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Optimality
in Carbon
Metabolism
Ron Milo
Department of Plant Sciences
Weizmann Institute of Science
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Arren Bar-Even
Elad Noor
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Uri Alon
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What limits maximal
growth rates?
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What governs the efficiency of
photosynthesis and carbon fixation?
Why is Rubisco slow and
non specific?
What governs
maximal growth rates?
growth
Design principles in
photosynthesis –
wavelengths used
and saturation
Synthetic carbon
fixation pathways
for higher efficiency
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Are there simplifying principles to the structure of
the central carbohydrate metabolism network?
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An illustrative example: the Pentose Phosphate cycle

Converts between 5 and 6 carbon sugars

e.g Ribose-5P is used for making nucleotides

e.g Fructose-6P is used for building the cell wall

Was analyzed as an optimization problem (Meléndez-Hevia & Isodoro 1994)

We use this as a starting point
The Pentose Phosphate Pathway defined
as a game
Goal:
5
5
5
5
5
5
Turn 6 Pentoses into 5 Hexoses
?
Rules:
Transfer 2-3 carbons between two
molecules
Never leave a molecule with 1-2
carbons
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6
6
6
6
TK
Optimization function:
Minimize the number of steps
(simplicity)
TA
E. Meléndez-Hevia et al. (Journal of theoretical Biology 1994)
Solution to Pentose Phosphate game in 7 steps



Corresponds to
natural pathway
Doesn't explain why
the rules exist
Supports the idea of
simplicity
Are there simplifying principles to the structure of
the central carbohydrate metabolism network?
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We develop a method to find shortest path from A to B
N
W
E
S
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But what are the “steps” allowed in
biochemistry?
?
?
?
?
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All possible reaction types are
explored
aldehyde dehydrogenase (CoA):
pyruvate ↔ acetyl-CoA + CO2
isomerase (keto to enol):
pyruvate ↔ enolpyruvate
kinase (carboxyl):
pyruvate ↔ pyruvate-P
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Hatzimanikatis et al. (Bioinformatics 2005)
EC numbers define 30 possible
enzymatic reaction families
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EC numbers define 30 possible
enzymatic reaction families
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EC rules were encoded into commands
C C O C O O
C C O C O O
C 0 1 0 0 0 0
C 0 2 0 0 0 0
C 1 0 2 1 0 0
C 2 0 1 1 0 0
O 0 2 0 0 0 0
O 0 1 0 0 0 0
C 0 1 0 0 2 1
C 0 1 0 0 2 1
O 0 0 0 2 0 0
O 0 0 0 2 0 0
O 0 0 0 1 0 0
O 0 0 0 1 0 0
Hatzimanikatis et al. (Bioinformatics 2005)
Optimization function finds minimal number
of steps between any two metabolites
The shortest path can be
found efficiently using a
customized BFS (breadth
first search)
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Are all pairs of metabolites connected by shortest
possible paths? (as allowed by biochemistry rules)
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Are all pairs of metabolites connected by shortest
possible paths? (as allowed by biochemistry rules)
•
•
Some pairs are connected by possible shortest paths
Other pairs can be connected in less steps via shortcuts
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Are all pairs of metabolites connected by shortest
possible paths? (as allowed by biochemistry rules)
•
•
Some pairs are connected by possible shortest paths
Other pairs can be connected in less steps via shortcuts
•
•
Cluster together pairs that connect via shortest paths
Define these as minimality modules
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minimality modules are defined to contain
shortest paths
A
A
B
B
C
B
C
Existing
reactions
(in organism)
D
E
E
Only metabolites
connected by
shortest possible
paths are contained
in an minimality
module
C
D
D
F
A
F
E
F
Possible EC
reactions
(biochemistry)
Minimality
modules
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Example: possible shortcut in glycolysis
break it into modules
GLU
DHAP
DHAP
GAP
GAP
BPG
EC 1.2
3PG
2PG
PYR
BPG
GAP  3PG (EC 1.2) is
biochemically feasible (exists
in plants), but is not part of E.
coli central metabolism
3PG
2PG
Therefore glycolysis is not as
short as possible and breaks
down into minimality modules
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Central carbon
metabolism network
breaks down to
minimality modules
Biomass
precursors are
key metabolites
• Design principle:
minimal number of enzymatic
steps connecting every pair of
consecutive precursors 
central carbon metabolism is a
minimal walk between the 13
biomass precursors
“Make things as simple as possible but not simpler”
Can carbon fixation metabolism
be “enhanced”?
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Can we find “better” ways to
achieve carbon fixation?
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There are several alternative carbon
fixation pathways
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We systematically explore all possible
synthetic carbon fixation pathways
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Future directions – metabolic networks
optimization and synthesis
• Try to implement alternative carbon fixation in-vitro or in-vivo
• “Test case”: can we convert E.coli to being an autotroph?
• Couple synthetic carbon fixation to energy sources  fuel
production from sunlight/wind
or at least learn something about the logic of evolution,
and how: “evolution is smarter than you are” (Orgel’s law)
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The number you need, with reference in just a minute
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