Identifying common structure in genome scale
metabolic models.
Mark Poolman, David Fell, Hassan Hartman
April 6, 2011
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
ABOLI
ET
H
WA
LY
S
P AT
2011
IS
C
M
http://mpa2011.brookes.ac.uk
Y ANA
Ru5Pk
PGM
TPT PGA
X5Piso
Rubisco
StSynth
G3Pdh
TKL2
PGK
Ald1
PGI
TPT DHAP
FBPase
TKL1
TPI
R5Piso
LReac
Ald2
SBPase
TPT GAP
StPase
0/ 1
0/ 1
0/ 1
0/ 1
0/ 1
1/ 1
0/ 1
0/ 1
0/ 1
0/ 1
0/ 1
0/ 1
0/ 1
0/ 1
0/ 1
0/ 1
1/ 1
0/ 1
0/ 1
0/ 1
1/ 1
3/ 1
0/ 1
0/ 1
2/ 1
3/ 1
0/ 1
6/ 1
1/ 1
6/ 1
1/ 1
0/ 1
0/ 1
1/ 1
1/ 1
2/ 1
1/ 1
9/ 1
1/ 1
1/ 1
1/ 1
0/ 1
3/ 2
-1/ 2
0/ 1
1/ 1
3/ 2
0/ 1
3/ 1
1/ 2
3/ 1
0/ 1
-1/ 2
0/ 1
0/ 1
1/ 2
1/ 2
1/ 2
9/ 2
1/ 2
1/ 2
3/ 2
1/ 2
3/ 1
0/ 1
0/ 1
2/ 1
3/ 1
0/ 1
6/ 1
1/ 1
6/ 1
1/ 1
0/ 1
1/ 1
1/ 1
1/ 1
3/ 1
1/ 1
9/ 1
1/ 1
1/ 1
0/ 1
0/ 1
3/ 1
0/ 1
1/ 1
2/ 1
3/ 1
0/ 1
5/ 1
1/ 1
5/ 1
1/ 1
0/ 1
0/ 1
1/ 1
1/ 1
2/ 1
1/ 1
8/ 1
1/ 1
1/ 1
0/ 1
0/ 1
2/ 1
1/ 3
0/ 1
4/ 3
2/ 1
1/ 3
4/ 1
2/ 3
4/ 1
1/ 1
1/ 3
0/ 1
1/ 1
2/ 3
5/ 3
2/ 3
19/ 3
2/ 3
2/ 3
0/ 1
0/ 1
3/ 2
-1/ 2
0/ 1
1/ 1
3/ 2
0/ 1
3/ 1
1/ 2
3/ 1
0/ 1
-1/ 2
3/ 2
0/ 1
1/ 2
2/ 1
1/ 2
9/ 2
1/ 2
1/ 2
0/ 1
1/ 2
7/ 16
-7/ 48
7/ 16
7/ 24
7/ 16
0/ 1
7/ 16
7/ 48
7/ 16
0/ 1
-7/ 48
0/ 1
0/ 1
7/ 48
7/ 48
7/ 48
7/ 8
7/ 48
7/ 48
0/ 1
7/ 48
artwork taken from the cover of Professor Brainstawm Stories by Norman Hunter, (c) The BodleyHead. Used by permission of The Random House Group Ltd.
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Overview
Work from some of the projects in our group.
Can we find common features in networks ?
What is their significance ?
Compare plant and microbial metabolism.
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Null space analysis
Most fundamental description of the problem.
Identification of invariant properties.
Enzyme (reaction) subsets.
Dead reactions.
Moiety conservation.
Encompasses all possible states of the system.
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Limitations of null-space analysis
Provides a rather ‘unfocussed’ view of the system.
Does not (implicitly) take into account
thermodynamics/irreversibility.
Hard to integrate experimental flux observations.
Less interpretable for large (genome-scale) models.
How to sample the solution space for solutions with particular
properies ?
(Genome scale models are challenging for other reasons)
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Limitations of null-space analysis
Provides a rather ‘unfocussed’ view of the system.
Does not (implicitly) take into account
thermodynamics/irreversibility.
Hard to integrate experimental flux observations.
Less interpretable for large (genome-scale) models.
How to sample the solution space for solutions with particular
properies ?
(Genome scale models are challenging for other reasons)
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Limitations of null-space analysis
Provides a rather ‘unfocussed’ view of the system.
Does not (implicitly) take into account
thermodynamics/irreversibility.
Hard to integrate experimental flux observations.
Less interpretable for large (genome-scale) models.
How to sample the solution space for solutions with particular
properies ?
(Genome scale models are challenging for other reasons)
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Application of LP to metabolic networks
Complementary to null-space analysis.
Identify solutions with specific properties.
Irreversibility accounted for.
Easy to incorporate experimental flux data.
Allows rapid, repeated sampling.
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Application of LP to metabolic networks
The problem of the objective function.
What objective to use ?
Clearly no single global objective.
How to identify objective for individual cells/organisms ?
Why bother ? (what would we do with all those numbers ?)
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Application of LP to metabolic networks
One solution.
Choose one reasonable objective.
Apply repeatedly with varying constraints, how do solutions
change ?
Do these solutions conform to expectation ? (hypothesis
generation)
Are such responses common to different networks ?
If they are, does this represent common underlying
organisation ? (hypothesis generation)
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Application of LP to metabolic networks
A reasonable objective function.
←− objective
: vtargs
Nv = 0
subject to
maxi ≥ vi ≥ mini ←− imposed flux limits
minimise
Where:
“targs” is typically all reactions.
“Imposed fluxes” are observed or assumed.
Reversibility and directionality are correctly handled.
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Application of LP to metabolic networks
A reasonable objective function.
←− objective
: vtargs
Nv = 0
subject to
maxi ≥ vi ≥ mini ←− imposed flux limits
minimise
Where:
“targs” is typically all reactions.
“Imposed fluxes” are observed or assumed.
Reversibility and directionality are correctly handled.
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Embedding LP in other algorithms
1: Simple constraint scan (pseudo-code)
for c in c o n s t r a i n t s :
lp . SetConstraint ( c )
l p . Solve ( )
s o l u t i o n = lp . GetSolution ( )
r e s u l t s . AddData ( c , s o l u t i o n )
Save ( r e s u l t s )
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Embedding LP in other algorithms
2: Recursive bisection search (Python)
def FindGLCMatch ( l p , alo , ahi , g l c , t o l =1e −6):
a = ( alo+ahi ) / 2
l p . S e t F i x e d F l u x ( { " ATPase " : a } )
l p . Solve ( )
g = l p . GetPrimSol ( ) [ " GLC_tx " ]
i f abs (1 −(g / g l c ) ) < t o l :
return a
i f g < glc :
alo = a
else :
ahi = a
r e t u r n FindGLCMatch ( l p , alo , ahi , g l c , t o l )
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Secondary analysis of LP results
Examine responses of individual fluxes to changing
constraints.
Determine corrrelations between flux responses - build
correlation trees.
Identify groups of reaction with similar response.
Treat the latter as sub-networks.
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Comparison of plant and microbial metabolism
Models of growing heterotrophic cell cultures grown on
minimmal media.
Basic characteristics:
Total metabolites
Biomass components
Other outputs
Inputs
Total reactions
Live reactions
Mark Poolman, David Fell, Hassan Hartman
Microbe
783
60
6
5
914
544
Plant
1249
34
1
6
1403
783
Identifying common structure in genome scale metabolic models.
Comparison of plant and microbial metabolism
Model analysis:
: v
 Nv = 0
v = tx
subject to :
 i..j
va = Ja
minimise
Where :
tx represents fluxes in biomass transporters vi..j
Ja represents an imposed flux in the ATPase reaction va
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Comparison of plant and microbial metabolism
Results 1 (general):
Solution size
ATP responding
Mark Poolman, David Fell, Hassan Hartman
Microbe
300
34
Plant
240
40
Identifying common structure in genome scale metabolic models.
Comparison of plant and microbial metabolism
Results 2 (correlation trees):
Microbe
-
-
-
Plant
2OXOGLUTARATEDEH-RXN
PYRUVDEH-RXN
CITSYN-RXN
- ISOCITDEH-RXN
Cytochrome_c_oxidase
- ACONITATEDEHYDR-RXN
O2_tx
R601-RXN
NADH_DH
CO2_tx
ATPSynth
ESS_2
Glc_tx
ACONITATEHYDR-RXN
SUCCCOASYN-RXN
ATPase
FUMHYDR-RXN
ESS_1
MALATE-DEH-RXN
THX
TRIOSEPISOMERIZATION-RXN
- PGLUCISOM-RXN
ESS_6 PEPDEPHOS-RXN
F16ALDOLASE-RXN
6PFRUCTPHOS-RXN
3PGAREARR-RXN
2PGADEHYDRAT-RXN
ESS_5
PHOSGLYPHOS-RXN
GAPOXNPHOSPHN-RXN
PGLUCONDEHYDRAT-RXN
6PGLUCONOLACT-RXN
ESS_4
KDPGALDOL-RXN
GLU6PDEHYDROG-RXN
ASPARTASE-RXN
ESS_1 GLUTAMATE-DEHYDROGENASE-NADP+-RXN-(NADP)
ASPAMINOTRANS-RXN
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Comparison of plant and microbial metabolism
Results 3 (Responding networks):
Microbe
x_G LC
Plant
PEP
Py r
G 6P
F6P
G L6P
FBP
6PG
D HAP
2-D -3-D -G l6P
G AP
Py r
D PG
3-PG A
CisAc on
2-PG A
Py r
IsoCit
αKG
Cit
PEP
Ac CoA
OAA
Suc CoA
Mal
G lt
Suc
Fum
NH 3
Asp
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Conclusions
LP can be used for broader investigations than simple flux
asssignment.
Investigating correlated responses in different networks
appear to show common features.
These can be shown to have defined metabolic functions.
Different areas of metabolism have the potential to interact
in unexpected ways.
“Pathways” may not be the independent entities text-books
suggest.
Future modelling.
Experimental.
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Acknowledgements
David Fell
Hassan Hartman
The Cell Systems Modelling Group
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.
Acknowledgements
http://MPA2011.brookes.ac.uk
Mark Poolman, David Fell, Hassan Hartman
Identifying common structure in genome scale metabolic models.