Metabolic networks
John Pinney
Theoretical Systems Biology group
j.pinney@imperial.ac.uk
341 Introduction to Bioinformatics: Biological Networks
25th February 2010
Part 1: Constructing metabolic networks
What is metabolism?
“Metabolism is the set of
chemical reactions that
occur in living organisms
in order to maintain life.”
Image: section through an Escherichia
coli cell
by David Goodsell
What is metabolism?
Key classes of biochemicals:
amino acids
• proteins
carbohydrates
• bacterial envelope
nucleotides
• genetic material
lipids
• membranes
coenzymes
• transfer chemical groups
minerals
• assist in biochemical
transformations
Enzymes
Metabolic reactions are catalysed by proteins called enzymes.
glucose
glucose 6-phosphate
Metabolic pathways
Traditionally, biochemists consider a series of consecutive metabolic
reactions to form a pathway.
Image: CK12.org
Metabolic networks
However, pathways
often overlap so much
that it is more accurate
to consider the set of all
metabolic reactions as
forming a network.
Image: Wikipedia
How should we represent metabolic networks?
Traditional textbook
representation:
Compounds are shown as boxes.
Arrows connect compounds to show
interconversions.
Arrows are labelled with the name of
the associated enzyme.
Cofactors (commonly-used
compounds) included with curved
arrows.
Image: Michal, G. (1993). Biochemical Pathways Poster. Boehringer Mannheim GmbH
Why should we study metabolic networks?
Fundamental to life
Since enzymes are encoded in the genome, metabolism is one
mechanism by which an organism’s genotype (specific set of genes) is
connected to its phenotype (how it behaves). Many metabolic processes
are common to all forms of life.
Biotechnology
Deep understanding of the metabolic networks of bacteria is needed if
they are to be genetically modified to produce a desired product with
maximum yields.
Medicine
Aberrations in human metabolism are fundamental to diseases such as
diabetes and some types of cancer.
Knowledge of the metabolic networks of pathogens and parasites can
help to select drug targets (or target combinations) that will be most
effective.
How should we represent metabolic networks?
Traditional textbook
representation:
Compounds are shown as boxes.
Arrows connect compounds to show
interconversions.
Arrows are labelled with the name of
the associated enzyme.
Cofactors (commonly-used
compounds) included with curved
arrows.
Image: Michal, G. (1993). Biochemical Pathways Poster. Boehringer Mannheim GmbH
Representing metabolic networks for systems biology
simple graph
metabolite
digraph
bipartite digraph
or more
complex still..?
reaction
enzyme
Metabolic reconstruction
Task:
Given the genome sequence for an organism, find its metabolic network.
Resources:
Sequence databases
Genome annotations
Databases of metabolic reactions
Tools:
Sequence similarity searches
Text extraction
Machine learning
Experimental data (high- and low-throughput)
Francke C et al. (2005)
Metabolic reconstruction from a genome annotation
For well-studied organisms, a great deal
of information about metabolism is
already known.
Genome annotations label each gene
with our current knowledge.
EC 5.3.1.9
glucose-6-phosphate isomerase
Enzymatic functions are often described
in such annotations using the E.C.
(Enzyme Commission) hierarchical
numbering system.
5
=>
isomerase
5.3
=>
intramolecular
oxidorecuctases
5.3.1
=>
interconverting
aldoses and ketoses
Metabolic reconstruction from a genome annotation
Once a set of enzymes has been
collected, they can simply be projected
onto a database of all known metabolic
reactions to give a “first-pass” network
reconstruction.
e.g. glycolysis / gluconeogenesis for
chicken, Gallus gallus, taken from
KEGG (Kyoto Encyclopedia of Genes
and Genomes)
www.genome.jp/kegg
Metabolic reconstruction from a proteome
Often a well-curated genome annotation is unavailable, but we have a good
idea of where the protein-coding genes are on the genome so can extract a
predicted proteome (set of all protein sequences encoded by the genome).
The task is now to assign enzymatic functions to these protein sequences.
genome sequence with
known protein-coding
regions.
predicted proteins
Metabolic reconstruction from a proteome
If a closely-related organism has a good annotation, it may be possible to
identify orthologous (i.e. functionally equivalent) proteins using basic
sequence alignment methods such as BLAST.
More sophisticated methods for orthology assignment are also available.
annotated
proteome
new
proteome
Functional assignment by
sequence similarity (e.g. BLAST)
Metabolic reconstruction from a proteome
However, using profile models for enzyme domains is a more sensitive way
to detect sequence similarities, especially across large evolutionary
distances.
Highly-conserved amino acids
multiple alignment of enzyme domains from many species
profile model (position-specific scoring matrix / profile HMM)
library of models for all enzyme functions with known
sequences
Metabolic reconstruction from a proteome
Known ligand-binding residues from bacterial structure
EPSP synthase
ATP/GTP binding motif
shikimate kinase
McConkey GA et al. (2004)
Limitations of sequence-based methods
Large evolutionary distances
Transfer of function from a distant sequence may not be reliable.
Enzyme may be too divergent to be recognised from sequence.
Multiple functions
Some enzymes have multiple protein domains that have different functions.
An enzyme may “moonlight” - i.e. catalyse several different reactions using the
same active site.
Reactions with unknown sequences
There are several known metabolic reactions for which no example enzyme
sequences
are known.
Unknown reactions
Across all kingdoms of life, there are many hundreds of metabolic reactions that
are as yet completely uncharacterised!
Manual curation
Computational assignment of gene function is not 100% accurate!
It will always be important to examine and refine initial automated metabolic
reconstructions carefully before attempting to analyse the resulting network.
Comparative genomics can be a powerful tool in network curation.
By comparing genomes between different species, we attempt to use their shared
evolutionary histories to help us identify gene functions more accurately.
What genes are close to this gene?
Has this gene ever fused with another one?
Which genes tend to be present in the same organisms as this one?
Which genes control whether this one is switched on?
What experimental evidence is there?
Gaps in a reconstructed network
Even after curation, a network may still contain obvious gaps, also known as pathway holes.
consumed but not produced
source
intermediate reaction missing
produced but not consumed
sink
Methods for gap-filling
Phylogenetic profiling (evidence for functionally associated genes)
Anticorrelation analysis (evidence for functionally analogous genes)
gene
species
g1
s1
+
s2
+
s3
g2
?
g3
g4
g5
g6
+
+
+
+
+
+
+
+
+
+
+
+
+
s5
+
+
+
s6
s8
+
?
+
g8
g9
+
+
+
+
shared pattern
Osterman A and Overbeek R (2003); Pellegrini M et al. (1999)
+
+
+
+
+
+
+
+
+
g10
+
+
s4
s7
g7
+
+
anticorrelated pattern
+
Methods for gap-filling
Evidence from various sources can be integrated using machine learning to give
an overall likelihood that a particular gene might fill a particular pathway hole.
For parasitic or symbiotic organisms, we also need to consider the possibility of
metabolite exchange with the host or subversion of host enzymes.
Green ML et al. (2004)
Part 2: Metabolic network analysis
Analysis of metabolic networks
Metabolic networks can be analysed on several different levels.
Topologically
Basic network structure
Stoichiometrically
Considering the numbers of molecules of each type consumed and
produced by each reaction.
Dynamically
Considering the rates of each reaction and variations in metabolite
concentrations over time.
Topological analysis
Metabolic networks can be studied
purely from the point of view of their
graph properties.
Degree distribution
Clustering coefficient
Shortest path length
Modularity
etc.
These types of investigations may (or
may not!) provide useful insights into
how metabolic networks have evolved.
Wagner A and Fell DA (2001)
Topological analysis
Chokepoint analysis can help to reveal potential drug targets
highlighted squares are all chokepoint reactions, as they have unique substrates
and/or products
Yeh I et al. (2004)
Petri net representations
The bipartite digraph representation of a metabolic network is
very close to a modelling paradigm from computer science called
a Petri net.
Various forms of Petri net representation have been successfully
used in the analysis of many biological networks, especially for
gene regulation, signal transduction and metabolic systems.
bipartite digraph
metabolite
reaction
Petri net
Petri nets for metabolic systems
Image: I. Barjis and V. Gehlot, SCSC 2007
Petri Nets
A tool for modelling a system:
•
•
•
•
•
simple.
easy to represent graphically.
represents concurrent processes.
mathematically rigorous.
large theoretical framework has been developed.
Peterson JL (1981) Petri Net theory and the modeling of systems
Prentice-Hall, NJ
Introduction to Petri Nets
Generic features of a system
Composite:
• A system is considered to be made up of separate, interacting
components.
State:
• Each component has its own state of being, which determines its future
actions.
Concurrency:
• Components in two or more parts of the system may be simultaneously
active.
Introduction to Petri Nets
Petri nets are usually described
mathematically using matrix
notation.
place
arc
transition
However, they can also be
represented as directed
graphs with two types of node:
places and transitions.
Introduction to Petri Nets
input place
output place
Transitions
Each transition has a set of
input places and a set of
output places.
Introduction to Petri Nets
marked places
Places
Places may be marked by tokens.
Each place may hold an integer
number of tokens.
A particular distribution of tokens
over a net is called a marking.
This represents the state of the
system.
Introduction to Petri Nets
enabled
transitions
Firing transitions
Transitions whose input places are all
marked by at least one token are
said to be enabled.
A transition fires by removing one
token from each of its input places
and creating new tokens at its
output places.
Introduction to Petri Nets
Firing transitions
Transitions whose input places are all
marked by at least one token are
said to be enabled.
A transition fires by removing one
token from each of its input places
and creating new tokens at its
output places.
Introduction to Petri Nets
Firing transitions
Transitions whose input places are all
marked by at least one token are
said to be enabled.
A transition fires by removing one
token from each of its input places
and creating new tokens at its
output places.
Introduction to Petri Nets
Firing transitions
Firing may continue until no transition
is enabled, at which point
execution halts.
Although the initial marking
determines the possible future
behaviour of the net, the order in
which transitions are fired is not
fixed: the same initial marking may
lead to different final states.
Introduction to Petri Nets
Firing transitions
Firing may continue until no transition
is enabled, at which point
execution halts.
Although the initial marking
determines the possible future
behaviour of the net, the order in
which transitions are fired is not
fixed: the same initial marking may
lead to different final states.
Introduction to Petri Nets
Firing transitions
Firing may continue until no transition
is enabled, at which point
execution halts.
Although the initial marking
determines the possible future
behaviour of the net, the order in
which transitions are fired is not
fixed: the same initial marking may
lead to different final states.
Introduction to Petri Nets
Firing transitions
Firing may continue until no transition
is enabled, at which point
execution halts.
Although the initial marking
determines the possible future
behaviour of the net, the order in
which transitions are fired is not
fixed: the same initial marking may
lead to different final states.
Introduction to Petri Nets
Firing transitions
Firing may continue until no transition
is enabled, at which point
execution halts.
Although the initial marking
determines the possible future
behaviour of the net, the order in
which transitions are fired is not
fixed: the same initial marking may
lead to different final states.
Introduction to Petri Nets
Firing transitions
Firing may continue until no transition
is enabled, at which point
execution halts.
Although the initial marking
determines the possible future
behaviour of the net, the order in
which transitions are fired is not
fixed: the same initial marking may
lead to different final states.
Introduction to Petri Nets
Firing transitions
Firing may continue until no transition
is enabled, at which point
execution halts.
Although the initial marking
determines the possible future
behaviour of the net, the order in
which transitions are fired is not
fixed: the same initial marking may
lead to different final states.
Matrix notation for Petri nets
Stoichiometric analysis
Elementary Flux Modes are formal definitions of minimal pathways that can
operate independently at steady state.
They are equivalent to the set of minimal T-invariants of the Petri net incidence
matrix describing the system.
Schuster S et al. (1999)
Part of E. coli metabolism
Stoichiometric analysis
Schuster S et al. (1999)
Stoichiometric analysis
Flux balance analysis (FBA) is a widely used stoichiometric analysis technique.
For a given growth condition (e.g. known input nutrients):
Assume that metabolic system operates in a steady state.
Assume certain constraints on system (mass-balance, flux limitations).
Assume an “objective” that is expected to be maximised by evolution (e.g. biomass
production).
FBA can be used to predict reaction fluxes and essential enzymes under a given
growth condition.
FBA example
anoxic
(no oxygen)
Grafahrend-Belau E et al. (2008)
hypoxic
(limited oxygen)
aerobic
(unlimited oxygen)
Pathways of starch storage at different
phases of development in barley seeds
Metabolic control analysis
Given kinetic parameters, we can calculate sensitivity of the flux through a
given pathway to the inhibition of any enzyme involved.
This replaces the concept of a “rate-limiting step” in a pathway with the idea of
control being shared to some degree between all enzymes, represented by each
enzyme’s flux control coefficient, C.
Requires detailed kinetic model: currently limited to a few very well characterised
pathways in specific organisms.
C=1
0<C<1
C=0
Bakker BM et al. (2000)
Metabolic control analysis
The human trypanosome parasite
Trypanosoma brucei has a unique
organelle called the glycosome,
which carries out the glycoloysis that is
essential for its survival.
MCA has been applied to the glycolytic
pathway in T. brucei to determine
which of these enzymes would be the
best drug targets.
MCA is potentially very helpful in drug
target investigations because it allows
us to consider the likely effects of
incomplete inhibition of enzyme
function.
Bakker BM et al. (2000)
Dynamic modelling approaches
There are many general software packages available for systems biology that
can be used to model and simulate the dynamic behaviour of metabolic
networks and to integrate them with processes such as gene regulation and
protein interactions.
Metabolic models can often be shared between different software using
Systems Biology Markup Language (SBML).
(see sbml.org for examples)
Modelling could be
Deterministic
or
Stochastic
e.g. ordinary differential equations (ODEs)
e.g. Gillespie algorithm, Petri net simulation
Systems Biology Markup Language
Summary
Metabolic networks are central to much of systems biology and have important
applications in biotechnology and medicine.
They can be reconstructed to some extent from genome sequences, but a
complete and accurate metabolic model is difficult to achieve and requires a great
deal of manual curation.
Metabolic networks may be analysed at various degrees of detail, using
topological, stoichiometric and/or dynamic approaches.
References
•Oberhardt MA et al. Applications of genome-scale metabolic reconstructions. Mol Syst Biol (2009) 5:320
•Francke C et al. Reconstructing the metabolic network of a bacterium from its genome. Trends Microbiol (2005)
13:550-8
•Bakker BM et al. Metabolic control analysis of glycolysis in trypanosomes as an approach to improve selectivity and
effectiveness of drugs. Molecular and Biochemical Parasitology (2000) 106:1-10
•Grafahrend-Belau E et al. Flux balance analysis of barley seeds: a computational approach to study systemic properties
of central metabolism. Plant Physiol (2008)
•Green ML et al. A Bayesian method for identifying missing enzymes in predicted metabolic pathway databases. BMC
Bioinformatics (2004) 5:76
•McConkey GA et al. Annotating the Plasmodium genome and the enigma of the shikimate pathway. Trends Parasitol
(2004) 20:60-5
•Osterman A and Overbeek R. Missing genes in metabolic pathways: a comparative genomics approach. Current
Opinion in Chemical Biology (2003) 7:238-51
•Pellegrini M et al. Assigning protein functions by comparative genome analysis: protein phylogenetic profiles. Proc Natl
Acad Sci USA (1999) 96:4285-8
•Schuster S et al. Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and
metabolic engineering. Trends Biotechnol (1999) 17:53-60
•Wagner A and Fell DA. The small world inside large metabolic networks. Proc Biol Sci (2001) 268:1803-10
•Yeh I et al. Computational analysis of Plasmodium falciparum metabolism: organizing genomic information to facilitate
drug discovery. Genome Res (2004) 14:917-24