Thermodynamics and Tradeoffs in Glycolysis

Thermodynamics and
Tradeoffs in Glycolysis
Avi Flamholz
Fall 2013
Friends and Collaborators
Arren
Bar-Even
Elad Noor
Ron Milo
Wolf Leibermeister
Why are there multiple pathways that
have the same function?
● Glycolysis:
EMP, ED, methylglyoxal, ...
● Carbon fixation:
Calvin, rTCA, 3HP-4HB, ...
● Carbon oxidation:
TCA, pentose-P, PEP-glyoxylate
Relatedly: which pathways are best for
metabolic engineering projects?
Stoichiometry and available enzymes give many options
Let’s talk glycolysis.
Glycolysis by the Book
● Single pathway
● Glucose to Pyruvate
● Glucose phosphorylated in cytosol
● Cleavage into 2 trioses
● Substrate level phosphorylation.
● Makes 2 ATP per glucose
Stryer’s Biochemistry, 5th ed.
Actually, there are several variants of
glycolysis
Especially among bacteria and archaea,
but also in plants, fungi, etc.
ED and EMP pathways are the most
common among bacteria and archaea.
Otto Meyerhof
1922 Nobel Laureate
Jakub Karol Parnas
Died 1949
in “Doctor’s Plot” Purge
Embden-Meyerhof-Parnas = EMP
Fully elucidated ~1940
http://www.nobelprize.org/nobel_prizes/themes/medicine/states/otto-meyerhof.html
Microbiology
Entner-Doudoroff = ED
First reported in 1959
http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/doudoroff-michael.pdf
ED and EMP pathways
Stettner and Segre, PNAS 2013
Same Same, But Different
Flamholz, Noor, Bar-even, Liebermeister, Milo, PNAS 2013
Nearly identical chemistry, too!
Flamholz, Noor, Bar-even, Liebermeister, Milo, PNAS 2013
But lower glycolysis produces ATP, while
upper ED pathway does not
Glucose + 2 NAD+ + n ADP
2 Pyruvate + 2 NADH + n ATP
Flamholz, Noor, Bar-even, Liebermeister, Milo, PNAS 2013
Score Card
Pathway
ATP per Glucose
EMP**
2
ED
1
**Winner!??
Yet many contemporary bacteria use
the ED pathway to eat glucose!
Fuhrer, Fischer, Sauer, J. Bac. 2005
And phylogenetic analysis shows ED is
no mere evolutionary fossil
* see appendix for more info
Flamholz, Noor, Bar-even, Liebermeister, Milo, PNAS 2013
?!?!?
Our Claim
● There is no free lunch.
● Extra ATP comes at a cost.
● The cost is high demand for EMP
enzymes.
Proof by analogy… to rivers.
From above, all rivers look similar
Iceland
Israel
A closer look shows how different
they can be
Gullfoss (32m)
Iceland
Jordan "river" (~0m)
Israel
Speed of flow increases with the slope
v1
large difference
in potential
v2
small difference
in potential
The flux is the cross-section times the
flow speed
v1
A2
v2
A1
large motive
force
small motive
force
J1 = A 1 ⋅ v 1
J2 = A2⋅ v2
G6P
F6P
From rivers to
biochemical
pathways
FBP
G3P
DHAP
BPG
2PG
3PG
PEP
PYR
<cue equations>
ΔG' is affected by reactant
concentrations
● Second law of thermodynamics:
ΔG' = ΔG'0 + RT ln Q < 0
where ΔG'0 = - RT ln Keq
Q - reaction quotient = [P] / [S] for the reaction P ⇔ S
Keq - equilibrium constant = [P] / [S] at equilibrium
● Physical limits on cellular concentrations
When we talk of irreversible reactions
We mean ones where directionality is unaffected by
physiological changes in reactant concentrations.
ΔG'0
ΔG'
ΔG'
Turns out we can say more about
the relationship between rates and
thermodynamics.
The flux-force relationship
Noor, Flamholz, Liebermeister, Bar-Even, Milo, FEBS Letters 2013
Beard, Qian, PloS One 2007
Small motive forces means you need
more enzyme
small motive
force
large motive
force
high enzyme
levels
low enzyme
levels
Small motive forces means you need
more enzyme
Maximum rate
Degree of substrate saturation
Effect of reverse reaction
E
v/kcat
-ΔrG'
Noor, Flamholz, Liebermeister, Bar-Even, Milo, FEBS Letters 2013
We know that the EMP pathway is
less exergonic than the ED pathway
It makes more ATP, after all. But does
this matter?
Maybe we can twiddle reactant
concentrations so EMP reactions are
far enough from equilibrium in cells.
The EMP pathway appears to be
thermodynamically constrained
Optimization shows ED ~twice as favorable as EMP in the
best possible (biologically-plausible) case.
The ED pathway skips a thermodynamic
bottleneck at the expense of ATP production
bottleneck
bottleneck
Model effect of thermodynamics on
enzyme levels
Minimize Λ, the total enzyme mass per unit
pathway flux. We call the optimum Λ*.
** requiring all reaction ΔG' < 0 and all metabolite concentrations within
bounds.
Our model predicts costs due to
backwards flux and non-saturation.
So how much protein is that, really?
Λ* minimizes enzyme mass per unit flux
Λ* has units (g glycolytic enzyme / (mol glucose s-1))
Vglycolysis ~= 8 - 15 mol glucose gCDW-1 s-1
Fprotein ~= 0.5 - 0.55 g total protein / gCDW
Λ* Vglycolysis / Fprotein
gram glycolytic enzyme / gram total protein
BNIDS: 109353, 109354, 109352
Fuhrer, Fischer, Sauer, J. Bac. 2005
ED pathway predicted to require ~3-5
fold less enzyme mass than EMP
EMP glycolysis accounts for 3-7% of
the measured E. coli proteome
Recap
● Rates are constrained by ΔG'
● Effect is significant near equilibrium
● Some EMP reactions must be near
equilibrium, requiring high enzyme levels
● ED pathway avoids bottleneck by forgoing
one ATP
● ED predicted to require much less enzyme
to catalyze the same flux
Resulting Hypothesis
Organisms that have a substantial nonglycolytic source of ATP will use the ED
pathway more often than those that do not.
Aerobes, for example.
We find that aerobic conditions do
favor ED much more than anaerobic
Closing Thoughts for Modelers
Variable Type
Coverage
Accuracy
Stoichiometric
high
high
Thermodynamic
medium
medium
Kinetic*
low
low
Concentrations**
low
depends
Fluxes
low
high
Thermodynamic data is higher quality than much other
data we have, especially kinetic data. Worth including
in your models, especially due to flux-force relation.
* usually measured in-vitro
** of enzymes and/or metabolites
Source code available
https://code.google.com/p/milo-lab/
http://equilibrator.weizmann.ac.il/
http://bionumbers.hms.harvard.edu
Questions?
Appendix
Nearly identical chemistry except for ATP
unique enzymes
Unique enzymes enable phylogenetics
ED species seem to prefer higher TCA
fluxes
ED
ED
EMP
EMP
ED
ED
ED
ED
Fuhrer et al., J. Bact. 2005
Derivation of the flux-force
relationship for a mass-action rate law
Beard, Qian, PloS One 2007
Derivation for a mass-action rate law
a.k.a the Haldane relationship
Beard, Qian, PloS One 2007
Derivation for a mass-action rate law
Ta-da!
Also true in general for reactions in steady state,
independent of reaction mechanism. See reference.
Beard, Qian, PloS One 2007
General derivation for 1:1 reaction in
steady-state
v = v + - vv
A
v+
v-
B
v
Consider a steady state with net flux v.
Beard, Qian, PloS One 2007
General derivation for 1:1 reaction in
steady-state
v
A
A*
v
v*+
B
v
v*-
1. Because of steady-state v*- = v*+, v = v+ and v- = v*2. So A* is in equilibrium with B, meaning B / A* = Keq.
3. Solution well-mixed, so v*+ = v A* / A
4. Therefore, v+ / v- = A / A* = Keq A / B = exp(-ΔG' / RT)
Beard, Qian, PloS One 2007
How do we know ΔG' ?
Tables of formation energies are
used to calculate ΔG'°
ATP + H2O ↔ ADP + Pi
ΔrG'° =
ΔfG'°(ADP) + ΔfG'°(Pi) - ΔfG'°(ATP) - ΔfG'°(H2O)
1957 - Burton
1977 - Thauer
2003 - Alberty
Assuming additivity of thermodynamic
properties helps estimate more ΔG°
Mavrovouniotis Biotech & Bioeng, 1991
Assuming additivity of thermodynamic
properties helps estimate more ΔG°
Mavrovouniotis Biotech & Bioeng, 1991
Using group decomposition more
reactions can be used
ΔrG'° = -ΔgrG'°(-OH) - ΔgrG'°(=n+<) + ΔgrG'°(-n<) + ΔgrG'°(=O)
1991 - Mavrovouniotis
2008 - Jankowski et al.
2012 - Noor et al.
Modellers choose method ad hoc
Accuracy Coverage
Suitable for
Formation
Energies
+
-
single pathway or
sub-system
models
Group
Contribution
-
+
genome scale
models
Map services were used as
inspiration
walking
bus
Component Contribution Method (CCM)
Noor, Haraldsdottir, Milo,
Fleming (PLOS CB, 2013)
Cross-validation shows an improvement (of
median error) over standard GCM
CDF of the cross-validation error for observations in TECRDB