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Elhanan Borenstein
Spring 2010
Complex (Biological) Networks
Some slides are based on slides from courses given by Roded Sharan and Tomer Shlomi
Analyzing Metabolic Networks
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Metabolism
Metabolism is the process involved in the
maintenance of life. It is comprised of a vast
repertoire of enzymatic reactions and transport
processes used to convert thousands of organic
compounds into the various molecules
necessary to support cellular life
Schilling et al. 2000
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Why study metabolism? (II)
Its the essence of life(and maybe its origins)
Tremendous importance in Medicine
Inborn errors of metabolism cause acute symptoms Metabolic diseases (obesity, diabetes) are on the rise
(and are major sources of morbidity and mortality)
Metabolic enzymes becoming viable drug targets
Bioengineering applications
Design strains for production of biological products
Generation of bio-fuels
The best understood of all cellular networks
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Metabolites & Biochemical Reactions
Metabolite: an organic substance Sugars (e.g., glucose, galactose, lactose)
Carbohydrates (e.g., glycogen, glucan)
Amino-acids (e.g., histidine, proline, methionine)
Nucleotides (e.g., cytosine, guanine) Lipids
Chemical energy carriers (e.g., ATP, NADH)
Atoms (e.g., oxygen, hydrogen)
Biochemical reaction: the process in whichone or more substrate molecules are
converted (usually with the help of an
enzyme) to produce molecules
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Pathways
Ouzonis, Karp, Genome Res. 10, 568 (2000)
EcoCyc describes 131 pathways
Pathways vary in length from asingle step to 16 steps (ave 5.4)
But ... no precise biological definition and
partitioning of the metabolic networkinto pathways is somehow arbitrary
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From Pathways to a Network
http://www.genome.jp/kegg/pathway/map/map01100.html
http://www.genome.jp/kegg/pathway/map/map01100.htmlhttp://www.genome.jp/kegg/pathway/map/map01100.html8/12/2019 ComplexBiologicalNetworks 2 Online
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Models
ofMetabolism
(and Metabolic Networks)
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Metabolic Network Models
required data/accuracy /complexityabstraction/scale
Topological analysis Degree distribution
Motifs
Modularity Reverse ecology
Conventional models Boolean models
Discrete models
Bayesian models Kinetic models Dynamic system
(differential eqs)
Requires unknowndata constants and
concentrations
Constraint-based CB-Models
Flux Balance Analysis
Extreme Pathways
Growth/KO effects
ApproximateKinetic models
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Reconstructing Metabolic Networks
Fructose + Glucose => Sucrose
A
B
C D
EIncomplete data
Noise
Large-scale
Simple directed
graphs
Simple Representation
Nodes=compounds
Edges=reactions
Topology based
Static
SucroseGlucose
Fructose
Describing the chemical reactions in the cell and thecompounds being consumed and produced
atgaaaaccgtcgttt
ttgcctaccacgatat
gggatgcctcggtatg
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Metabolic Network (E.Coli)
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Environment
& EcologySystem Topology
& Structure
Environments from Networks
Can the structure/topologyof metabolic networks be used toobtain insights into the ecology in which species evolved/prevail?
inference
(Borenstein, et al.PNAS, 2008)
Reverse Ecologyof
Metabolic Environments
d
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Seed Sets
&Metabolic Environments
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Env
ironment
set of exogenously
acquired compounds
(seed set)
proxy for the environment(operational definition)
Seed set:a minimal subset of the compounds that cannot be synthesized from
other compounds and whose existence permits the synthesis of all other
compounds in the network.(Borenstein, et al.PNAS, 2008)
d if i d d
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Identifying Seed Compounds:
A Simple Synthetic Example
Id if i S d C d
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Identifying Seed Compounds:
Strongly Connected Components (SCC)
K j l i h
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Kosarajusalgorithm
for SCC Decomposition
Given a graph G:
1. Run a Depth-First Search (DFS) on G to compute finishing
times f[v] for each node v
2. Calculate the transposed network G (the network G with
the direction of every edge reversed)
3. Run DFS on G, traversing the nodes in decreasingorder
of f[v]
Each tree in the DFS forest created
by the second DFS run forms a
separate SCC
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Identifying Seed Compounds:
Strongly Connected Components (SCC)
SCCs are equivalent sets(seed-wise)
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Identifying Seed Compounds:
Strongly Connected Components (SCC)
Directed Acyclic Graph (DAG)
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Identifying Seed Compounds:
Source Components
Candidate seeds are members ofsource components
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Identifying Seed Compounds:
Candidate Seeds
Id tif i S d C d
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Identifying Seed Compounds:
Seed Confidence Level
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Metabolic Network with Seeds
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Multi-Species Large-ScaleSeed Dataset
Oxygen
L-Glutamate
Sulfate
Leucine
Sucrose
Glycerol
Methanol
Thymidine
B. aphidicola - - -
S. pneumoniae - - -
R. typhi - -
S. aureus - -
M. genitalium
2264 compounds
478s
pecies
accuracy 79%
precision 95%
recall 67%
478species (networks); >2200compounds
Seed compounds for each species
Large-scale dataset
of predicted metabolic
environments
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Applications of Reverse Ecology
Reconstructing ecology-based phylogeny
Predicting ancestral environments
Identifying evolutionary dynamics of networks
Predicting species interaction
Analyzing genetic vs. environmental robustness Quantifying ecological strategies
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Constraint-Based Modeling
Living systems obey physical and chemical laws
These can be used to constrain the space of
possible behaviors of the network
How often have I said to you that when
you have eliminated the impossible,
whatever remains, however improbable,
must be the truth?Sherlock Holmes (A Study of Scarlet)
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Evolution Under Constraints
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1 Glucose + 1 ATP 1 Glucose-6-Phosphate + 1 ADP
Reaction Stoichiometry
Stoichiometry - the quantitative relationships
of the reactants and products in reactions
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Stoichiometric Matrix
S
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Stoichiometric Matrix and Fluxes
vSdt
md
m: metabolite concentrations vector (mol/mg)
S: stoichiometric matrix
v: reaction rates vector
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Kinetic parameters
),( kmfSvSdt
md
Reaction rate equation
Requires knowledge of m, f and k!
A set of Ordinary Differential Equations (ODE)
A Full Model? Not Really
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Constraint-Based Modeling
Assumes a quasi steady-state!
No changes in metabolite concentrations
Metabolite production and consumption rates are equal
No need for info on metabolite concentrations,
reaction rate functions, or kinetic parameters
0 vSdt
md
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Constraint-Based Modeling
In most cases, Sis underdetermined:a subspace of Rn(possible flux distributions)
0
0
0
Sv=0
Thermodynamic constraints:
a convex cone vi> 0
Capacity constraints:
a bounded convex cone vi< vmax
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Flux Balance Analysis
But this still leaves a space of solutions
How can we identify plausible solutions withinthis space?
Optimize for maximum growth rate !!
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Flux Balance Analysis
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Flux Balance Analysis
How do we
solve this?
Linear Programming
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Linear Programming (LP)
Assume the following constraints: 0
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Application of CBM & FBA
Predict metabolic fluxes on various media
Predict growth rate
Predict gene knockout lethality
Characterize solution space
Many more
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Available CBM Metabolic Models
Bernhard Palsson
UCSD
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