Metabolic modelling
Metabolic networks, reconstruction and analysis
Esa Pitkanen
Computational Methods for Systems Biology
1 December 2009
Department of Computer Science, University of Helsinki
Metabolic modelling p. 1
Outline: Metabolism
Metabolism, metabolic networks
Metabolic reconstruction
Flux balance analysis
A part of the lecture material has been borrowed from Juho Rousus
Metabolic modelling course!
Metabolic modelling p. 2
What is metabolism?
Metabolism (from Greek "Metabolismos" for
"change", or "overthrow") is the set of chemical
reactions that happen in living organisms to
maintain life (Wikipedia)
Metabolic modelling p. 3
What is metabolism?
Metabolism (from Greek "Metabolismos" for
"change", or "overthrow") is the set of chemical
reactions that happen in living organisms to
maintain life (Wikipedia)
Metabolism relates to various processes within the
body that convert food and other substances into
energy and other metabolic byproducts used by the
body.
Metabolic modelling p. 3
What is metabolism?
Metabolism (from Greek "Metabolismos" for
"change", or "overthrow") is the set of chemical
reactions that happen in living organisms to
maintain life (Wikipedia)
Metabolism relates to various processes within the
body that convert food and other substances into
energy and other metabolic byproducts used by the
body.
Cellular subsystem that processes small molecules
or metabolites to generate energy and building
blocks for larger molecules.
Metabolic modelling p. 3
Why should we study metabolism?
Metabolism is the ultimate phenotype
Metabolic diseases (such as diabetes)
Applications in bioengineering
Diabetes II pathway in KEGG
Lactose Ethanol pathway, 2009.igem.org
Metabolic modelling p. 4
Cellular space
Density of
biomolecules in the
cell is high: plenty of
interactions!
Figure: Escherichia
coli cross-section
Green: cell wall
Blue, purple:
cytoplasmic area
Yellow: nucleoid
region
White: mRNAm
Image: David S. Goodsell
Metabolic modelling p. 5
Enzymes
Reactions catalyzed by enzymes
Example: Fructose biphosphate
aldolase enzyme catalyzes reaction
Fructose 1,6-biphosphate
D-glyceraldehyde 3-phosphate +
dihydroxyacetone phosphate
Enzymes are very specific: one
enzyme catalyzes typically only
one reaction
Specificity allows regulation
Aldolase (PDB 4ALD)
Metabolic modelling p. 6
Fructose biphosphate aldolase
Metabolic modelling p. 7
Fructose biphosphate aldolase
Metabolic modelling p. 7
Metabolism: an overview
metabolite
enzyme
Metabolic modelling p. 8
Metabolism in KEGG
KEGG Pathway overview: 8049 reactions (27 Nov 2009)
Metabolic modelling p. 9
Metabolism in KEGG
KEGG Pathway overview: 8049 reactions (27 Nov 2009)
Metabolic modelling p. 9
Metabolism in KEGG
KEGG Pathway overview: 8049 reactions (27 Nov 2009)
Metabolic modelling p. 9
Metabolic networks
Metabolic network is a graph model of metabolism
Different flavors: bipartite graphs, substrate graphs,
enzyme graphs
Bipartite graphs:
Nodes: reactions, metabolites
Edges: consumer/producer relationships between
reactions and metabolites
Edge labels can be used to encode stoichiometry
Metabolic modelling p. 10
Metabolic networks
Metabolic network is a graph model of metabolism
Different flavors: bipartite graphs, substrate graphs,
enzyme graphs
Bipartite graphs:
Nodes: reactions, metabolites
Edges: consumer/producer relationships between
reactions and metabolites
Edge labels can be used to encode stoichiometry
r10
NADPP
r1
r3
NADPH
R5P
r4
X5P
r9
6PG
r5
r8
bG6P
r7
6PGL
r2
aG6P
r6
bF6P
H2O
Metabolic modelling p. 10
Stoichiometric matrix
The stoichiometric coefficient sij of metabolite i in
reaction j specifies the number of metabolites
produced or consumed in a single reaction step
sij > 0: reaction produces metabolite
sij < 0: reaction consumes metabolite
sij = 0: metabolite does not participate in
reaction
Example reaction: 2 m1 m2 + m3
Coefficients: s1,1 = 2, s2,1 = s3,1 = 1
Coefficients comprise a stoichiometric matrix
S = (sij ).
Metabolic modelling p. 11
Systems equations
Rate of concentration changes determined by the set
of systems equations:
dxi X
sij vj ,
=
dt
j
xi : concentration of metabolite i
sij : stoichiometric coefficient
vj : rate of reaction j
Metabolic modelling p. 12
Stoichiometric matrix: example
r10
NADPP
r3
NADPH
r1
R5P
r4
X5P
r9
6PG
bG6P
r5
r8
6PGL
r7
r2
aG6P
r6
bF6P
H2O
r1
r2
r3
r4
r5
r6
r7
r8
r9
r10
r11
r12
G6P
-1
-1
G6P
-1
-1
F6P
6PGL
-1
6PG
-1
R5P
-1
X5P
-1
NADP+
-1
-1
NADPH
H2 O
-1
Metabolic modelling p. 13
Modelling metabolism:
kinetic models
Dynamic behaviour: how metabolite and enzyme
concentrations change over time Kinetic models
Detailed models for individual enzymes
For simple enzymes, the Michaelis-Menten equation
describes the reaction rate v adequately:
vmax [S]
,
v=
KM + [S]
where vmax is the maximum reaction rate, [S] is the
substrate concentration and KM is the Michaelis
constant.
Metabolic modelling p. 14
Kinetic models
Require a lot of data to specify
10-20 parameter models for more complex
enzymes
Limited to small to medium-scale models
Metabolic modelling p. 15
Spatial modelling
Bag-of-enzymes
all molecules (metabolites and enzymes) in one
bag
all interactions potentially allowed
Compartmentalized models
Models of spatial molecule distributions
Metabolic modelling p. 16
Increasing detail
Spatial modelling
Bag-of-enzymes
all molecules (metabolites and enzymes) in one
bag
all interactions potentially allowed
Compartmentalized models
Models of spatial molecule distributions
Metabolic modelling p. 16
Compartments
Metabolic models of eukaryotic cells are divided
into compartments
Cytosol
Mitochondria
Nucleus
...and others
Extracellular space can be thought as a
compartment too
Metabolites carried across compartment borders by
transport reactions
Metabolic modelling p. 17
Modelling metabolism: steady-state
models
Steady-state assumption: internal metabolite
concentrations are constant over time, dx
dt = 0
External (exchange) metabolites not constrained
Metabolic modelling p. 18
Modelling metabolism: steady-state
models
Steady-state assumption: internal metabolite
concentrations are constant over time, dx
dt = 0
External (exchange) metabolites not constrained
Net production of each internal metabolite i is zero:
X
sij vj = Sv = 0
j
Is this assumption meaningful? Think of questions
we can ask under the assumption!
Metabolic modelling p. 18
Modelling metabolism: steady-state
models
Steady-state assumption: internal metabolite
concentrations are constant over time, dx
dt = 0
External (exchange) metabolites not constrained
Net production of each internal metabolite i is zero:
X
sij vj = Sv = 0
j
Is this assumption meaningful? Think of questions
we can ask under the assumption!
Steady-state reaction rate (flux) vi
Holds in certain conditions, for example in
chemostat cultivations
Metabolic modelling p. 18
Outline: Metabolic reconstruction
Metabolism, metabolic networks
Metabolic reconstruction
Flux balance analysis
Metabolic modelling p. 19
Metabolic reconstruction
Reconstruction problem: infer the metabolic
network from sequenced genome
Determine genes coding for enzymes and assemble
metabolic network?
Subproblem of genome annotation?
Metabolic modelling p. 20
Metabolic reconstruction
Metabolic modelling p. 21
Reconstruction process
Metabolic modelling p. 22
Data sources for reconstruction
Biochemistry
Enzyme assays: measure enzymatic activity
Genomics
Annotation of open reading frames
Physiology
Measure cellular inputs (growth media) and
outputs
Biomass composition
Metabolic modelling p. 23
Resources
Databases
KEGG
BioCyc
Ontologies
Enzyme Classification (EC)
Gene Ontology
Software
Pathway Tools
KEGG Automatic Annotation Server (KAAS)
MetaSHARK, MetaTIGER
IdentiCS
RAST
Metabolic modelling p. 24
Annotating sequences
1. Find genes in sequenced genome
(available software)
GLIMMER (microbes)
GlimmerM (eukaryotes, considers intron/exon
structure)
GENSCAN (human)
2. Assign a function to each gene
BLAST, FASTA against a database of annotated
sequences (e.g., UniProt)
Profile-based methods (HMMs, see InterProScan
for a unified interface for different methods)
Protein complexes, isozymes
Metabolic modelling p. 25
Assembling the metabolic network
In principle: for each gene with
annotated enzymatic function(s),
add reaction(s) to network
(gene-protein-reaction
associations)
Metabolic modelling p. 26
Assembling the metabolic network
In principle: for each gene with
annotated enzymatic function(s),
add reaction(s) to network
(gene-protein-reaction
associations)
Multiple peptides may form a
single protein (top)
Proteins may form complexes
(middle)
Different genes may encode
isozymes (bottom)
Metabolic modelling p. 26
Gaps in metabolic networks
Assembled network often contains so-called gaps
Informally: gap is a reaction
missing from the network...
...required to perform some function.
A large amount of manual work is required to fix
networks
Recently, computational methods have been
developed to fix network consistency problems
Metabolic modelling p. 27
Gaps in metabolic networks
May carry steady-state flux Blocked Gap
r10
NADPP
r1
r3
NADPH
R5P
r4
X5P
r9
6PG
r5
r8
bG6P
r7
6PGL
r2
aG6P
r6
bF6P
H2O
Metabolic modelling p. 28
Gaps in metabolic networks
May carry steady-state flux Blocked Gap
r10
NADPP
r1
NADPH
r3
R5P
r4
X5P
r9
r3
R5P
r4
X5P
r9
6PG
r5
r8
bG6P
r7
6PGL
r2
aG6P
r6
bF6P
H2O
r10
NADPP
r1
NADPH
6PG
r5
r8
bG6P
r7
6PGL
r2
aG6P
r6
bF6P
H2O
Metabolic modelling p. 28
Gaps in metabolic networks
May carry steady-state flux Blocked Gap
r10
NADPP
r1
NADPH
r3
R5P
r4
X5P
r9
r3
R5P
r4
X5P
r9
r3
R5P
r4
X5P
r9
6PG
r5
r8
bG6P
r7
6PGL
r2
aG6P
r6
bF6P
H2O
r10
NADPP
r1
NADPH
6PG
r5
r8
bG6P
r7
6PGL
r2
aG6P
r6
bF6P
H2O
r10
NADPP
r1
NADPH
6PG
r5
r8
bG6P
r7
6PGL
r2
aG6P
r6
bF6P
H2O
Metabolic modelling p. 28
In silico validation of metabolic models
Reconstructed genome-scale metabolic networks are
very large: hundreds or thousands of reactions and
metabolites
Manual curation is often necessary
Amount of manual work needed can be reduced
with computational methods
Aims to provide a good basis for further analysis
and experiments
Does not remove the need for experimental
verification
Metabolic modelling p. 29
Outline: Flux balance analysis
Metabolism, metabolic networks
Metabolic reconstruction
Flux balance analysis
Metabolic modelling p. 30
Flux Balance Analysis: preliminaries
Recall that in a steady state, metabolite
concentrations are constant over time,
dxi
=
dt
r
X
sij vj = 0, for i = 1, . . . , n.
j=1
Stoichiometric model can be given as
S = [SII SIE ]
where SII describes internal metabolites - internal
reactions, and SIE internal metabolites - exchange
reactions.
Metabolic modelling p. 31
Flux Balance Analysis (FBA)
FBA is a framework for investigating the theoretical
capabilities of a stoichiometric metabolic model S
Analysis is constrained by
1. Steady state assumption Sv = 0
2. Thermodynamic constraints: (ir)reversibility of
reactions
3. Limited reaction rates of enzymes:
Vmin v Vmax
Note that constraints (2) can be included in Vmin and
Vmax .
Metabolic modelling p. 32
Flux Balance Analysis (FBA)
In FBA, we are interested
in determining the
theoretical maximum
(minimum) yield of some
metabolite, given model
For instance, we may be
interested in finding how
efficiently yeast is able to
convert sugar into ethanol
Figure:
KEGG
glycolysis
in
Metabolic modelling p. 33
Flux Balance Analysis (FBA)
FBA has applications both in metabolic engineering
and metabolic reconstruction
Metabolic engineering: find out possible reactions
(pathways) to insert or delete
Metabolic reconstruction: validate the
reconstruction given observed metabolic phenotype
Metabolic modelling p. 34
Formulating an FBA problem
We formulate an FBA problem by specifying
parameters c in the optimization function Z,
Z=
r
X
ci vi .
i=1
Examples:
Set ci = 1 if reaction i produces target
metabolite, and ci = 0 otherwise
Growth function: maximize production of
biomass constituents
Energy: maximize ATP (net) production
Metabolic modelling p. 35
Solving an FBA problem
Given a model S, we then seek to find the maximum
of Z while respecting the FBA constraints,
(1)
(2)
(3)
max Z = max
v
Vmin
r
X
ci vi
such that
i=1
Sv = 0
v Vmax
(We could also replace max with min.)
This is a linear program, having a linear objective
function and linear constraints
Metabolic modelling p. 36
Solving a linear program
General linear program formulation:
X
ci xi such that
max
xi
Ax b
Algorithms: simplex (worst-case exponential time),
interior point methods (polynomial)
Matlab solver: linprog (Statistical Toolbox)
Many solvers around, efficiency with (very) large
models varies
Metabolic modelling p. 37
Linear programs
Linear constraints define a
convex polyhedron (feasible
region)
If the feasible region is empty,
the problem is infeasible.
Unbounded feasible region (in
direction of objective function):
no optimal solution
Given a linear objective function, where can you find the
maximum value?
Metabolic modelling p. 38
Flux Balance Analysis: example
r10
NADPP
r1
r3
NADPH
R5P
r4
X5P
r9
6PG
r5
r8
bG6P
r7
6PGL
r2
aG6P
r6
bF6P
H2O
Lets take our running example...
Unconstrained uptake (exchange) reactions for NADP+ (r10 ),
NADPH and H2 O (not drawn)
Constrained uptake for G6P, 0 v8 1
Objective: production of X5P (v9 )
c = (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
Metabolic modelling p. 39
Flux Balance Analysis: example
r10
NADPP
r1
r3
NADPH
R5P
r4
X5P
6PG
bG6P
r5
r8
6PGL
r7
r2
aG6P
r6
bF6P
H2O
r1
r2
r3
r4
r5
r6
r7
r8
r9
r10
r11
r12
G6P
-1
-1
G6P
-1
-1
F6P
6PGL
-1
6PG
-1
R5P
-1
X5P
-1
NADP+
-1
-1
NADPH
H2 O
-1
Metabolic modelling p. 40
r9
Flux Balance Analysis: example
Solve the linear program
max
v
r
X
ci vi = max v9
subject to
i
r
X
sij vi
=0
0 v8
for all j = 1, . . . , 10
i=1
Hint: Matlabs linprog offers nice convenience
functions for specifying equality constraints and
bounds
Metabolic modelling p. 41
Flux Balance Analysis: example
r10 2.00
NADPP
r1 1.00
r3 1.00
NADPH
R5P
r4 1.00
X5P
6PG
r5 0.57
r8 1.00
bG6P
r7 -0.43
6PGL
r2 1.00
aG6P
r6 0.43
bF6P
H2O
Figure gives one possible solution (flux assignment
v)
Reaction r7 (red) operates in backward direction
Uptake of NADP+ v10 = 2v8 = 2
How many solutions (different flux assignments) are
there for this problem?
Metabolic modelling p. 42
r9 1.00
FBA validation of a reconstruction
Check if it is possible to produce metabolites that
the organism is known to produce
Maximize production of each such metabolite at
time
Make sure max. production is above zero
To check biomass production (growth), add a
reaction to the model with stoichiometry
corresponding to biomass composition
Metabolic modelling p. 43
FBA validation of a reconstruction
If a maximum yield of some metabolite is lower than measured
missing pathway
Iterative process: find metabolite that cannot be produced, fix
the problem by changing the model, try again
6PGL
NADPP
r2 0.00
r3 0.00
R5P
r4 0.00
X5P
r9 0.00
r3 1.00
R5P
r4 1.00
X5P
r9 1.00
6PG
r1 0.00
H2O
r5 0.00
r8 0.00
bG6P
r7 0.00
NADPH
aG6P
r6 0.00
bF6P
r10 2.00
NADPP
r5 0.57
bG6P
r1 1.00
NADPH
r7 -0.43
6PGL
6PG
r8 1.00
r2 1.00
aG6P
r6 0.43
bF6P
H2O
Metabolic modelling p. 44
FBA validation of a reconstruction
FBA gives the maximum flux given stoichiometry only, i.e.,
not constrained by regulation or kinetics
In particular, assignment of internal fluxes on alternative
pathways can be arbitrary (of course subject to problem
constraints)
r10 2.00
NADPP
r1 1.00
NADPH
r3 1.00
R5P
r4 1.00
X5P
r9 1.00
r3 1.00
R5P
r4 1.00
X5P
r9 1.00
6PG
r5 0.57
r8 1.00
bG6P
r7 -0.43
6PGL
r2 1.00
aG6P
r6 0.43
bF6P
H2O
r10 2.00
NADPP
r1 1.00
NADPH
6PG
r5 0.00
r8 1.00
bG6P
r7 -1.00
6PGL
r2 1.00
aG6P
r6 1.00
bF6P
Metabolic modelling p. 45
H2O
Further reading
Metabolic modelling: course material
M. Durot, P.-Y. Bourguignon, and V. Schachter:
Genome-scale models of bacterial metabolism: ... FEMS Microbiol
Rev. 33:164-190, 2009.
N. C. Duarte et. al: Global reconstruction of the human metabolic
network based on genomic and bibliomic data. PNAS 104(6), 2007.
V. Lacroix, L. Cottret, P. Thebault and M.-F. Sagot: An introduction
to metabolic networks and their structural analysis. IEEE
Transactions on Computational Biology and Bioinformatics 5(4),
2008.
E. Pitknen, A. Rantanen, J. Rousu and E. Ukkonen:
A computational method for reconstructing gapless metabolic networks.
Proceedings of the BIRD08, 2008.
Metabolic modelling p. 46
