 Glu 32 37
Glu 24 33 NADH 21 39
Pyr 14 43 CoA 21 33
CoA 22 24 NH4+ 14 39
NH4+ 7 34 AMP 13 37
AMP 7 33 KG 25 25
KG 20 17 O2 32 8
AcCoA 17 14 AcCoA 20 14
Succ 8 18 ACP 2 26
PEP 21 4 Pyr 11 15
Stoichiometric constraints
Hubs in metabolism
E. coli (1167 reactions) S. cerevisiae (1123 reactions)
Metabolite Consumed Produced Metabolite Consumed Produced
H+ 225 370 H+ ? ?
H2 O 229 82 H2 O ? ?
ATP 173 38 ATP 138 36
Pi 35 142 Pi 37 106
ADP 35 140 ADP 40 103
NAD+ 49 42 CO2 15 76
NADH 39 47 NADP+ 19 62
PPi 8 72 NADPH 60 17
CO2 8 58 PPi 10 63
NADP+ 19 45 NAD+ 43 26
NADPH 44 18 Glu 32 37
Glu 24 33 NADH 21 39
Pyr 14 43 CoA 21 33
CoA 22 24 NH4+ 14 39
NH4+ 7 34 AMP 13 37
AMP 7 33 KG 25 25
KG 20 17 O2 32 8
AcCoA 17 14 AcCoA 20 14
Succ 8 18 ACP 2 26
PEP 21 4 Pyr 11 15
Some hub metabolites are not so simple!
Stoichiometric constraints
Hubs in metabolism
E. coli (1167 reactions) S. cerevisiae (1123 reactions)
Metabolite Consumed Produced Metabolite Consumed Produced
H+ 225 370 H+ ? ?
H2 O 229 82 H2 O ? ?
ATP 173 38 ATP 138 36
Pi 35 142 Pi 37 106
ADP 35 140 ADP 40 103
NAD+ 49 42 CO2 15 76
NADH 39 47 NADP+ 19 62
PPi 8 72 NADPH 60 17
CO2 8 58 PPi 10 63
NADP+ 19 45 NAD+ 43 26
NADPH 44 18 Glu 32 37
Glu 24 33 NADH 21 39
Pyr 14 43 CoA 21 33
CoA 22 24 NH4+ 14 39
NH4+ 7 34 AMP 13 37
AMP 7 33 KG 25 25
KG 20 17 O2 32 8
AcCoA 17 14 AcCoA 20 14
Succ 8 18 ACP 2 26
PEP 21 4 Pyr 11 15
Simple metabolites are rarely directly incorporated in other metabolites…
Stoichiometric constraints
Hubs in metabolism
E. coli (1167 reactions) S. cerevisiae (1123 reactions)
Metabolite Consumed Produced Metabolite Consumed Produced
H+ 225 370 H+ ? ?
H2 O 229 82 H2 O ? ?
ATP 173 38 ATP 138 36
Pi 35 142 Pi 37 106
ADP 35 140 ADP 40 103
NAD+ 49 42 CO2 15 76
NADH 39 47 NADP+ 19 62
PPi 8 72 NADPH 60 17
CO2 8 58 PPi 10 63
NADP+ 19 45 NAD+ 43 26
NADPH 44 18 Glu 32 37
Glu 24 33 NADH 21 39
Pyr 14 43 CoA 21 33
CoA 22 24 NH4+ 14 39
NH4+ 7 34 AMP 13 37
AMP 7 33 KG 25 25
KG 20 17 O2 32 8
AcCoA 17 14 AcCoA 20 14
Succ 8 18 ACP 2 26
PEP 21 4 Pyr 11 15
...rather, they are usually transferred from carrier molecules
Stoichiometric constraints
Hubs in metabolism
Metabolic networks have many two-reaction cycles
Stoichiometric constraints
Hubs in metabolism
Metabolic networks have many two-reaction cycles
% consecutive multi-substrate, multi-
product reactions that form a cycle:
E. coli: 67% S. cerevisiae: 63%
Reactions participating in 2-reaction cycles:
E. coli: 75% S. cerevisiae: 67%
Excluding:
• Ubiquitous metabolites H2O, H+
• Reverse reactions
• Redundant reactions
Stoichiometric constraints
Hubs in metabolism
Some cycled intermediates are shared among many reactions
X2
X1
Stoichiometric constraints
Hubs in metabolism
Top cycled pairs of metabolites
# reactions
ADP / ATP X2 103
NADP+ / NADPH 71
NAD+ / NADH 48
CoA / AcCoA 26
AMP / ATP X 25
1
KG / Glu 21
Glu / Gln 13
Data for S. cerevisiae
Stoichiometric constraints
Hubs in metabolism
Top cycled pairs of metabolites
ADP / ATP X2 R~Pi
NADP+ / NADPH R~H
NAD+ / NADH R~H
CoA / AcCoA R~Ac
AMP / ATP X R~PPi
1
KG / Glu R~NH2
Glu / Gln R~NH2
All good group-transfer molecules
Stoichiometric constraints
Hubs in metabolism
NADP+/NADPH
ADP / ATP
CoA / AcCoA
...
metabolic currencies
Biosynt. precursors,
Facilitated moiety transfer mediated by carrier molecules
Nutrients Catabolism Anabolism Macromolecules
Stoichiometric constraints
Hubs in metabolism
Three alternative ways to transfer a moiety (M)
between a donor (D:M) and an acceptor (A)
D:M C A:M
D C:M A
cells
Why do A:M prefer this one?
D:M D:M A
D M A D A:M
Stoichiometric constraints
Hubs in metabolism
Three alternative ways to transfer a moiety (M)
between a donor (D:M) and an acceptor (A)
D:M C A:M
D C:M A
D:M A:M D:M A
D M A D A:M
Stoichiometric constraints
Hubs in metabolism
Q: How many enzymes are necessary to permit transferring a
moiety from any of n donors to any of m acceptors…
… by direct transfer?
n donors m acceptors
…
…
Stoichiometric constraints
Hubs in metabolism
Q: How many enzymes are necessary to permit transferring a
moiety from any of n donors to any of m acceptors…
… hub-mediated?
n donors m acceptors
…
…
Stoichiometric constraints
Hubs in metabolism
Q: How many enzymes are necessary to permit transferring a
moiety from any of n donors to any of m acceptors…
… by direct transfer?
n donors m acceptors
…
…
nm enzymes
Stoichiometric constraints
Hubs in metabolism
Q: How many enzymes are necessary to permit transferring a
moiety from any of n donors to any of m acceptors…
… hub-mediated?
n donors m acceptors
…
…
N+m enzymes
Stoichiometric constraints
Hubs in metabolism
This arrangement creates a moiety ”market”,
which facilitates regulation of supply and demand as function
of overall availability of the moiety
n donors m acceptors
…
…
Stoichiometric constraints
Hubs in metabolism
Three alternative ways to transfer a moiety (M)
between a donor (D:M) and an acceptor (A)
D:M C A:M
D C:M A
D:M A:M D:M A
Requires too many enzymes,
complex regulation
D M A D A:M
Stoichiometric constraints
Hubs in metabolism
Key points:
Hierarchical dis/assembly bowtie architecture
Few metabolites participate in many reactions,
most in a few
Most of former metabolites mediate transfer of
molecular parts (moieties)
Compared to direct transfer, hub-mediated
transfer requires less enzymes, increases
versatility, simplifies regulation